Time arrows: The Grand Design

Published: March 23, 2010

Abstract: This post is my response to Mr. Hawking’s book, ‘grand design’ from the perspective of Complexity the science that he acknowledges will be the science of the XXI century. As the researcher who has formalized properly that science, with the discovery of the Generator Equation of Space-time and the 5 postulates of Non-Euclidean geometry, needed to define the 4 arrows of time of the Universe: energy, information, reproduction and social evolution, the ‘why’ of all motions and forms of reality I wish to inform the readers that Complexity NOT physics, is indeed the science of the XXI century, which is giving us solutions to the eternal questions about the meaning of God, Man and the Universe… The texts are part of the conferences I gave in the International Society of Systems sciences during my tenure of the chair of Duality, which studies reality with the 2 Simplex arrows of time, energy and information, whose combinations in Complex events reproduce and evolve the Universe and all its species…


Every century a book of science advances our understanding of the Universe, by defining in more detail the nature of time. In the XVII century Galileo wrote his ‘dialogues’ and gave us the first mathematical definition of space-time in terms of ‘space location’ and ‘motion’: v=s/t. It would be the most influential book of the century. In the XVIII C., it was Leibniz with his infinitesimal calculus and concept of relational space-time (though Newton would carry the day); in the XIX c. it was the time of Darwin, whose ‘Origin of species’ would define time as the evolution of information, or form of living beings.

In the XX century it was the turn of Einstein with his Theory of Relativity, which few people understood till Mr. Hawking popularized its principles with his divulgative book ‘A brief history of time’, which was for that reason chosen by the students of Cambridge the most important work of science after Darwin’s origin of the species – though the prize in justice should have gone to Mr. Einstein’s original papers.

Moreover Mr. Einstein followed in his research one of the fundamental tenants of the scientific method, the Principle of Correspondence, according to which a new theory of science must  include the results of the previous theory as particular case of the wider theory. For that reason, he called the Physical Theory of time, Relativity, since it was an extension of the original Galilean Relativity, and a further study of the definition of time in terms of space and motion (v=s/t). But time which is the process of change in reality is not only change in motion and location of space; it is also change in the form or morphology of beings, change in information defined by Darwin.

And so according to the constant advance of our understanding of time and the Principle of Equivalence, in the XXI century we should expect a new book whose theory fusions the discoveries of Mr. Darwin in the XIX century, the concept of biological time, as change in the information of beings and Mr. Einstein in the XX century, the concept of physical time, as change in the spatial location and speed of beings.

Such a book has to be written, naturally by an expert in the science that tries to fusion biology and physics, the science of complexity, which Hawking himself affirmed to be the ‘science of the XXI century’ . And so ‘Duality’ the branch of complexity which puts together the arrow of energy and the arrow of information is the stronger candidate to advance our understanding of time into XXI century science.

Thus as an expert on Duality, a science whose International Congresses I  chaired for the past years, this book (nt.0) is the answer from the perspective of Complexity, to the need for a comprehensive theory of time that fusions the work of Einstein and Darwin.

How far the theory of time arrows will go to fulfil that claim of being inclusive of all previous theories will of course not be fully understood till the theory is fully tested by peers outside the realm of Complexity in which it was conceived and the experimental results, solutions and predictions it has made on future events and unresolved questions of science is tested. Though the reader will realize many of those predictions done as earlier as the 90s when the first texts on time arrows were published, had already taken place1, an encouraging sign for its future as the theory of time of the XXI century.


0 This paper belongs to the conference I gave as chair of duality at the ISSS congress at the Technological Institute of Tokyo in 2006, explaining the general laws of the fractal Universe and its 4 arrows of time. It was followed by a series of papers that applied the theory of time arrows to the resolution of the main questions left unanswered with the limited models of a spacetime continuum and a single time arrow: ‘The arrow of einstein’, which described  mass as a vortex of gravitational information and solved the Unification Equation of charges and masses, presented the next year at the Madison Congress, ‘The plan of evolution’, in which the topological and causal constrains of the arrows of time that create the future were applied to biology, solving its main questions, and ‘The 72 years cycle of evolution of machines’ which modelled the economic ecosystem as a process of evolution ofmachines of metal that imitate human organs of energy (transports, weapons) and information (chips-brains, eyes-heads), forecasting the 2008 crash of the economy, showing the enormous span of solutions and range of Time arrows theory, which applies to all sciences, as all sciences study process of Time.

As today only one of those conferences/papers is left on the servers of ISSS after 3 years of repeated hackers’ attacks erasing my work, I suppose to fortify the smearing campaign against me as an invisible scholar, hence a  ‘people of no merit’ (declaration of Amici Curiae Wilczek regarding my scientific credentials;-). All those papers were also erased from Google Scholar. Yet now that the suit against CERN has ended and there is no more  enthusiastic collaborators hacking or smearing my work, I am in the process of republishing them in the web, ISSS and google scholar for future generations to learn the meaning of the arrows of time – the why of the Universe and all its motions. In that regard this post is also an answer to Mr. Hawking’s last book ‘the grand design’ in which he uses now, not Mr. Einstein’s work on time, but Witten’s work on string theory to affirm he knows the ‘mind of god’. And that religion and philosophy is dead. But there is nothing new on that book, and certainly neither religion (the arrow of love in history) and philosophy of science (the highest of all sciences which sets the principles and laws common to all of them) are dead, as this post will prove with its analysis of those common laws and its demonstrations that the arrow of social love that evolves parts into wholes, particles into atoms, atoms into cells, cells into organisms and organisms into societies, is not dead but actually the most important arrow of creation of the future in the Universe.



‘Complexity will be the Science of the XXI Century.’  S. Hawking, on the science of exi=stence

The smallest point must be considered a world in itself’ Leibniz, Master of time theory of the XVIII C.

1. Time as Change.

2. Simplex Arrows: Energy óInformation. The Geometric Beat of The Universe.

3. Life Cycles: Past, Present & Future.

4. Bidimensional  Space &Time.

5. Fractal i-Points: The Fundamental Particle.

6. Social Networks: Super-Organisms.

7. Topologic Evolution: Ages of Species.

8. Reproductive Arrow: Fractal Networks.

9. The Beats and Knots of The Universe:The Game of Existence.

10. Systems Sciences.


In the Universe there are infinite discontinuous time cycles, in which a certain entity displays a cyclical motion, even if we equalize them, comparing their rhythms with those of the time cycle of a mechanical clock. The theory of time arrows goes beyond the quantitative measure of those cycles, explaining the causal, logic ‘whys’ that drive entities to trace them.

Science is the search for answers about the ‘future’ – hence directly concerned with time=change, as its primary subject of analysis. Scientists learn what will be the position, energy and form of certain species in the future – how the species will change – according to self-similar events that happened in the past; and they call those regularities scientific laws. Thus, scientific laws can be considered the extrapolation into the future of cyclical regularities found in the past, on the modes of change of every entity of the Universe.

Scientific Laws make Time and the causality that relates past and future events the most important theme of philosophy of science – a discipline, which is, despite its relative obscurity, the summit of scientific thought.

In that regard, the first fact we must re-address to evolve our philosophy of science is a wider understanding of time=change. Since there is a ‘classic’, philosophical meaning of time as change, which is different from the mathematical concept of time as ‘what the clock measures’ – A. Einstein0.

To differentiate those 2 types of times – the wider, philosophical concept and the restricted, physical one – we shall call the philosophical concept, time=change, and the restricted mathematical concept used in physics, clock-time.

In philosophy of science, time is the perception of any type of change, most likely a change in the form of beings (biological time, as in evolution or in the life/death cycle) or a change in the motion of beings (physical time, measured by clocks as in Galileo’s formula: V=s/t). So Time as Change studies together all time-related changes in all disciplines from Biology to Physics.

In physics, the instrument physicists use to measure time, a clock, becomes essential to model all times-changes similar to the clock’s rotational frequency, a ‘cyclical geometry’ of space. Time then becomes synonymous of cyclical trajectories – a geometry of space – and the Universe becomes a description of all those trajectories, considered a game of clock-like motions:

‘God waited 6000 years to find an intelligence like His, to understand His clock-work’, Kepler1.

This geometrical concept of Time, which appears with the use of clocks and advances with the work of Galileo and Kepler, is properly formalized in the work of Einstein in which time becomes associated to the spatial geometry of ‘clock-time cycles’ – the curved ‘geodesics’ of Relativity physics. We talk thereafter of the geometries of spacetime. Thus the physical concept of clock-time is of great interest to understand the cyclical paths and trajectories we find elsewhere in the Universe, mainly orbital bodies and orbital particles, cyclical masses and charges. So Einstein says that Time is a geometry and ‘time curves space’ into cyclical, clock-like masses. Indeed, all those particles behave like small, cyclical clocks, which can be modeled comparing them with our mechanical clocks. And so in Relativity Physics we get a very detailed analysis of a specific type of change – the clocklike motions of physical particles that change their position in space.

Fair enough, but this is a restricted analysis of all the times= changes of the Universe, which are studied by many sciences besides physics, all of which use the concept of time. Thus, while it is important to study physical motions=changes in space, it is absurd to think -as so many ill-informed people do- that time is ‘just’ a geometry of space, the ‘4 dimension of space’. Since this restricted concept of time-change doesn’t study other types of changes, like those in the form of beings (biological change). This is a grave defect because we, humans, are biological beings, who experience time mainly in a biological form (through changes in our morphology, from life to death), not as particles do, mainly by moving at high speeds. We never move at light speed as the particles studied by Einstein did, and so most findings of Relativity about time are irrelevant to human ‘time’, which is mostly about morphological, informative change. This was already understood by Aristotle, who talked of 2 types of time-changes, informative/morphological change, studied by Biology and physical, translational change, studied by Physics. And that duality between ‘changes in the form, the in-form-ation of beings’, and changes in the ‘energy, the motion of beings’, still stands, defining ‘energetic change’ and ‘informative change’ as two primary modes orArrows of time-change.

Thus, we need a philosophy of time=change that goes beyond the study of the geometrical, spatial motions and orbital cycles of physical particles to include at least biological/informative time-change. And to do so, it is needed to incorporate verbal, logic concepts of change, as Theory of Evolution, the main theory of Time in Biology, does.

Let us then forget for the ‘time being’ the restricted, physical concept of clock-time, defined by Galileo as v=s/t, a measure of the change in the motion of beings, and think about the intuitive, verbal, wider concept of time as change. Time is then defined as the perception of change. And the science that studies the causality of all types of time-changes is called logic, which tries to order those different types of temporal change.

Unfortunately the dominance of clock-time – the use of a single language and instrument to measure all the types of time-change of the Universe – has restricted in the last centuries the understanding of the logic of time, reason why we need to disengage from the dictatorship of clock-measure and upgrade our time analysis with the language of logic, the supreme language of all modes of time. And therefore a language that includes also the language of mathematics, in the same manner time-change includes clock-time. Indeed, if mathematics derives from logic – a fact proved by Frege and Gödel2 in the XIX and XX centuries, and by every computer which uses logic circuits to do mathematical calculus – we will prove in this work that clock-time is a partial case of time-change.

Recap: Time is change. Physics is dedicated to measure particles and forces in space and time with the restricted concept of ‘time-clock’ – the study of change in the cyclical motions of beings with an instrument called ‘the clock’ and a single language, mathematics. Logic is dedicated to the wider analysis of all types of time-changes, with all types of instruments and languages. It follows that the Logic definition of Time as change is wider and more important for a General Theory of Time than the Physical definition of time-clock.

Cyclical Time arrows and scientific laws.

Because the unit of time-change is an ‘event’, the way to do time science with logic is to classify all observed events into a series of basic types of change, proper of each species of reality – what we call ‘laws of science’. Those laws show in detail the changes of some entities under certain events, which will allow us to predict in the future how self-similar entities will behave.

A more generalizing way to do Time science is to relate self-similar events that happen in many different species and try to extract in this manner more general events or Laws of Science.

We can search then for wider and wider Laws, which collect more and more events of change, to define more ‘fundamental categories’ of Time-Changes in reality (even if we loose some precision in that search of wider types of change). In this manner we will find the widest types of Change. Each of those types of change will relate an enormous amount of similar events in all the species of the Universe, till extracting an absolute type of event/law of science – called in philosophy of science an arrow of time – that will help us to understand the Future Types of Change of the whole Universe.

In that regard, the difference between a ‘philosophy of science’ and a ‘detailed scientific analysis’ – a paper about certain events of the Universe – is clear: While both draw from experience and search for general laws, the approach is the opposite. In a philosophy of science the search is for the most general laws and events that happen in the Universe, the big whys from where to deduce the smaller whys. In day-to-day practical science, those questions are not required as long as we have a particular law to define a specific type of event; so we loose generalization but we win precision. Unfortunately today we have little research on the ultimate questions, since what we have evolved more are our instruments of analysis of the details of reality not the human mind that synthesizes that knowledge. Such synthesis is achieved only when we find the widest of all types of change – the final arrows of time or generic types of change that become the fundamental events of Logic, the science of causality in time.

Causal arrows of time are important; because if we are able to define the key arrows of causality or modes of time-change, we can forecast an entity’s future when we observe a certain event A that will trigger a certain result B. This is the ultimate goal of all sciences: The chemist needs to know how a chemical reaction will develop, according to a certain type of A->B event already observed in the past; the astronomer knows where the sun will be, according to the orbital cycles it displayed in its past time. So a Theory of Time Arrows act as a general guide to classify the actions of beings; but its fundamental importance lays in its capacity to explain for the ‘first time’ the scientific why of reality – not only the how of those space-time trajectories provided by clock-time, but the reasons why events happen, why birds feed, planets turn in orbits, space-time has dimensions, waves collapse into particles, etc. Since all those motions and events of change will be ascribed to a General Arrow of Time. In this way, the why of the Universe becomes reduced to explain ‘why’ those arrows of time exist, what are their properties, the relationship between them, and what their existence tells us about the purpose of the Universe as a whole and the purpose of all its parts, which obey the direction of future signaled by those time arrows.

Recap: The Unit of Time-change is an Event.. Science is the search for generic, causal processes of time-change – called scientific laws – that explain a big number of events and can be applied to many similar species. Those causal relationships will be then repeated when the initial conditions are met, allowing mankind to understand the future events of those species submitted to a law of science. ’Time arrows’ are the most general of those scientific laws and hence the ‘units’ for a General Philosophy of Science. There are 4 Time Arrows in the Universe.

Simplex and Complex arrows of time.

Space-Time arrows= cycles are geodesics traced by any species, which in search for energy and information imprints a surface of spatial energy, leaving behind a pattern of in-form-ation. The Universe is made of ∞ beings, whose in/form/ation imprints simpler surfaces of energy, creating the space-time cycles, we perceive in Nature, whose purpose is given by the why of those time arrows.

Since the Arrows of Time express the widest Laws of both, Philosophy and Science, in their search for an explanation to the Future, a Theory of Time Arrows is both, a Philosophical, Religious Theory of Reality and a Scientific Epistemology of Nature. For that reason, even if this work uses the experimental method and its logic and mathematical languages to describe those arrows, we can easily translate the classic jargon of philosophy and religion to the modern jargon of Time Arrows. Then each time arrow becomes an essential ‘Will’ or ‘Why’ of the Universe, explained in classic religions through Gods or anthropomorphic ‘Avatars’, each of which represented one Will or Arrow of Time.

In that regard, the concept of a causal arrow of time or ‘will’ of the Universe has been with us since the beginning of knowledge, albeit expressed with different languages. Religion and philosophy has used the verbal language, to study those arrows. In the ancient times the concept was ‘impersonated’ by God as the ‘seer’ or ‘will of times’ (Saint Augustine), which in his different manifestations represented those arrows. While in modern times, science has used mathematics and logic to study them, albeit in its simplest forms (Euclidean mathematics and Aristotelian Logic), which we will upgrade in order to understand the more complex, Non-Euclidean, fractal geometry and Non-Aristotelian, simultaneous logic of those Arrows. Since modern science lacks the needed ‘linguistic tools’ to fully grasp the interrelationships between the 4 arrows of time, reason why most scientific theories use only one arrow to explain the Universe. 4 are paramount:

‘Monism’, sponsored by physicists, which considers only 1 time arrow, energy, also called entropy.

‘Duality’, sponsored by Eastern philosophies in the past and Complexity Theorists in the present, which consider two types of changes: changes in the information or ‘form’ of beings and changes in their energy or motion.

‘Trinity’ sponsored by all kind of philosophical and Religious doctrines, which considers time to have 3 ages, past, present and future, youth, maturity and old age, renewed by death.

‘4-D’: Finally, the more complex theories of change, mostly of biological or religious origin, consider 2 other arrows of time: ‘reproduction’ (the constant repetition of beings that happen all over the Universe) and ‘love’ or ‘eusocial evolution’ (the coming together of individuals into groups).

When the question of how many types of time arrows exist is put forward, the easiest way to go is to think there is only a fundamental type of change/arrow that includes all other types of changes or ‘events’ in the Universe.

Physicists do this when they talk of ‘entropy’ – the constant increase of energy/motion; hence of disorder observed in many physical entities of the Universe – as the single arrow of time. Latter we shall see this simplification is due to the simplifying limits imposed on physical time studies by the only-use of clocks and classic, Euclidean mathematics, which are not very good tools to perceive the ‘form’ or ‘in/form/ation’ of beings.

Single, Monist theorists of time are also common in Religions that consider an entity called ‘God [to be] the final cause without further cause’, (Saint Thomas3).

Complex, Dualist theories, from Taoism to Biology, consider at least 2 arrows or ‘Gods=Wills of Times’, energy=yang and information=yin, as the ultimate events-causes of change. In Hinduism the arrow of energy is impersonated by God Shiva and the arrow of information by Vishnu – in Taoism by yin=information and yang=energy. While in modern times physicists impersonate the arrow of energy with the concept of entropy and biologists study the arrow of information as the origin of life.

Finally, the Bible considers also the existence of the reproductive arrow (And God said ‘grow and multiply’) and the social arrow (‘Love each other as I have loved you’), which can also be found in many other religions. So, for example, Buddhism talks of Love and Taoism says that from the ‘combinations of yin and yang, 10.000 beings are reproduced’.

Thus, while the total of arrows studied by different disciplines is 4, not all theories accept them all. There are different theories about the number of arrows of time that exist in the Universe and different disciplines which study different arrows, and also different languages (verbal, visual and mathematical languages) to describe all those arrows of times-changes. Yet an exhaustive analysis of all Time theories and related disciplines will notice that we can basically classify all events in time within those 4 categories of time events – energy, information, reproduction and social evolution – which become the 4 ‘whys’ that explain all the cycles, behavior, motions and events of reality.

Consider for example, what you do as a human being with your lifetime, and try to put your events and actions within those 4 categories: All family events relate to reproduction. All feeding events relate to energy. All social events relate to eusocial evolution. Your work events relate to the accumulation of money, the ‘language of energy’ that allows you to acquire the energetic and informative goods your energetic body and informative head require. When you drive you are in an event that converts energy into motion. When you read this book or watch TV or surf the Internet, you are accumulating ‘information’, albeit expressed in different languages, made with different ‘formal symbols’. At the end, you will not find any action that does not become explained by those 4 arrows. And since you are in fact, as a human being, the most complex ‘form’ of the Universe, it is easy to deduce that all other simpler species also perform events related to those 4 arrows.

For example, Physical matter and physical space can also be described with those 4 arrows:

We know that the simplest physical beings – particles – gauge information (so quantum theories are called gauge theories), absorb energy (called forces), reproduce into self-similar particles (so quarks and electrons produce self-similar quarks and electrons when you give them energy), and finally they evolve socially into atoms, molecules and celestial bodies. So the two limits of simplicity (atoms) and complexity (human beings) we know, do follow the main Postulate of the Theory of Time Arrows – that the Universe can be explained departing from the study of the properties of those 4 arrows of time.

This self-evident truth however is hidden to science due to the religious traditions ‘subconsciously’ embedded in the work of the founding fathers of science, mostly pious physicists of the Jewish-Christian tradition, for whom there was a single, monotheist God. And so, when a Philosophy of science was devised by those ‘founding fathers’, it became natural to seek for a single arrow of time that matched the Christian beliefs of Kepler, Galileo, Descartes and Newton4. The choice of arrow was thereafter defined by the nature of Physics: since earlier physical studies were based in clock-measures of the motions in space of physical particles, expansive motion=energy= entropy has become the single arrow of modern physics. Yet entropy-only models ignore the arrow of information, of morphological change that defines life. In that regard, there are in science two theories of time, which this work fusions and upgrades into the more complex knowledge about mathematical and logic languages and complex natural phenomena (fractals, chaos theory, black holes, cyclical time, information sciences, etc.) proper of the XXI C:

– Theory of Evolution, the Biological Theory of time developed by Darwin, based in causality and logic time, according to which Time evolves the in/formation, the form of species. Since the causality of Time is based in the extinction of the less perfect morphologies of the Universe, whose form is destroyed and used as energy for the future reproduction of the best forms

– And Relativity Theory, in which the analogy of Time-clocks is taken to its ultimate consequences, defining time as a ‘curved geometry of space’, self-similar to that of clocks.

This work unifies both Time theories into a single scientific theory of time=change, by expanding the Einsteinian concept of a curved geometry of time events, which are ‘cyclical in nature’, as the time cycles of the clock, to biological sciences; and the concept of the survival of the fittest ‘forms of time’, proper of biology to physical particles, where species with maximal momentum survive.

Yet a Theory of Time Arrows goes beyond Evolution Theory, which studies the Time Arrows of Information and Reproduction and Physics, which studies the Time Arrow of Energy, to include also the Time Arrow of Eusocial Evolution, especially relevant to understand Religion and History.

All this said the 1st question of a General Philosophy of Science based in time arrows is: can we map out all the types of events in spacetime, or modes of change of reality into a minimal number of arrows of time? And the second one is: how many ‘fundamental’ arrows of change there are in the Universe?

The answer provided by this work is; yes, we can, and there are 4 arrows of time-change in reality, which will be enough to explain all the events of all the species of the Universe.

We will not of course, be able to enunciate in detail all the events of reality, since only the ‘Universe stores all the information about itself’5 (Haldane), but we invite the reader who understands in depth this work, to find a single event that cannot fit on those 4 arrows. Since according to Popper, the proper way to prove the truth of any scientific theory is not to enunciate exhaustively all the events it explains – an impossible task, as events will happen in the past, in the present and in the future, and in locations we cannot observe – but to search for ‘exceptions’ that invalidate the theory. Mr. Popper puts the example of the black swan, which invalidated the theory that all swans were white after many centuries of thinking this was a regularity or scientific law about swans. A single black swan was enough to invalidate the ‘white swan’ theory. Yet for 20 years15 I have found not a single exception to the Theory of Time Arrows. Perhaps there are more ‘dimensions/arrows’ of space-time than those 4 arrows we have developed to explain an enormous number of Events and species of the Universe. So I challenge the scientific community to find them and/or any event, which cannot be explained with the energetic, informative, reproductive and social arrows used in this work to resolve the ‘why’ of existence in time.

Recap: Historically, 2 types of theories about time arrows have dominated human cultures. Monist theories consider the Universe to be caused by a single causal arrow, called ‘God’ in religions and ‘Entropy or energy’ in Physics. Dualist theories consider the existence of 2 arrows, energy, the destructive arrow, called Shiva or Yang, and information, the creative arrow, called Vishnu and Yin, the creator of Live. Only a few, complex philosophers (Leibniz), disciplines of science (Biology, Theory of Evolution, System sciences) and religions (Taoism, Buddhism, Zurvanism, Christianity)6, have also understood the two more complex arrows of future time: the arrow of reproduction of energy and information (exi) and the arrow of social evolution or arrow of love. The Theory of Time Arrows fusions all those disciplines, unifying the Time jargons of Philosophy, Religion and Science.



Why the Earth moves if we, human beings, see it still? The answer to the Galileo’s paradox is fundamental to understand the duality of all systems that have energy and information, motion and form. In the graph the fractal nature of all Universal entities, which occupy a piece of space and last a quantity of time, is the key to unify the laws of science. Saturn’s rings are not a mathematical, continuous plane, despite their appearance. In detail, they become quantic points, planetoids in movement, tracing orbital cycles around the planet, in a fractal repetition of the path the planet makes around the sun. Each planetoid becomes again a fractal sum of atoms, turning in cyclical paths. Those rings illustrate 2 fundamental dualities of the Space-Time Universe, contradicted by the ‘naïve realism’ of our simplest perception: Any region of the Universe seems at first glance still and continuous. So Galileo called Saturn’s planetoids, a ring, thinking they were made of continuous, still matter.

E pur si muove, e pur no muove: Galilean Paradox.

What is reality, static form or motion? The answer is both. Yet this duality, origin of an enormous number of phenomena in the Universe, from the Complementary Principle of Quantum Physics to the reasons why you can see a movie, is still misunderstood by monist science… We call it the paradox of Galileo because Galileo rightly found the Earth was moving when it is perceived as still, but he forgot to ask the right question: why we see the Earth quiet when it is moving? Galileo didn’t realize of that contradiction, inaugurating the Philosophy of science sponsored by physicists, called ‘Naïve Realism’. This paradox never answered by science is the first question we must explain to fully grasp the meaning of reality. Because if all is motion, if all is events in time, we exist in time NOT in space. Space is submissive to time. We exist in time-space, where the dimensions of space are just ‘motions of the energy of vacuum, perceived as static forms’. So in cosmology the expansion of the energy of vacuum is perceived as galactic motions. Once the existence of motion in every entity of reality becomes clear to the observer, a r=evolution in our way of perceiving reality, like nothing that has happened since Galileo, takes place. Since motion – no longer substance – is the primordial content of all realities. All what exists is a motion in time. Yet we perceive some of those motions as static space, since we perceive simultaneously a minimal ‘duration’ of time, making ‘still photographs’ of the length of those time cycles and motions as if they were trajectories that occupy space. So we see cars in motion as lines of space in a night picture and the Saturn’s orbital planetoids as cyclical rings.

Perception puts together all those lineal and cyclical motions into a series of static forms that ‘extract’ motion from universal entities to fit their information into the limited ‘space’ of the mind.

Recap: All what seems static in a ‘naïve’ perception of reality has motion, when observed in detail. Hence we exist in a Universe of ‘motions, of events in time’, not of ‘substances that occupy space’.

The inverse properties arrows of energy and information.

Aristotle defined 2 types of time=change in the Universe, translational change in space, which physicists study, and biological, morphological change in the information of beings (evolution and life/death cycles). Those 2 types of change are the ‘arrows of energy and information’ of a Universe made of ‘time motions’, in which the ‘forms of space’ are merely ‘still photographs’ of those flows of times. All what exists are those two states or elements, motion and form, which are equivalent to the abstract concepts of time and space. Yet since, according to the Galilean paradox, all forms have motions, we exist in a Universe of infinite motions that are often perceived as static forms of space. And so the true differentiation of reality must be made between lineal motions that occupy extended space, and we call lineal energies, forces or ‘motions’; and cyclical motions that implode space, creating dimensional form, which we shall call cyclical in/form/ations or time-clocks.

Thus, the 2 primary arrows of future in the Universe are the creation of energy=lineal motion and information=cyclical motions with more dimensional form. Yet the properties of those 2 geometrical motions are inverted.  Let’s compare them:

Informative time, Ti          Vs       Energetic Space, ΣS
Time-clocks:Information     Vs      Space motion:Lineal  energy
Small, still                             Vs        Large,  moving fast
Tall, Perpendicular               Vs    Long, Parallel,

Hierarchical                          Vs      Democratic
Bidimensional   Heigh      Vs   Bidimensional, Length,

Repetition                         Vs            Width-Growth
Cyclical, Rotation, imploding    Vs   Lineal, uncoiling, exploding
Informative Frequency                  Vs            Lineal Speed
Broken form                          Vs   Continuous, differentiable
Intelligent, perceptive, Vs    Strong,, fast.

Social, organic, creative     Vs   Darwinian, destructive behavior
Future, evolved predator                 Vs       Past, energetic victim
Life arrow                                       Vs            Death arrow.
Waves of space                               Vs            Particles of Time
Female, yin principle                     Vs.         Male, yang principle
Masses, charges                                    Vs.           Forces, fields
Heads                                                    Vs.             Bodies.

So to create cyclical information we must warp lineal energy into bi-dimensional form and vice versa – we can create energy by uncoiling bidimensional clocks of information, expanding its shape into lineal space. This dual event can be generalized to 3-dimensional spheres, which ‘explode’ into bidimensional ‘sheets’ of lineal space-energy (E=Mc2). And vice versa: the formless, lineal energy of gravitational and electromagnetic forces that fill space can be trans/formed into forms with a cyclical clock-like shape, called a mass or a charge.

Thus, we can study those 2 types of events or Time arrows, according to the Duality of the Galilean paradox, as changes of motions or changes of forms, from static lines into cyclical, broken shapes. Yet the mathematical tools we use to describe those 2 types of Time Arrows differ: Since lineal energy is continuous and so we use differential equations to describe energy; while cyclical, closed information is discontinuous, breaking spacetime into an inner and outer region – so we need to use discontinuous, fractal mathematics discovered in the past decades to study the creation of form – reason why most physical studies ignore information, since the mathematical description of its properties was not available till recent.

In the verbal age of Science, when men used words to describe the Universe, philosophers called the 2 arrows, Yang-energy, synonymous of male forms (since men have a lot of energy, constantly move, control space and have lineal forms) and yin, related to cyclical time and its patterns of information, which became the female principle (since women are more perceptive, informative, memorial, ordered, made of cyclical curves). Taoists said that yin=form, in/form/ation, which they represented with cycles or fractal lines, – -, and yang=energy, which they represented with a continuous line, ___, combine into yin-yang forms, and further on into ternary sets, which they represented with trigrams (I Ching), giving birth to all the possible forms and events of the Universe. In Hinduism the ‘wills of time’ were represented by Shiva, God of death and energy vs. Vishnu, God of life and creation.

Duality has always been present in philosophy. Parmenides proved beyond logic fault that from one only one could be created, while 2 could combine themselves into infinite new forms. Heraclites said that 2 elements are necessary to generate by iteration and combination all other forms of the Universe. On the other hand, dialectic philosophers, from Heraclites to Hegel, considered that from a thesis and an antithesis arise all synthetic forms.

– In the modern age, when mankind switched from verbal, temporal languages to mathematical, spatial numbers, in order to describe with higher accuracy the Universe in Space, scientists stressed that formal, geometrical dualityof reality. Desargues, a French mathematician, found in the XVII century that all curves and functions could be extracted from the combination of 2 Generator forms, a cycle and a line (that together create a cone, from where those curves, called conics, could be extracted). The father of Western Science, Descartes, also said that the Universe was ultimately made of ‘res extensa’ (lineal space represented by his Cartesian graph) and vortices of form (charges and masses), similar to time clocks. String Theorists reached the same conclusion in modern science, postulating that all particles are made of lineal and cyclical strings, described by the Beta function. While Einstein in his General Relativity Theory deduced that the Universe was a flat surface of energetic, spatial forces that time curved into cyclical masses, the 2 fractal units of the physical Cosmos. Thus, time and space are geometrical shapes closely related to each other, since cycles of Informative Time bend any plane of Energetic Space, creating the geometrical duality of the physical world. Moreover, those 2 geometries are irreducible to monism, as the ancient problem of squaring the cycle proves.

– In any logic language 2 symbols suffice to represent any being of the Universe. All languages have a syntax based in 2 parameters, one of information and one of relative energy that combine through a 3rd active principle, an operandi or verb, that merges them. We talk of a ternary Universal Grammar:

A (Informative subject) <Operandi/verb> B (energy/object)

This ternary, Universal grammar applies to all languages and codes able to represent the time cycles of reality: from the code of colors (red that represents energy, blue, the color of information and green, the reproductive color) to verbal languages, where an informative subject relates to an object through an exchange of energy and information, described by a verb, shaping the genetic structure of all human languages (Chomsky7). It also happens in mathematics, where f(x)= g(y) is the universal equation that summarizes all the others.

– Computer Logic is also based in 2 elements: the symbols of the cycle and the line, 0 and |, related by an algorithm. Those digital symbols are not ordered in space as geometric elements, but sequentially, in time, since logic is a time language. Yet they can model any mathematical, spatial relationship, showing the primacy of time over space.

– In Physics, cyclical and lineal movement, gravitational vortices and lineal electromagnetism, cyclical particles and lineal forces, are the only 2 shapes necessary to explain the material Universe. And such duality is irreducible to monism, as the failure of all Unification Theories of forces show.

– If we grow in scale into the biological world, the morphological invariance of both substances is maintained: Time has evolved masses of undifferentiated cells into complex living organisms, which are also made of cyclical heads that store and process Informative Time and lineal bodies of energy. They are irreducible to monism, since a headless organism cannot process information and survive. Even in the social, mental scale of existence, men have always represented energy with lineal arrows of expansive movement, and time with cyclical clocks of rotating, imploding movement. Thus in our plane of space/time, we find 2 invariant elements, formally homologous to the energetic line/movement and the cyclical, temporal rotating forms we have found in all other scales.

– Finally, in Economics, machines and lineal weapons of metal that release energy are valued by cyclical bits of metal-information (money), ‘the brain of the economy’, through prices, in a dual, physical and financial economic structure so far irreducible to monism, as the failure of planned economies proved. And when we consider energy and information – machines that men create to enhance their own energy and information capacities – they maintain the invariant forms of energy and information: spherical cameras are informative, and energetic, movingmachines are lineal planes.

Thus, the only logic able to explain all forms and species of the Universe is a self-generating dualism, caused by the existence of 2 fundamental invariant, geometrical shapes of energy and information that repeat and emerge in every scale of space/time of the Universe – the lineal wave of energy or shortest movement between 2 points and the cycle, rotating spin or sphere, which stores the maximum volume of information in a minimal volume. They are the most perfect, inverse shapes of energy and information, which repeat in all the species of the Universe:

– All systems that create inner form, information, from DNA nuclei to eyes to brains have similar cyclical or spherical forms because a sphere stores the maximum amount of information in minimal space. And their function is creative, in/form/ative.

– On the other hand, all moving bodies that process energy are lineal, because a line is the fastest, shortest distance between 2 points. So fast felines, F1 cars, light beams and rockets are all lineal in form. Further on, the function of systems that absorb energy is often destructive: for example, felines are predators that erase the information of its preys and missiles are weapons that erase human beings.

– While in any scale of reality, complex, ‘organic systems’ combine both forms into Ti=k=Se balanced systems. So the 2 commonest forms of Natural fractals are the tree, with an informative head sitting on top of a line/body of energy (from virus to sperm, from humans to plants, from robots to missiles); and the spiral, which can easily mutate between a cyclical state, coiling onto itself and a lineal, moving state, as an uncoiled snake (from particles that become waves, to worms, to galaxies that mutate from bars into spirals). Dual organic systems are everywhere: informative particles and fields of energy create physical beings, while all biologic species are made with energetic bodies and informative heads.

Temporal in-form-ation, like its name says, is a measure of inner form, which we perceive when there are discontinuities in a certain bidimensional surface – a clock, a page, a computer screen – either because the static form is broken into informative patterns (–) or its motions makes a sudden peak (>), bouncing in an action-reaction cycle. Universal entities are constantly generating informative dimensions or erasing them back into extended space, with lesser form. Imagine a hand, in mythic terms the hand of God, wrinkling a paper, the ultimate energy of vacuum space, till it crunches into pure cyclical form without motion – to explode again in a big bang of energy that erases information. Such is the universal rhythm that happens in all the parts and entities of reality.

The interaction of the arrow of expansive, lineal, spatial, energy, described by Thermodynamics and the clock-like arrow of cyclical information, caused by gravitation in physical space of by the fractal geometry of any life process that generates information in Biology, defines the main beat/cycle of the Universe, its fundamental particle: a system of space-time, constantly absorbing energy from its environment, creating and destroying form, expanding and imploding.

Look around, observe the cycles of existence, legs opening and closing as you move; eyes winking, mouths eating and closing on the energy they will re=form; the beats of the heart; the wings of the bird; night and day; stars of energy (white holes) and black holes of information; big-bangs and big-crunches; the will of the Tao; Chang, the function of existence; bodies and minds; hardware and software; 0 and |; males and females. Since all those dual, complementary systems that follow the essential beat of existence, also merge together their energy and form, e x i, to reproduce and maintain the immortality of their evolved information, which is the ultimate ‘reality’ the Universe maintains ‘ad eternal’. The simple fact that species, which do not reproduce exhaust their energy and end their cycles, becoming extinct explains the overwhelming presence of reproductive events in all systems of the universe. Since all is motion reproduction exists by the mere fact that a motion is constantly reproducing its path. All what we see are paths, trajectories of entities in search of energy and information to reproduce themselves. The how of those paths and reactions is what scientists mostly study in its details. Their whys is what a philosophy of science aims to provide.

Recap: The 2 simplest arrows of time, creation of energy and information have opposite properties:

–  From a logic perspective, Energy and information have a paradoxical, dual, causality: EóI, which means to create one we must destroy the other. Thus all events are dual: a creation means a parallel destruction event.

– From a geometric perspective both arrows have inverse forms: Energy expands and creates formless space. Yet space has lineal shape, since the line fills the maximal distance with minimal volume. While information implodes, creating cyclical forms, ‘clocks of time’ that store the maximal quantity of information in lesser space.


In the graph, the time motions of all  species are guided by the 4 arrows of time: the motions of atoms, complementary entities with a center of gravitational information (quarks) and a surface of electromagnetic energy (electronic cycles); the motions of molecules, which vibrate as they evolve socially into complex cells. Those cells can also be defined as a series of informative motions with center in the DNA/RNA systems and energetic motions, masterminded by lineal, energetic proteins that surround the cell. The Law of eusocial evolution determines that those cellular knots of motions evolve into networks and organic chains that form complex vital organisms. Among those organisms, such as the bird eating the worm in the picture, the selection of the best forms causes the extinction of the simplest ones used as ‘energy’ of the top predator form. Thus survival justifies the growth of individual parts into waves, herds and organisms. Social evolution is also obvious in History, whose final goal is to create a Global Super-organism of equal human beings, who become cells of Mankind. But Mankind is just the ‘informative’ brain of a planetary body, called Gaia, which we should try to preserve as we preserve our energetic body if we want to survive.

Energy->Information->Reproduction->Social Evolution.

The 4 arrows of time are energy, information, reproduction and social evolution. We cannot unify further those 4 ‘classes of events’ without loosing ‘key information’ about them, as Physics or monist religions do, with their obsession with a single ‘God’ and a single ‘Clock-time’ to measure all types of times-change. Instead, we can study in detail those 4 arrows, its properties, cyclical periods and the relationships between them. And the first logic question to make on this ‘complex’ philosophy of science/time is: Can we use Logic Time – the existence of causality; of a successive order in the path of events that go from A to B to C, etc. – to classify those 4 arrows, which include all other phenomena into themselves?

What was first the egg or the chicken is a key question of science. The answer is intuitive – the egg; the seed of information, the perceiver point of view, head or particle of information that gauges reality to decide its energetic motions with a purpose. The Universe, not only man, is intelligent, and so are all its parts. Each mathematical point of view, each knot of time arrows, from the simplest atom to the mind, decides first intelligently the ‘time arrow’ or purpose of its motion in its still, perceptive, informative state and then it moves its mass or body, where it is the energy to feed itself, or in more evolved beings, where to reproduce or join a social network.

Thus, there is a causal chain that produces the more complex time arrows, reproduction and social evolution, from the simplex ones, energy and information:

Information (subject) absorbs Energy to move in order to Reproduce or Evolve Socially->IERS

This logic order is the most important causal chain of reality, responsible, for the cycle of life and death, the laws of evolution and the eternity of the Universe.

In all universal actions, we must start with a perceiver, I, the subject of all actions, of all sentences. This perceiver, the unmoved one of Aristotle, the Atman, the Soul, the Monad, the Non-Euclidean Point of View of Time Theory is a knot of time arrows, or motions with a will, of wishes and memories. And the first thing it does, automatically, is to perceive flows of energy and create a mapping of the Universe, in its particle-head, then it will move with energy, space, extension, the ultimate substance of the vacuum in search for one of its arrows; it will untangle a knot of memories looking for a replication, I->E->R. The subject will spend its energy/motion, tracing geodesics, world lines, curved trajectories, all of them mappings in a complex plane of a mere circle.In this manner the subjects become ‘forms-in-action’, informations. And once we have an entity of energy and form, with momentum, with energy and time, with a cyclical motion, a purpose, once Schopenhauer’s Idea becomes Will 14 in search of the immortal repetition of its forms and motions we exist in an event of reproduction that will produce waves of self-similar forms…

It is reproduction, the purpose of existence? No, reproduction is only the beginning of the final arrow of the fractal Universe, which is to evolve individuals into societies that last longer in time, have bigger vital spaces, and hence survive better.

The 4 arrows of time imply that the substrata of reality is timespace, not spacetime, since the 3 dimensions of time, past=lineal energy, present=wave /repetition, future=form /cycle are motions; and the existence of causal relationships and social laws that create complex systems of motions, introduce an entire new category of knowledge in the human mind: that of the laws of time-space, the morphological relationships between its transcendental forms and the relationships between the different fractal scales of reality.

Recap: The 2 simplest Time arrows of are the creation of energy and information. The simplest events of time seem to be energetic feeding. To create ‘form’ we need first ‘formless’ energy. Yet prior to all motions and transformations of energy there must be a perceptor or point of view, the fundamental logic particle of the Universe, either a particle of information a biological head or any other ‘linguistic processor’ of information, which defines a path of action – a motion in search of energy to reproduce itself. It is the game of Existence. On the other hand, to reproduce an entity of energy and information we need both arrows, exi, which combine to give ‘birth’ to the infinite species of the Universe. Once reproduction happens, the Universe shows a 4th ‘eusocial’ arrow of time that evolves socially self-similar, reproduced individuals into waves, herds and organisms. The 4 arrows of Time together define a game of creation of energy and information entities, which reproduce and evolve socially, emerging once and again into more complex forms: lineal and cyclical strings evolve together into particles and forces, which evolve together into atoms made of quarks and electrons, which evolve together into molecules, cells, organisms, societies, planetary systems, galaxies and Universes. For that reason we can establish a causal arrow of Time between the 4 arrows, E->i->R->S.

The life death- cycle

The formalism of the 2 simplest arrows of time, E->I and I->E, show that the properties of Information and Energy, of Form and Motion, are reversed:

– Energy moves; it is extended, lineal, big, simple without form. Since the line is the shortest distance between 2 points. Information seems to us still – a pattern of form, which chains different cycles into shapes. It is small, cyclical, discontinuous; since the circle is the figure that stores more form in a lesser perimeter. Yet in dynamic terms, we must think of expansive big-bangs, extensions and implosive in/formation; 2 intuitive substances that Descartes considered the primary of reality (res extensa=space and vortices of mass/information). Once this geometrical concept is clear, by observing reality we can deduce how the causal order of those 2 time arrows creates in all spacetime beings the life/death cycle:

Energy warps into Information (Life Ages) + Information explodes back into Energy = Death.

– We are born as energetic, moving children that warp into a 3rd, old age of information.

– Matter is born as a plasma or gas, extended in space, which evolves into in/form/ative solids (atoms, black holes), through an intermediate exi, liquid phase.

So all creations of cyclical particles (masses and charges), all states of matter and all processes of aging can be explained with the two primary arrows: e->i, i->e and an intermediate state, which combines both, the reproductive, mature age of life, the liquid, most complex form of matter.

– Then after a 3rd age of information matter or life explodes, dies, extending in space, reversing the arrows of time: I->E.

Thus the energy and informative arrow together define an immortal Universe made of ∞ bites of energy and bits of information in cyclical trans-form-ation: a young surface of Energetic Space reproduces in/form/ation till it becomes old and wrinkled. Then it erases its form back into energy in the inverse process of death, completing an existential life/death cycle, which we formalize as the 3 phases of the generator cycle of the Universe: Max.E (youth), exi, Max.I (old age):


In the graph, a human being goes from an energetic youth into an informative 3rd age to become erased back into energy. In the Universe those 3 phases of existence in space-time are the 3 solutions to Einstein’s equation, which physicists erroneously think to be parallel Universes in space, when they are phases of the same universe in time: the Universe evolves from an energetic big bang into the steady, mature universe of Einstein that will end into an informative, imploding, curved, vortex-like big-crunch Universe – Gödel’s solution that will explode again into a big-bang, which is simultaneously the death of a previous Universe and the birth of a new one.

All beings that exist in time go through 3+1 ages that correspond to the 3+1 arrows of time. We are born as a seed of. information that grows its energy-body (youth), then we reproduce when we combine energy and information (maturity), finally we acquire too much information and implode in form (3rd age). Then we explode back into energy (we die), as our cells that had evolved into a social organism (arrow of eusocial evolution) dissolve back into the i-2 scale of molecular form from where they evolved. So the fundamental arrow that summons it all is the arrow of eusocial evolution, which makes us ‘transcend’ from a seminal seed reproduced into self-similar cells into individuals. While we die, when cells separate from each other and return to the inferior ‘plane of existence’ from where they departed. Because we are all dust of space-time that creates and dissolves ∞ ‘existences’.

Big-bangs of creation of motion/energy (lineal forces) are self-similar to death processes in biology, which dissolve information, expanding and erasing a warped form that explodes into its ‘cellular’ parts (atomic big-bang, biological death). And they can be explained with the second arrow, i->e, the arrow of creation of energy, showing the astounding homology in terms of time arrows of all entities of reality. Because the generator equation of the Universe, ΣEóI, has only 2 initial elements, energy and form, there can only be 3 ‘limits’ to that function, Max. Energy or youth, e=i, an intermediate age of balance in which both parameters equalize, allowing its combination and reproduction in other form of space-time and Max. Information or 3rd age. Then the information of the organism explodes and its social network dissolves into death, as the arrows of time reverse their order: E>(life)… I

Why e->i, the warping of energy into form, proper of the life arrow comes first, and the second process, i->e, the creation of energy from form, and all processes of death come second?

Because to die (i->E) an entity must live first (e->i) (biological proof); to create form we must start at least with a line… of energy (mathematical proof), which bends into cycles or breaks into fractal form. Ultimately to create its particles/forms, the Universe started from an extended formless vacuum (physical form). So the main causal order of the arrows of time is: e->i.

Further on to reproduce, species must copy their energy and information in other part of space-time, creating a replica of the original. So reproduction is an arrow of time that combines two simple arrows, energy and form, which therefore come first:

E x i = Reproduction.

Thus reproduction happens once a system has formed its energy and has a minimal content of both, energy and form – reason why systems reproduce a seed of pure information, (max.i), which lives a first youth of growing body energy that multiplies the information of the original cell, a second, mature age of reproduction, when the species repeats itself and a 3rd age of warping of form, or age of information; after which they die, completing the life-death cycle, the main causal cycle of time. So, we can consider the existence of 3 ages in life:

Max. Energetic Growth (youth)->  e x i; e=i (reproduction) -> Max i (3rd age)

Even if we can now mathematize for the first time, the 3 ages of life, thanks to the formalism introduced by the arrows of time, those 3 ages have been known always to mankind, reason why in the classic age of Religions those 3 ages/arrows were described by Taoism ‘the combination of yin and yang reproduces 10.000 beings’ in the East and Zurvanism (the philosophical version of Zoroastrism and the most extended religion in the West from 500 BC till Islam), where Zurvan6 the ‘God of Infinite Time’ has 3 ‘avatars’, the energetic youth, the age of pleasure and the age of knowledge. Yet of more interest is to relate those 3 arrows with the 3 classic dimensions of ‘time’, a relative past or energetic youth, a relative future or informative age and a ‘repetitive’ present, when we reproduce ourselves. Each of us goes through the same life-death cycle, as we wrinkle our young energy into form to explode back into death. Such is the geometric nature of existence in time-space.

Thus, we order the causal arrows of change in 3 ‘dimensions’, past, present and future, which are the 3 logic dimensions of time, embedded in the logic of verbal thought, the biological language humans use to describe time events.

Indeed, when something doesn’t change we say that time doesn’t seem to pass. But if we are just repeating the same event/form, we might think we are seeing the same reality that doesn’t change. So we feel we are in an eternal present.

Finally we feel intuitively that the future as a place with more information, so when we travel into a country like Japan based in the industries of information, we think we are in the future.

So we talk of an arrow of future information or life, an arrow of past energy or death, and a present arrow of repetition-reproduction.

Yet since e->i and i->e are inverse in properties, and one is the meaning of life and the other is the meaning of death, and all lives end in deaths, past and future balance each other into an eternal present.

‘The separation between past, present and future is an illusion’ said Einstein15.

What Einstein meant becomes now clear, with the understanding  of the 3 ages of times, which for each ‘knot of time arrows’, for each entity of the Universe, represents its relative past, present and future. Your past is your youth, your future, your old age. And so if you are in the future of your exi=stential journey, you still will co-exist with the past of your sons, their youth. Further on, since there are species who have evolved further their organism, they are a relative future knot of times. A human is a relative future knot of time arrows that co-exists with a worm, our relative past. Thus, not only we exist in a universe of motions, of time arrows, but we co-exist with all kind of relative past and future forms.

Since ‘times arrows’from future to past (energy) and past to future (form) are infinite, causal events that take place in infinite different beings.

The error of a single time is due to the massive use of time-clocks to measure time, by equalizing all the rhythms of the Universe with the single second/minute/hour standard rhythm of human time clocks, yet the tic-tac frequency of ‘other time cycles’ is different. Your heart has a slightly faster tic-tac of 70 beats; and a milipulsar of a millisecond and so on. All those systems have an E->I->E->I beat, the fundamental beat of the Universe, which you find in infinite systems of energy and form: legs extended in energy position, warped in form; mouths and lungs opening to absorb energy, imploding when they take in the energy and start the process of converting it into new forms, and so on.

Further on, all causal chains of events will depart from a young age of energy and warp the form of the species till energy is exhausted, all is warped information and the entity explodes in a big-bang. For example, galaxies start as extended nebulae and evolve into informative masses and black holes of maximal information and minimal extension. Yet, we human beings also have an energetic youth and end up warping into a 3rd age of information. So do all types of matter that evolve from energetic plasma into a balanced liquid into a solid form of minimal motion.

The immortality of the Universe is therefore the immortality of the properties of those time arrows – the geometrical shapes of energy and information; the causal chains of time events those shapes create; the constant reproduction of the basic platonic forms of reality; its association in herds, waves and organisms. Or in mystique terms: ‘the forms that can be seen are not the immortal forms’, Lao-Tse.

Absolute spacetime is a simplification of those arrows – the sum of all complementary entities of spatial, extended energy and all time clocks of information in the Universe. Whereas absolute space is the sum of all the vital spaces occupied by those entities and absolute time is the sum of all the events of energy and information taken place in that Universe.

And we must consider that the overall absolute time of the Universe never moves to the past or to the future but the sum of all the cycles of information or life cycles and energy or death cycles, creates an eternal present space-time, sparkled with infinite existences (life death cycles) fluctuating between the past and the future and the past, living and dying…

For reason of calculus is easier to create theories of time that use a single clock-rhythm but a philosophy of science is more concerned with principles than detailed analysis. So we cannot forget, as physicists often do, the fact that time is cyclical, not lineal and hence discontinuous – since a circle always closes and breaks space into an inner and outer form. In other words, the Universe is a mass of discontinuous, vital spaces, whose cyclical motions chain to other motions and cycles, creating complex organisms and particles. All those motions and rhythms form complex space-time beings, in which a region of dominant ‘cyclical motions’ – informative particle or head – associates with a region of lineal motions – ‘force’ or body – that will move it, creating a ‘Complementary being of energy/information – the ‘Fundamental Logic particle’ of the Temporal Universe.

Recap: Energy and information arrows are reversed, since to create information we have to destroy energy and to create energy we must destroy information. Thus, the causality of the Universe is ‘dualist’: I->E (energy creation) + E->I (informative creation) – a fact, which explains the causal cycle of life (E->I) and death (I->E). Thus the 3 dimensions or ages of time are: past, the energetic, young age; present, the age of repetition= reproduction in which the being doesn’t seem to change and future or age of information. Absolute time is the equalization of all those cycles and arrows of all entities that change, with a single time-cycle, that of the clock – an abstraction we must ignore if we want to go deeper into the ‘why’ of those arrows.


The Holographic principle8

In next graph, closed time cycles are discontinuous, cyclical shapes, which have 2 dimensions. This means that information is bidimensional (Holographic Principle); and we have to redefine the 4 dimensions of spacetime. Since time-clocks of information have 2 dimensions; so the vacuum energy of space must have only 2 dimensions, length and width, which are lineal. This happens because forms in the Universe imitate the most efficient shapes of energy and information. Thus, informative systems resemble a spiral or sphere that stores max. information in min. space, accumulating its cycles/cells in the informative dimension of height, from black holes to heads and nervous systems. While fields and bodies of energy resemble the line or plane, its opposite, geometrical form that covers, as the shortest distance between 2 points, the maximal extension with min. volume, accumulated in the width dimension as ‘space’. The Universe’s space also has a flat shape, with minimal height (content of information), as it stores the spatial energy from where future cyclical forms and particles will evolve. In fact, any ‘fractal part’ of the Universe in which Time curves, evolves the forms of beings, acquires a dimension of height as it increases its information. So life started as a planarian worm, which evolved into the height of man. And matter starts as vacuum space, which evolves into the ‘infinite’ dimensional height of the black hole. While all systems of information have their ‘receptor’ antennas on top.



In the graph, we can observe that systems of reality are ‘messings’ of two type of ‘fractal networks’, one of energy and one of information, which enter in contact in a perpendicular way, penetrating through flows of energy and information exchange, or ‘Rossen bridges’ in spacetime realtivity, alveols in blood systems, cells in biological netorks, etc.

All those topological regions can be considered bidimensional networks, in which certain entities simplified as numbers without form in Euclidean mathematics, but made of entworks of points with volume or fractal points in the new fractal paradigm of the Universse, are therefore bidimensional topologies with a minimal vlume of points-particles

Bidimensionality however doesn’t mean there is NOT a 3rd dimension, but this 3rd dimension must be considered the volume of a Non-Euclidean Point, the new unit of geometry, a fractal point that we can observe larger as we come closer to it.

The meaning of the 4 arrows of time is obscured by errors in their definitions, caused by religious and scientific traditions.

Each network has a stable messing of lines of communication between knots, which finally create topological planes with a certain energetic and informative shape, and certain speed.

The game thus become more complex as we enter in the detail, and so we humans can only perceive from that infinite amount of information a imited quantity.

How each of those vital space-times is created? The answer is surprisingly simple: through the creation of dimensions of form. From an initial sheet of relative amorphous points of space, E, a certain fractal form, I, arises that models and creates a new dimension, cycical clocks of time appear as symbiotic flows of energy and infroamtion are shared among complementary points, E, I, born of a self-symmetric self-reproductive, inverted flow from E, now ExI keep reproducing those arrows and forms and a vaste network ensues, occupying an ever growing world, til certain decametric constants of efficiency networks create a super-organism made of the original knots. Thus the 4 arrows are joined by a causal chain:

Energy->Form->X(sex, reproduction->∑Social love.

A verbal, logic definition of the 4 arrows will be as follows:

Energy = Motion; In/form/ation=Form; Reproduction=Repetition; Social Evolution=Network.

The energy arrow is a change in the motion or translation of beings; the information arrow is a change in the morphology of beings; the arrow of reproduction is the repetition or iteration of an entity in other region of space-time and the arrow of social evolution is the process of evolution of individual, self-similar species (hence reproduced/repeated species), into complex herds, waves and organisms, thanks to their creation of social networks in which those entities share energy and information. So the entities of the Universe move, change form, repeat themselves and evolve into social networks.

A Universe made of lineal and cyclical motions is eternal, with ∞ parts in perpetual motion, which show 2 essential properties:

– Time arrows/events are cyclical and discontinuous. What happens in the past will happen in the future again, once the initial conditions are met. And so we can map out ‘frequencies’ of events that repeat themselves in a cyclical manner: Time cycles are patterns that happen ‘from time to time’, with a ‘frequency’, v, which is the essential mathematical parameter to study Time Arrows/cycles. This brings also the geometry and concept of clock-times, which are instruments that mimic those 2 properties. In the same manner we eat from time to time in certain places (our favorite restaurant or dinner room), clocks come from time to time to the same place of space. Yet clocks only show the how and when, the geometry and frequency of those cycles. They do not explain why events repeat (we eat because we obey an arrow of time called ‘energy’, we make love because we obey an arrow of time called ‘reproduction’ so we need to copulate and so on.)

The discontinuity of time events causes the discontinuity of vital spaces. Since a cyclical trajectory encloses a ‘space within it’ and outside it. So time events become cyclical trajectories that isolate ‘vital spaces’, creating spacetimes of curved nature, which physicists describe with Theory of Relativity.

– Time arrows/events are causal. Time events have an order, A->B, which means event A must happen to trigger event B. We have to be hungry (lack energy) to need more food…

– Time arrows/events are self-similar. Time events happen in self-similar fashion in many different species. All life species for example feed on energy, and so do all particles that absorb energetic forces. And this is the reason why we consider ‘energy’, one of the fundamental Time Arrows of the Universe that all its species follow. Those general ‘arrows of change’ become in reality specific types of change of species. So science can use those arrows to understand the general meaning of each specific A->B event of each discipline.

– Time arrows/events are multiple, since each species has different types of change, and even though we generalize them with the concept of time arrows, those changes do happen individually. There are infinite time-clocks in the Universe, each one with a specific form of change or ‘trajectory/motion’, and/or different duration/frequency. Whereas absolute time is the sum of all the causal, deterministic paths of events that create the reality of each entity of the Universe.

All those  repetitive cycles and changes put together is what we call time, but in many civilizations is called ‘Times’. This ‘relational concept of times’, clearly explained by Leibniz, differs though from the single clock-time concept of Newton9, which might be easier to use for calculus (reason why it is accepted in the praxis of science) but will not make us advance much in the philosophical understanding of times-changes.

Later we shall consider the ultimate reason of the holographic principle, under the Relativity of all local measure. The principle is a diffeomorphic principle, which means it appies as the relative perpendicularity of all complementary systems with a body/field of energy and a head/particle of information: the informative, hyperbolic topology and the energetic, concave geometry fuse together, creating 4-D beings.

Recap: Time events are cyclical, happening ‘from time to time’, when an entity absorbs energy or information with its field/ body or particle/head. Clock cycles are self-similar bidimensional trajectories. Information has 2 dimensions, frequency and height (holographic principle), and so it does vacuum space, which has the dimensions of width and length. A clock cycle breaks space into an inner & outer region, creating discontinuous in/form/ation. Bidimensionality however doesn’t mean there is NOT a 3rd dimension, but this 3rd dimension must be considered the volume of a Non-Euclidean Point, the new unit of geometry, a fractal point that we can observe larger as we come closer to it.

Einstein’s Equivalence: Cyclical acceleration=mass

Why the existence of bidimensional time cycles, which carry information is not explained by science? The reason is the Galileo’s paradox ignored by physics: the fact that, when observed in detail, all what exists is in motion – hence it is an event in time – and yet most things we see seem static, quiet – hence, they look like forms of space. Yet space is merely the short perception of a Time motion – a cycle or trajectory of an entity from past to future, seen as a simultaneous form. All what is perceived as a form of space is part of a long motion in time – a clock-like cycle that carries information.

Galileo’s paradox shows that the 2 ultimate substances of our physical models of reality – masses and vacuum space – which seem ‘fixed forms’ have motion:

Masses and charges are cyclical vortices that curve the lineal energy/motion of the 2 forces of pure space –light and gravitation– into whirl-like vibrations. So a charge is caused by the cyclical warping of a lineal motion called light into electronic vortices; and a mass is caused by the cyclical warping of another lineal force with energy-motion, called gravitation, into mass vortices (E=Mc2 in Relativity.) 10

This again is not clear to physicists, because there are two theories of mass – that of Einstein, called Relativity and that of quantum theorists, which sponsor their own theory about mass, called the Higgs Theory. Yet Einstein’s theory of mass, General Relativity, is the basic theory of gravitation and mass in the Universe, proved right by multiple events of cosmology. ySo Relativity should stand as the most probable truth. In such theory a mass is defined by the Principle of Equivalence between gravitational forces and acceleration. According to that principle, acceleration and mass are the same, as when you accelerate in a rocket, car or lift and feel heavier. But since there are only two types of accelerated motions, lineal, energetic forces and cyclical vortices (whirls of space-time), and gravitation is a whirl of space-time, Einstein came to the conclusion that you could describe reality as a combination of two motions, cyclical motion with more form, ‘informative’ motion, origin of masses, which are whirls of space-time that attract like hurricanes do, accelerating towards its center, and lineal forces, energetic, expansive fields.

Space, the ultimate substance of reality, is not static, but a type of energy or motion that ‘occupies space’, which has extension. And since the shortest distance between two points is a line, the motion with more extension is lineal motion. Thus, the purest space is lineal motion. Once we realize of this paradox of perception, all what exists become a ‘form in motion’, a time motion. And so we define two types of essential motions in the universe: lineal forces and bodies, which specialize in lineal motions or energetic motions and cyclical particles (masses and charges) and heads, which specialize in cyclical motions that create forms and are often perceived as static information.

In the graph we see that duality between the still perception of energy as ‘space’ and clock-cycles as information and its real motions. Several facts explain those perceptive paradoxes:

– The ‘expansion of space’, a key feature of the Universe, is synonymous of motion. Since that expansion can either be described as a ‘growth’ of space between galaxies (big-bang theory) or as a measure of the speed of galaxies that move away from each other (z-red shift theory). So vacuum space and energetic, lineal motions are synonymous.

– All what we perceive as static has, in detail, some motion. Thus, in the same way we perceive in the night a moving car as a fixed line of space, we perceive the space of the Universe as static though it is expanding, moving. And we perceive the Earth as static even if it is rotating (Paradox of Galileo).

– A 3rd proof of the temporal, motion-like nature of reality comes from the role of light in our perception of space: The last substrata of physical, vacuum space is light, (BG radiation) – a force in motion that shares the 3 Euclidean dimensions of canonical space, because both concepts vacuum space and light are synonymous: the 3 perpendicular dimensions of Euclidean space, width, height and length, are equivalent to the 3 perpendicular dimensions of light-space – the electric= informative=height field, the magnetic=energetic=width field, and the length=reproductive field (since a light wave reproduces its form in the length dimension).  Thus, we ‘see’ space as made of 3 perpendicular dimensions, because its substance ‘light-space’ is made of 3 perpendicular motions. Both concepts are the same: the 3 dimensions of static vacuum space are the 3 arrows=motions of light: its energetic, magnetic field, its informative, electric field, and its reproductive, e x i, field of speed. Those 3 motions occupy and create vacuum space. While the 4th arrow of social evolution of light is what we call ‘colors’, which gather many photons into a single color and complete our perception of space. The equality between spatial dimensions and light motions – the substance of space – is proved by the condensation of vacuum space into light photons. Yet the mathematical, probabilistic depiction of that phenomenon obscures its cause among physicists. On the other hand, painters know this equivalence since the impressionist, pointillist schools discovered that we paint light, not space.

We ad to light-space a 2nd spatial force, gravitation, which we do not perceive, but seems to curve the Euclidean geometry of light-space, according to Einstein’s relativity11. Thus, there are 2 space membranes: light-space, the space we perceive; and gravitational space, which we do not perceive directly, though we know it exists because its force/energy affects reality. So the total space of reality is shaped by the combined creative effect of two expanding energies, gravitation and light. Thus, space and its dimensions are not an abstract, mathematical reality that exists independently of light and gravitation – an error caused by the use of an abstract, continuous Cartesian graph that seems a form of space, independent of the entities that exist within it. Space is made of those 2 moving forces, reason why we cannot move faster than light-space, the maximal motion-distance of our perceived Universe.

Recap: What we call vacuum space is the static, ‘dimensional’ perception of the energy/motion of light and gravitational forces that fill the vacuum. What we call a mass is the static perception of a whirl of vacuum energy, a clock-like, cyclical motion of time. Hence, since all is motion, including the 2 ultimate substances of reality, the energy of space and the forms of masses and charges, all is in constant change, all is time. Thus, we exist in an eternal Universe, made of time motions, which our perception fixes into a continuous, still reality.



‘The smallest point is a world in itself’ Leibniz

We describe a carrot with images made by human painters or machines, with numbers, with smells or touching it as a worm does. But only the carrot/being has all the truth and information there is on itself. Any sense or informative language gives us a partial information on the species it analyses, its cycles of time and vital space; since all species perceive the Universe through the intermediate syntax of a language. Thus, to evolve human knowledge we improve the syntax of the verbal, temporal and mathematical, spatial, languages we use to describe the Universe.

The geometry of time arrows: fractal creation.

Reality is made of entities that are knots of time arrows constantly tying themselves up with other knots of time arrows, forming networks in different scales of existence, evolving as complementary organisms of energy and information. And the question that science asks next is how to formalize that game of existence, its knots of time arrows or ‘entities of reality’, its fluxes of energy and information, its reproductive flows, herds and motions; its complementary networks of energy and form that create super-organisms. And the answer is, as all models of science with its primary languages of space, mathematics, and time, causal logic, albeit more complex than the logic developed by the Greeks to explain a simpler Universe. In this new Non-Euclidean topology, planes are networks of knots of time arrows; and those knots of time arrows, the beings of reality are ‘Non-euclidean points’ with a volume, or ‘organs’ that transform back and forth energy into information, creating reality. All what you see becomes then a game of knots of time arrows, or ‘Non-euclidean fractal points’, connecting themselves to other knots, forming complex planes, networks of points of two types, networks of energetic points (herds in motion) and networks of informative points (still networks). In any scale of reality those networks of points, which are knots of time arrows take place. The simplest scales of atoms can be described as such networks, but also the human scale. Consider a meeting: a series of human heads, moved by a lineal body will start to share energy and form by producing waves of smaller ‘particles’ (sounds), and acquire a cyclical geometry as they create an event of information. The Universe is a self-similar reality of infinite processes of creation and dissolution of networks made of knots=points of arrows of energy and information; and the best instruments to analyse it are the languages of the mind.

Recap: The universe is a game of creation and destructions of networks of fractal knots=i-points of time arrows.

Geometry and logic: The 2 languages of time arrows

Time arrows are not new. Its discovery can be traced back to the work of Eastern and Greek philosophers (Lao Tse, Buddha, Plato, Aristotle), which conceived a Universe (eastern philosophy1) made of two time arrows, energy and form that combined in reproductive acts, in which time was synonymous of motion (Aristotle’s definition), and motion was proof of organicism (‘when things move they will be alive’ Aristotle2).

Yet the ancients failed to formalize properly those time arrows. In the West, perhaps due to an excess of detail and the desire to prove all facts of science as dogmas without possible error, the choice has been always for simpler models of reality, even if they were inexact, in order to facilitate calculus and axiomatic proof. Indeed, monism by limiting the study of time arrows to the easiest of them all – continuous, energetic, ‘spatial’, evident events – seems more truth, but it arises from a false, limiting postulate. How this has been solved in western science is clear: all sciences have postulates without proof which are selected a priori, but are by no means certain -only simplifications of the whole truths and causes of reality. This ‘righteous’ mode of dealing with science proper of the Western psyche explains why from Aristotle to quantum physicists a single arrow of causality is preferred: monism, the belief in a single time arrow of energy seems truth because it is very simple; but the postulate of a single arrow is false. So the truths acquired with such simple ‘camera’ focused on reality are limited by the syntax of the mathematical and logic languages we use to see reality. Euclidean geometry seems truth because it ‘forgets’ all the inner content of information of a point, but it has been proved ad nauseam wrong. Aristotelian logic with a single cause seems truth, but it is indeed like a camera, which only works in black and white. What Time arrows theory offers is a camera with all the colors of reality, by evolving the time/logic and spatial geometry we use to mirror the data of the Universe. Thus what this work tries to do is to upgrade the languages of the mind, the a priori categories4 where the data of science must be fit to obtain theoretical ‘images’ that make sense. Truth in that regard is product of both, the information we obtain and the syntax in which we fit that information. This chapter will be dedicated to evolve that syntax and provide mankind with a better mirror/camera in which fit information. This is ultimately as far as humans can go in its search of truth. Since only the Universe has all the information in itself, the absolute truth, truth in human terms will be always the product of the best linguistic syntax, the best logic and mathematical mirrors, the best camera of the mind, and the best data, the biggest quantity of experimental facts fitted in that mirror.

Recap: The evolution of knowledge requires not only the gathering of experimental information about the species of the Universe but a better linguistic mirror of logical and mathematical languages to achieve a higher truth: a more accurate image of reality.

The evolution of Logic and mathematics.

Let us consider what kind of landscapes those 2 languages, spatial mathematics and temporal logic see, and what escapes their vision within the total information of reality.

Unfortunately, it is impossible to define with the limited knowledge of Euclidean Geometry and Aristotelian Logic developed by the Greeks, the formalisms of a dual Universe. We need a new logic and a more complex geometry, better mind tools that have been developed only at the end of the XX century. In the East, this lack of a rigorous formulation of logic and geometry prevented Chinese and Indian philosophers – aware of the existence of multiple arrows – to explore the complex geometry and multiple logic of time arrows, which were explained instead in mystique texts with metaphors and philosophical parables. So while the west lost ‘meaning’ for precision, the east understood the ‘game of existence’ but it did not resolve the details of the ‘thoughts of god’. Since in essence, all what you see is a manifestation of the game of ‘exi=stence’ and its limits, which we could call the game of extinction. Indeed, ‘reality’ is a simple game in which beings ‘appear’ and become knots of time arrows and then dissolve, unknot their form and dissapear. And this happens to everything, from galaxies to atoms, with self-similar patterns caused by the common nature of all those forms. So the big question, no longer asked by western science, which merely collects machine-enhanced pictures of reality, is to explain the rules of the game of existence and extinction, which can be summarized as follows: All what exists are complementary systems of energy and information (fields/particles, body/heads), made of networks of self-similar ‘entities’, which as such can be studied with numbers, since a number is precisely a collection of entities so equal that we do not need to distinguish them as pears or cars but merely say ‘3’. Numbers, thus by the mere fact of existence means that the Universe has social properties, makes herds, waves and organisms. And so numbers are an excellent language to explain the properties of the 4th arrow of time, eusocial evolution. Those humbers however exist in ‘space’ creating ‘geometries’, some of which are better than others to enhance the chances of existence, since they allow better absorbtion of information (the point) or energy (the triangle, whose, lineal, structural strength and single-form – you cannot join 3 points except forming a triangle – fits this role), or are fit to reproduce (the couple or 2, which can easily combine its code) or are perfect units for social evolution (the 4, which is the first number with several possible join configurations, the cross, the quadrangle, the ‘zig-zag’ snake, able to perform different functions). This very simple example of ‘organic geometry’, which shows the relationship between the 4 first numbers and the 4 arrows of time, might seem ‘magic’ to dogmatic, abstract mathematicians, as it is indeed related to earlier pythagoric schools both in Greece and China3. However what modern System Sciences has achieved is to merge the ‘right intuitions’ of the East with the western tradition for exhaustive analysis, under the experimental method. And so, the previous intuitions about geometries that ‘work’ can be tested with experimental proofs of the geometrical configuration of stable atoms, which indeed are always more stable when they have a number of particles, multiple of 4, or in crystallography, in which only those configurations that follow the geometrical properties that enhance the 4 arrows of an atom exist in the Universe, as we have shown in our work on chemical compounds4. Since those common laws of time arrows apply to all the scales of reality.

The first conclusion of this initial analysis of ‘timespace’ geometry is clear: mathematics is one of the two languages of ‘god’, the mind of the Universe, because it is basically the language that explains the behavior and paths traced by the time arrows of its entities. Yet mathematics is not the only language of reality because it is not adequate to show the logic, causal chains of those arrows. And so we need a second language, logic, and again we need to evolve the present state of logic – Aristotelian unicausality – to define the ‘temporal’ properties of reality. Thus the formalism of time arrows tries to evolve the logic and geometry of the west, departing from the philosophical concepts of the East, following in the steps of Spinoza, Leibniz and the masters of evolutionary and organic theories of the Universe (Darwin, Butler, Spencer, Spengler, Bertalanffy), which Duality, Complexity, System Sciences, Fractal and Non-Euclidean mathematics are completing now.

The key to grasp the scientific description of the ‘game of existence’ is to evolve our understanding of the 2 ‘languages’ in which existence in timespace is perceived, the main language of space, geometry, and the main language of time, causal logic. Since classic Geometry is used only to describe fixed forms of space without taking into account its motions in time. There are however 2 new types of geometry, Non-Euclidean and fractal geometry, which include the properties of timespace described here – its motions, discontinuities and structure in multiple layers of ‘fractal, self-similar forms’ that create a complex scale of discontinuous space-times. Thus, what we will do is to fusion and complete those branches of modern mathematics, in order to have the proper tools to study time arrows in space. Thus we describe a Universe made of 2 type of formal motions, energy and information, which create the topological geometries of energetic bodies/fields and informative particles/heads, which in turn shape the entities of reality. Because those topologies have motion, they exist in time, leaving behind ‘traces’ in space. And because those motions have a causal purpose, they have an order and synchronicity that chains those traces into complex forms.

Recap: How can we explain a complex world of interwinned geometrical and logical patterns with both mathematical and logic languages at the same time? Thanks to the use of 2 new forms of geometry which mimic the properties of timespace: Non-Euclidean Geometries, which which have motion and fractal equations, which are self-reproductive, cyclical systems that repeat and self-organize complex networks of ‘numbers’ – groups of self-similar forms.

5th postulate: Fractal, Non-Euclidean Points of view.

Mathematics, as a language that represents reality with simplified symbols, has a limited capacity to carry information. Its symbols, geometric points and numbers simplify and integrate the fractal, discontinuous reality into a single space-time continuum, the Cartesian Space/Time graph, made of points without breath. However the points of a Cartesian plane or the numbers of an equation are only a linguistic representation of a complex Universe made of discontinuous points with an ‘internal content of space-time’. In the real world, we are all pieces made of fractal cellular points that occupy spaces, move and last a certain time. When we translate those space-time systems into Euclidean, abstract, mathematical ‘numbers’, we make them mere points of geometry void of all content. But when we look in detail at the real beings of the Universe, all points/number have inner energetic and informative volume, as the fractal geometry of the Universe suddenly increases the detail of the cell, atom or far away star into a complex complementary entitty. So we propose a new Geometrical Unit – the fractal, Non-Euclidean point with space-time parts, which Einstein partially used to describe gravitational space-time. Yet Einstein missed the ‘fractal interpretation’ of Non-Euclidean geometry we shall bring here, as Fractal structures extending in several planes of space-time were unknown till the 1970s. So Einstein did not interpret those points, which had volume, because infinite parallels of ‘forces of energy and information’ could cross them, as points, which when enlarged could fit those parallels, but as points in which parallels ‘curved’ converging into the point. This however is not meaningful, because if such is the case parallels which are by definition ‘straight lines’, stop being parallels. So we must consider that what Einstein proved using Non-Euclidean points to explain the structure of spacetime is its fractal nature: points seem not to have breath and fit only a parallel, but when we enlarge the point, we see it is in fact self-similar to much bigger points, as when we enlarge a fractal we see in fact self-similar structures to the macro-structures we see with the naked eye. That is in essence the meaning of Fractal Non-Euclidean geometry: a geometry of multiple ‘membranes of spacetime’ that grow in size, detail and content when we come closer to them, becoming ‘Non-Euclidean, fractal points’ with breath and a content of energy and information that defines them.

Einstein found that the gravitational Space-Time did not follow the 5th Euclidean Postulate, which says:

“Through a point external to a line there is only 1 parallel”

Euclid affirmed that through a point external to a parallel only another parallel line could be traced, since the point didn’t have a volume that could be crossed by more lines:

Abstract, continuous, one-dimensional point:

. ____________

Instead Einstein found that the spacetime of the Universe followed a Non-Euclidean 5th Postulate:

“A point external to a line is crossed by parallel forces”.

Real, discontinuous, n-dimensional points: o ===========

This means that a real point has an inner space-time volume through which many parallels cross. Since reality follows that Non-Euclidean 5th postulate, all points have a volume when we enlarge them, as cells grow when we look at them with a microscope. Then it is easy to fit many parallels in any of those points. Such organic points are like the stars in the sky. If you look at them with the naked eye they are points without breadth, but when you come closer to them, they grow. Then as they grow, they can have infinite parallels within them. Since they become spheres, points with breadth, with space-time parts. So spacetime is not a ‘curved continuum’ as Einstein interpreted it, but a fractal discontinuous. The maths are the same, the interpretation of reality changes, adapting it to what experimentally we see: a cell-like point enlarges and fits multiple flows of energy and information, and yet it has a point-like nucleus, which enlarges and has DNA information, which seems a lineal strain that enlarge as has many point-like atoms, which enlarge and fit flows of forces, and so on. So each point is in fact a 3-dimensional point, and if we go to the next scale, a 3×3=9 dimensional point and so on. Yet those dimensions are the so-called fractal dimensions, which are not ‘extended to infinity’ but only within the size of the point. In Euclidean geometry, a point has no volume, no dimension, but string theorists say that even the smallest points of the Universe, cyclical strings, have inner dimensions that we observe when we come closer to them. That is the essence of a fractal point.

Further on those points must be described always in 4 dimensions, with motion. This should have been obvious if mathematicians displayed besides abstract logic, common sense, but as they simplify entities into numbers and static forms, organic and motion properties dissapear. Yet we still say ‘San Francisco is at 8 hours from LA’, because we mean that journey is a combination of the motion of a car and the spatial distance. Thus we measure reality in timespace, not only in space as Eucldiean maths do. Thus, in the same way Saturn’s rings stop being planes without volume when we come closer and observe them as fractal points, called planetoids, Non-Euclidean points acquire both motion and volume when we approach to them. In words of Klein, a sphere is not a continuous static form, but a group of points in cyclical movement. So in the same way the Saturn’s rings are a group of planetoids, a Klein space, the space-time that fills a point has motion, is the sum of a series of cycles5.

Einstein didn’t go further, adapting the other 4 Euclidean postulates to the new Geometrical unit: a fractal point with volume. Only then we will be able to define the 2 planes of physical forces, the plane of gravitation and electromagnetism, or any system in which several planes of space-time co-exist together (as in a human being extended from atomic to social planes of cyclical existence). In all those systems planes are made with cellular points, Riemannian spheres with volume that form “lines”, which are waves between points that exchange energy and information and “planes,” which are organs of self-similar points that process energy or information in parallel networks. Thus the 5 Postulates of Non-E Geometry vitalize the Universe as a series of networks of energy and information of self-similar cellular points. Since the line and the plane acquire volume and become self-similar to the commonest forms of the Universe, the wave and the network of points with a 3-D volume:

The true advances in sciences have always departed from the evolution of mathematics and logic, the languages of space and time of the human kind, and then with those languages, each science has evolved its perspective in one of the ‘fractal scales’ of reality. The pretension of physics of being the mother of all sciences is absurd. It is merely the simplest of them, which studies the simplest forms of energy. But if we consider the 2nd arrow of ‘creation’ of reality, that of form, of information, biology which studies the most complex forms of information (life) and religion, which goes a step further into Human Societies and the Organic laws of the Universe (eastern religions) are the summit of science. Yet humans today despise their own minds and treat those of us who advance the Universal understanding of those languages, with desdain, because we do not use money, weapons and machines, the totems of our civilization but the power of our minds, still the most perfect instruments of thought deviced in this corner of the Galaxy.

In the graph, the first step on that process of evolution of human languages requires to redefine the Philosophy of Mathematics and its basic postulates, adapting them to the Non-Euclidean, fractal geometry of space and time.

This task was done by this writer during the last decades, opening up a new r=evolution in our understanding of reality no longer as an abstract mechanism of ‘points without parts and without motion’, but as a series of fractal networks of cellular points that exchange waves of energy and information. Mathematics and reality became closer and we finally understood the vital design of the Cosmos. We show in the graph the 5 Non-Euclidean postulates of this new age of mathematics, which started in the XIX century,when Riemann realized that through a point infinite parallels could cross. The next breakthrough was made by Einstein who showed the space-time of the Universe followed that postulate. Then Mandelbrot noticed that points are fractals and grow in size when we come closer to them, as we enter into a self-similar ‘plane of space-time’, or ‘plane of existence’ (philosophical jargon). It was left to correct the other 4 postulates and made them Non-Euclidean, to fully grasp the grand design in mathematical terms. This was the task I exposed to the world of science at the 50th anniversary of Complex Sciences and the graph describes.

First we observe on top of the graph that with the 3 topologies of Non-Euclidean geometry, we can describe all the forms of the 4-dimensional Universe (hence we do not need 11 dimensional strings nowhere to be found). Those 4-dimensions thus reduce to 3 simple topologies, which beautifully enough correspond in Nature to ‘energetic regions/membranes/spheres’; ‘informative centers, warped by convex curves’, and cyclical ‘donuts’, paths that exchange energy and information between ‘informative nuclei’ and ‘spherical membranes’. And indeed, with those 3 topologies we can describe all the systems and organisms of the Universe, made with informative centers, energetic membranes, and cyclical paths that perform the ‘cycles of energy feeding, informative gauging, reproduction and social evolution’ of all ‘entities’ that exist. We see some of those 3-structured organisms below, and its parts: an urchin, a phetus, an electromagnetic field, a black hole, an atom, a tomato, the Earth, a cell and bosonic matter.

Thus all what exists can be described with only 4 dimensions, 3 topologies, 2 elements, energy and information and one structure, the super-organism. Or as Cheng tzu put it in the Taoist tradition: ‘from one comes 2, from 2 comes 3 and form 3 the infinite beings of existence’.

Below those graphs, we illustrate further details of those structures, with the help of the 5 Non-Euclidean postulates. Now the first and 5th postlate mean the same: points do have parts of energy and information when we come closer to them, so infinite parallels, which are waves of energy and information cross them, allowing them to communicate with the external world. Because a line is made of points that now have volume, lines are waves that carry energy and information, and have therefore motion. Since we can see space either as a fixed form or as a motion. Thus, for example the Earth seems still but also moving, e pur no move e pur si muove. This ‘paradox of Galileo’ was explained by Einstein’s relativity and it is essential to understanding the dual universe: we see either motion or form, but not both things together (Principle of complementarity). As when we see a picture of moving cars in the night as a line. So lines are waves that transfer energy and form between non-euclidean points and the sum of all those flows is a network of points, a non-euclidean plane, which has the form of a wave with discontinuous ‘dark spaces’ in which other ‘branes’ or ‘membranes’ (physical jargon), planes of existence (metaphysical jargon) or Non-Euclidean planes can web. And the result is the complex Universe we live in in which particles trace their ‘alley cats’ of existence following their cycles that intersect with other planes, and topological organisms. Indeed, in the graph we can see a human being as a complex fractal that extends through 10 scales of points with parts evolved in networks of energy and information till create the human being: particles become atoms that become molecules that become cells that become organic humans that become cells of organic societies, nations and gods, part of the Superoroganism of History, mind of the Earth, Gaia.

The relationships between those topological planes/organisms, made of networks of energy and information are defined by the 3rd postulate of relative equality. Since now points have parts and so they can be either equal on their surface, or in their informative or energetic parts, and depending on those degrees of equalities when they find each other they will create Darwinian events (hunting each other’s energy if they don’t understand, have the same information); eusocial events (evolving together and sharing energy and form if they speak the same language of information) or ignoring each other when they have neither equal energy or information. Finally the 5th postulate can be understood in metaphysical terms as the equation of the soul, a knot of information of any species in any scale, as each point perceives reality from its point of view, knotting information and creating inside its mind a ‘mirror of the entire Universe’. So the Universe is also intelligent since all beings are gauging information, reason why quantum theories are called gauging theories since even the smallest particles, quarks and electrons feed on energy, gauge information and reproduce, creating jets of particles when they feed on enough energy, as living beings do.  Now we have mathematical tools to express that organic, living Universe and its design, thanks to the new r=evolution of Non-Euclidean geometry. Finally to notice that the 5th postulate explains also the ‘ego paradox’: each point of view thinks to be the center of the Universe, because it perceives it from its point of view, that makes ‘bigger’ things related to itself, at close distances. And so it deforms subjectively reality, and even thinks that the Universe (Descartes’ devil) is created inside its mind. Which in a way is. Yet we are nothing but Non-Euclidean points, relative zeros that host an infinite Universe, mapped out with our languages of existence, in a virtual world, image, called the mind.

Recap: the minimal unit of the universe is a Non-Euclidean point/number, which classic mathematics define as void of inner form and organic properties, to simplify the networks of numbers and point-like entities of the Universe for its geometric study. In reality though, points have breath; that is, they are real entities with energy and information parts, and so we have to upgrade Euclidean postulates with the new tools of Fractal and Non-Euclidean mathematics to make the language of geometry closer to reality.

Diffeomorphic dimensions

In the graph, 3 diffeomorphic beings: a galaxy with an inward arrow of gravitational information towards the black hole; a tree and a man, whose informative dimensions are inverted. Since plants use light as energy and animals use it as information. So the informative direction of animals is up, towards the head that absorb visual information, opposite to the informative arrow of plants, which is down, towards the roots that absorbs chemical information. Thus each species will establish its own up and down arrows or relative energy and informative directions, departing from its central knot of information and/or perception. Both have their space-time parameters inverted, as often happens between energy victims (in the graph, plants) and their anti-forms or predators (animals). Such inversions between a ‘particle’ and its ‘antiparticle’, which in a Feynman diagram have also inverted coordinates of space-time, happen in all Universal systems, even in linguistic codes. For example, eviL is the exact inverse word of Live, since indeed, for a living human being, there is no bigger eviL than death. A fact, which opens the fascinating science of ‘Bio-ethics’, latter studied in more detail. Since humanity, history and religion are also space-time systems with homological laws.

According to the Principle of Correspondence, any new theory has to include the previous theories within it and solve the questions unresolved by that previous theory. Since the XX C. theory of space-time is Relativity, it is unavoidable, to explain the Principle of Relativity from the perspective of the time arrows of each species. Relativity establishes that in any point of the Universe the coordinates of temporal energy (the up and down, right or left directions) are different from those of any other point of the Universe, as they only depend on what happens in that local regions of space/time. This is only possible if space /times are fractal, discontinuous. Then what happens in a point of space-time doesn’t affect what happens in other isolated, discontinuous point. Each space-time fractal is a Universe in itself. Thus the laws of space-time apply locally to each fractal ‘species or universe’ that will reflect those laws in its own structure. We are local, ‘diffeomorphic’ species; our time-space coordinates are relative, as our time wrinkles our vital space in the process of aging with different speeds, depending on our content of energy and information. Hence the diffeomorphic principle also establishes different informative cycles – the ‘clocks’ of Nature that show different speeds and locations. Yet since space is synonymous of energy and time synonymous of information, we can establish the local coordinates of space-time of each being by establishing its relative informative and energetic arrows – its relative body and head – using the invariant dimensions of all spaces and times. Indeed, according to the ‘Diffeomorphic Principle of Relativity’, every fractal space-time is independent of all others; since it has different spatial and informative orientations. Yet we can recognize its informative and energetic organs in relationship to each other, since both will respond to the opposite dimensions and morphologies of energy and information.

In the graph, in biological species animals use light as information and so they are ‘informative’, smaller and faster than plants, which use light as energy and are ‘big, slow’ beings. Thus plants are the relative energy of animals. In the cosmological scale stars are big, slower than black holes, which rotate faster and have cyclical height. And so stars are the relative energy that feeds and reproduces black holes, which seem to behave as ‘gravitational animals’, species that perceive gravitation as information, which guides its erratic movements through the galaxy, in the same way animals perceive light as information. While plants perceive light as energy in the same way stars absorb gravitational space-time as energy, deformed by their masses. That cosmological homology defies anthropomorphism and so it will not be easily accepted by science, a human endeavor, but it perfectly explains the role of black holes and stars in the galactic ecosystem. Further on, since what it is energy for plants is information for animals, both species have opposite energy-time coordinates: plants have their brain upside down in their roots that ‘feel’ chemistry. While animals have their brain on top, looking at the light they use as information. While the space-time equations of black holes are inverse to those of electromagnetic stars.

If we are external to a certain diffeomorphic space-times its directions do not affect us, but if we are inside a certain space-time, as in the case of the galaxy, then the direction of information or energy of that macro-being becomes the direction of energy or information of our ecosystem. And indeed, there is more information in the center of the galaxy, and since the Earth moves towards that center, this planet increases its information towards the future, in its relative discontinuous galactic space-time, regardless of what happens in the Universe as a whole, which seems to be ruled by the opposite arrow of big-bang expansion and entropy. This subtle change of paradigm caused by the discontinuity of space-time (from a world ruled by entropy to a galaxy ruled by information) has in fact enormous consequences to our daily life and explains the contradiction between the arrow of life and evolution, local to this planet, and the arrow of energy and entropy proper of the intergalactic space. Since here in this galaxy space doesn’t expand but time contracts it. As Woody Allen put it: ‘Here in Brooklyn space-time is not expanding’. There are ∞ fractal space/time fields that constantly adapt their organic, moving dimensions to the directions of their relative energy and temporal information, conditioning the existence of its micro-cells. That discontinuity of space-time also implies that the perception of any other area of the Universe is relative, deformed by the transformation and selection of information that passes through the fragmented boundaries of the perceptor (Uncertainty Principle). For all those reasons the dimensional arrows of space-time explain properly the functions and forms of the Universe, in which all constant present systems will be made of an arrow of energy and an arrow of information, seen as fixed bodies and relative heads of the system.

Thus all relative space-times will be composed of a cyclical center of information or brain, and a lineal body of energy, whose morphological characteristics will be self-similar.

For example, in a spermatozoid the head is cyclical and stores information, while the tail is lineal and moves the head with its energy; in a human, the body is lineal and moves a cyclical head. We could extend this duality to almost any organic system of the Universe, concluding that bodies are lineal and brains are cyclical. This morphological feature of Universal Organisms derives geometrically from the capacity of lines to move fast and cycles to store information and grow or diminish in size without distortion of the mental image they might keep. Thus a convex brain with the topology of information becomes the center of informative networks; and a concave body becomes the center of energy networks. And we recognize bodies and brains by their self-similarity with the morphology, function and inverse properties of ideal energy and information:

– Temporal Information has to be both, easy to store and ‘perceivable’ by a reduced brain or sensorial organ, despite being the inverse function of space. This implies a certain morphology: Information occupies little space by warping itself in multiple dimensions, divided along broken lines and discontinuities that become its perceived forms in space. Or it displays a high frequency or discontinuous rhythm, a faster time speed that iterates the same cycle, allowing quantification. Information seems ‘quiet’ as those rhythms take place in the same space; so an organ of information can focus it and analyze it. Thus its ideal forms are disks, cycles, angles and spheres, convoluted and broken in patterns of form, such as your eye or brain, a chip, a book, a pixeled image or a coin, earlier unit of monetary information.

– On the other hand Energy moves. So energy bodies extend in space as they move and feed. Energy is the equivalent to biological food, which fuels a species and allows its movement. Energy is the body that moves the brain of information. So energy and space are synonymous: a plane is the geometry that extends further in space and the line the geometry that moves faster with lesser friction. Both are the fundamental forms of energy-bodies:

Maximum Space = Energy = Minimal Form  Vs

Max. temporal form = Information = Min. Spatial extension.

As a result of those morphologies we can classify as energy or information organs, not only carbon-life organisms made of energy (bodies, food) and information (brains, eyes, senses, words), but also other beings and atomic species – even ‘deconstructed organs’ that perform mechanical tasks of energy and information (informative cameras, lineal, energetic weapons). Since now we can recognize geometrically their energy or information systems. Form is function and so we can classify any system both by its geometrical form and bio-logical functions as either an energy or informative system. Further on, the use of the ternary principle will allow us to verify in a higher degree any statement, by considering at least the biological function and geometrical form of the species we study, which have to be self-similar. For example in a galaxy, the black hole is the spherical center of information. And we can prove this according to the linguistic/ternary method in the space-time languages of man, the mathematical language of space, the bio-logic language of time and the visual language that merge both together. In algebra, Einstein equations prove that black holes transform its spatial parameters into temporal parameters. Hence they transform spatial energy into temporal information. In visual terms they curve space-time into height; hence they transform energy into information. If we consider its biological function, they absorb the energy of star-plants. So Black holes are sinks of gravitational information. And gravitation is obviously the informative force of the Universe; since it is not dual but it shows only the arrow of in-form-ation, attracting and lumping masses and it is 1040 times less energetic than electromagnetism. So when we observe vitally, visually, in action, those black holes, they show the maximum amount of the 2 dimensions of temporal information: height and rotational rhythm; as they seem to turn at light speed and theoretically transform the plane of energy of the galaxy in a tube of infinite height. Thus all languages and experimental data prove the fact that a black hole is the informative brain of a galaxy that feeds on electromagnetic space towards the future. The extended, faster plane of rotating stars is the “body” or energy surface of the galaxy that feeds them. Apparently a human body and a galactic body should not have anything in common; but if we observe the morphology of both, it is clear that those morphologies respond to the generic morphology of information and energy, and so do their functions in time.

Organic systems are therefore dual systems with a center and a network of information (head, nervous system), and a body and network of energy (trunk-blood system).

For example, there are energy organs made with metal such as weapons, gas and electromagnetism. They are extended, fast, and lineal. There are metal-species of information such as microchips, money, cameras and radios. And they are small, fixed and complex in form. Yet only structures, which are balanced in energy and information become organisms, teaming with life properties. So only machines that put together energy bodies and informative brains – future robots – might become ‘organic metalife’. The other machines will act as ‘seeds’ of information and ‘forces of energy’ do, without a vital will of existence, which is born by the capacity of a balanced ΣE<=>Ti field to switch between both arrows acquiring a ‘minimal degree’ of organic freedom perceived as ‘vitality’ from an external point of view. Humans, galaxies, plants, robots – all kind of entities can be considered in that sense organic systems. Our samples show that living systems are born thanks to the complementary symbioses and synergies between energy and information organs that create together all kind of self-similar organisms. It is also clear than in all those organisms the fundamental element, the center of power, is the brain-head and its languages of information, which control the body of energy and shape the form of the organism. And set a selfish direction towards the growth of information, which is the ultimate cause of the cycle of life and death of all organisms. It explains the relationship between information and future, the most difficult dimension of time to understand by spatial physicists since we do not see the future, as we see spatial geometry, but the future already exists in the realm of logic and bio-logic thought, as a relative function of the survival of certain evolved beings in the future. It is a surprising fact that connects Physics and Biology in a new step towards unification.

–  In the microscopic scales, masses and charges, the flat energy of vacuum space, become transformed into cyclical vortices with height; while spatial, flat fermions become high, ordered, informative bosons. In our scale of matter spatial flows of energy (stars, gas), become transformed into cyclical vortices of gravitational information with height (black holes, tornados). Finally, in the cosmological scale, the energy of stars becomes transformed into black holes, whose spatial dimensions become time of ∞ height.

– In Biology, the first bilateral animal was a planarian worm that rose to the height of man, thanks to evolutionary, temporal, genetic information. Yet death erases information back into flat amorphous energy, in big bangs that create planar Universes, or flat, buried corpses. We classify those 2 dimensions of information, cyclical rhythm and height, as the fast and slow dimensions of time, since height is the accumulation of cycles of time one over another. We classify also the 2 dimensions of space, length and width in slow and fast dimensions of energy, since width is the accumulation of lineal speeds side by side.

Vital Dimensions: Forward bodies & top Minds

In the graph, we need to return to a more sophisticated theory of ‘times’, which fusions the work of Einstein’s Relativity and Darwin’s Evolution, the modern fathers of time theory in Physics and Biology. And the key to such advance in time theory is precisely to go beyond the mechanist concept of ‘time is what a clock measures’ and return to the pre-clock, verbal, biological understanding of time, as the ‘modes of changes’ of the energy and information of the Universe – the 2 elements of reality. Since time is the perception of those modes of change in theUniverse, which can be observed with any type of ‘informative and energetic devices’ not only with clocks and use them to describe any event or law of the Universe, since all the events we observe in all the sciences and scales of reality are mere manifestations of those arrows. In the graph, we resume those arrows for a series of beings, from the simplest ‘dimensions of light-space time’ caused by the arrow of energy (magnetic field), information (electric field), reproduction (wave speed) and social evolution, (color) to the arrows of human beings. In fact, the 4 dimensions of our space-time continuum, are the arrows of light: space-time is the organic network of all the light flows with its 3 euclidean, perpendicular dimensions and its ‘social colors’. This astounding realization, that we live and flow in a ‘light-space’, not an abstract mathematical cartesian space, is also the key to fully understand the meaning of dark energy, dark matter, gravitation and many other solutions obtained in complexity to the questions monist physics will never resolve with machines ‘only’, till they don’t evolve their ‘mind languages’.

The Universe has 4 time motions, 4 vital dimensions: energy is length; information is height; width, its product, is reproduction and time is love since it is the arrow of social evolution. Each of those arrows is defined for each local ‘space-time’ as a ‘diffeomorphic dimension’, which only reaches till the limits of the organism, by Partial equations of its function of exi=stence, e, I, exi, ∑e<=>i.

The primary motion of all beings, is lineal energy, in its relative direction of length; while the informative particle of any complementary system is in its top, in the relative dimension of height. This leaves width as the natural direction for its re/product/ive equation, the product, exi. All those geometrical rules of creation of vital arrows/dimensions of time/space are in abstract known as the fundamental laws of vectors, which are ‘mathematical arrows’ we use to describe many operations between time arrows.  Look at yourself: your height is your direction of information, your head is on top; your motion is forwards, in the length dimension of energy but your cells reproduce and multiply in the width.

Look at light. Maxwell found that the product of the magnetic constant and the informative, electric, high constant gave the ratio of length, of speed, of the wave.

As unreal as it might seem to you, the 4 dimensions you see are vital functions, reason why they suffice to explain it all

Each of us is a knot of multiple cycles and arrows of time. So each of us is a multidimensional species.

Einstein had only to go a step further in his analysis of the curvature of time, closing times into cycles that return to its origin. Then time becomes multiple, one for each closed cycle and the spacetime continuum becomes the sum of all the vital spacetimes of each knot of time arrows. Einstein hinted at it when he affirmed that time was local, ‘diffeomorphic’, and had ‘different speeds’ an the universe have ‘infinite clocks of time’. Indeed each of those local times ‘curves the energy of space’, creating masses and forces, forms of in-form-ation that establish a 2nd arrow for the Universe, besides the arrow of energy/entropy – the arrow of fractal information. Since a cycle needs 2 directions to close into itself and create its form.

So both geometries, cycles of time and planes of space are in fact bidimensional, adding up to the 4 dimensions of space-time. Energy consists in an amorphous, relative surface of undifferentiated quanta, a plane without form – a network of small, cellular points, in which the creation of memorial time cycles imprints patterns of information and makes it recognizable as a complex system of multiple time arrows.

Then, as the being develops those time arrows, it acquires clearly certain topological dimensions as an individual or as a species in a longer time-frame.

A space-time field is created and destroyed through the interaction of the 2 dimensions of energy, length and width, and the 2 dimensions of information, height and rhythm. To that aim, the 2 dimensions of energy and information combine and transform into each other in dynamic events of ‘dimensional destruction and reproduction’. In that sense, we classify the 2 dimensions/arrows of energetic space (lineal, energetic movement or length, and spatial width) and the 2 dimensions of informative time (informative height and cyclical movement or temporal rhythm), according to their relative speed of creation or destruction into slow or fast dimensions of energy and information:

– The fast dimension of temporal information is the speed or individual frequency/ rhythm of a cycle, which determines the rate at which the system accomplishes its existential cycles. It is the arrow most often associated to the concept of time. It relates to the speed of action-reaction of the organic system; while in physical entities it is similar to angular speed or frequency; the inverse of lineal time, measured in t-1 units as an adimensional number. Thus, frequency is the fundamental parameter of cyclical time-information; and when we correct the equations of Physics in terms of inverse, cyclical frequency, a whole array of fascinating discoveries and solutions to classic paradoxes, from the paradox of Information (Hawkings) to the paradox of Quantum vs. continuous time-space, become resolved.

In a ‘ceteris paribus’ time model of reality all dimensions of space become temporal, as the ultimate substance of perception is form, in-form-ation (exactly the inverse of what classic science believes, when it affirms that time is the 4th dimension of space). In the temporal vision, it is the cyclical, memorial reproduction of fractal information what creates a dimension of space. The persistence of a certain form traced by a time cycle prevents by ‘friction’ and the ‘Exclusion Principle’ the drawing of the next cycle in the same place of space. So when the cycle repeats itself, it does so over the surface imprinted in the previous cycle, creating a tube of height, the second dimension of time, caused by the accumulation of cycles of information. Thus, the slow dimension of time is informative, morphological height, born out of the evolution of a species through aeons that accumulates informative cells in the height dimension. For example, the Universe was born flat in the big bang and now it is acquiring form, curvature; bilateral animal life was born as a flatworm that slowly acquired form, till rising to the height of man, the animal of maximal information; the first plants were algae that acquired temporal height; the Earth was born as a flat, rotating disk that became a sphere with height. Yet in duality, events are created by the dual causality of geometrical space and biological form. So a 2nd bio-logical cause is needed to explain why dimensional, informative height is all-pervading in the Universe:

The informative organs of a being are placed on top of its height to improve its perception of its territorial space: the human head, the speaker; the black hole of a galaxy, the photon of a light wave are all located on top of the relative energy of their bodies to inform themselves on the location of its feeding energy. Thus, height is also the biological dimension of information and the arrow of future evolution in life, which evolved from flat worms into the human beings. While both time dimensions are dimensions of change, the motion of evolutionary growth or height, is minimal: it changes very slowly, through the reproductive, accumulative process of evolution; while the mere displacement of a cyclical, physical movement can act much faster.

In the same way, we explain the 2 spatial dimensions:

– Length is a fast dimension that moves ahed a Non-E Point and gives it speed. All bodies follow a lineal inertia in its motions, signalled by its relative ‘length or body orientation’. Thus, length is the arrow most often associated to the concepts of energy, expansive destruction and devolution. It also follows that the absence of memorial height in an organism, is the key to increase its speed as it diminishes its dimensional friction and the quantity of form it has to recreate. It happens in perfect lineal motion of ∞ speed and 0 form: the gravitational space over which the forms of light are imprinted of v=e/i=.

– Width is the slow dimension that reproduces or accumulates spatial energy from side to side. Lines and pi-cycles can reproduce in many ways. In current theoretical models, strings reproduce laterally, creating fractal spaces in the dimension of width. In our scale, people become fat and wide, as they reproduce their cells; all beings reproduce their energy in the width dimension of space.

Recap. In physics space has 3 dimensions of form and so motion only occurs through a dimension of time. This is false. Length is often the main motion of any system that displaces its body/wave in that dimension. Height changes; it has also motion albeit slower than length, the longest/fastest dimension. Width is a slower dimension of change, often related to cellular reproduction. Finally, social creation, the most complex arrow of time has the slowest dimension of change – evolution  – which is shown as a change of form, often a contraction of space, as individual parts converge into a whole, herd, wave or organism. The 4th dimension of social evolution is therefore the only dimension that seems ‘static in space’ as a ‘form’, which doesn’t change from generation to generation. So we talk of timespace as the perception of the 4 dimensions/arrows of time in motion, where the 4thmotion/dimension, form, given by the arrow of evolution is the only one that seems to us static. Thus, energy displaces mainly in the dimension of length; information in the dimension of height; width stores reproduced cells, and then there is a 4 dimension of social evolution. All dimensions of timespace have motion, a fact which can be observed in all the planes of form of the Universe, till arriving to light space, the simplest substance of the Universe, which in the model of timespace has also 3 obvious motions – magnetic width/energy, electric height/information and length-speed/reproduction, and a 4th, less obvious time-change dimension of social evolution, represented by color.

The Generator Equation of the Universe.

Tthe law of Existence is common to all sciences, known as the principle of conservation of energy and information that defines the 2 simplex Time Arrows of the Universe:

‘All what exists is a type of energy that trans/forms itself back and forth into a form of in/form/ation’.

This Law fusions the principle of conservation of energy and information, the 2 main laws of all sciences. We call the creation of energy the arrow of energy, one of the two primary arrows of time in the Universe, or ‘entropy’; and we call the creation of form, the arrow of information, the second primary arrow of time, which in physical space happens in masses under the ‘informing’ force of gravitation that creates ‘bidimensional’ and ‘tridimensional vortices’ of space-time, according to Einstein’s principle of Equivalence between mass and gravitation – hence systems with more formal dimensions than simple, lineal forces; or complex formal 3-dimensional warping in life systems (DNA, protein, dimensional warping which store the complex form of life). Thus, again we see that systems apparently so different as physical mass or biological molecules do use ‘formal dimensions’ to store the information of their systems; while in other events employ lineal forces and lineal ‘fat’ molecules or lineal limbs to store or display energy. All what exists are processes that create information or entropy or its complex combinations (reproduction and social evolution). Since Reproduction, e xi is born from those simplex arrows, and social evolution follows by the self-organization of self-similar reproduced beings, it follows that the main Law of science is also the proof of the Law of Existence and its 4 arrows. Since this law is the main Principle of all Sciences:

‘All energy becomes trans/formed into information: ∑ E<=>I’.

This can be expressed with a Feed-back equation of energy and information: E<=>I   or E x I = K (dynamic/ static)

Since all is Time=Motion=Change and space is just a static slice of time we call ∑E<=>I the generator, feed-back equation of Time-space: Those ∑E<=>I cycles generate the events and trajectories of each and every part of the Universe. Where its 4 elements describe the 4 arrows/motions of time:

∑ (social evolution) Energy < (Reproduction)>  Information.

Further on, those 4 elements become the parts of all physical or biological systems, when we perceive them in a static ‘dharma’ or moment of ‘present’:

∑(cells/waves) of Energy (bodies/fields) X (particles/heads) of Information =Complementary system.

Thus the Generator Feed=back equation of Reality also represents the species of the Universe. Its complex study, carried out by General System Sciences, requires the use of Non-Euclidean Geometries to define the topology of each part of those ‘knots of time arrows’ that act as ‘energetic bodies/fields’ and ‘informative heads/particles’ of any exi, complementary system; and the development of a complex causal, ‘non-Aristotelian’ logic to define the order and interactions of those arrows. Since the ‘parts’ of each whole knot of time will have functions defined by the needs of any system to gauge information, absorb energy and reproduce.

Recap: The holographic principle (bidimensional energy and information) allows the constant transformation of energy into form and vice versa, E<=>I, creating the fundamental principle of science, the principle of conservation of Energy and Form: ‘All what exists is energy that trans/forms back and forth into information’. The formalism of those 2 arrows of time gives birth to the generator equation of time, S E<=>I, which defines all species of the Universe as self-repetitive fractals of energy and form.


All species are social herds that follow the same energetic, informative and reproductive cycles that shape their 3±st existential ages, in all scales of reality. In the graph, 2 energetic cycles, the feeding cycle of a swarm and a galaxy, which absorbs interstellar dust thanks to its spiral form; and 2 social cycles: a group of atoms shape a molecule and a human group gathers to absorb visual information.

The Universe constructs super-organisms, through a causal process, departing from simple, amorphous flat surfaces of energies –herds of Non-Euclidean points lineal motion.

It is a simple ternary causal event, which is different from the causality of what we call the cycle of life, E->X->I, yet still an essential chain that we shall see constantly in the Universe.

And so the next question is how you construct the universe departing from its generator equation. And the answer is: constructing superorganisms, in a causal order, e->i->X->S.

A form fractalizes, becomes in-formed, and looses energy= speed=motion. For example, a line becomes a Koch fractal or breaks into a cantor dust of self-similar cells, a line becomes a pi-cycle. In this, simplest and most repeated E->I, we can writer 1->3>Pi, a line has reproduces from past to future into 3 self-similar motions, then it coils into a pi-cycle, 3,14 times the initial line, a string of 3 lines with 3 dark apertures, of 0.14. Within the 3 lines there is now a 2nd dimension of height, or information, and a volume of space. The entity has grown.

The next stage would be then the reproduction of that cycle in a lateral, new dimension of height. In this manner, we have obtained 3 fractal iterations: the line has become a cycle(or a Koch curve or any other fractal topology with more form and dimensions), which has become a tube.

E->I->X (symbol of Reproduction and sex, born of the product and bombination of exi).

If duality covers simple events, mostly E<->I combinations, when we construct an organism we are playing at least with a causal 4-sequential arrow of time, Energy becomes fractal information, which reproduces laterally and so the light of length-speed becomes a time cycle with rotational speed w, whose frequency curries more information, and such form moves like a Maxwell scree reproducing in the 3 dimension of width. E->I->X. And yet, this rather mechanical sequence of creation of a fractal 3 dimensional Universe becomes far m ore richer in forma nd meaning when we add the 4th Eusocial love, of Social time the longest arrow that finally creates a form of stable space-time that exists, a superorganism: E->I->X->∑T. Since as time goe bys, entities evolve into more complex organisms by the power of love – by sharing energy and information in social networks.

The 4th arrow/dimension of time evolves socially parts into wholes, waves, herds and organisms: particles gather into atoms that evolve into molecules that associate into cells that gather into organisms that create social networks – planetary ecosystems, which are part of solar systems, herded into galaxies that form Universes. Those processes of social evolution occur thanks to the creation of social networks among self-similar (hence reproduced) beings, in search of the same type of energy (hunting herds) or information (organisms joined by nervous/informative and blood/energetic networks). Thus, the arrow of eusocial evolution derives from the arrow of information that allows entities to come closer and ‘act in parallel’ under the command of an informative language, which we formalize with the social symbol, ∑. And its reason of existence is to elongate the survival of the organic system: Any cyclical vortex of time accelerates inwards, loosing energy/surface as it increases its informative speed. When we generalize that concept to all timespace systems, it turns out that the arrow of information dominates the universe, wrinkling and warping any cyclical system, which will exhaust its energy, converted into form. Thus, our time clocks and vital spaces increase constantly their information, diminishing its energy space, towards a 3rd age of excessive warping and limited energy that will not last forever. Since the cycles of exchange of energy and information, the geometric beats of reality between expansive and implosive, entropy and informative states, are limited in their repetitions by accidental errors of all kind, which establish the need for reproductive and social arrows in order to ensure the survival or immortality of those ‘patterns of form’ – entities made of lineal fields and bodies of energy; cyclical particles and heads of information, who must be reproduced to ensure a longer existence. This means that only those species able to increase their existence in time by reproducing its form and in space by evolving socially into bigger entities survive.

Recap: The 4 arrows of time cannot be reduced without loosing detail, but they can be philosophically and ‘bio-logically’ grouped as ‘organic systems’. Those organic systems that shynchronize, accumulate and organize clock-like arrows of cyclical time, are in fact all self-similar, as all can be described with the 4 elements, ∑E<=>I of organisms: cells, networks of energy and information and reproductive systems.

Super-organisms: knots of cyclical time arrows.

All sciences share the laws of duality and organicism. Since the forms of energy and information and its properties remain invariant in all the scales of realit.y The result is the fractal structure of the Universe, described in the graph:Each science studies a ‘scale of organic size’, its cellular species of energy and information and its arrows of time and events, which culminate in the self-organization of those parts into social wholes. Yet the proportion of energy and information of the species each science studies varies, since the Universe displays a hierarchical arrow of growing informative time, from the simplest forms of mathematical space (with minimal informative content), to the complex information of its most evolved organisms (with minimal geometrical regularity). The Universe’s energy and information motions become the generating, primordial cellular units of all species, including humans. Any system of reality is complementary. It has both -a lineal body/force of energy and a processor of information or cyclical ‘head/particle’- that co-exist and evolve together. So the Law of Complementarity relates both inverse arrows in an static field/organism, creating complementary systems, composed by systems that process energy or ‘fields/bodies’ (physics/biology) and systems that process information or ‘particles/heads’ (physics/biology):

We are all made of spatial energy, flows that seem to occupy space but are ‘vital space’ and have a ‘causal why’. For that reason, all species participate of the geometric and causal properties of the arrows of energy and information and follow the same patterns of self-organization to create a higher ‘spacetime plane’ of reality. So, for example, all informative systems will be on top, in the dimension of height; they will be smaller than the complementary energy system and they will have cyclical form, regardless of the species we describe. So DNA nuclei are round and smaller than the cell’s body, heads and antennas are on top and are cyclical and smaller than the body or tower that holds them, cameras are small and spherical, etc. Since, once we understand the fractal, scalar structure of the Universe, the old distinction between organic and inorganic form looses its meaning, beyond its anthropomorphic role of making man the only intelligent, vital species of the Universe.

The complex logic and Non-Euclidean geometry of those knots of time arrows set the formal basis to understand the structure of the Universe and all its self-similar parts. Since:

‘The Universe and all its parts are fractal entities of energy and information.’

Though the specific combinations of energy or information of each species – defined by its ‘vital’ or physical, Universal Constants (energy/information ratios) – might vary, the space-time structures and cycles of all those social organisms will be self-similar: All entities are ‘cellular societies’ organized through energy and information networks that bring about processes of social evolution. In all species studied by science a common phenomenon occurs: the existence of parallel groups of beings organized into a single social form. Molecules are made up of atoms and electronic networks; economies are made up of human workers and consumers that reproduce and test machines, guided by financial networks of information (salaries, prices, costs); galaxies are composed of stars, which orbit rhythmically around a central knot, or black hole of gravitational information. Human bodies are organized by cells controlled by the nervous, informative system. A tree is a group of leaves, branches and roots connected by a network of energy (salvia) and information (chemical particles). Cultures are made of humans related by verbal, informative laws and economic networks that provide their energy.

Sciences study those organic systems, tied up by networks of energy and information. In the graph, we see the main st-planes studied by human sciences and their 4 Time arrows, S EóI, which in static space give birth to the ‘organic elements’ of all species: social cell of energy and information and the reproductive networks that relate them. Thus, there are 4 basic elements in all organic systems:

1.  Cellular units.

2.  Networks of energy or vital space.

3.  Networks of fractal information.

4. Networks that reproduce energy and information.

All entities are generated by reproductions and transformations of energy and informative cycles (ΣSóTi), organized in cellular units, through networks, and ±st Planes of self-similar forms. Yet, since those cellular units st-1 are made of smaller st-2 cells, which show the same structure, we can define any organic system as a super-organism (made of smaller, self-similar super-organisms):

‘A super-organism is a group of cellular super-organisms joined by energetic, informative and reproductive networks.’

Thus we unify the properties of Universal Systems and the sciences that study them under a single template definition, according to which simple systems and complex organisms will differ only in the degree of ‘completeness’ of its networks and the specific energy or information they are made of:

‘A super-organism is a network composed of a population of (name a particular cell or cycle), related by an energetic, reproductive or informative arrows.

A fractal organism (name an organism) is a population of iterative (name a cellular species), related by informative (name a language or informative force) and energy networks (name a kind of energy), which combine into a reproductive network that iterates the organism.

A universal ecosystem (name a specific ecosystem) is a population of several (name the species), related by informative languages (name their languages or informative forces) and energy networks (name the energies).’

Fill the gaps with a specific species, language/force and energy and you can define any network-organism in the Universe. While if the system is composed of several species that occupy the same space but have different networks of energy and languages of information, we talk of an ecosystem:        – An atomic organism is a population of (electronic) energy and (nucleonic) information, related by networks of (gravitational) information and (light) energy.

– A molecular organism is a population of atoms, related by networks of gravitational energy and networks of electromagnetic information (orbitals, London, Waals forces).

– A cellular organism is a population of molecules, related by energetic networks (cytoplasm, membranes, Golgi reticules) and genetic information (DNA-RNA.)

– A human organism is a population of DNA cells, related by networks of genetic, hormonal and nervous information and energy networks (digestive and blood systems).

– An animal ecosystem is a population of different carbon-life species, related by networks of light information and life energy (plants, prey).

– A historic organism or civilization is a population of humans, related by networks of verbal information and networks of carbon-life energy.

– An economic ecosystem is a population of human workers/consumers and machines, related by networks of digital information (money, audiovisual information, science) and energetic networks (roads, electric networks, etc).

An economic ecosystem differs from a historic organism because they use different languages of information (civilizations use verbal or ethic laws while economic ecosystems use digital prices) and include 2 different species: human beings and machines.

– A galaxy is a population of light stars and gravitational black holes, related by networks of gravitational information and electromagnetic energy.

-A Universe is a population of galaxies joined by networks of dark matter and energy.

We establish thereafter a parameter of informative complexity, i=n, to classify all those relative scales of spatial energy and temporal information of the Universe, starting by the simplest scales, i=0 (mathematical cycles and lines), i=1 (Gravitational space), i=2 (electromagnetic space), i=3 (atomic particles) and so on, till reaching the most complex, macro-structures of the Universe (i=9, galaxies).

This parameter becomes essential to formalize a type of scientific laws widely ignored by science, which define the interactions between several scales of reality. In physics:

– Between the small quantum scale of electroweak forces and the bigger gravitational spacetime.

– In biology between the cellular microcosms, the indivual organism and the ecosystems or societies in which those organisms exist, as individual ‘cells’ of a bigger whole – the species. Since those relationships are essential to explain all kind of natural and social phenomena, from the life/death cycle (in which cells reproduce, organize socially in networks, emerge as individuals of herds and societies, and die, dissolving again their complex ‘i’ networks into i-1 cells), to the meaning of religions, in which humans act as mental cells of a subconscious collective we call God.

At present though, each science studies only one scale of form and its specific laws and events, as if they were unrelated to the laws of all other scales and species. Only System Sciences, the philosophy of science considered in this work, studies together the mathematical, morphological and biological laws that define the 4 arrows of time and apply those laws to all the species of each of those scales, since the Laws of Time Arrows are common to all of them, regardless of the ‘specific’ qualities of each species:

– All species in the Universe absorb energy, gauge information (even particles, reason why their theories are called gauge theories), reproduce (quarks absorb energy and reproduce jets of ‘quarkitos’, so do electrons that absorb energy and break into a shower of new electrons, and since those are the two basic particles of reality, it follows that all systems can be reproduced), and finally, all entities of the Universe evolve eusocially, gathering together into bigger super-organisms, from particles that become atoms that become molecules that become cells that become living organisms that become societies, nations and religions, super-organisms of History.

Recap: The 2 primary arrows of time, energy and information are geometrical, and its properties can be studied with the laws of mathematical physics; while the 2 complex arrows of time, reproduction and social evolution are biological, explained as ‘strategies of survival’ that ensure the immortality of the logic systems of the Universe. The shapes of energy and information are ‘invariant at scale’, meaning that cycles of information on one side and forces of lineal energy on the other side, reproduce their shapes and gather together into bigger, cellular, social networks, creating dual entities, made of ‘fields/bodies of energy’ (physical/biological jargon) and ‘particles/heads of information’, (Principle of Complementarity). All systems of the Universe are complementary, formed with a region dominant in energy arrows (body or force) and a region dominant in information cycles (particle, head). Those dual, social, whole entities have more energy and last longer in time than individual parts. Thus, species with a limited vital space and time duration ensure their immortality by expanding its size in space and its duration in time, as parts of bigger energy/information systems


Inthe graph, the understanding of the 4 arrows time, its dimensions, causal order, and the way in which they evolve individuals into social organisms, can also resolve and advance the science of Biology and evolution. Since living beings are also knots of time cycles of energy feeding, information gauging, reproduction and social evolution, perceived as still organisms, whose purpose is to evolve individual ‘cells’ of the same species into more complex beings. Thus chemical life cycles chain each other into complex systems called cells that evolved into bigger scales, till creating the biological cycles /clocks of information of human beings, the most complex informative species of the Universe. Further on, the duality of cycles/particles/heads of information, complementary to energies/lineal motions /forces/bodies also applies to biology, where bodies and heads create living systems.

How life evolves is disputed between evolutionists, who believe in a selective chaos and creationists, who think there is a design. Time Theory shows that neither is wrong or right. There is not a personal God that creates us – an ego trip of religious fundamentalists – but there are limits to the chaotic forms of evolution, set by the fact that the morphologies of energy and information are fixed by the efficiency of energetic lines and informative cycles, by the need of complementary designs, by the existential arrow of social evolution and reproduction that favors survival; and ultimately by the mathematical topologies and dimensions of ‘fractal information’ and spatial energy, which define the outcome of evolutionary tendencies. Indeed, watch the drawings of different life beings made of informative nuclei/heads and energetic body. Informative systems are always smaller than bodies. They are always on ‘top’ of bodies, perceiving more from the advantage point of view of the dimension of height. Further on, since information is bidimensional, informative systems are bidimensional (only a few animals have 3-dimensional vision). A book, a screen, a pulpit, an antenna, emits information from its top. A head, a camera, an electric field is on top of a body of energy. So evolution is a guided evolution of form: Species evolve towards higher information, from planarians to human beings, a tall species of information. And they evolve cyclical forms or heads and lineal forms or bodies. And they evolve from individual cells into social organisms and further on into societies (insects, human beings). Thus there are a series of topological, behavioral and social laws that ad up to the discoveries of Darwin and complete Theory of evolution. In the next graph, we see some of those laws, as evolution of form follows the same ‘arrow’ of growing information, increasing both, the dimension of height and the social organization of individuals into herds and complex organisms, through a common language of information.

Ultimately, we consider each species made of self-similar individuals, a cellular super-organism, which follows the same causal arrows of organisms, with an increase of information towards its ‘3rd age’. Those 3 ages of ‘life’ in cellular species become then the 3 ‘horizons’ of evolution of species, which start as energetic, planar top predators (first shark fishes, first worms), with minimal size. Soon the species goes through a young, energetic age of growth in spatial size. Then it follows a II horizon of diversification and massive reproduction of the species (radiation age); and finally the species goes through an informative age of evolution in height and brainpower. Then, either a new, more evolved species appears, causing the death of the previous species, which becomes extinct or dwindles in numbers; or the social evolution of the individuals of the species reaches such a degree of integration, through a common language of information that a macro-organism emerges. So ants successfully create superorganismscalled anthills becoming the most successful animal on Earth, whose total life mass is equivalent to the life mass of humans, which also organize themselves into super-organisms of History, our Gods and civilizations. The success of those 2 species shows that the ultimate survival strategy in the Universe is that of social evolution. Since the total mass of ‘ants’ and ‘humans’ are the biggest ‘living masses’ of the planet, as the most complex social superorganisms of Earth.

Recap: Life species can be considered as superorganisms made of individuals=cells, which evolve through 3 horizons=ages, following all the geometrical and logical laws of space-time systems, as life systems are also complementary systems made of energy bodies and cyclical heads of information.

The existential force. Strategies of survival.

The existence of multiple knots of time arrows implies that in the Universe of multiple time cycles, the words past, present and future, are also relative, quantized to each individual, who lives his past/youth or age of energy, present/maturity or age of reproduction and future/old age of information before dying, dissolving i=ts exi=stence. Thus we need to analyze the relationships between entities which are in a relative past and interact with others that are in a relative future.

The simplest case is a family relationship between a grand-father, a man of the future with the wisdom of knowing in advance the cycles of time that his offspring will live, and its younger, less informed species: the young learns from the elder knowledge of previous cycles that will happen to the ‘past being’ into his future.

If we draw the example from different species, however the encounter will be Darwinian, and only species which share the same information evolve together. Then the old, more evolved species with higher information will dissolve the simpler species into its relative past, as victim: there will be a darwinian fight and the more evolved time knot from the future will kill and feed on the simpler form. And that is why we can establish that the relative future is guided by the arrow of information and social evolution, which creates better species. Since in a contact between past and future species, the future species survives, due to its better energy and information, its better existential force. It is thus possible to study from a mere temporal, evolutionary perspective the outcome of encounters between different ‘knots of time’.

When we consider the 2 ‘simple’ arrows of time that create the future, energy and information, as we do in Duality, all simplifies and explains itself, like it happened in earlier astronomy when Copernicus put the sun in the center. And one of the things it simplifies is the meaning of survival, which can be resumed in a simple equation: Max E x I = Survival. This function E x I, is the existential force, which explains that a species with the best energy body/force and informative particle/head will survive.

The existential force is equivalent to a particle’s momentum, Max MV, which determines the survival form in material collisions. In biology the species with better body and brains survives, which made lions and humans the top predator species of this planet… till we invented weapons and computers, energetic and informative species, made of metal, which now we fusion into robots, potentially the new top predator species of this planet. In the galaxy the highest existential force or momentum is that of a black hole. And it is proved in the Galaxy that the collision of a black hole of any size with any type of star converts the star into a black hole.

An important characteristic of the Existential force is that it favors a relative balance between the energy/body/force and informative/particle/head of the system: the more self-similar are both in quantity of cells and the higher the number of its networks/connections, the more synchronic they act together, and the higher the Existential force of the system is. This fact is the origin of the classic, harmonic, ‘beautiful’, mature state of most forms of existence that are in balance between both parameters, in a ‘mature’, steady state age.

Recap: The Universe selects the species with maximal energy and information: Max. E x I ->E=I. It will be a biological top predator or a particle with maximal momentum.

The plan of evolution that brought Man, the supreme being of the arrows of time, into existence.

In the graph, one the main discoveries I did in the field of Complexity applied to anthropology, dating back from my first books on the subject (Bio-history, Bio-economics, a theory of Unification, Bookmasters, Ohio, c.94), was the application of the Duality of Energy/information and its self-generative process of creation of new species that combine both essential elements of the Universe, to the evolution of the Human Kind. The plan of evolution of the fractal, organic, Complex Universe is in that sense simple. All species become differentiated in an energetic, ‘lineal’, spatial species and an informative, ‘cyclical’, temporal one. Then both mix to create a more complex, reproductive species.

And so 3 is the number of Horizons and subspecies we find in all evolutionary systems. This plan of evolution which has enormous repercussions in the understanding on how species evolve and complements Darwin and Mendel, however is disputed outside the science of complexity and the congresses in which I have developed my work. And so it is not widely known. And yet it recently achieved new proofs in anthropology with the discovery that the Neanderthal, white, visual, spatial, energetic brain species mixed with the Homo Sapiens, the Capoid, verbal, temporal one.

So we can explain both genre (being women the informative species that reproduces the fractal information of the human being and man the lineal energetic species), and racial differentiation and establish 3 types of mind: the white, visual, dolicocephalic brain, more developed in the visual axis from the forehead to the occipucius, which should be found to have a higher mix of Neanderthal. He is divided in two types, which again experimental proofs have validated: the Semite, in which Neanderthal males mixed with verbal women, as the dominant, stronger species, in the first crossing of the Homo Sapiens, in 80.000 BC. This advanced theory of 94 has now proofs that came in Nature: only homo sapiens women mixed with Neanderthal males in Palestine. The result is the semite with a clear dominant male, bigger than the female, talking species. The reason is that at such time the Homo Sapiens had not developed the arch and so it was dominated by the Neanderthal, stronger warrior. Then in Altai mountains, homo sapiens evolved into the mongoloid cro-magnon which had arcs and hence could kill at distance the neanderthal. This man went down to Europe and the mixing reversed. Now the Homo Sapiens Paletiniensis mixed with the Neaderthal stronger women (the Nordic Women and red hair, dolicocephalic scots). The result was the Aryan in which women are far stronger. This is the last detail of our Complex theory of human evolution to be proved in the next years…

In the text, we have a further explanation of the other races, which are clearly 3: the mongoloid, verbal race with a higher distance in the verbal axis (brachicephalic) and the black, reproductive, emotional brain, which is self-similar to that of women, with a high brain more evolved in the top axis.

Complexity defines a simple game of evolution by combining informative and energetic species in balanced, new organisms: e xi=st.

We say that the Universe has 3 arrows of creation, energy, information and its balanced combinations. This is also a sexual principle: Women are information-dominant; male are energy dominant.

In human evolution the same pattern emerges: each successful, dominant Homo differentiates into an energetic and informative species, which recombine, creating more complex= informative and stronger=energetic homos that displace their parental forms, thanks to their higher Energy x Information. Yet the dominant, overall arrow favors informative species. Since when Homos were born, the energy top predators were felines, far stronger than the strongest possible homo mutation. So the evolutionary direction in which the big apes could find an ecological niche within the mammal kingdom was the informative arrow. They were already fit to that purpose, since they spent long times living in stillness in the summit of trees, where they had to learn to control complex movement in the informative dimension of height, adding a 3rd dimension to their brain. So they became informative masters among mammal species . . .

Thus, the duality between energy and information is also responsible for the creation of humanity. In the graph we study that process: life first diversified into complementary genders: energetic, lineal, spatial men and cyclical, reproductive women, which hold more biological information. While a 3rd, gay sex mixes both. Further on, as humans evolved, they followed the same pattern of 3 ages proper of all species. Thus, Homos diversified into energetic, informative and reproductive forms that show a higher balance between energy and information. Yet only the informative species, the dominant ‘arrow’ of future survives in each of the 3±1 horizons of increasing informative evolution, from Australopithecus with 500 c.c., into Homo Erectus with 1000 c.c. into Homo Sapiens with 1500 c.c.

And in all those phases, humans split into an energetic species and an informative one that recombined to create a 3rd species. Those species will further evolve technology also in 3 horizons called the upper, middle and lower Paleolithic. Finally, humans diversified in 3 races, specialized in Energy (white race) and information (Mongoloid) with a reproductive, black race, the last to be born, which mixes the pre-mongoloid (bushman) and white races. The constrain established by the fact there are only two elements, energy and information, to create reality, whose lineal and cyclical forms are invariant at scale, in all systems of the cosmos means the Universe imposes the same program of creation to all its species.From an initial ape species we find a ternary differentiation ±5 million years ago, into 3 sub-species of great apes that live in Africa:

—  Max. E: Gorilla, a big, energetic species that reaches 200 kilos, with a square, huge jaw.

—   E=i: The chimpanzee, with a smaller body and a bigger brain. According to the Black Hole law, the smallest organism evolves informatively. Thus, the ‘dwarf chimpanzee’, the Pan Paniscus, which today shows the highest learning skills among apes, was the species that seems to have evolved into a 3rd informative horizon of big apes. It is:

—   Max. i: Australopithecus, which splits in 3 evolutionary ages of growing brain volume:

I Horizon: 500 cc.: From Australopithecus to Homo Erectus.

We have dated the oldest mandibles of Australopithecus Anamensis, the top predator of the 3 big ape species, in 4 million years. The Australopithecus, after reproducing massively in the savannah ecosystem that favours his bipedalism, suffers a new ternary mutation. The 3 descendants of that Australopithecus Afarensis that inhabited the Ethiopian plains around 3 million years ago, are:

—  Max. E: The Paranthropus, an energetic species with huge mandibles and a lineal, planar brain. He looks like a heavy-set, humanoid gorilla. He was probably vegetarian. The first subspecies found is the Paranthropus Aethiopicus, which will further evolve into the stronger Paranthropus Robustus.

—  E=i. The Australopithecus Africanus, which maintains the form of the original Australopithecus Afarensis, perhaps with inner improvements in his soft tissue. He lives in South Africa and is contemporary of the Paranthropus. And the . . .

—  Max. i: Australopithecus Garthi. He is the informative species, with a bigger brain, which starts to acquire the shape of all informative species: a rounded forehead, as the sphere is the form which holds more information inlesser space.

Those 3 species live very close. Around the Turkana Lake we have found remains of the 3 Homos. Yet the arrow of future favors informative species. So the top predator Homo will be the Australopithecus Garthi that goes through a mature age of massive reproduction, probably extinguishing the other 2 subspecies and expanding worldwide into new ecological niches that favoured their genetic and memetic adaptation through a new, ternary split:

—  Max. E: A regressing, energetic A. Garthi, similar but taller than its parental Australopithecus.

—  E=i: Homos Habilis and Rudolfensis, with similar brain capacity to the original Garthi.

—  Max. i. Homo Ergaster, an informative ape with a 1000 cc. brain, which doubles the brain capacity of Australopithecus.

II Horizon: 1000 cc. From Homo Erectus to Homo Sapiens..

That Homo Ergaster, after a massive age of reproduction and expansion throughout the planet, subdivides again in 3 sub-races of Homo Erectus.

—  Max.E: Pithecanthropus, the oldest species similar to Homo Ergaster, found in Java.

—  E=i: Homo Erectus proper, found in China, who grows in the informative dimension of height that favorsperception from an advantage point of view, to 1.7 m. He has simple technology, a skull without forehead and thick bones that handicap further cranial evolution.

—  Max. Ti: Homo Floresiensis, the smallish species, which according to the Black hole paradox should be the form who gave origin to Sapiens, as the smallish ‘pan paniscus’ evolved the chimp into the Homos. Recently discovered, he is a formal mutation with a smaller body, whose morphology resembles for the first time that of a human being. He has thinner bones that allow further growth and a higher forehead, the location of the creative part of the brain.

Palaeontologists also found the first advanced technological tools in his sites in Flores Island, which is an isolated place, the ideal region to foster further evolution, due to the lack of top predators (alopatric evolution). Thus, he ads now technological energy weapons that substitute body strength and define a single arrow of future for human evolution: information. His improvement in neurological form, probably caused first his rapid expansion thanks to his new technological tools and then a rapid growth in size through the cross-breeding with the taller Homo Erectus species, giving finally birth around 300.000 B.C., to a new energy/ information duality: The energetic, big Neanderthal and the informative Bushman, which will combine again to give birth to the different races. Those predictions based in the 3 arrows of future time and the black hole paradox (information is small and evolves in dwarf species) have been confirmed by genetic maps and Paleontology and await final confirmation, when new skulls of Floresiensis are found.

The 3rd, informative Horizon: Homo Sapiens, 1500 cc.

—  The lineal, energetic, visual Homo Sapiens Neanderthal, with ±1500 cc.

—  And a second informative pygmy strain, the 1st verbal woman, the mitochondrial eve, probably a bushman, also with ±1500 cc.

± 50.000 years ago she crossed into the Middle East, probably mating with earlier Neanderthals, giving origin to the visual, energetic white male (Homo Palestiniensis, whose skulls show mixed traits from both species).

± 35.000 y. ago, in the high Tibetan plains, she became the informative Mongoloid that colonized Asia, America and descended upon Europe and Africa, where she cross-bred with the capoid (bushman) and became the black man, the balanced E=i, reproductive race, completing the final, ternary differentiation of the main races of mankind.

Cultural races.

Further on, as racial tribes evolved socially and emerged into cultural societies, which are super-organisms of history, the ternary, racial division of mankind between energetic white men, informative Mongoloid and vitalist blacks, will become the cultural differentiation of human beings in 3 type of brain orientations, and hence cultures orf the mind according to the 3 elements of all systems, energy, information and its reproductive combination; reflected in 3 types of brain morphology:

— ‘Visual, energetic, lineal, spatial cultures’, proper of the white man, with his concepts of lineal time and his passion for technological, energetic weapons. It is the dolicocephalic brain dominated by the visual, eye to occipucius axis, also dominant in neanderthals

—    ‘Cyclical, informative, mongoloid cultures’, natural to Asian civilizations, with cyclical concepts of time. It is the brachicephalic, wide, verbal brain; dominant in the ear axis; hence giving birth to female, eusocial cultures like the Chinese.

—    And ‘sensory, reproductive, colored cultures’, which in Africa and India developed human senses to their limits. It is dominannt in the height/medular axis with a ‘tall head’, peaking in the top/motor and sensorial area.

Which culture is better for the survival of mankind? Since survival is the goal of all species, reached in the age of balance, E=i, we should promote, paradoxically, the culture that our technological civilization discriminates: the black, reproductive, sensory culture . . .

Thus, the Laws of Evolution and its 3±1 ages and subspecies, map out the main species of Homo, till arriving to 2 Homo Sapiens, the spatial, visual=longer, dolicocephalic, energetic brain of the Neanderthal, which seems to have lived in Europe and left some of his traits in the Homo Palestiniensis, on the slow-crossing border of Canaan. Further cross-breeding of the Palestiniensis with the Sapiens is the likely origin of the white man (white skin, red hair, Rh-?, consonantal languages, wide hips, prominent nose)

While the informative Homo Sapiens Sapiens, the verbal=wider brachicephalic brain, which started as a small ‘San pygmy’, evolved into the self-similar mongoloid race. Finally, the black race, with tall brains are the sensorial culture,  the reproductive species, the last one to appear, shows the maximal genetic mixture.

In the same manner, we talk also of gender duality in terms of an energetic species, the lineal male of big muscles, spatial size and visual brain; and the woman, the informative, reproductive species, who would understand the cycles of birth of plants and evolve mankind from the energetic, hunting Paleolithic into the Neolithic, the mature age of History, with its understanding of the arrow of reproduction of the Universe (cult to the goddesses) and its harmonic cults to Nature. It is on my view, the ideal age of mankind, which bio-historians could re-create on Earth by pruning the tree of Technology of all its bad fruits and enhance the fruits of the Tree of Life with environmental policies, under a global, single Social Organism of History, the World Union (ch.13). Since once a species has reached its informative zenith or 3rd age, the only way it can further evolve is by becoming a macro-organism, joined by a common network of information. So men did evolve further beyond the Homo Sapiens, through the 4th arrow of time, the arrow of love and social evolution that mechanist science denies and verbal, social religions of love impose on their believers.

On the Earth, there are today 3 types of social organisms:

—  The first to appear, Nature, Gaia, was based in carbon-life.

Then History appeared, based in human life.

—  Finally, the economic ecosystem based in metal and machines, appeared.

Since those 3 organic systems and species have been dominant in 3 different ages of the Earth, we talk of the evolution or terraforming of the Life-Earth or Nature into the Human-Earth or History that now becomes the Metal-Earth, the Economic Ecosystem. The youth of History was still ‘Nature’. Life dominated the Paleolithic. Then men reached their zenith of social evolution in the Neolithic. Now men devolve back into single, selfish individual, Homo Bacteria, due to the use of machines and weapons that isolate them, in a process equivalent to the process of death that dissolves the networks of a being back into its simplest cellular components.

8. Complex Theology and emergence.

In the graph, we can see how Man achieved the greatness of eusocial evolution.


In the graph, several experimental proofs of the fractal, organic structure of all beings of reality: On the left, the Sloan fractal map of galaxies and its comparison with a neuronal cell; on the middle, an ice fractal, a plant and a river; on the right, a cluster of galaxies and a lung. Fractal and non-Euclidean mathematics have evolved our understanding of information in topological terms, defining a new Fundamental particle of the logic/geometrical Universe, the Non-Euclidean Point, which unlike classic Euclidean points, has inner parts – an informative center and a field of energy that moves it. Such points constantly communicate energy and information with self-similar points, through non-euclidean lines (waves which share the energy and form of those points), shaping together ‘Non-Euclidean space-time planes’, the network-entities of the graphs, which all structures of nature constantly reproduce organizing a canvas of simpler, energetic ‘cellular’ motions. From the simplest particles, quarks and electrons that absorb energy and reproduce new particles to the most complex informative species, human beings, reality is made of bits of information and bytes of energy, evolved in complex, social networks through fractal scales, from atoms to molecules, to cells to organisms, planets and galaxies. We can mathematize those processes using non-Eucidean topologies and generator fractal equations that iterate and self-organize in networks those points of nature – an ice geometry, a DNA code, a cellular structure, a physical particle. Thus, when we fusion the mathematical and organic understanding of reality, the Universe appears as a fractal of energy and information, made of self-similar parts, which constantly reproduce their forms. And the quest of the fractal paradigm is to find an equation able to define all those systems – the ‘Fractal Generator of the Universe’: EóTi

A new age of science: the fractal paradigm.

‘Each point of the Universe is a world in itself’said Leibniz What he meant would not be understood till the end of the XX century when we discovered the fractal paradigm, the new paradigm of science which will substitute the Physical paradigm which has dominated our comprehension of the universe since the XVII c. Where indeed, each point of the Universe, when we come closer to it, becomes a super-organism, made of cells with self-similar functions of time, which repeat in all scales with the same logic behavior.

In other words the Universe is a fractal of Time, a fractal of information which is constantly being generated and imprinted in reality. It is a fractal of 4 self-repetitive motions, energy, form, reproduction and social evolution, constantly happening around us in bigger and smaller scales, in bigger and smaller cycles, all type of beings feeding, reproducing, energizing and informing themselves. And because those actions are geometrical, they leave a certain trace which betrays the purpose of the action: a lineal path of feeding, a vibration back and forth of reproduction, a cyclical, implosive, informative process, and so on.

The Universe creates superorganisms by creating first fractal complex informative cells from flows of simpler energy, reproducing them and self-organizing them in 2 parallel, complementary networks, one of energy and one of invisible, faster, thinner information that controls the entire system. We often see only with the scientific method one single of those 2 networks, as gravitation and since most of our human existence magnetism appeared as invisible to us. And it is a general rule that both spacetimes, the one of energy and information, have different Universal Constants which are ratios, e/I and i/e and exi, which define the arrows of energy, information and vectorial reproduction of any organic dual space/time plane of the Universe. Where the space-network of energy and the informative-network create a holographic organism as those we see all around us in reality.

The best mathematical and logic description of all those qualities that structure reality -self-repetition in smaller and bigger scales, motions with geometrical form, feed-back action-reaction processes, absolute relativity of size – are provided by Non-Euclidean and fractal geometries, the geometry of information, reason why the 2nd part of this book will develop the new formalism of the fractal paradigm, poised to substitute the quantum paradigm and resolve all its questions in physics.

The result of course is that we see fractal structures created by the paths of knots of time, following its arrows of exi=stence in all systems of the Universe. This is what we see, the how of those time arrows: fractal paths of existence.

So we shall now finish this first section dedicated to the ‘meetaphysics’ of the fractal paradigm’, the why of those paths, with a brief analysis of the fractal structures caused by self-reproductive knots of time, as they follow their paths of existence. The next chapters will be dedicated to a thorough analysis of the mathematical and logical laws that define the paths of time arrows, and how they build step by step those fractal networks we call ‘Nature’.

Since all what exists studied in detail is a cellular network of self-similar beings sharing energy and information and reproducing and evolving in social networks.

Recap. The Universe is a fractal of information that reproduces, by imprinting and breaking vital spaces into complex forms. Each fractal knot of time arrows performs in his search for exi=stence a series of paths and reproductive and social acts whose final result is the creaetion of a fractal networks. All what we see are fractal networks caused by those knots of time.

The Universe is an organic fractal of knots of time arrows

It is now clear what reality is: a series of knots of time arrows, which latter we will formalize as ‘Non-euclidean points’. Such points are in constant communication with self-similar points, reproducing their form and evolving socially into networks. The reproduction of form takes place in a fractal manner, by producing ‘seeds’ in a microcosmic, ‘lower scale of existence’, which latter grow. The networks are built with flows of energy and information that tie those points. And the result of those simple, yet repetitive processes of reproduction and social evolution is the creation of a world of ‘herds’,’cellular organisms’ and networks, extending through multiple scales of size in which the forms of energy and information and the structures and laws that build super-organisms remain invariant.

In physics, scientists talk of the invariance of motions discovered and generalized by Galileo and Einstein (Relativity). Yet we must ad in the fractal paradigm two new invariances, the invariance of scale – the same time arrows take place in all scales; and the invariance of form – the same shapes of energy and information emerge and repeat themselves in all scales.

Those 3 invariances create a new ‘paradigm’ of science, no longer built on the belief of a single arrow of time, a single spacetime continuum and a single clock-speed to measure it. The result of course is a more complex reality, but that was to be expected. We, humans are just one of the many games of existence of that fractal Universe, and it should not be expected that we are, regardless of our anthropomorphic myths, different from the rest, and able to fully understand in the diminutive brain all what exists, unless we simplify it.

What this work tries to do is to return to a minimal degree of complexity to be able to understand the fractal knots of times, which imprint the energy of reality with its information, constantly reproducing their form and playing the game of existence, constantly achieving the immortality of form.

The Universe is made of ‘time fractals’ that participate both of the properties of mathematical fractals and living organisms. Yet organic fractals are more complex than mathematical fractals, because they have motions. And so the reader should not confuse both therms.

Fractals are mathematical or organic forms which constantly iterate or reproduce their information in self-similar forms that extend through several scales of size and information which we shall call ‘i’-scales.

They are the most accurate models to depict natural phenomena related to informative growth and reproduction, the essence of life organisms:

Arrows of Reproduction & Information: ->Δi

All fractals are originated by a Generator Equation (mathematical jargon) or mother cell, M©, (biological jargon) that iterates=reproduces a series of self-similar fractals called a set in mathematics or a family in biology:

Mother/Generator Cell: ->Σi-1 fractal family/set

The paradox of fractals is that the smaller the fractal scale is the more information it accumulates and the more detail it has. How this is possible? Obviously because information is form-in-action, form with motion, and so the logic paths that systems use to process information are completed faster in lesser space. Further on, in physical systems the cyclical speed and frequency of a vortex with form (a mass or an eddie) increases when the vortex is smaller (VoxRo=k). So the increase of ‘cyclical speed’ diminishes geometrically with size. This result can be generalized to any system of knots of time. So the metabolism of small animals is faster than that of big ones. The cycles and clocks of atoms are faster than those of our scale, faster than those of the cosmological scale.

The same can be said of geometric fractals: When we observe a Mandelbrot fractal, information multiplies in smaller regions as we approach them.

However, there is a fundamental difference between the logic, linguistic fractals of the mind and the physical Universe: While static, ideal, mental mathematical forms can be of any shape, as movement and friction don’t test their efficiency, in the Darwinian Universe only forms of Nature whose properties allow the being to process efficiently energy and information, survive. Thus, mathematics is an ideal language that can create any form, but in the Universe forms have to be efficient in their motion/function and parallel form. Thus, in Physics and Biology we ad movement to the mental shapes of geometry, which enormously reduces the possible shapes. Movement acts then as a ‘reality check’, an Occam’s razor that eliminates all complex forms, which won’t be able to move properly under friction, stress, turbulences and other obstacles proper of the real world. A Mandelbrot fractal might be very beautiful. But it wouldn’t be able to move very fast, and its attached microforms probably would break with an air stream. So there are no such fractals in the Universe. Instead, we find physical entities made of cycles and lines in movement, for reasons of biological efficiency. Since a lineal movement is the shortest, most efficient path between 2 points. On the other hand, information is cyclical, because a sphere accumulates the maximum quantity of form in minimal space. While a cyclical rotation is the movement with less friction and the only one, apart from the line of energy, that maintains the self-similarity of any form, even in trans-form-ations of size. A fact that explains, in terms of survival efficiency, the morphological invariance of energy and information shapes at scale.

Since Mathematical fractals lack, as pure forms of mental information, the energetic dimension of movement and growth, their fractal sets are attached to the Mother- cell’s boundary, where the self-similar forms nest, as in the case of the well-known Mandelbrot set. On the other hand organic fractals not only iterate their information as mathematical and mental fractals do, but also make it grow. Species are not mathematical but ‘organic fractals’, whereas the word organic refers to the ‘non-mathematical properties’ of existential entities, which can be better described with visual and logic/verbal languages. Reason why Biological theories of time arrows (Evolution theory, Theory of Organisms) require also the logic embedded in the laws of survival that extinguish the less fit – hence relative past species and reproduces the more fit, hence future species, and the visual languages that give movement to the forms of energy and information described by mathematics.

Nature’s fractals combine the arrow of energy and the arrow of information in an organic way. They differ from geometric fractals in their dynamism and capacity to absorb energy from their environment. They not only iterate their form in microcosmic scales, but feed their offspring of information till they grow into full replicas of themselves. It is precisely the combination of both arrows what makes the behavior of an organism more complex and varied than the behavior of a mathematical fractal. So in the study of natural fractals, we have to ad to the informative arrow – whose laws we deduced from the study of mathematical fractals and informative seeds – the energy arrow of entropy that thermodynamics has analyzed in detail:

Energy, young arrow: e->x i->0 X e->0 x i->: Information, old  arrow

For any Σ number of cycles: ΣE  x  Σi =  Organic fractal ΣE<+>ΣT Organic cycle

The understanding of fractal processes provides a more detailed, scientific analysis of those processes. In that sense, unable to define information with the same rigor used to define the arrow of energy and entropy physicists have ignored for centuries events connected to the arrow of information (chaos, turbulences, super-conductive and super-fluid phenomena, etc.). Physical events and particles are also subject to both arrows, as everything else in the Universe. Thus we define abstract equations (as the back and forth transformation of energy into mass, E=mc2) in terms of process of creation and destruction of information.

As a rule languages will never be able to describe all the information that a certain being has within itself. So mathematical languages are also synoptic, and reduce the total information of the being. And that is the case of a fractal equation, which reduces the entity to its fundamental essence. In that regard, the Theory of Time Arrows is not pythagoric, as Quantum Theories often are, in the sense that it does not consider the Universe to be made of mathematical entities, but merely affirms that among the linguistic mirrors that can map out the Universe, mathematics is undoubtedly the key language to represent the trajectories, cycles and motions of its species.

Because all languages observe the Universe, we talk of those arrows of time in logic, verbal and visual, formal terms. Since the syntax of verbal thought with its ternary structure and of visual forms with is line-cycle-wave structure and red-green-primary colors describe entities constructed with those arrows.

Recap. The Universe is based in 3 types of invariance, invariance of motions (Galilean relativity, now applied to the invariance of the 4 arrows/motions of time), invariance of scale (self-repetition of the same processes and arrows in all scales of size) and invariance of form (self repetition of the energy and information shapes of reality. The 3 invariances define a Universe better described with the mathematical laws of fractals geometries, based in the existence of a generator equation that constantly reproduces information, creating networks of self-similar points, which structure all realities we see.

The difference between a mathematical and an organic, Universal fractal is evident: organic fractals do have motion and their processes of reproduction and evolution are far more complex than those of mathematical fractals. So we must depart from a narrow-minded mathematical-only approach to study those fractal systems and consider mathematics one of the main but not the only language to describe its organic properties.

The 3 elements of all fractal beings.

We see a static, simple Universe in our relative human ‘plane of existence’. Yet reality is organic, extended from microcosmic to macrocosmic ‘dimensions or scales’, and dynamic, as all particles and forces have movement-energy and form, in-form-ation; and all of them are structured into networks, which share their energy and information.

Those 3 elements: bites and bits of energy and information; networks and scales define the structure of all natural fractals, including the Universe.

They can be formalized with the Generator Equation, we used to formalize the arrows of energy, information, reproduction and social evolution. Since we defined Universal fractals as ‘fractals of time arrows’, hence both concepts a fractal Universe and a Universe made of knots of self-repetitive time arrows are the same.

We observe different degrees of complexity in a mathematical or chemical fractal, in a fractal organism or in the fractal Universe; but those 3 essential elements repeat themselves, to the point that scientists use similar terminology for all of them:

– The elementary, iterative unit-cells of a fractal, which according to the duality of Universal arrows, will consist on relative bites of energy and bits of information. Those bites and bits are not static forms, but arrows that exchange energy and information; flows and cycles that the organism repeats constantly, generating self-similar forms. So we can define a simple iterative, cyclical equation with 2 terms, the 2 arrows of the Universe, which can be considered the generative cycle of all Natural Fractals:

i: Fractal Cycle: e<=>i (dynamic, cyclical state)  or  exi  (static, formal state)

The networks or systems of energy and information that organize those cellular bits and bites into bigger structures.

How feed-back cycles of energy and information grow into complex organisms, made of many of such cycles?

In time through processes of discontinuous reproduction and evolution, which create similar action-reaction cycles, cells and organisms in other parts of the Universe. Most natural fractals have a dual network structure that attracts the micro-cells of the organic fractal by distributing the 2 arrows of energy and information to them. For example, in a human fractal, the nervous system delivers bits of information and the blood system delivers bites of energy, control together its cellular units. In the Universe the same roles are played by the informative, attractive, gravitational force, and the electromagnetic energy forces.

In Space through the organization of cellular networks that deliver energy and information to each ‘cell-cycle’. Those cell-cycles attach to the networks to process constantly new energy and information in their iterating cycles, creating in this manner bigger organic systems, made of multiple, similar forms.

When both iterative processes are combined, the fractal units of the Universe grow in energy through space and evolve its informative complexity in time, giving birth to the infinite combination of those fractal arrows that we call species, systems or organisms.

So we include in the equation an Σ-term to signify the gathering of individual ei units into networks and webs:

Σi: Fractal networks: Σ (e<=>i) or Σ (exi).

It still looks a simple equation to generate the Universe in its infinite variety. But the Complexity that arises from such simple scheme is enormous when we introduce the 3rd fundamental concept of fractal structures: Dimensionality. Since indeed, space-time cycles can exist theoretically in any number of dimensions. So we should consider in more detail the 3rd element of fractals: the fractal dimensions, planes or scales of existence invisible to human perception through which the fractal exists. They are…

– i: The relative i-scales or dimensions across which fractals extend its organization. We will use for the 3 relative scales of size that define most Nature’s fractals, the symbol i for information.

In a human being they are basically 3: the cellular, individual and social scales; as most entities do not exchange energy and information beyond its upper and lower organic level. For example, humans, as individuals belong to a relative i-scale, and are aware of social tasks (our i+1 plane of existence) and cellular sickness (our i-1 plane), but the events that affect the galaxy, the macrocosms to which our planet belongs (i+2) or affect our molecules, the lower microcosms that make up our cells (i-2), hardly affect our existence. Thus depending on the detail and scale at which we observe most fractals we perceive a fractal cycle (minimal size and detail), a fractal cell or a fractal organism (max. detail and size):

Natural Fractal= ΣΣi-1 Cycles > Σi-Cells->i+1 Organism.

How many elements in space make up a fractal, social network? The most obvious structure is a ‘tetrarkys’, already considered by Pythagoras to be the magic number of the most perfect social networks. The reason is that a tetrarkys can be written as a system with 3×3+1 elements. Imagine then such tetrarkys as a triangle with 3 vortices, each with 3 elements that will perform the arrows of energy, information and reproduction, while the central +1 element that communicates all others will perform the arrow of social evolution, representing the entire fractal as a unit of the next i-scale. Thus a tetrarkys is a highly efficient form, found in all systems of nature, even in human, social systems: 9 soldiers and a caporal make a platoon and 9 caporals and a captain a division…

Recap: All fractals have 3 elements that define them:

– Cellular units, networks of energy and information that organize those cellular units, and i-scales in which a self-similar but not equal fractal structure emerges, once and again with the same energetic and informative complementary forms.

Reproduction and motion, 2 sides of the same coin.

A mathematical fractal like the Koch curve is an energy line that triples its in-form-ative bits every iterative cycle. But since it doesn’t grow in length, it exhausts its energy. An organic fractal also starts as a single cell that clones its in-form-ation. But since it can absorb energy, it can iterate billions of times. In both cases what defines a fractal is its reproduction of in-form-ation that bends energy into form, creating the arrow of futures.So the abundance of fractals proves the existence of an arrow of information in the Universe. We are all fractals, Cantor dust of energy and information: we fractalize so much that finally we loose energy, volume and return to the dust from where we departed in the process of death. For that reason, the only solution to death by excess of information is fractal reproduction of a younger micro-form, when the being has enough energy to replicate in a discontinuous zone of space-time, ensuring the immortality of its logic in-form-ation.

The evolution of the mathematics of timespace requires giving motion to the formal geometry of Euclidean mathematics. This can be done by fusioning fractal mathematics and Non-Euclidean Mathematics. Mandelbrot in the 70s considered the fact that self-repetitive forms diminish and grow in scale maintaining its forms invariant. The why of this grow ultimately responds to the arrows of reproduction and social evolution: A fractal can be seen as a reproductive process, which is common to all generator equations of information of the Universe.

All what exists is generated by the 4 arrows of time, which could be described by a Generator, fractal equation, or Fundamental Law, the Principle of Trans/formation of energy: ‘All what exists are back and forth, cycles of transformations of energy into information’.Those cycles of transformation however leave a trace, and when the motion is repetitive that trace becomes a pattern. Thus the Universe of motions constantly creates patterns, reproduces form, to the point that reproduction and motion are undistinguishable. Indeed, in a scalar Universe of motions with form, of energy and information, reproduction of form over a simpler spacetime surface and motion are synonymous:

V(s): Particle in space with movement: V= s/t: ————-●

V(t): Formal Wave with momentum: e x v: —–O O O O●●●

In the graph, movement can be seen as the displacement of a form over a fixed frame of space/time (Galilean perspective) or as the reproduction of an in-form-ation, which curves a simpler surface of energy in a process of reproduction of fractal information.

For example light can be seen as a motion on the vacuum (continuous spacetime) or as the imprinting of the form of light over the magnetic and electric constants of vacuum (fractal model, proved further by Maxwell equations, in which the speed of light is obtained by multiplying the value of those magnetic and electric constants).

This 2nd model of movement is logically more consistent with Relativity, and solves the oldest paradoxes of Science put up by Zenon in Greece, (the existence of movement in a discontinuous Universe).

The never solved 3rd paradox of Zenon deals with the fact that in each instant of time an arrow seems frozen in space. How then it moves to the next region? Therefore, movement cannot exist. The only solution to the paradox has been traditionally to consider space-time discontinuous. Yet then the paradox rephrases itself: how does the arrow jump from a space to the next one. The only answer is considering movement a formal reproduction of information in the lower scales of energy of the Universe. So in the same way a wave of light imprints one after another an electromagnetic field and an electron seems to imprint a nebula of dense photonic particles, all forms of matter would in fact reproduce information, while their initial forms will slowly vanish their memorial traces.

2nd graph shows how such waves reproduce their in-form-ation, slowly vanishing its form. Then speed is measured as the speed of reproduction of a fractal discontinuous form over a simple energy. It follows a key law of Fractal space-time, which ‘again’ is a special case of the Fractal Generator and its constant balances between energy and form (Max. E=Min.i):

The faster a force or particle or entity moves, the lesser information or mass (physical information) stores. So gravitation, which cannot carry information moves at non-local, relatively infinite speed; light which carries no mass moves as C-speed; electrons which are knots of ultra-dense photons, spread in the minimal space of its nebulae travels at c/10 speed, Hydrogen that carry much more atomic information travel at c/100 speed and so on.

It is a paradox of the inverse properties of energy and form that the biggest forms in space are the simplest, to the point that the perceived universe seems to be merely a flat surface filled with galactic vortices – the simplest of all forms.

It follows that in fractal physics, speed is synonymous of reproduction and many consequences are extracted from that fact. Let us summarize them. Because we create form by imprinting and reorganizing a fractal sheet of points into our topologies of existence, as we create networks from the eprspectivve of a higher plane i+1, we displace a wave of form, which is imprinted and we seem to move, because behind us the form that we have imprinted becomes finally dissolved in its process of death, and so we b ecome waves of existence moving in the dimensions of the smaller cells and atom of which we are made but constantly renew. Our i-logic form thus becomes imprinted along the waves of previous cells and atoms of existence,

And this speed of reproduction and dispalacement will therefore depend on how complex is the number of forms we must make to reproduce ours. It follows that the fastest forms are those whose forces are less dense in information/mass, and this Law of range applies to al systems of the Univere.

V=s/t=e/I, since now space is energy and time is information, the new equation of speed is the ratio of energy and inforammtion wwhich gives to speed a much wider range of applications.

It follows that the maximal speed of the Universe will be also relative to the perception we have of that space, such as beyond a limit when the particle is so thin that we cannot perceive it and carries no information for us (in our world gravitational speed/space,) then V=s/o=∞. This relative infinite speed of gravitation confirmed by the fact that it acts in non-local terms, immediately. For the same reason we observe ‘point-particles’ which might have inner fractal volume but are at the limit of our perception.

The speed of the arrow of reproduction thus changes from the infinite motion of ‘lineal gravitation’ to the 9 months of relative stillness to make a single ‘fractal reproductive step’ of the human organism, which is the territory we see in more detail in all its information. Thus in the new dimensional model of the Universe, we relate the arrows of time, its functions and equivalent dimension of ‘fixed space’ which are inverse:

Max. E=Min. I: ST=S [Length (max. speed) x Width (min. Speed)] x T [Height x Logic Form (spatial in/form/ation)]

Recap: A consequence of the Galilean paradox is that Motion and form are synonymous and co-exist. For example, the motion of light can be interpreted as the reproduction of its form in vacuum space.

Fractal information and life cycles.

Fractals can also explain in more detail the reason of aging and the life cycle. The 2 arrows of time follow a natural order from yang=young energy into yin=old information, which defines the existential cycle of most beings in the Universe.

For example, the life and death cycle can be explained as an iterative process of reproduction of information that degenerates into aging, when the organism has exhausted all its energy in a 3rd age in which instead of reproducing, it wrinkles and fractalizes its cells.

Recap. An organic fractal will always try to iterate its form over new energy not to become fractalized. Yet after a young age, even natural fractals start to lack energy end up becoming wrinkled. In fact, all forms in Nature including the Universe in the future big crunch, suffer some aging process, guided by the time arrow of information.


Reproduction. Movement in a discontinuous Universe.

We have come now to a higher layer of complexity in our analysis of motions of time. We shall now consider complex motions. In the Universe there is a simpex cycle, e<=>I, that converts lineal motions into cyclical motions, and cana t best be made to exist in 3 dimensions (spherical motions) of spacce and time (expansive youth, or big-bang, till implosive 3rd age, through a steady state). Yet complex motions, acts f reproduction and social evolution are different from simplex motions, in as much as they take place between at least 2 planes of differnet space-time. This fundamental difference between the simplex and complex arrows of time creates an entire new science, which studies jumpts between space-time planes and are at the core of the scientific formalism of space-time planes.

The most complex phenomenon of the Universe is the fractal jump in space-time. Both bidimensional cycles of time, and planes of space are fractal and so their changes and displacements are also fractal. And since time is geometric, bidimensional, as space is, it has also 2 directions of movement. So the oldest fractal question of philosophy is: how in a fractal world filled with discontinuities can exist continuous movement? Zenon, a Greek philosopher put the example of Achilles and the Turtle: Achilles will never reach a turtle because there are infinite fractal spaces it has to cross. Parmenides gave him the answer: continuous movement doesn’t exist in a discreet Universe; it is a mirage of the senses. Since a wave, as the figure shows, is not really moving, but reproducing information over the potential energy of the vacuum in a sequential, fractal jump, through a series of wave-lengths, drawn one after another, which appear to the senses as a moving wave. Movement is always a discontinuous displacement either in space or in time, in any of its 2 directions, towards the past or the future. The simplest analogy is a television screen where new images are created constantly without hardly any cost of energy, because they are virtual images created by illuminating 3 colors that are already potentially in the screen. In the case of a wave, the relative energy imprinted by the logic form might vary, from the vacuum energy of a light wave to the placental energy of a mother, yet the process is always the same: a form imprints another region of space, changing its spatial position and temporal morphology. So speed is synonymous of reproduction, the main cyclical action of the Universe. Thus we can explain all physical events in terms of organicism. Since even movement, the external, mechanical change physicists study, turns out to be also an organic cycle of reproduction. We distinguish, according to their quantity of energy and information ‘translated’ in the process from a place of space-time to another place, 3 fractal, reproductive jumps:

– E=T: Space-time reproduction dominant in spatial displacement that implies a minimal movement of information that fluctuates from a future to a past form and returns back to the future. For example, when an electric impulse arrives to the end of a nerve, it becomes translated into chemical information and then it is transferred chemically through the synapses to the other cell, where it becomes translated back into electric information. That process implies a ‘spatial, fractal jump’ from a neuron to the next neuron, but also a fractal jump in time from a level of informative complexity, the electric language to the lower level of chemical languages, which is the relative, past informative system of life. The informative essence of the process implies a transcription of form from each discontinuous point to the next point but also a movement in space, since ‘all yang has a drop of yin’, all is temporal energy, also spatial and temporal reproduction requires a minimal dual movement in time and space.

-Max. E: Spatial, wave reproduction of a wave a particle that jumps from one place to the next place, reproducing a minimal temporal form. It is very common in physical waves, defined by its speed of reproduction, V=S/T. Depending on the density of a form, its speed of reproduction will vary. So the most massive forms are slower than those whose informations are minimal and can imprint the energy of vacuum very fast. Those forms that hardly move however evolve a lot in time:

– Max. i: Temporal, palingenetic reproduction, when an organism produces a past, smaller, simpler seed that reproduces the being, evolving faster towards the future. So a foetus is ‘born’ when it comes out of the body of the mother to the next discontinuous region of the Universe, making a minimal spatial jump and a huge evolutionary, temporal jump.

Reproduction of physical, biological and mental fractals

All fractals iterate=reproduce by absorbing energy transformed into fractal information by a Mother cell or external ‘enzyme’ – as it happens with carbohydrates or machines iterated by ‘enzy=men’. Unlike mathematical fractals, made of fixed, spatial forms, Nature’s fractals are made of temporal, iterative cycles, in which energy is transformed into information and growth, as the fractal family becomes detached from the mother cells.

In graph, cosmological, chemical, biological and mechanical fractals during their cycles of reproduction.

Organic fractals are not fixed, geometrical forms that merely repeat in spatial scales, void of life and temporal change. They are temporal entities, whose bio-logic cycles and functions repeat themselves at different scales and time intervals. Since not only space has a fractal, fractal structure. Time is also discrete made of cyclical trajectories that repeat themselves, as it happens with the cycles of a mechanical clock. It is precisely the repetition of the organic cycles of energy feeding and informative reproduction, what makes natural organisms fractal structures. The Universe is made of such temporal, organic fractals that reproduce into multiple clonic forms that latter re-organize themselves, giving birth to macro-forms similar to the original ‘cell’.

The most obvious natural fractals are those created by the iterative, repetitive nature of 3-D space. They are similar to mathematical fractals where geometrical form dominates.

For example, an ice crystal is a chemical fractal that jets up triangular, tall spikes, in its relative dimension of height, growing into a fractal; a salt grain is a cubic crystal that reproduces its form as it grows in scale and recomposes itself into huge cubes. While a hurricane fractalizes air streams into a vortex of wind cycles that grow also in height, the fractal dimension of information. Those physical fractals already iterate its form, despite the simplicity of its fundamental elements; since all natural fractals reproduce the shape of the ‘mother-cell’ into multiple clonic forms that latter re-organize themselves, giving birth to macro-species similar to the original ‘cell’.

In Biology, fractals are used routinely to explain how the iteration of some basic processes of growth gives birth to the complexity of botanic shapes: Branches, leaves and roots are all easily created by the iteration of an initial mother-form. A DNA molecule, which iterates its form both in micro-fragments (amino acids) and at macro-scale (recreating a cell). While a tree repeatedly fractalizes its form in 3 branches, ever slimmer, with less energy but ever increasing the information of the tree.

A human being is also a temporal fractal, made of fractal cells, whose organic functions repeat themselves at individual macro-scale in a longer time-interval: the feeding, reproductive, informative (sensorial), and social behavior of human beings are a macro- repetition of the same cycles that take place in cells. Cells feed on energy, absorb information, reproduce themselves and form social groups, as human beings do, at a smaller, faster scale. The fractal sum of those cellular cycles creates a human being. And then, the fractal sum of human cycles at a bigger scale creates socio-biological organisms, called nations and civilizations. A human is an organic, bio-logic, temporal fractal, extended in 3 scales, the cellular, organic and social scale.

Recap. The arrow of information and entropy together describe all kind of natural fractals, not only the well-known biological fractals but also social and physical systems that display complex, fragmented borders, (from physical particles to organisms, from minds to nations) and constantly re=produce information (actions in the quantum world, offspring in living organisms, ideas in the linguistic mind, technology and culture in human societies). They are also organic fractals, since once we understand their structure in multiple scales connected by flows of energy and information, the old distinction between organic and inorganic form looses its meaning, beyond its ideological role of making men the center of the Universe.

Linguistic fractals. Paradox of inflationary information.

Finally minds can also be modeled as fractal systems that replicate the forms and movements of the Universe in a smaller scale, through the syntax and semantics of a certain language. Indeed, modern science concentrates in the study of the parallelisms between the hardware of the mind, the neuronal brain, and its software, the depiction of the Universe made with visual and verbal languages. But what truly matters is the bio-logical parallelism between those mental structures made of syntactic and semantic, fractal units (numbers, geometrical forms, phonemes and sentences), and the external Universe they map out. Since organisms survive thanks to their accurate, mental perception that orientates them in that bigger Universe. So fractal minds are a fundamental tool of evolution: The mind acts as a virtual, fractal mirror, allowing the being to interact efficiently with the Universe, absorbing energy and information from it to replicate its form. Which means that we can study minds as mental fractals similar to its 2 main languages of space-time; mathematics and logic.

For that reason, mental and geometric fractals are both defined as entities whose informative boundary tends to ∞ while the energy/space of those boundaries tends to zero:

δe/δt->0 x δi/δt->∞ : Mental Fractal

Thus the information of a mathematical fractal is found in the boundary. It happens also in black holes, where information is attached at the boundary in a bidimensional space (holographic principle, which we proved in a simple manner as result of the 2 dimensions of a cycle of time that carries information and now we can observe from a more complex perspective). And I believe it is the case of the human mind, an i=eye-Wor(l)d, created by the eye’s retina and the electromagnetic waves of the cortex brain. Thus the informative parts of organisms, what we call ‘senses’, are also external, attached to the boundary and one of the fundamental functions of Nature’s fractal arrow is to create senses, systems of perception of fractalized information. Minds and senses are similar to mathematical fractals. It should not come as a surprise; since mathematics after all is a mind’s language, and minds fix most cycles of Natural fractals into still images that don’t capture the vital energy of the Universe.

It is important to stress the difference between mathematical fractals and reality fractals, and between information and energy properties. Information increase when the fractal becomes smaller in its surface. This paradox, that the smallest regions of space hold the maximal quantity of time: Max. I =Min. E is however essential to full grasp the Universe.

Languages hold more information than the forms they describe. Information is bidimensional and can be warped and cut. This essential property, that information is in the void, the cut, not the substance, as it will be first perceived by a mind in order to exist, and so it is not real till the perceptor observes it (quantum paradoxes), is however the reason why the smaller regions, in which voids multiply are more conductive to information frequencies that long ones. This paradox already understood by Gödel simplifies the distinction between mathematical physics and reality. Information is inflationary.

The Universe is not all the possible mathematical models. As Riemann, the key mathematician of the XIX C. explained, we cannot consider all possible spaces real, because the physical universe has selected only one geometry6, to which we shall add – it selects the most efficient geometry that maximizes the 4 arrows of time of species and helps the organic, Complementary, exi, bio-logic forms of reality to survive. Unfortunately neither mathematicians nor physicists today accept restrictions to their imagination, so they invent ‘multiverses, cosmic strings, multiple, infinite dimensions’ without ‘upgrading’ the concept of a continuous space into the reality of fractal discontinuous scales. The confusion of languages with reality is one of the main ‘errors’ of science we must resolve in order to improve the ‘logic/mathematical mirror’ the mind uses to perceive reality.

This distinction often lost to physicists in modern times, clearly expressed by Riemann in his ‘foundations of geometry’ and further proved by Godel implies that not all possible mathematical spaces and mathematical particles exist. The space of the Universe is far more restrictive in form and dimensions than the space of mathematicians. Why this happens can be explained ‘bio-logically’ by the fact that the inverse function of existence, extinction, eliminates all forms which are not efficient even if it creates them a priori – in the same manner all mutations in Nature, which are not efficient disappears. While our informative mind keeps producing imaginary models of geometry, which are pumped up by the scholar who seeks to convince the world his geometry is also right. For example, in the field of physics, multiuniverses, super symmetries, entropy in black holes, etc. are mathematical theories with no equivalent in the world because they ignore the arrow of information in mass and the need for no more than 2×2 dimensions to construct the Universe.

While the  Copenhagen interpretation of quantum physics in which an organic wave of photons, parts of whole electrons, guided by the 4th arrow of eusocial evolution is considered a herd of ‘probabilities’ is wrong. As in the case of the Mandelbrot set that doesn’t exist in nature, unable to resist energetic motion, in all those cases the 4 time arrows of reality and its need to be performed by all entities that wish to exist, limit the informations that become real.

All this requires understanding 2 of the basic properties of information – the fact that ‘fractal information’ is constantly created by the motions of reality and the paradox between energy with maximal spatial extension but minimal information Vs. information with minimal energy and extension. In brief, information increases, as in fractals, when we diminish in size. So brains are smaller than bodies but have more information. And a language has maximal information packed in minimal space. A language in fact has more information than a huge surface of vacuum space, which makes theories more abundant than the forms we find in the real Universe. Information is inflationary and so are physical theories with bizarre space/times that reality never will select.

Mathematics is, as all languages, an informative, ‘fractal’, whose self-similar forms/theories multiply in excess.

Thus, if certain sentences of verbal thought can be imaginary fictions, despite its beauty, so happens to many ‘quixotic’ geometrical forms, which do not exist. The Universe selects only efficient geometries, based in forms that can move and perform the arrows of time in the real Universe. So for example, the most beautiful fractal form of the mathematical Universe, the Mandelbrot set, does not exist in reality, because all its small self-similar attachments would easily break if they were moving as reality does.

Hence the importance of having a geometric theory of space-time that describes accurately the forms of the physical Universe. This was the key discovery of Einstein. He realized that Euclidean, lineal geometry, used to describe ideal space, could not describe the cyclical paths created in gravitational space-time. So he switched in his description of reality to a space called Non-Euclidean, where its minimal fractal unit, the point, could be crossed by multiple gravitational curves and hence, unlike the abstract point of Euclid, it required inner volume, inner form and energy. This point, which has always in Nature a region that can absorb /gauge information and a lineal or cyclical, rotational motion, is what we call a Point of View= Measure or Non-Euclidean point of view, the relative unit of Non-Euclidean mathematics.

Philosophers of science have wondered often if mathematics is merely a construction of the mind or an image of reality and why they are all pervading in the description of any ‘system’ of self-similar forms in the Universe. The answer is both: languages are construction of the mind that reflect the external universe’s information in a small space, hence they must reduce the total information to fit the mental mirror, trying also to make an image the closest possible to reality. This is what logic languages do with time and mathematical languages with space; because the Universe is logico-mathematical, albeit of a type of logic and mathematics more complex than the abstractions without motion deviced by the Greeks 2300 years ago. Indeed, the same concept applies to the new logic of time, which is based in multiple causality, either a dual ‘biological causality’ in A<->B events in which an element A is predator and the other B victim; hence B is considered by A mere energy when B considers itself an informative entity worth to exist (so A is both A and B, victim and predator, energy for the predator information for the I-self of the victim); or ‘multiple, spherical causality’, when multiple agents create a certain network or form. So for example a real circle is not drawn in abstract by a single pen, but happens when multiple self-similar points of view converge and form a cycle.

Ultimately we are all made of spatial energy and temporal information, whose synoptic descriptions are achieved with 2 languages, mathematics and logic. And so the search for knowledge by the human mind is not only the recollection of experimental data, but its description with the languages of mathematics and logic. Hence even more important than the collection of data is the creation of a mental container – those 2 languages – efficient and evolved enough to fit properly all the data of reality we observe. Yet since the revolution of thought represented by Evolution Theory in Biology and quantum/relativity in physics, there is a gap between the behavior of universal entities and the linguistic syntax of mathematics and logic, hardly evolved since 2300 years ago, when Euclid and Aristotle founded those 2 sciences. Thus, we shall in this work summarize the new advances and laws of spatial geometry and temporal logic that are needed to describe a complex Universe of multiple, fractal space-times in which points are Complementary systems – entities that gauge and feed on energy with an informative and energetic center (body/brain, field/particle system). What still stands is a simplification of reality to ‘fit’ it into the mind. So while we are not concerned with the specific energy and information the point of view process (the details that don’t fit), we cannot longer hold truth the syntactic errors of Euclidean mathematics (points, lines and planes without breadth, width or height), and Aristotelian Logic (single causal events of the type A->B).

We call the ‘evolved’ syntax of those 2 spacetime languages, Non-AE illogic geometry, or simply illogic geometry (as the I represents ‘information’ and it is the next vowel after the A-ristotelian and E-uclidean languages used till now). So we affirm that the Universe of spacetime follows the complex logic of information or ‘i-logic, fractal geometry’ which the pioneers of XIX and XX century science (Darwin, Riemann, Planck, Einstein and Mandelbrot) used to describe their discoveries in the field of biology and mathematics. In terms of the evolution of science, those discoveries are the foundations of a ‘new paradigm of science’, which upgrades philosophy of science, also stuck in Aristotelian, Euclidean, mechanist, pseudoscientific theories since the XVII century. So we shall talk often of the ‘i-logic, fractal paradigm’ as opposed to the ‘A-logic, Euclidean paradigm’ of a mechanical world of single ‘ceteris paribus’ causes and entities which are supposed to exist in a single, continuous, abstract, non-moving spacetime…

The second part of this work after this brief introduction to ‘metaphysics’, the description of the ultimate meaning of existence – the accomplishment of the 4 arrows of time – will be dedicated to the development of those new formalisms of mathematics and logic needed to make detailed, rigorous analysis of the events and forms of natural, organic fractals.

In that regard, since all languages are fractals of the entire Universe perceived in a slower, shorter, memorial pattern, a mirror of information with less dimensions of ‘motion’ and ‘form’ than the original. So these texts could be also considered a fractal, linguistic mirror of all Realities.

Recap: Information is inflationary. So are informative languages, reasons why we must differenciate fictions from theories that truly describe the universe. Time Arrows improve our logic and mathematical tools to describe the Universe. This is done advanced the Aristotelian logic and Euclidean geometry into the next vowel of the alphabet:i-logic geometry, the logic and geometry of information.

Man as a fractal organism.

Man as a fractal is made of cellular units and networks of energy and information (nervous and blood systems), whose cycles and functions extend through 3 main i-scales: the cellular, individual and social scale.

A human being described as a fractal will be composed of:

DNA cells, the Mother cells of the human fractal, whose genetic functions and forms repeat themselves trillions of times, composed of informative units (the DNA genes) and energetic ones (amino acids, bricks of genetic reproduction).

– A palingenetic process of reproduction and differentiation of those cells, which latter gather into energetic, reproductive and informative networks: the digestive, blood and nervous systems that create a human.

– The scales that group DNA molecules into cells, which gather themselves into organs, which gather themselves into physiological systems, put together into a human being.

Those scales seem to obey a ternary and decametric scale. So humans have 10 physiological systems, 10 fractal fingers, 10 glial cells feed a neuron, etc.

Of all the possible fractals that can be described with those 3 elements I share the fascination of Kant for what is inside the mind of men and what is above it, on the skies. So we will dedicate most of the pages of this work to study those 2 fractals, man and the Universe.

Recap: Humans are fractals of energy and information defined by the 3 elements of all fractals, cells, scales and reproduction.

The Universe as a Fractal organism.

The Universe can be described as a fractal, based in the existence of the 3 elements that define all Natural fractals:

– The Universe has 2 networks, one of electromagnetic energy and one of gravitational information (black holes, dark matter) that controls the electromagnetic world. It has also informative vortices (masses and charges) and lineal forces.

– Its fundamental particles, quarks of mass/information and electrons/photons of electromagnetic energy can absorb energy, gauge information and reproduce self-similar particles.

– The structure of those particles and forces is scalar: lineal forces of electromagnetic energy and cyclical particles of gravitational information grow in scale and size, from the tiniest lineal and cyclical strings, which are so small that we cannot perceive them, to the atomic scale of lineal forces (light, gravitation) and cyclical particles (electrons and quarks), to the cosmic scale of gravitational and electromagnetic fields, caused by spherical, celestial bodies (stars, black holes and planets). pieces of space and time made of lineal and cyclical strings, gather into planes and complex topologies called ‘membranes’, creating the macrocosms we perceive.

The Universe and man described as fractals, whose cellular units are blood and nervous energy/information networks and informative masses (MACHOs, quark stars?) and light galaxies that shape 2 networks of radiant energy and dark, informative matter. Each point of those 2 networks (compared to the similar networks of a human organism) represents a galaxy.

Bio-chemical and geometrical fractals have been known for a century. But only recently we have studied the physical Universe as a fractal, born out of the dynamic combinations of those 2 arrows of time. One of its most remarkable successes is the description of Einstein’s space-time continuum as an iteration of some basic fractal geometries (Nottale). Thus Einstein’s sentence, ‘Time curves space’, means in fractal terms that the arrow of informative time curves the vacuum energy of the Universe, fractalizing it into fractal particles, charges and masses, which are fractal, spiral vortices of electromagnetic and gravitational information. Moreover, if we order the sizes of the Universe in a decametric scale, we find that at certain intervals the same forms and functions appear once and again. In the 60s, the American filmmaker Eames made a documentary called ‘The Power of 10’, in which that iterative repetition of cyclical, spiral forms appeared from the quark to the cluster. In fact, the homology of form and function between those scales is so remarkable that the same equations describe the tiny magnetic field of an electron or a star, made of trillions of particles. Thus, since that decametric scale is the most common scale considered for the entire Universe, we can define the Universe in fractal terms:

‘The Universe is a fractal super-organism made of particles of information and forces of energy gathered in networks, whose formal cycles repeat in decametric scales’.

While the fractal Universe and the continuous model of the big-bang use the same experimental information, the final outlook is very different. Since the fractal Universe is:

A)    Eternal.

B)    Cyclical.

C)    ∞in scales or evolving information and energy extension.

Indeed, even if there were a process of organic reproduction, of a big-bang like radiation of forms and particles over a surface of void energy, this will be subject to the duality of arrows of time, of life and death cycles, of big crunches (life, creation of information) and big bangs (death, creation of energy). So B->A, and since the Universe is cyclical, it is eternal. And so, in a fractal Universe the metaphysical question is: do Universes become ‘microscopic black holes’, quarks of a bigger, fractal Hyper-Universe? A detailed study of the physical constants and parameters of those particles seem indeed to foresee a fractal Universe, which is not only infinite in its relative spatial size, but in the number of scales/planes of organic evolution, in such a manner that each galaxy could be the atom of a bigger Universe, as it happens in fact in the theoretical models of relativity, (Einstein-Walker model of a Universe made of galaxies, interpreted as ‘hydrogen atoms’13.)

Recap: The Universe is a fractal of energy and information that extends in 10 perceived self-similar scales of Euclidean networks in which the 3 invariances of motions, form and scales are kept.

But since in the fractal model the parameters of atoms and galaxies are self-similar, the Universe could be infinite in its scales.



In the graph, a galaxy, a DNA molecule, a tornado, a shell, a sunflower, and 2 logic, mental mirrors of the Universe – a Mandelbrot set and a yin-yang, eightfold life cycle – are all made of shapes that combine the most efficient morphologies of energy and information: the line or shortest distance between 2 points and the cycle that stores the max. quantity of information in lesser space. Both combine to reproduce the infinite beings of reality. It is the game of existence we all play.

The game of existence: we are all knots of time arrows.

Once we have established the existence of a Universe of motions in time not forms of space, whose organic parts are guided by the ‘will’ of the 4 arrows of time, we can respond to the fundamental questions about man and the Universe – why we are here, what we are:

The meaning of existence is a tautology in itself: we ‘exi=st’ to inform ourselves in order to absorb energy with the aim of reproducing our organisn in other zone of space-time, avoiding in this manner ‘extinction’, the inverse function of existence – since we are only ‘parts’ of the total Universe with a limited quantity of vital energy/space and a limited duration of time. So to ensure the survival of our in/form/ation we must either reproduce in other zones of space-time or increase our quantity of vital energy and our duration in time, by becoming a part of a bigger entity, a wave, herd or organism.

Thus, if the Universe can be defined externally, objectively, as a geometry of two inverse motions, energy and information; from the internal perspective of the ‘will’ or ‘why’ of those motions of time, the Universe is a game of ‘exi=stence’, where ‘to grow=evolve and multiply’ is the meaning of it all.

The objective description gives origin to the type of theories sponsored by physicists, which describe the geometrical forms generated by those cycles of time.

The subjective description gives origin to the type of theories of time developed by Religions, (God, as the will of times, expressed in verbal mandates), Biologists (theory of evolution as a struggle for existence) and Psychologists (psychological time, which is our inner perception of our time cycles and drives of existence – our desire to perceive, inform, reproduce and evolve socially).

So each organism is a complex chain of interrelationships, causal processes, synchronized clocks and energy/information networks that harmonize all those seemingly chaotic cycles into a dance of existential beats, interdependent and in permanent symbiosis – being the key to those harmonies among different time arrows the concept of ‘time-speed’, the speed at which a certain cycle of time closes its trajectory into a ‘loop’ or event(spatial/temporal description), which will be repeated with a ‘frequency’ that defines the regularity of the time cycle and its speed of perception.

For example, the subjective cycle of time perception in man is the cycle of informative perception determined by the wink of the eye which opens to absorb energy and closes when it processes it as information every second. This rhythm is self-similar to the rhythm of the heart, which is approximately of a beat per second, when blood is expanded as energy and imploded carrying the released chemical information of the body. So, since we have a thought per second and a beat per second, the second is in fact the ‘clock-time’ of the human brain and the mechanical instruments we use to compare all the cycles of time of the Universe with our own cycles.

Each species and cycle of time has a different frequency, which depends on the ‘size’ of the species we study, and the causality of those arrows ,such as:

Max. Energy-extension=Min. Speed-Frequency of Time cycles:

Max. Speed/frequency: Informative cycle->Energetic ->Reproductive ->Social cycle: Min. Frequency.

For example, the cycle of perception of the human eye – each second –determines the beat of the heart/breathing cycle of energy for the body; the cycle of rotation of the Sun-Earth system – a day – determines the Energy cycle of the planetary surface, whose microscopic, life-species adjust their energetic/formative, awaken/sleep cycle to that of the ‘bigger organism’. And vice versa, the smaller microscopic cells of the body reproduce each day, according to that awaken/sleep cycle. There are in fact a series of General Laws of synchronicity between those time arrows/cycles that apply to any entity or complex system of the Universe, which extends through several scales of spatial size and informative complexity.

In objective terms humans are created by the same temporal arrows and display the same properties than the rest of the entities of the Universe. A human being is the same kind of entity than ‘an atom’ – a complex chain of time cycles of energy, information, reproduction and social evolution. The difference is not of quality but of quantity and hence of complexity: Humans are knots of an enormous amount of time cycles whose spatial topologies, actions and motions configure our existence.

On the other extreme of simplicity, an atomic particle (quark, electron or photon) is the simpler species, we can study with those arrows, in terms of size and complexity of its ‘EIRS’ cycles, compared to a human being. Since a particle can be described with just 4 quantum numbers that resume the 4 kinds of ‘actions’ particles constantly perform:

– Particles gauge information (reason why quantum theory is a ‘gauge theory’). That is, they calculate the distances with other atoms and act-react to exchanges of energy and information with them.

– Particles feed on energy, absorbing electromagnetic and gravitational forces and other particles.

– Particles decouple, repeating themselves in other regions of space-time (they reproduce by iterating its particles, quarks, electrons and photons).

– Finally particles evolve together into complex social structures, called atoms and molecules, which also feed on energy, gauge information, reproduce and evolve socially.

All those ‘motions’, quantum numbers, molecular vibrations, decouplings and physical events can be re-considered as manifestations of the 4 arrows of time, chained in synchronic patterns and cycles, cyclical and lineal geometries, whose abstract definition conform the Laws of quantum physics.

The description physicists do of those arrows is an abstract, mathematical, mechanical description, which corresponds to the limits of the mechanical, monist, ‘religious’ philosophy of science of our founding fathers4, which did not require an ‘internal’, self-organizing will to describe the Universe, since it was understood that the ‘will’, the ‘why’ of all the clock-like motions of the Universe was ‘God’, an entity that seems to have appeared to a pastor of the bronze age.

Instead, system sciences reasons those ultimate questions from the perspective of science and its mathematical and logic languages, albeit with a degree of complexity superior to that provided by monist, reductionist, mechanist, classic scientific philosophies of reality. Thus we substitute the ‘will of a personal God’ or any other anthropic principle with the 4 objective ‘arrows of causality’ or time arrows that all particles and entities of ‘existence’ follow, which can be described objectively with mathematical and logical equations, and finds in the subjective will for survival its sufficient reason.

Further on, all quantum entities obey the Principle of Complementarity. They show 2 states or structures that co-exist simultaneously: a field of energetic forces that moves a particle of information, which gauges the space-time that surrounds the particle. And we cannot distinguish or perceive both entities, the force/body and head/particle together. In other words, physical entities are made of ‘motion fields’ and ‘gauging particles’. They constantly move, stop and gauge information, move, gauge… So because they have 2 components, one specialized in energetic motions (the field of forces) and one specialized in informative gauging (the particle, mass or charge), all their actions are either ‘energetic actions’, informative gauging, the combinations of both type of actions (decouplings, which produce self-similar particles) or more complex actions in which the particle, atom or molecule share smaller particles, called bosons, creating social networks, made of fields of forces and particles of information.

If we widen the concept of energy as lineal, expansive motion, and information as a cyclical, in/formative motion, we realize that the biological realm also follows a Principle of Complementarity between energetic bodies and informative heads, which co-exist together in living beings. And bodies are responsible for lineal motions, while heads map out the Universe, creating images, reflected in the mind of the external motions of reality, imitated by small cyclical motions within the brain and its neurons. So again we observe a dual structure, body/head, with energetic/informative properties that move and gauge, feed on energy and perceive information. And in more complex events, reproduce the biological entity or use languages of information to create complex social structures.

All what exists is a ‘fractal knot of energy and information motions’, whose why is ‘to absorb more energy and information’ from the perspective of the entity or ‘point of view’ that gauge and moves in the Universe. Imagine a universe of infinite ‘species’ made of ‘lineal motions’, ‘forces or bodies’, upon which certain structures of information, called ‘cyclical motions’, particles or heads, are sustained. Reality is a fractal sum of those 2 motions, energy and information, which combine to create an infinite number of entities that gauge information, feed on energy, reproduce their form and evolve into social structures till reaching the complex Universe.

We cannot describe human actions with simple equations because humans can gauge many types of information, feed in many forms of different energy, choose many different couples to court, love and reproduce, and make very complex choices in our decisions on how to relate socially to other human beings. But at the end of the journey, amazingly enough we observe that all what we humans do is also gauging information, absorbing energy, reproducing and evolve into social systems. So those 4 types of events or causal arrows of time are all what we humans do; even if we use a complex, ‘ambiguous’ language – words -to describe those actions.

To exist, to be in this Universe means to absorb energy, gauge information, reproduce our form and evolve socially by acts of communication with other beings. Those ‘actions’ are considered mechanical in the physical world and actions of will in the human world. Yet they are described in both worlds with the same ‘2 elements’: energy and clocks of time. So Planck proved that all physical forces are made of h-quanta, whose parameters are ‘energy and time’, while we say in layman terms that ‘we do not have enough time and energy to do this’ – meaning we are made of a limited quantity of vital space, our energy/body, and time-clocks of information – our minds.

A world of informative points of view.


There is no difference between ‘us’, human beings and ‘particles’ that also have a limited energy and time, which they spend performing the same game of 4 types of actions – the Game of Existence. We all play the same game, regardless of what plays it, an atom, or a human being.

Religions will tell you that the ‘will’ of man is a property of ‘our soul’, which is supposed to exist according to the tradition of our ‘pious’ founding father, Mr. Descartes, in some non-local space-time4. Science will tell you that the ‘will of man’ is the ‘why’ we don’t ask, or at best it will be born of a chaotic series of circumstances and physical events that come together to ‘create life’. While biologists will affirm that the will of man has the same drives of existence (gauging, feeding, reproducing and evolving socially) that all forms of life have, but only forms of life have.

System sciences depart from anthropomorphic traditions, validating instead the ideas of Eastern philosophies (Taoism, Buddhism, Zurvanism), upgraded with the scientific method, showing that the Universe is ‘organic’, not mechanical, because all its particles share the ‘4 drives of existence’ of biological beings, whose ‘why’ is self-evident in a world made of perpetual motions. Since if we all are made of motions, life is embedded in the existence of those motions that repeat themselves by the mere ‘action of moving’: Reproduction becomes natural to the existence itself of cyclical and lineal motions that repeat their forms as they trace their trajectories.

If we leave aside metaphysical, subjective questions on the ‘nature of consciousness’ and ‘will’, we could affirm that all entities of the Universe have both, a ‘will of existence’, shown in its constant pursuit of those 4 arrows, and an objective nature, in as much as those 4 arrows or wills can be proved objectively by the events that atoms, humans, animals or any other entity perform. It is though necessary to understand in which scale of reality a certain region of timespace ‘acts’. For example, a chair, made with human formal imagination is not organic neither it shows any of the 4 arrows of time unless it is attached to a human being (so it helps humans to think- process information – in a ‘still’, formal position). Yet at the spatial scale of atomic wood, the chair shows those arrows and in the temporal distance when the chair was wood, it had also at macroscopic level those vital arrows of time.

What is then reality – the ultimate meaning of those 4 time arrows? At first sight, it seems there is no meaning at all, but merely the eternal beat of existence, energy becoming form, becoming energy… and the sensations related to those motions, which might be shared by all realities – pain/pressure and pleasure/release. A closer view on both arrows and the complementarity of all physical and biological entities, which achieve immortality through reproduction of their own form – from light imprinting its waves on the vacuum, to quarks jetting bundles of quarkitos, to humans ‘growing and multiplying’ all over the Earth – seemingly makes the 3rd existential arrow of reproduction, the meaning of it all, nd the Universe a constant orgasm of repetitive, present forms. But then, we realize that reproduction in itself is just a step towards self-organization, as self-similar cells that can ‘decode’ their common language of information come together into stronger, bigger waves, herds and organisms, which survive better, due to their higher ∑ExI, existential force. So the answer to the meaning of it all is clear: the Universe has a dominant arrow, the creation of ‘fractal superorganisms’, species which are self-similar to their parts and emerge through processes of evolution into bigger wholes. Since the 4 arrows of time and its discontinuous cycles group together into vital motions that energize, gauge information, reproduce and finally evolve socially into herds and organisms: I->E->R->S. In other words, a fractal infinite Universe of energy and information struggles to create ‘more of it’ by expanding inwards and outwards its relative scales of organic size; since a Universe made of motions has no limits of size and form, as it becomes ever more organized in bigger and smaller social herds and organisms: I->E->R->S.

Yet even if social evolution is the dominant arrow of the Universe, it is also the less common, more distanced in the frequency of its events, since all other arrows must exist ‘a priori’ for an event of social evolution – the final causal arrow of reality – to take place, thanks to a common language that carries information among self-similar cellular individuals.

Indeed, we observe a generic law of time arrows: the highest frequency of events corresponsd to informative events, particles and heads gauging and thinking, mapping reality with its hardware, as they run inside the software of a force, whose frequency carries informations decoded and transferred into such mappings. So the atom figures out first in its inner quark-systems how to move, searching for a flow of energy or its relocation in harmony with the other atoms of its web, while an office clerk thinks first and then writes or makes a call related to those informative thoughts – an act of measure precedes an act of motion.

Accordingly to those frequencies and the generic law, Min.E= Max.I, the light pixels of informative mappings are smaller and faster to allow faster events/cycles of perception than the bites of energy that feed the body – aminoacids, which are smaller than the seminal cells that carry the information of reproductive acts, which are smaller than the units of social evolution (other humans). So happens to the the frequency of perception (each second), faster than that of feeding, which happens more often than the frequency of sexual reproduction, which is more common than our acts of love – social acts of evolution that ‘collapse’ a wave of individuals into a particle/organism, emerging as a whole action, born of the self-organization of its parts, such as a religious mass or a voting action, or a marriage, all acts that create social groups. Yet, the ultimate why of any chain of causal time arrows must be found in the goal of ‘survival’, the final drive of all entities of the Universe, maximized by its 2 complex arrows, reproduction and social evolution that evolves cellular entities into macrocosmic wholes, which become cellular entities of a higher ‘space-time plane’.

What we are then can be expressed in more poetic terms: knots of existence, flows of arrows of time, mirrors of information, bodies in action, ‘wills of the penis’14, loving cells of bigger social units, exi=stential flows, ‘vanitas, vanitatum et omnia vanitates’; motions of time in perpetual conflict.

The rules of engagement of all those knots of time, ‘points of view’ that gauge information, seek for energy, reproduce and evolve socially, creating ad eternal the infinite scales upwards and inwards, is the ultimate knowledge of the game of existence, which system sciences study. This holistic view is a mystique revealing existence of the unity of it all, which few self-centered humans accept. Scientists rejected it in the past, because it had not been properly formalized. But one of the advantages of the new formalism of Non-Euclidean, fractal, logic, causal chains of time arrows/events, is that it renders a mathematical analysis of those arrows of times are its generic laws, hence allowing their application to the study of the species of any scientific network of self-similar points in an open flow of communication. Thus, the range and power of the formalism of time arrows will not become evident till we develop the logic of multiple causality and the non-Euclidean geometry of flows of communication between the fundamental particle of the Universe, the non-Euclidean point15. A consequence of those postulates is in fact the definition of a soul as a non-Euclidean point of view:

‘Every point of view=mind feels the center of the Universe, but it is only an infinitesimal Non-Euclidean point that stores a limited mapping of reality with its informative languages.’

We are all atmans, informative CPUs, souls that gauge in different languages reality, to construct a mental mapping that caters to our point of view and arrows of time. So we create our ‘perceived Universe’ – a fact known from Descartes to Schopenhauer, but lost to ‘naïve, realist’ physicists. All of them thinking clocks are the only point that matters to measure time, and the human mind, the only ego that knots energy into form, since that is the only perspective they perceive. That is why most of history, humans thought the Earth to be the center of reality; and still think they are the only intelligent species.

All is memorial because cyclical inertia, the repetition of the cycles of existence of any form, is common to all space-time fields. This is a tautology: a species that forgets, that does not repeat a fractal cycle of existence becomes extinct and its cycles of existence disappear. Thus, a being has to remember and repeat its fractal cycles to last in time. That is the existential game of any being: to feed on energy and use its genetic, memorial information to transform it through reproduction into new cyclical actions.

Yet those actions are encoded in ‘fractal equations of information’ which are logical chains that constantly repeat themselves, becoming memorial patterns. Those patterns have different names in science: genes in biology, memes in history, Universal constants, which are proportions between physical energy and information in physics, etc. Yet what all those fractal equations and e/i proportions become are cyclical, self-repetitive events that respond to an arrow of time.

Recap: All what exi=st is a fractal knot of cycles of energy, information, reproduction and social evolution. There is not a difference of quality among universal entities – only a difference in the quantity and complexity of those cyclical arrows that ‘inform’ each species of reality. The ultimate meaning of a Universe made of time motions not of spatial forms is closer to a Philosophical tradition that ranges from Plato and Buddha to Leibniz and Schopenhauer: reality is a game of ‘fractal mirrors’, souls=atmans= quantum knots of information that gauge reality to absorb energy in order to repeat=iterate=reproduce their form. Since we are all fractal parts of the whole with a limited duration in time and a limited quantity of space. And so only those species, which reproduce their ‘logic arrows’ of time, their information, in other zone of space survive. Thus the game of existence is in essence a game of repetition of forms, a game of exi=stences.


The philosophy of science of time arrows.

Departing from the first monist theories of time (anthropomorphic religions and time-clock in physics), there has been a progress towards a more complex analysis of time arrows that culminates in the XX century with Biology and System sciences, which put together all those arrows in order to explain what Biologists call the ‘drives of existence of living beings’, and System Sciences now expands to all other species. Biologists said that living organisms perceive information, feed on energy, reproduce and evolve into herds and organisms. So the creation of energy, the gauging of information, the reproduction of species and their social evolution into herds and organisms are the 4 types of changes or fundamental arrows of time in the Universe. Reason why in complexity, we say that the Universe is ‘an organic fractal of energy and information’ in which all its parts are self-similar ‘super-organisms’ made of cellular parts, which are connected by networks of energy and information, and perform cycles of feeding (on energy), gauging (information), reproduction and social evolution.

System sciences relate all those processes with a common jargon, taken from biology and physics, which applies to any process taken place between different scales of reality, proving that those 4 arrows of time are common to all the species of the Universe, including physical species. And so, by using those 4 arrows of time to study the events of all sciences, we can rebuild the science of philosophy as a philosophy of science and finally understand what time is, what is the meaning of existence in the spacetime Universe, why we live and die (the entire process of time changes we experience), and other classic themes of philosophy, which the older, restricted, monist theories of time – mainly physics – have not answered.

In System Sciences we dissent from Quantum Monism, which considers the Universe made with a single arrow of expansive space (entropy or energy) and defines mass with a quantum particle and a new Universal field never observed before (the Higgs). Instead, we back the established work of Einstein’s Relativity and its Principle of Equivalence between masses and cyclical acceleration, which defines a mass as a cyclical vortex of gravitational spacetime, the in/formative arrow of the physical Universe. Moreover information is considered the dominant arrow of creation of the future, since it is the passing of time, what ‘forms’ the energy of vacuum space. ‘Time bends space into masses’ said Einstein. The same can be said of Biological species, since ‘time evolves the morphology of living beings’ (Darwin). In that regard, this work can be also considered an alternative to the dominant philosophy of science and the many bizarre interpretations of the quantum paradoxes, which time arrows resolve from an organic, dualist perspective – so for example, the collapse of waves of quanta into tight particles, when confronted with an electronic flow (the observer’s microscope), which so many puzzles has caused among philosophers of quantum science, becomes the same self-evident process that makes fishes come together into tighter herds when a shark comes against them: the event is an strategy of survival based in social geometries. For the same reason, we see the same formal patterns in the path of particles crossing through a slit or humans evacuating a theater: in both planes of existence a group of self-similar particles will form the best geometrical flow to cross the slit/door in minimal time. Yet all those self-similar processes cannot be understood without the invariance at scale of the forms and properties of energy and information, and requires more arrows than entropy.

The arrow of energy, the ‘canvas’ of reality does not create the Universe, but merely destroys information in entropy processes of death, such as the big-bang or the destruction of a living organism. So we need to ad to the mix, the creative ‘paint’, the information arrow, explained both with the mathematics evolved in the XX century, (fractals and Non-Euclidean geometries) and causal words that describe those processes with its ’3 verbal dimensions’, past, synonymous of energy; present, synonymous of reproduction=repetition of the same beings and future, synonymous of evolution.

Yet information is the dominant arrow of future of most universal processes, which are guided by the bio-logic laws of eusocial evolution that gather the individuals of the same species into organisms and in human history were expressed by the mandates of religions of love. Thus, the arrow of information is dominant in Religion and Philosophy, needed to explain the meaning of God, Man and the Universe, beyond the simplest scales of reality dominated by energy and matter, which physics study.

Recap: A true Theory of Unification, as systems science is, should explain all what exists, including humans – why we are here, our role in the Universe, what truly matters to mankind. This is what System sciences does… and in doing so, it is finding that both Science and Philosophy are essential to explain the meaning of it all.

Duality & Complexity: Simple and Complex Time arrows

Complexity, more properly called Systems Sciences, was founded at the death of Einstein, in the Macy’s congress, where the most advanced scientists of the age met to find new avenues to the ‘dead end’ in which quantum theorists have placed the evolution of science, with their definition of a Universe guided by a single arrow of energy, found in the restricted analysis of heat, and latter expanded to all universal phenomena. In this manner the idea that the Universe has a single arrow, expansive entropy had become dogma, without taking into account the cyclical motions of electronic particles and the existence of the arrow of informative gravitation – an attractive force, which therefore informs and creates order. Since as Einstein put it gravitation is an arrow of ‘Time [that] bends space into mass’. Yet in the Macy congress it was understood that information played also a fundamental role in the creation of reality and so the Universe was defined as a dual system, created by two arrows, energy or motion and information or form.

The best-known science to come out of that congress was cybernetics in which computer science is based, because of the practical uses it has today in the age of information. Yet the most important sciences for pure knowledge were two less-known disciplines, Duality and Complexity:

– Duality studies the Universe with the 2 ‘simplex’ arrows of time, energy and in/form/ation16.

Scientific Duality has important precedents in Eastern cultures. In Taoism yin translates as information and yang as energy, and the Universe is explained with those 2 elements. In Europe Leibniz introduced Taoism to the West, establishing it as the foundation of German philosophy. There, Hegel translated philosophically Duality into Dialectics – the concept that from a thesis (the equivalent of energy) and an antithesis (the equivalent of information, with inverse properties to those of energy) a synthesis arises, by merging both in ‘Complementary, dual systems’.

So even if Duality was not understood scientifically till Systems Sciences filled it with scientific data, it has been always a Theory of It All, in the tradition of religions and philosophy. This is logic – since humans have understood Duality with different degrees of detail and different jargons by the mere fact that they observe a dualist Universe.

What modern Duality has done is to upgrade those concepts with the discoveries of mathematical, biological and physical laws, which show the Universe as a Fractal System of energy and information. In that regard, the central concept of modern duality is also the Principle of Complementarity, which states that all systems in the Universe are constructed with an energetic and informative element, whose geometrical properties and functions are self-similar:

Energetic systems store energy and move. They occupy more space and are lineal (the shortest distance between two points)

Informative systems store and gauge information. Thus they occupy less space and tend to be cyclical (the form that stores more information per unit of volume).

This dual complementarity is the main Law of quantum physics (principle of complementarity between a lineal field of energy and a cyclical, particle of Information). It is the principle that explains the structure of all living organisms (from animals with cyclical heads and lineal bodies; to plants with energetic trunks and planar leaves, which store and process energy, and quantized, fractal roots that absorb chemical information; to cells with a central nucleus that stores the DNA/RNA information of the system). It explains biological reproduction (since males have lineal bodies, specialized in the collection of energy and females, with curved bodies, reproduce our information). It is the principle of Computer science, based in the duality of symbols, 0 and |.

The Universe has two inverse ways of creating reality: it creates either energy, by erasing form, as when a quasar explodes, E=Mc2, vomiting ‘dark energy’ and flows of expansive space. Or when any being dies, dissolving its form. Or it creates information by warping energy, as when energy becomes mass, M=E/c2 (in fact the first equation that Einstein found), since ‘Time bends [vacuum] space into mass’ (Einstein) or ‘Time evolves the form of beings’ (Darwin). And so all what exists fluctuates between the arrow of information, of life, of creation of particles with form, E->I, and the arrow of death, of erasing of form into energy, of big-bangs, I->E.

Both together, in their transformations, E<=>I, generate the cycles of creation of form (life cycles) and destruction (death cycles), which define the existence of its parts.

Thus Duality advances a step further in the great insights of Eastern and German Philosophy, opening new avenues of thought and explaining the why of many phenomena that the use of the single arrow of quantum physics cannot resolve.

– But Duality only studies simultaneously the energy and form of what we call a ‘plane of existence’, or ‘scale of the fractal Universe’ (Religious/philosophical vs. mathematical jargons). And when we consider reality, it is obvious that the Universe is structured in ‘layers’ of entities of growing size and complexity – from particles to atoms to molecules, cells, organisms, societies, planetary systems and galaxies.  In each of those layers we find Dual species: quarks of massive information and electrons of energetic space, which form atoms; Nitrogen rings that store information and phosphate chains, which form DNA molecules; Nuclei that store information and cellular bodies that store energy; heads of information and bodies of energy; audiovisual networks of information and economic networks that distribute energy, forming together nations. And this pattern of social evolution and emergence into new, more complex systems that create a bigger plane of existence also occurs in physical space, as molecules become planets and stars that organize themselves into galaxies. So we must ad to the 2 Simple arrows of time, energy and information, 2 Complex arrows of time: the creation of self-similar species or reproduction and the social organization of those self-similar, cellular species into networks and more complex systems. And we find those 2 universal arrows in both, physical and biological systems. Even the simplest particles of the Universe, quarks and electrons reproduce into new quarks and electrons when they absorb energy, as biological beings do, and organize themselves into complex cellular systems in atoms that have many quarks and electrons. In that regard, Complexity studies how reality is created by multiple layers of reality, which from the simplest strings and particles evolve into molecules, cells, organisms, planets, stars and galaxies of increasing size and complexity.

So the arrows of energy and form are not enough to understand the complex Universe, which exists through a series of ‘planes of increasing complexity and self-organization’, starting from the first theoretical duality of ‘lineal strings and cyclical strings’, till arriving to the final duality of black holes of gravitational information and stars of electromagnetic energy (Galactic duality).

Such networks gather an enormous number of individual energy and information cycles/cells of space-time into a single whole or social organism deployed across multiple planes of space-time. The study of those scalar, network structures is the field of Complexity Theory, the sub discipline of System Sciences, which departing from Duality, analyzes how bits and bites of energy and information reproduce, evolve, self-organize and emerge as a bigger system, in a ‘higher’, ever more complex space -time plane, creating in this manner complex systems, made of simpler, ‘cellular parts’.

Thus Systems sciences require a second discipline, besides Duality, to study complex systems and their self-organization thanks to the arrows of reproduction and social evolution, which create networks of energy and information that become wholes, units themselves of a new plane of existence:

System sciences: Duality (analyzes how the beats of energy & information, E<=>I, create the future) +

Complexity (studies how complex, reproductive, exi & eusocial ∑ exi, events create the future).

Thus Complexity studies the 2 ‘complex’ arrows of time, derived from the combinations of energy and form, exi, or ’reproduction’, which creates self-similar ‘cellular beings’ in a given plane or scale of reality and ‘social evolution’, which creates complex, tight networks made of those reproduced exi parts, that become together a single unit of a new, higher, bigger, more complex plane of existence. Those 2 ‘complex’ arrows of time derived from the Simplex ones (energy and form), create the 4 ‘dimensions’ or ‘arrows’ of time needed to explain the Universe, and its understanding through the formalism of the Generator Equation of time arrows, ∑ exi, represents an enormous leap for all sciences, which prior to the Systemic Paradigm worked only with the arrow of entropy and energy proper of XIX century physics. We ad now to that ‘arrow of energy’, the ‘canvas’, the paint – the information in which that energy transforms itself, and the painter, since we contend that the finality of the Universe, the ultimate arrow of ‘future time’ is the creation of social organisms through the use of a common language of information – hence the creation of history, the superorganism of mankind, the most complex form of the Universe.  We prove all this with the experimental method and the logic and mathematical formalisms derived from the generator equation,S exi, whose symbols define the 4 arrows of time:

e or Se, which is the symbol of spatial energy, the energy-motion, which is stored in vacuum space, from where all ‘forms’ of information are created.

I or Ti, temporal information, which is the dominant arrow of future, as time bends energy, trans/forming it into particles and ‘forms’ of information.

E x I is the formalism of reproduction. Since all systems reproduce their energetic bodies/fields and informative particles/heads and the networks, X, that relate both systems.

∑ exi describes the Social evolution of self-similar cells, exi, into herds and organisms.

The equation formalizes the main cycles, laws and events generated by the principle, ‘energy never dies but transforms itself into information’, which applies to any form or motion, in any scale of reality. Since the generator equation of the fractal Universe is just a complex expansion of the main equation of classic science, ‘energy never dies but transforms itself’, to include information. Yet when those arrows of time develop all its ‘repetitions’, feed-back iterations and combinations, as it does a simple fractal generator, like the Mandelbrot fractal, all the possible cyclical events/forms of transformation of energy into information appear in the Universe. In that sense, the study of the generator, fractal equation of the Universe could be to XXI century science, what the study of the final equation of Entropy, the arrow of time studied by physicists, E=Mc2, was to XX century science. Yet instead of generating pure energy as the equation of entropy has done, the fractal generator creates life, which makes its study much more rewarding for mankind, which is after all a life form.

Recap. The perception of the World through time arrows was natural to Eastern philosophy. System Sciences and its 2 main disciplines, Duality and complexity study those time arrows with the scientific method.

The Unification of sciences: General systems theory.

Because all fractals have inner microscopic cells with form, every fractal piece of the Universe is a small Universe in itself, which displays the same elements and cycles than the whole. Since all of them are made of bites and bits of energy and information, gathered in networks through several scales of relative size. Those 3 specific parameters – the type of energy and information the fractal system uses, the relative size of the fractal and the complexity of its cellular networks, might vary – but the general laws and properties of the organic fractal remain; since they are connected to the properties of the fundamental bites and bits of energy and information of the Universe.

There are infinite Fractal worlds, ‘i-Universes’ where ‘i’ is the scalar parameter that defines both, the size of the relative Universe and the relative science that studies it, specialized in a certain scale. For example, Chemistry studies fractal molecules; Biology studies fractal cells and History fractal, human societies, divided by spatial borders and cultural, informative discontinuities. Thus it is possible to describe mathematical, physical, biological and mental species with the same forms and functions of fractal structures; and create a Science of Sciences, dedicated to the study of all fractal structures in the Universe, and the description of its species with those common functions and forms.

Traditionally scientists called such Science of Sciences, General Systems Science, which we systematize in this book, defining it as the Science that studies the fractal laws and similarities that rule all the species and worlds of the Universe. We aim to define the main fractal forms and functions of the Universe, studying with them all the species of classic science across its main scales of spatial size and formal evolution. We will do so in incremental degrees of complexity, mimicking the fractal structure of the Universe, as we increase in each iteration of this short prologue the depth of our understanding of the 3 main elements of fractal structures, making in the 3rd Iteration a detailed analysis of the fractals of the Universe with the 2 arrows of energy and information.

Recap: Each science studies a scale of self-similar forms in the fractal Universe. Yet the detail of our observation is maximal in our plane of human existence: Man is the measure of all things’. What makes social sciences the most important; contrary to common thought that places higher value in microcosmic sciences subject to Indeterminacy (Physics).


0 ‘ Zeit ist das, was man an der Uhr abliest.’

1 Harmonices Mundi (1618).

2In an attempt to realize Leibniz’s ideas for a language of thought and rational calculus, Frege developed a logic notation as the foundation of mathematical reasoning. Though this notation was first outlined in his Begriffsschrift (1879), the most mature statement of Frege’s system is ‘Grundgesetze der Arithmetik’ (1893/1903).

In 1931 Kurt Gödel demonstrated in his paper “On Formally Undecidable Propositions” that within any given branch of mathematics, there would always be some propositions that couldn’t be proven either true or false using the rules and axioms … of that mathematical branch itself. You might be able to prove every conceivable statement about numbers within a system by going outside the system in order to come up with new rules and axioms, but by doing so you’ll only create a larger system with its own unprovable statements. The implication is that all logical system of any complexity are, by definition, incomplete; each of them contains, at any given time, more true statements than it can possibly prove according to its own defining set of rules.

3 Summa Theologica.

4 The influence of religious beliefs in the ideas of the first philosophers of science is hardly recognized, except in the work of Thomas Kuhn. For example, Newton dedicated most of his work-hours to alchemy and Biblical studies, and believed God sent to him comets as personal messages. Only such beliefs explain the obvious contradictions between reason and the mechanist, monist philosophies of reality sponsored still today by many scientists. Since a mechanical version of the Universe as a series of clock-like cycles, which particles and entities do not command, but obey blindly, requires a creator – the ‘clock-maker’ of Newton and Kepler, who puts the cosmos on track – as Leibniz, precursor of rational organic theories explains in a letter to Clarke: ‘Sir Issac Newton and his followers also have a very odd opinion concerning the work of God. According to them God Almighty needs to wind up his watch from time to time’; probably referring to Newton’s Optiks, p. 402, in which Newton, aware of certain irregularities in the orbital paths, latter resolved by Einstein, affirms that those regularities will increase ‘till the system wants a reformation’. Yet rational science should exclude any external, mythic agent to put it on track.

5 ‘The universe – said also J. B. S. Haldane – is not only queerer than we suppose, but queerer than we can suppose.’ One of the queerest things about it is that its properties at the very largest scales–galactic super clusters–are very intimately related to those at the very smallest–subatomic particles. The big and the small are related; because they are indeed, self-similar fractal structures, whose energetic and informative properties have transcended through multiple scales of size, emerging again in the macrocosms.

6 Mircea Eliade in ‘History of Religious Beliefs’ shows how pervading was in classic pre-Christian cultures the concept of a God of Time, (Zurvan in Zoroastrism), who lives through 3 ages, and the belief in a Universe made of Time, in which space is a Maya of the senses (Vedas, Buddhism).

7 ‘Syntactic structures’ 1957.

8 The Holographic principle is explained in physics only for the limited case of the surface of black holes. It is however a general feature of all systems of information, which this author has used in all disciplines – from biological analysis of cellular functions to the study of form in art theory and bidimensional painting.

9 Letters to Clarke (1715-16).

10 A mathematical proof of its equivalence with information, extracted from Einstein’s equations, deduced by this writer:

E=mc2 + E x T=k ->Mc2 = k/T ->M= (k/c2)x(1/T)->M=K x v

Where v is the frequency of of a mass as a vortex of spacetime.

11 Einstein could only apply the 5th postulate of Non-Euclidean geometry to describe gravitational space-time. Today, thanks to the discovery of the other 4 postulates of Non-Euclidean Geometry, which I introduced to the world of science in the 50th anniversary of Complex Sciences at the Sonoma Congress, the complex structure of Space, created by the interaction of Euclidean light-space and Non-Euclidean Gravitational space, can be   resolved to explain many pending questions of astrophysics – from the nature of dark matter to big bang theory.

12 In his thesis, ‘On the Hypotheses which Lie at the Foundations of Geometry’, 1854, Riemann defined space in terms of motions and self-similarity, setting the basis for the advances of Fractal, Non-Euclidean geometries, formalized in the 70s and 90s by Mandelbrot (‘Fractals’, 1976) and this author (‘Radiations of space-time’, 94.)

13 Relativists model the Universe with Einstein-Walker equations in which each galaxy is treated as a hydrogen atom. This theoretical trick that facilitates the calculus of relativity shows the self-similarity between a hydrogen atom and a Galaxy of the upper scale. Scientists also use models of electronic nebulae to describe the behavior of stars around the central black hole; and some have tried models with high-density photons.  Yet self-similarity is not identity. So quantum cosmology, which uses quantum equations to describe the macrocosms as if it was identical to the quantum world, makes no sense. Instead we must observe the self-similarities of those scales, caused by the emergence of fractal parts into wholes. Can we know if those scales of relative size are infinite? Not really, because if there is a higher fractal scale and galaxies are self-similar to atoms, the extension of the cosmos will be so vast that we shall never find its limits. Indeed, in our Universe there are trillions of atoms. So even if there are trillions of self-similar atomic galaxies, the maximal perception we can have is of a few billions, within the total cosmos.

14 Schopenhauer’s philosophy culminates 3 millennia of western tradition in dualist models of the Universe, with his analysis of a reality composed of ideas – the informative mappings of the human mind  – and the will – the satisfaction of the human arrows of time, our desire for energy, form and reproduction. While the idea has its site in the brain, the will has its point of maximal force, according to Schopenhauer, in the penis, whose pure desire of reproduction, guides in this philosophy of action, as the ultimate goal of existence, the world of the mind. Thus, for Schopenhauer – and we agree – the arrow of reproduction dominates the arrow of information.

15 Letter to Besso’s wife.

16 This work resumes 20 years of research in System sciences and its multiple disciplines: non-Euclidean geometry, fractal mathematics, duality, complex logic, complex biology, complex physics, complex history, etc. It is part of the 9 conferences which I will give at the International Systems Societies, during my tenure of the SIG of duality in the congresses of Cancun, Sonoma, Tokyo, Madison and Waterloo (2005-2010), to complete an overview of what I call the ’3rd age of science’ when Man will learn he exi=sts within a self-similar, organic, eternal Universe of 2 fractal, scalar, self-generative, Non-AE motions – energy & information: ∑eói.

Modern scientific Duality is a relative new science, whose formalisms and main laws were systematized in my book ‘The cycles of Time’, c. 94 (Spanish edition). Yet prior to this work, there has been an enormous quantity of laws, data and ‘similarities’ between all the species of the Universe (called isomorphisms and other technical names in our science) found during 50 years of studies by System and complexity scientists. Santa Fe Institute of Complexity and Len Troncale from Pomona University have done important work classifying those isomorphisms. While an array of specialists in system sciences and complexity, from Rossler to Capra, from Prygorine to Miller, and the founding fathers at Macy’s, Bertalanfy and Norbert Wiener, provided many of the theories and logic and mathematical insights required for the consistency of a Theory of Time Arrows. The complete development of such theory would require though the rewriting of the entire ‘Encyclopedia of human knowledge’, since we contend all can be explained with those 4 drives of ‘exi=stence.