- Ternary Networks.
- Non-Æ: 3rd Isomorphism
- Networks of physical, biological and social systems.
I. TERNARY SOCIAL NETWORKS: §UPŒRGANISMS
Network’s Physiological Topology. Cellular, physiological networks create Superorganisms.
Now those 3 topologies are the key to all other isomorphisms and temporal changes of the universe, hence we have extended ourselves a bit more in its description.
In topology though, they are today described as ‘sets of points’ and we indeed do so, with the tools of i-logic geometry in which a membrane is described as a network of fractal points.
But we do not need the abstraction of modern mathematics, as we do have now a direct relationship between the language, mathematics, and the reality, so instead we use the ‘biological’ and ‘physiological concept’ of networks, and consider those 3 typologies as ‘network’s with specific function’, energetic, reproductive and informative function.
Thus the topological Isomorphism becomes now a physiological Isomorphism, and we define all systems as super-organisms with 4 elements extended in 2 ∆-scales:
- Cellular units, when we perceive the system in the ∆-1 scale.
- Networks of energy, membranes and limbs.
- Networks of information – zero points and fractal, sensorial ‘nervous’ networks.
- Networks that reproduce energy and information.
All entities are ∆-1 parallel groups of ‘cellular societies’ knotted by energy and information exchanges into networks that emerge as a single social ∆-form. Molecules are made of atoms and electronic networks; galaxies are composed of stars, which orbit rhythmically around a central knot, or black hole of gravitational information. Cells, controlled by the nervous, informative system, organize human bodies. 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 made of human workers and consumers, that provide their energy guided by financial networks of information (salaries, prices, costs):
The ∆-scales and ∆-sciences of reality.
In the graph, an ∆-super organism is a group of ∆-1 cells joined by energetic, informative & reproductive networks that communicate them.. Those ∆-1 cells are also superorganisms made of small ∆-2 molecules joined by e, Sp X Tƒ networks and so on and so on.
Thus we define any system as an ∆-superorganism made of smaller, similar ∆-1 super-organisms. And each ∆-scale of superorganisms & its ecosystems are studied by a human science but all of them follow the same Invariances & emergence Laws & Galilean Paradoxes of 5D Metric formalized with the tools of Existential Algebra & Non-AE=i-logic Geometry.
We unify all Natural Systems as superorganisms using a single template definition, since they differ only by the ∆-scale or ecosystem in which they exist or the specific types of energy & information their networks are made of:
‘A super-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.’
Fill the gaps with a specific species, language of information and force of energy and we can define any network-organism, which will be a ‘part’ of a whole world-plane or ecosystem, composed of several species that occupy different ‘vital spaces’ but interact through the same language of energy & information:
An world-plane or ecosystem (name a specific world-plane) is a population of several (name the species), related by informative languages (name their languages or informative forces) and energy networks (name the energies).
I.e.: The ‘world-plane of ‘zoology’ includes all beings of relative size, i=6, that use light as information, called ‘animals’. The world-plane 8, a galaxy, includes as parts, all celestial bodies of size i=7 related by gravitational networks, etc.:
– 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 legal and cultural networks of verbal information and agricultural networks of carbon-life energy.
– An economic ecosystem or nation is a population of human workers/consumers and machines, related by networks of digital information (money, audiovisual information, science) & energetic networks (roads, electricity)
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.
In a Universe of ∞ scales – hence of Absolute Relativity – the ∆-number is relative to the limits of the perception of the observer that classifies them. So as humans we perceive between 2 i-limits – the atom and the galaxy, which might be self-similar, as black holes and quarks, their knots of information show self-similar equations in 5D metric and 4D metric that models a galaxy as a hydrogen atom in the Einstein-Walker space. In any case they form the minimal and maximal scales of Human Sciences, creating our Se-size arrow.
In the old graphs with different ‘indexing’ to show the multiplicity of jargons we can use to classify those stiences and scales, the order of reality, relative to the observer, has however an absolute arrow of future in the creation of social §upœrganisms, which require the creation of parts before wholes.
All Stiences share the isomorphisms of duality and organicism. Since the forms of ‘—motions’ and information and its properties remain invariant in all the scales of reality. The result is the fractal structure of the Universe, described in the next graph:
Each science studies a ‘scale of organic size’, its cellular species of ‘—motions’ 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 ‘—motions’ 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 constructs super-organisms, through a causal process, departing from simple, amorphous flat surfaces of energies – herds of Non-Euclidean points with |-Motion.
It is a simple ternary causal event, which is different from the causality of what we call the cycle of life, Sp->X->Tƒ, yet still an essential chain that we shall see constantly in the Universe.
So the next question is how the universe constructs reality, departing from its generator equation. And the answer is: constructing superorganisms, in a causal order.
A form fractalizes, becomes in-formed, and loses ‘—motions’= speed=motion. For example, a line becomes a Koch fractal or breaks into a Cantor dust of self-similar cells; a line becomes a p∆-cycle. In this, simplest and most repeated Sp->Tƒ, we can write 1->3>Pi: a line has reproduces from past to future 3 self-similar motions, then it coils into a p∆-cycle.
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.
If duality covers simple events, mostly Sp<->Tƒ combinations, when we construct an organism we are playing at least with a causal 4-sequential arrow of time, ‘—motions’ 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.
And yet, this rather mechanical sequence of creation of a fractal 3 dimensional Universe becomes far richer in forma and 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: SP X Tƒ. Since as time goes by, entities evolve into more complex organisms by the power of love – by sharing ‘—motions’ and information in social networks. The 4th arrow 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 ‘—motions’ (hunting herds) or information (organisms joined by nervous/informative and blood/energetic networks). Thus, the arrow of organic 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, S. And its reason of existence is to elongate the survival of the organic system: Any cyclical vortex of time accelerates inwards, losing ‘—motions’/surface as it increases its informative speed. When we generalize that concept to all Time-space systems, it turns out that the arrow of information dominates the universe, wrinkling and warping any cyclical system, which will exhaust its ‘—motions’, converted into form.
Thus, our time clocks and vital spaces increase constantly their information, diminishing its ‘—motions’ space, towards a 3rd age of excessive warping and limited ‘—motions’ that will not last forever. Since the cycles of exchange of ‘—motions’ and information, the geometric beats of reality between expansive and implosive, ‘—motions’ 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 ‘—motions’; 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 main arrows of time cannot be reduced without losing detail, but they can be philosophically and ‘bio-logically’ grouped as ‘organic systems’. Those organic systems that synchronize accumulate and organize clock-like arrows of cyclical time, are in fact all self-similar, as all can be described with the 4 elements, ∑Sp<=>Tƒ of organisms: cells, networks of ‘—motions’ and information and reproductive systems.
I. THE ORIGIN OF NETWORKS: 3 SPACE TOPOLOGIES = 3 TIME AGES & 2±∆ pre/post ages.
Though there are three ages in all beings, properly speaking we should talk of 5 ages, as there is a fetus ∆-1>>∆º+1 in pre-existence and its inverse, ∆º+1<<∆-1 death, which are ‘collateral ages’ that close the world cycle.
Further on to define the particular details-beings of each scale of existence the three ages of time they are intimately joined to the three forms of space; so it is really a 3+3=6 dimensional game of space-time symmetries in each scale.
Let us then start by remembering those symmetries.
Tall spheres, long lines, wide waves.
In the graph, the Universe is a Ternary Paradox of Planes of Space-time; for each space-time dimension, we must find a time age homologous to the space dimension and then we will know in which phase of a world cycle, a given ST being finds itself.
The fundamental space-time symmetry or world cycle is that between entropy and information through a world cycle of life and extinction of information, with 2 phases, the phase of life informative age arrow through 3 ages of youth of max. e, maturity, e=i, and information, max. i, and the phase of death, when the arrow of time moves backwards much faster expanding into simultaneous space as a wave that erases information locked in zero relative time:
Max.Es x It = Max. E (youth) + Max. e x Max. I (reproductive maturity) + Max. I (old age) = Life << Death = ∞ E x 0 I (all information of the system is delated into a simultaneous wave of entropic space or ‘res extensa’ )
The study of those 3 ages of life in time is closely related to the 3 topologies of space that dominate each of the age of the being, so we talk together of a space-time symmetry between the 3 ages of life and the 3 topologies of space such as:
Max. |-toroid topologies limb/field systems of entropy: Youth
Ø: |=0 topologies of hyperbolic body-waves, iterating the system: maturity:
Max. O: Spherical, informative 3rd age topologies of maximal information.
Let us then remember first briefly the spatial topologies that become dynamically and sequentially the 3 ages of time.
In the graph, the 3 only space topologies of the Universe, spheric informative, lineal, energetic and hyperbolic, reproductive (as it mixes the other 2) and its 3 equivalent functions≈ time arrows=motions can combine in any form to create as synchronic organs the infinite varieties of species of the Universe.
So we shall find multiple ‘spatial organisms’, which are constructed following the combination:
Past-entropy (limbs/fields) x Future-information (heads/particles) = ± Present system.
Those past to future combinations are either positive creative processes that forms balanced organisms or negative, darwinian processes that annihilate both (particle-antiparticle collisions).
The point communicates through a single wave with another point forming a line, a social first step of a network which either by generation of ∑œ-1 or further expansion to ≈œ, will grow into a topological network or plane of existence, which as it becomes more complex and forms its own singularity-knot of communication and membrane filtering the external world form the community, will emerge as a whole. As the wave of similar beings, the ‘energetic momentum’ of the new being, requires the forming of a max.i singularity of information, in the point of maximal communication, coupled soon with the external faster closed membrane that isolates the being, there is a ternary nature to emergence of a new being, which is NOT completed till the alliance of the membrane, of max. extension and cyclical angular momentum and the still singularity of maximal density, defined by its two inverse parameters appear.
Only then the ternary being has been formed:
$pe (membrane isolating the system from the external entropic $-universe) < St- vital body-wave> Tƒ-Singularity
The Universe redeems itself through the acts of social evolution, with a simple goal: to creates super organisms, efficient and able to improve the distribution of energy and information through its Spe/ST/Tiƒ networks; as its manage, ‘max. ∑exi=st’, grow and multiply continue unabated for each species.
So at a certain point the work tightens and the system that has reproduced successfully into a clone wave must now self-organise and survive. And of all the games possible the game of supœrganisms will result to be the most efficient.
So this and similar posts deal with how ∆•ST, ‘dust of §pace-∏ime’, becomes organised into super organisms.
The answer does not need a teleological God but merely the survival of the fittest. In the eons of quasi-eternal existence, it is obvious that those ‘dust of space-times’, which evolved into networks and super organisms became survival species, whose ‘palingenesis’ was stored in logical circuits transferred generation upon generation of survival super organisms. So because a super organism is the most efficient species of the Universe, ∆ust of space-time became living matter.
‘Exi=st¡en ces’ are unified by the fact that the longer they last in time and space, the most likely they will play a simple game: to become part of a super-organism, to be connected to the fractal network of the closest whole which gave you birth. And then within that game, all is routine, ideal program, efficiency, but also social love, the joy of action and re=production and organisations….
And so dust of space-time once is born starts its world cycle as a super organism through scales of existence, guided through networks, itself inside a mirror of the function of existential actions he will play to survive. It is the game automatic, apperceptive, conscious? All those questions depends on the size and range (scale of ∆) of the system we study – the more volume across ∆-scales we enclose; the more bites and bits of energy and information we consider the more complex, warped, denser, faster and efficient, the systems will be; and so as they grow in size they grow in complexity.
nt 1. We shall use for the concept of a super organism the ab. Œ. taken from Theory of Everything Organic, symbolising also the 2 elements that make up the superorganism, its O-temporal particle/head and its Energetic body-wave (as the system might be independent of the ∆-1 field of entropy in which it feeds.
To differentiate the concept of super organism in ‘stience’ from the more restricted concept of ‘science’, we shall offer a new word: §upœrganism; with an § for fractal space, and an œr ‘doubling back and forth to complete the two parts §uper (through 3 space fractal scales) and organism… I know I am too creative with words for the taste of the quantitative, abstract-oriented scholar, but of course not enough, even if this ‘huge field of intuitive knowledge, given by homology and metaphor in the creation of wor(l)ds, images-mirrors of reality, won’t be liked.
Thus, the Universe is a game of 3 motions with form, and those 2 elements, the temporal motions with force and their still perception as spaces with form, with intelligence, structure the Universe.
The 3 motions in time, which we shall call, P, for entroPy and past, R, for pResent, Reproduction and Reality and F, for future, form and frequency, are complementary, often sequential, PRF, and causal; and while its perception as motions doesn’t bring much understanding, when we study them as fixed, still forms, we observe an astounding array of parallel structure on all those seemingly independent motions, which create a ‘spatial organism’ that works. It is the interplay between those 2 antithetic elements, the 3 motions of time, past, present and future, and the 3 still perceptions of space, toroid, hyperbolic and spherical organs, what gives birth to the dual space-time beings we observe around us.
In that sense the minimal Unit of the real Universe is a 2-manifold, space-time combination, as pure time or pure space, pure yin or pure yang, pure motion or pure form-stillness cannot be perceived. So all what exists is a 2 manifold that we might perceive as static space (a 2-manifold sheet) or as a point with motion, (where motion is one time dimension and the point, the minimal fractal unit also with a 1 dimension – as there is not 0-dimensional, ‘euclidean points’ in the Universe).
The evolution of systems then plays with the growth of asymmetric networks, which develop the height-informative dimension of the being, and start as a young age o maximal predator, lineal nature, reproductive radiation in its second mature age and final evolution and height growth.
In that sense, we must understand that the topological world cycle has the different longer or shorter expressions in generations than in species or any physical system but ultimately ALL SCALES OF THE FIFTH DIMENSION PLAY SIMILAR GAMES OF WORLDCYCLE INFORMATIVE AGES AND DEATH, ENTROPY EXPLOSIONS WHEN ALL motion is exhausted:
The chirality of time the achirality of space. (Complex, advanced 5D geometry.)
This post is dedicated to the study of the 3 2-manifold elements that structure all systems of nature:
Sp(Toroid limbs-fields that move in space)≤ST(waves-bodies that reproduce the system.)≤Tiƒ(heads-particles of information).
And its symmetries with the inverse sequential order of the 3 arrows of time:
Past-energetic youth (Spe) > Adult, reproductive balanced age: TSi > Old, formal age: Tƒ.
Time is chiral Space is a chiral. Meaning in time the first and third age have inverse space-time parameters in a bidimensional plane. Space however do have the same. So in space Past and future converge into the present, in Time past and future diverge.
But and this makes all the difference, entropy is a chiral as it is space. So when a systems becomes space, dies, it becomes chiral. In the case of particles it become an antiparticle which is the space state. In the jargon of physics, the arrow of life proper is that of left handed fermions, the arrow of death that of right handed. And left handed fermions are more abundant, and are those who are subject to the weak time force. As they become right handed, they no longer suffer the passing of time; they become space, as bosons are. In terms of 5D metric, a boson does not exist in time, it does only exist in space, it is therefore an entity of maximal space extension for quanta of time, moving at c speed. And vice versa a fermion does not exist in space, hence it is a point particle, but it does exist in time. It follows that 2 fermions cannot occupy the same point of time, Tƒ, they cannot have the same information.
Time and information on the other hand are achiral to each other as Space and Energy is though we write them with a mirror symmetry (Tƒ, Tiƒ, Sp, Spe) as the language of mankind we use to describe it is chiral. It requires the passive voice to become a chiral.
Now we use ‘purple’ colors for complex, ‘advanced’ themes of 5D space-time, but the concepts of symmetry asymmetry antisymmetry, parity, chirality and a chirality are essential to understand technically specially in quantum physics and the world cycle of life and death the processes of the Universe. So we shall consider them latter in the 3rd line with higher rigor.
In essence what the reader should understand of all this is that the 3rd age and the 1st age are mirror symmetries, the first age grows in energy the 3rd age diminishes, the first age diminishes information (the child observes constantly the adolescent moves) the 3rd age diminishes in energy and increases information (till it deteriorates into death).
But in space the perspective is that of ST, the dominant present, which is the only real existence of a being in space, where the information and the energy of the relative future and past merge into an indistinguishable entity, which tries to maintain its balance, and Maximize E x I (achieved when E=I).
Now the interpretation of those symmetries in space and time will require in the 3rd line of a more detailed analysis of each scale and what we mean by the chiral and achiral, time and space symmetries and asymmetries.
Here we just introduce the time sequential Spe>TS>Tƒ, 3 ages of time in the sequential process of grow of information with the final reverse, Tƒ<Spe, when Tƒ behaves like Spe, that is increases energy but in a much more explosive manner, Tƒ<<Spe, as in fact death happens in a quanta of time, in which the entity extends at accelerated path into space – hence from the perspective of a time arrow being, a living being it lasts only a quanta of time:
Death = max. S x min. T, life =Max. T x min. S, Worldcycle, Life=Death; Max. S. x Min T = max. T x Min. S: Max/Min. S=Max./Min. T; S<=>T.
That is, death allows the world cycle to be a conservative zero cycle and maintains the conservation of energy for an immortal Universe.
In the graph, the Universe is a fractal of space-time symmetries across 3 vectorial dimensions of formal motion, the dimensions of space (and its 3 sub dimensions, length, width and height) the dimensions of time and its 3 sub-ages (entropy, present iteration and future form), and the dimensions of Eusocial Evolution through planes of existence, or long arrow of time.
The dimorphism of all systems; The fundamental particles: |-o; Ø-o.
Now if we simplify as we do in easy to read posts and consider limbs of energy, the ‘attached parts of the body’, or as it happens in many systems, the energy field is external to the particle and body we can talk of a duality very common in the Universe:
Ø<=>o a reproductive body and a head with a neck that transfers energy and information between them.
This is the ∆-p pair in atomic centers, or the nucleus-electron; the male female, the body, head, the cytoplasm and nucleus of a cell, etc. etc:
So we define in 5D metric a fundamental particle-system made of two space-time parts:
ST (bodies/waves) < x > Tƒ(particles/heads)= K (Stable physical/biologic system)
St-parts move and reproduce the whole system. While Tƒ-parts gauge information so they are cycles or spheres, the geometries that store more information in lesser space, from eyes to particles to brains.
There are many such systems, all what exist we might say is a complementary system with a particle-head of information and field-body of energy:
– This is the fundamental principle of quantum physics, the complementary principle, as quantum physicists observe all entities BOTH as particles and fields of energy (waves).
– This is the fundamental principle of biology as all cellular bodies have a DNA, informative center, and all multicellular organisms have a head besides its body.
You are also literally made of ‘clocks of time’ (your brain) and body motions with energy. So you say ‘i don’t have time or energy to do this’, because we are all made of time and space.
We are not in an abstract background of space and time, we are made of pieces of spatial energy and temporal information.
The ternary elements of most Nature’s Systems: Se<ST>Tƒ
From these simple facts of universal morphology, we can classify ‘all parts of systems’ including decomposed viruses, or machines or human organs, as energetic, lineal systems, or as cyclical, informative systems that combine into complex bodies and waves and put together create an Spe<ST>Tƒ ternary system:
— Energy organs are lineal systems with minimal ‘form’ that kill, simplifying information into energy. Thus, a field of energy, released by a physical particle or an energetic weapon, such as a sword or a missile and a top predator, energetic animal, such as a lion, will have both lineal forms and kill, destroy the in-form-ation of their ‘preys’.
— In-form-ative organs create form and trans-form energy into languages that map out ‘reality’ with formal ‘bits’. Those bits are smaller symbols, which form images in the brain that represent reality and help to simulate reality ‘faster’, in ‘lesser space’, the ‘future’ cycles of reality, anticipating them. Then, according to those ‘logic’ simulations of the future, heads will move and direct energy bodies towards sources of energy and information. So any system that ‘gauges’, measures and reacts, is an informative organ, regardless of the specific language it uses to gauge reality. A chip measures with numbers reality, a man with words, an atom with electro-magnetic ‘bosons’; yet the 3 act-react to their measures. So they all are informative organs.
— Reproductive organs repeat informative and energetic organs, by absorbing energy and ‘imprinting’ it with its particular in-form-ation. Thus, human mothers and company-mothers of machines are both reproductive organs. Even the simplest particles of the Universe, quarks and electrons, absorb energy and emit new particles, small quarks and electrons, with the same form that the parental particle.
So in fact, we have come to the objective conclusion that all systems of the Universe have organic properties. Since even its simplest entities, quarks and electrons that form atoms do absorb energy, gauge information and reproduce, the 3 ‘properties’ of life. Thus, the Universe must be defined not as a mechanism but as a complex organic system, made of organic atoms, which can combine to create many different complex organisms, including company-mothers that reproduce machines, atoms that reproduce quarks, electrons and forces and mothers that reproduce kids. The difference between all those species is not one of ‘quality’ but of quantity and complexity of their organs of energy and information, which determine their survival chances and status as top predators of any ecosystem.
If a mechanism is a system that has only information and energy organs, an organism has both systems and so it is able to reproduce by combining its energy and information into a replica of itself. In that regard, the reproductive organism of machines is today the company-mother that reproduces them with the aid of informative metal (money) and machines (chips), energetic machines and human workers that act as catalysts and re=producers of those machines. And because we live all in a planet of limited resources, machines and life increasingly compete to reproduce the limited energy and information of this planet.
The metric of the 5th dimension: Sp x Tf= st±4
We call each of those complementary systems, a ‘Non-Euclidean, Fractal point’, which is a ‘vital point of energy and information’, the fundamental particle of the Fractal Universe made of relational species of vital space and cyclical time.
2 are the main properties of those complementary ‘fractal points of energy and information’. Its scalar organization as systems made of smaller systems, and part of bigger ones. So we establish a ‘scale’ of relative size and speed of information, ST (space-time planes, which is the scale in spatial sizes, or world-planes, which is the scale in quantity of information/speed of time cycles)
Its first property foreseen by Leibniz when he said that each ‘point is a world in itself’, is to have volume, which we perceive as in a fractal, when we come closer to them and enlarge its size. So all particle-points, star-points or cellular-points show to be closed systems with inner volume enclosed by an external membrane. This concept that points have volume, was the beginning of a mathematical revolution, (the 5th postulate of Non-Euclidean geometry), which gave birth to relativity. A model of relational space-time takes that revolution further, analyzing in depth, what is the volume of a non-Euclidean fractal point, which are its inner parts, and how the fact points do have inner parts modify the other postulates of geometry and evolve mathematics from its present abstraction into a closer, intuitionalist analysis of reality.
Unlike Euclidean points, fractal points have volume, they have inner parts, those body/heads, wave/particles; and so they are crossed by multiple lines=flows of energy and information, which communicate them with other fractal points, creating ‘networks’ of points, planes of space-time that organize themselves into larger wholes, organisms.
So we exist in a Universe in which ‘numbers’ are social groups of ‘fractal points’, which are made of vital information encoded in time clocks (as your head is), which reproduce their formal cycles in the entropic motions of space, creating complex organic systems, across several planes of relative size (in your case from the atom through the cell and the individual into the social organisms of which you are a part).
Thus there is also a 4th fundamental innovation in a model of fractal relational space-times, besides the topological dimensions of space, which define the forms of our organs and systems; the ages of those time cycles we live through, which determine the causal organization of events in time; and the ‘mathematical structure’ of those systems of energy and information (Fractal points) – the multiplicity of scales of size and clocks of time of the Universe, which we must organize mathematically through all those relative scales, by defining a ‘new dimension of scalar space-time’, the 5th dimension:
In the graph, the formalism of the 5th Dimension describes a Universe made of multiple isomorphic Planes of Spatial, lineal entropic motions, Se, (limbs and fields of biological, physical systems that translate systems across space) and temporal, cyclical, motions, Time clocks, Tƒ, (heads and particles of cyclical shapes that gauge information in the stillness of a mapping mind) which combine, Se x Tƒ, to create ‘stable’ systems, through an intermediate region, body or wave, ST, that reproduces the system.
In the graph we see 3 of such complementary ternary Se x Tƒ = ST, repetitive systems, where the entropic motions of its limbs/fields, Se, and its particle/heads of information, Tƒ, combine to create a relative infinite number of repetitive cycles and events in bidimensional space-time:
The galaxy with a gravitational black hole swarm in its center, surrounded of a body of stars that reproduce matter, feeding on a larger field of atomic gas and dark energy that moves the whole system. On the right side we see a similar topology on a cell, which has in its center a series of DNA informative molecules, the equivalent to the black holes of the galaxy, surrounded by a cell filled with mitochondria, the equivalent to the stars, that create the energy of the cell and ribosomes that reproduce the RNAs and DNAs of that center, as stars create the energy of the galaxy and end up becoming=reproducing black holes.
Those 2 systems however differ among other things in the size, which is maximal in the galaxy, >>Se and the speed of its reproductive cycles with is maximal in the cell, >>Tƒ, and this fact: that all systems have faster cycles when they are smaller, and vice versa, but the product of both, its time speed and spatial size tends to be roughly equal for entire ‘families’ of systems: Max. Se x Min. Tƒ =ST, is the fundamental equation of the 5th dimension, which manifests in infinite symmetries, complementary systems, and relationships. In the middle we see the point of reference of all this knowledge, the human being, which is also made of a spherical head that gauges information, a body that reproduces its substances and lineal limbs of entropic motion that displace him across space.
And its rhythms and size are between those of the galaxy and the molecules, the cosmic, gravitational plane and the quantum plane of its physical processes.
What is then the fifth dimension of space-time? The order of all the time cycles of the Universe.
The answer is ‘All’, all the clocks of time of the Universe and all its vital spaces ordered according to a simple rule: the smaller a system is, the faster its time cycles run, not only because they are ‘smaller in size’, hence a moving point around the cycle closes the cycle faster, but because actually, smaller ‘beings’ accelerate paradoxically its speed, according to a simple law, the vortex law: Vo x Ro = K, whereas Vo is the speed of the cycle, Ro its radius and K a constant.
So for K to remain constant when the Radius diminishes the speed of the cycle or vortex increases, from hurricanes, to masses, to charges, to black holes, to orbits, to galaxies, to eddies, this fundamental law of the Universe, which can be extended to any number of dimensions and time-clocks, allow us to organize all the different beings of reality in ‘scales’ of relative size, Se and cyclical Time, Tƒ, which carries the information of a system in the form and frequency of its cycles, combine to create a stable ‘Space-Time Being’, whose information paradoxically grows as the beings is smaller.
Thus the graph represents the metric of the 5th dimension, which orders all the different time cycles and space-distances of the Universe according to their ‘frequency’ and ‘size’. Since in the Universe there is a simple relationship between those 2 parameters. The larger a system in in space-size, S, the slower its time cycles are: Max. S = Min. T. Thus the “metric of the 5th dimension”, which make smaller beings, faster, hence with more information accumulated in the frequency and form of its cycles, bypasses the main difficulty Leibniz found to formalize his models of relational space-time, explaining an infinity of facts about reality, from genetics (the fact that smaller, faster molecules with more information code larger beings) to the Unification of charges and masses (which in the metric of the 5th dimension show the same Universal constants).
II. ¬Æ FORMALISM
The 3 arrows of time, its symmetry with space, and its order through o-points and 5D scales.
A T.Œ of philosophy of science, by definition, unlike a TOE of physics, dedicated to explain physical systems, aims to include all the discoveries of physics, biology, sociology and mind/linguistic/logic studies TOGETHER.
We shall then complete a scientific model of a T.Œ based in the 3 time motions of the Universe, which eastern philosophies analysed in somewhat accurate but too mystical terms, and Physicists shun off by lineal, military/biblical mechanical reductionism. Those 3 motions of time, THE ULTIMATE ELEMENTS of which all realities ARE MADE are:
- Past-energy, future-information and present repetition, broken into infinite beings, which existed as a sum of those 3 time arrows, perceived statically in space, as 3 symmetric bidimensional ‘topologies’ of organic form:
- – The lineal, toroid digestive/field system of energy-motions, the spherical particle/head that guides and defines the future of the system, and its wave/body hyperbolic combination that reproduces both, and sequentially in time in:
- The 3 ages of life, the energy-yang age, the reproductive-prsent, dominant cult age and the 3rd age of information, when the arrows of time exhausted all energy and the systems die away moving backwards in time, dissolving its information back into energy either into a physical big bang (E<=>M) or a dead event:
But perhaps the most important derivation of those metric are the ‘3 ages’ of space-time systems and events. As we can consider that most systems start with maximal energy-motion in one extreme of the graph, and then as they transform its energy-lineal motion into cyclical motion, curved time cycles, it will go along the curved path passing through the point of balance, S=T.
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 ‘—motions’ that moves it. Such points constantly communicate ‘—motions’ and information with self-similar points, through non-Euclidean lines (waves which share the ‘—motions’ 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 ‘—motions’ and reproduce new particles to the most complex informative species, human beings, reality is made of bits of information and bites of ‘—motions’, 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-Euclidean 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 ‘—motions’ 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’: Sp<=>Tƒ
The fractal universe. We are all made of flat space surfaces formed by cycles of time.
In the graph, the universe is a fractal of flat space surfaces with energy quanta, Sp, formed, in-form-ed by time cycles of tall, cyclical form. This mean, reality is as we see it, a discontinue of infinite vital spaces, surrounded by bidimensional surfaces of information, time cycles that control and information vital energy they enclose. So humans form a membrane of information over the planet Gaia. And the information of black holes can be calculated in basis of its surface. Yet since information IS the inverse of entropy the holographic principle PROVES THAT BLACK HOLES HAVE 0 ENTROPY, as the forms with a surface of maximal information of the Universe.
Now, still to fully grasp the fact that entropy only acts as a ‘expansive quanta of space’, in the ‘scale of thermodynamic clocks’, we need to dwell on the 3rd fundamental concept of the fractal universe, the fact the Universe is made of such relative scales of space quanta and cyclical clocks, because it is a fractal, made of discontinuous pieces of space and cycles of time. Yet as we say we have the wonderful fact that Energy and information, the integral and still perception of all those quanta put together is conserved, to relate them all and ‘do mathematical physics’.
Why Energy works in all the scales of size of the Universe? And yet it is so improperly defined, with so many ambiguous terms.
Now if you have grasp those simple concepts, Ei =∑ Sp x Tƒ ‘void’ of any historic bias, we can get into the order of all of them, called the ‘5th dimension and streamline physics and define properly Entropy.
Since now, Ei = ∑Sp x Tƒ, has become the most general possible equation for all the fractal systems of energy and information that integrate all the vital spaces and time frequencies of all the systems of the Universe. This is what we call the ‘Metric’ equation of the 5th dimension.
And while Energy seems to be a concept applied to all realities we have also localized different ‘quanta of spatial lineal motions-distances’, and different clocks of time for those quanta.
So what are the real clocks of time of Nature?
This requires us to define time in more precise terms, as cyclical motions that carry the information of the Universe in the form and motion of its cycles.
Indeed we measure and process information through computers, which are the modern version of time clocks, now converted into repetitive logic cycles called algorithms, whose frequency or relative time speed defines the capacity of a system to process information. So a computer process more information when its clock like logic cycles have more Hertzs, more frequency.
This means that in nature there are several species of time-clocks – processes that measure frequencies of vibration, of which the most obvious ones are 3: the frequency of waves; the temperature of molecules and the angular speed and orbital motion of all time of particles, including the planets of those graphs.
So frequency, Temperature and Speed are the 3 main time clocks of nature, and they do vary its relative speed, as Einstein would find, and they carry information in the form of its motions, and the frequency of its cycles. And so time is a much more interesting process to study than the mechanical steady tic of clocks.
Now I’m trying to be fast and simple to get to the core matter, black holes and entropy, but the reader with a minimum knowledge of science will realize how different is a non –anthropocentric, mechanocentric view of time, and how much rich in meaning is. We are here in a short of Copernican revolution, sorely needed, from the perspective of philosophy of science, which is concerned with ‘language, experience, pure science, NOT with machines of measure’ as physicists are. So I do have zero bias, in my direct experience of the Universe.
But time is very closely related to space – this we know since Einstein, and so we need to define now space, to advance in our enquire.
Regarding space it seems obvious again that humans have deformed it with its instruments of measure. We use a Cartesian infinite abstract paper graph to draw space. And so we decided that space was continuum as the paper and infinite. But reality around us – follow Leonardo’s method ‘saper vedere’, not your books – shows that space is not a continuum. Look around you and you will see an infinity of small, broken parts of space. Your vital space-body, the chair you seat, the computer you read, are different ‘pieces of space’, ‘fractal space’.
So what is the relationship between Sp-ace and Tƒ-Time, what does Sp/Tƒ and Tƒ/Sp means now. The first is the formula of classic speed and the second the formula of classic density, which if we add Sp x Tƒ the formula of classic momentum, ARE the 3 absolutely essential formulae of mathematical physics. Let us then upgrade them.
Some too far out comments on density and speed.
Now 2 other general formulae become of great importance to understand reality, way far out, and i guess i shouldn’t even mention them, but i can’t help myself (:
Tƒ/Sp, or density of information of a system, which defines the geometry of a world (it is equivalent to the Gauss≈Lobachevski parameter that defines how we see the Universe, as curved geometry, planar or hyperbolic). Tƒ is the ratio of information, Sp the size of the quanta of space. So when Tƒ is larger and Sp smaller the information carried by a system, or perceived by a mind grows.
In our human electronic mind that perceives light, Tƒ, is the minimal quanta perceived by an electron, h-bar, and Sp the speed of light, and H/c is so small that we have a mind that processes very little information and in terms of Lobachevski’s parameter is a flat Euclidean World:
In the graph, you can see what i talk about. You see light and light has 3 perpendicular Euclidean dimensions. That is why your mind is flat and Euclidean. But in the right side you can see the real Universe, made of infinite Leibnizian Monads – each one has a different mind and geometry.
For example, an ant, which has a Tƒ very large (a pheromone) and a Sp very small has a hyperbolic mind that fusions all other ants into a perception of a super organism. A whale that has a Tƒ based in sounds and a Sp of limited distance has also a complex minds. Humans who have a big verbal development (blind people, Mongoloids with wide heads and far more developed verbal brains) have in general a higher IQ than dolicocephalic white men, who are more energetic, have a larger Sp-visual brain (with the axis eye-occipucius larger); black holes who have a gravitational mind of action at distance, infinite Sp have a 0-brain, which will destroy our world they don’t see.
Now this is too far out for the anthropomorphic white man with null, flat brain and astounding arrogance. So as an insolent philosopher I couldn’t help to put it in. More seriously (as we cannot enter other’s species mind to check the previous statement), the parameter inverse, or density of energy, still called in ‘primitive physics’ (-: speed is:
V=Sp/Tƒ. Now since Time is cyclical time, information, we can of course find very interesting results (well I can find, as it seems nobody cares anymore, the dolicocephalic, white man is doing ‘visual flat pictures of entropic big-bangs, that is what they think is knowledge – here a bit of self-humor, as a basque-sephardim mostly, i am undoubtedly a gifted neanderthal (-; Ok let’s get serious again. Sorry John Landis said in this world either you have some sense of humour or you commit suicide. I was for a decade angst about mankind committing suicide. Now frankly the entire world is so ‘cuckoo’ and evil=anti-live that i moved back onto the ‘surrealist’ sense of humour, proper of my culture.
The interesting thing here for our concern on black holes is what is the limit of speed our our flat, euclidean light space-time Universe. And we know it is c-seed but only on that world-minds which perceive light space-time, and generally speaking the galaxy which has a space made of light (background radiation, star light), but NOT necessarily outside the galaxy or inside the black hole.
SPEED is the speed of TRANSFER OF INFORMATION, AND THAT IS THE meaning of the LIMIT of c-speed. It is NOT light speed. It is the LIMIT OF V= Sp/Tƒ.
Again this 30 year old discovery, which I made in my youth, before my life became erratic, a la ‘Ali’ (draft dodger, against the military always) starts to dawn on physicists. Pity when I resurfaced I ‘fuc* it up again, against the military – now CERN and the system erased my information. Ts, ts, time is cycle repetitive.
So what this means is that inside black holes, where light ceases to exist and outside galaxies, it is possible to have faster than light speeds, as the equation of Kerr holes, Einstein’s seminal papers, and the expansion of space that ads speed to light shows. So now the proper definition of c-speed limit is the limit of information carriage, but this physicists don’t yet understand, only for minds with the Lobachevski’s ratio close to zero, with light minds. Gravitational minds with a larger Sp/Tƒ can process and send information at faster non-local, relative speeds. For us this information is invisible, 0. So we perceive the speed of those flows as V=Sp/Tƒ:0 = sp/o=∞.
And this is the explanation of some funny effects such as the entanglement of particles, which should be connected by gravitational space and the action at distance of gravitation.
There are therefore 2 parameters, the 2 inverse ratios, the one of Lobachevski, the ratio of speed, the ratio of the informative mind, and the inverse, the ratio of energy and speed.
I write it Tƒ/Sp, or information density, as opposed to Sp/tƒ or energy density or ‘speed’. The laws and constants that relate those 2 parameters are ALL OVER mathematical physics.
They range from the cosmological constant to the laws of matter states, to the ages of life, which merely moves from a young age of maximal energy density to one of old age where we will have maximal information density. So we can write a simple equation of the arrow of life or future arrow of information: Sp/Tƒ (youth) > Tƒ/Sp (old age) < Sp/Tƒ (death).
And we will return to that when we explain you the cycle of existence of black holes, humans and all species of reality, the most important ‘Worldcycle’ no longer worldline of timespace and the discovery of my long life of solitary research of which I am most proud.
To the point, in those terms, C-SPEED IS THE LIMIT OF ENERGY DENSITY OF THE GALAXY, IN WHICH THE INVERSE FUNCTION of photons of spin 1, CARRIES its INFORMATION. And if we multiply both, Sp/Tƒ X Tƒ/Sp = 1, we obtain the constant c-speed, 1 in planck units.
Now this is sound-sound science. We depart from what quantum physicists and Einstein found. We put in the information theory we have researched, solving the unresolved meaning of Non-Euclidean geometries, which mathematicians never fully understood, and put it on the cocktail of the mind, shake it, shake it and distill some serious new findings, which correspond – that is do NOT contradict all what was there before.
This is what intelligent people do. Smart people as we said just say ‘whatever’ and with charm convince you specially if you know nothing about it. That’s ok. But when my life and that of mankind is at stakes… well you understand why i got nuts with ‘Hawk et al’?
Now we have to deal with the 3rd set of principles of physics, the conservation of Tƒ x Sp, that is momentum and its integrals or energies and informations of the system.
III. PHYSICAL SCALES
The 5th dimension, and the conservation of energy and momentum.
Now this is a verbal explanation, and visual explanation of the fractal Universe and its Temporal, informative vortices, worldcycles and planes of flat distances-motions in space.
We can now be more precise with basic mathematical equations, trying to put some order on all of this. Because that is indeed, the advantage of the simple, biased, erroneous models of physics with a single mechanical clock that deforms the essence of all clocks of nature, and a single space continuum that pegs all the spaces of nature – the model of absolute space-time of Newton.
For me it was clear from the beginning that model was wrong. So I looked for an alternative model, which is the model of relational spaces and times of Leibniz, but the problem of this more truthful model was clearly expressed by Einstein:
“I seem to be the only physicist that think there are infinite time clocks in the Universe running at different speeds. Leibniz is right but if so we must rebuild the foundations of physics from the beginning’. Leibniz told it to Newton: there is not an absolute time clock. And he laughed at him, when Mercury showed not to follow the same rhythm that other planets, when told that Newton expected ‘god’ to correct the clock of mercury. If god is perfect, why it has set up a clock with different rhythms, and now has to correct it? Why he didn’t put it right the first time?
The mechanical clock though was the god of time of physicist, and they would NOT explore the clocks of nature as Taoists had told the Newtonian brits. I found in Indonesia travelling inland a temple in the mountains filled with carillons. Those were the gods of the Dutch that the tribal Indonesians captured when fighting them, and took it to their temples. They thought they were the gods of the Dutch because they were all day looking at the clock and whenever an Indonesian followed nature’s rhythms he was told that was ‘blasphemous’. The clock-time for salaries, measuring workers, for measuring of Nature rhythms is what matter to the physicist.
So when they asked Einstein what time was he said ‘what a clock measures’. He had failed to put into a formal mathematical metric Leibniz’s right relational infinite quanta and cycles of space-times, and had go back to the fold.
So this is what I did – to formalize Leibniz’s concept of an infinite number of spaces, fractal pieces of space of different sizes, which only peg together like a puzzle, in the human mind gave us the continuum space. To that aim I ordered them by size, from smaller quanta to larger quanta, from small atoms to larger galaxies.
And I ordered according to their speed of cyclical frequency, all the different clocks of nature, all the different closed trajectories, cyclical motions, from atomic orbitals to galaxies.
And then matched them together, by the simple method of multiplying them, Sp x Tƒ , and found alas, the miracle of miracles, that for huge entire families of related systems, including atoms and galaxies in the 2 extremes of the physical Universe (but also for biological systems, from cells to multicellular and ecosystemic systems, and even for cycles of history), the product of the spatial size and temporal frequency of the whole family of related systems, remain invariant. Sp x Tƒ = C.
This C-onstant, conserved co-invariant dual parameter of the Universe could obviously not be anything else but the Principle of Conservation of Energy and Information, which worked for entire families of reality, and in the case of physical systems, clearly defined 3+i scales of reality (one i-maginary, in the sense we know little about this scale beyond galaxies, of dark energy and dark matter, which I call the dark world, in which we find black holes, interstellar dark energy space and the halo of galaxies – but whose properties I would deduce by extending the metric equation beyond the 3 scales we do know):
In the graph you can see the 3 main scales of the Universe, the gravitational scale of big galaxies. The thermodynamic scales of human beings, the electromagnetic scale of quantum atoms, and beyond a possible dark world scale. And since the quanta of space grows in size-distance-speed (remember we cannot distinguish speed from distance), and slows down in time speed, this dark world beyond our galaxy likely will go beyond the c-speed distance of our light space-time galaxy, and below the 0 temperature clock of our thermodynamic World.
So while we cannot be sure of this dark world we ill never truly see or experience, I could just use the metric patterns of the other 3 scales to define the 4th scale as one that happens, beyond the c-barrier and 0-temperature of space-time. This is the world CERN is working on, and the danger is obvious: the expansion of such world will erase our ‘other side’ of the c-speed barrier, the electromagnetic world.
Thus there are only 3 known-known scales, where the invariant Sp x Tƒ constant product gives us the ‘Energy and information’ conserved in the Universe.
And so for each of those scales I just had to find an equation of “energy’ that describe the system, in each relative plane of size and time speed, and then find its ‘parameters to measure’ the frequency of its motions and the constant quanta of fixed space of each scale:
Ei = Sp x Tƒ. And once such equations were found, I found the main clocks of time of the Universe for each scale of the fifth dimension, and resolved the conundrum of the meaning of mathematical physics, Energy, the Universal constants of space and the different clocks of time of the Universe that have existed well before humans invented their mechanical clock:
In terms of energy, Space and Time, I had resolved the details of the general equation, Ei=Sp x Tƒ for each scale:
Now you can see in the graph, the ‘specific’ equations of the 3 known-known scales of the Universe, which we call:
The ∆+1 gravitational sale (∆ being the symbol for a relative scalar plane of size and speed of time of the 5th dimension, which is the sum of all of them). Here the quanta of ‘space’ is obviously mass, which is what occupies the volumes of space of this scale, and the quanta of time motion, is speed, angular frequency or wave motion, with the limit of c-speed. So the equation is:
E=1/2mv2 or mc2 in Galilean and Einstein’s’ relativity.
Now the reader should realize that speed, angular or wave speed DOES change the frequency of its steps. A wheel turning cyclically to move a car can move at higher r=evolutions per minute
Let us then return to those graphs and clocks of time, as we are now close to the more strict concept of entropy.
The ∆-thermodynamic human scale is the next scale of the 5th dimension’s relative planes of size and speed. And here we realize while Energy is conserved, the total quantity of formal motions, angular and lineal momentum clocks of time and quanta of space are conserved, as the speed of time clocks and the quanta of space change, we need new ‘concepts’, new ‘clocks’, new Universal constants of space-quanta to measure it.
So in thermodynamics we have a new equation, E=nkT (with small variations fro specific fractal species of thermodynamic matter, gas, liquid etc.). And here obviously n being a number of atoms, is really E=KT, where T is the temperature of the system, the thermodynamic clock, so cold systems are slow in time, hot systems are fast in time, hot mammals have fast metabolic clocks and thoughts, cold reptiles and plants slow, but alas the beauty of the Universe is that this big cold plants and dinosaurs do live longer than the fast, small humans, since roughly speaking for each family of reality, Tƒ x Sp = Constant.
So Temperature is the clock of time of the thermodynamic scale and its constant of space, lineal, expansive motion is K, the Boltzmann constant, which has the dimensions of ENTROPY. So ENTROPY is the quanta of expansive spatial motions, of the thermodynamic scale, and only makes sense for thermodynamic systems.
Any attempt to transfer a clock of time or quanta of space of one scale into another larger or smaller space as physicists do unaware of the fractal structure of space-time of its multiple time clocks and quanta of space, without the slightest idea of what those Universal constants and terms mean is speakeasy bull$hit as Neumann told to Shannon. Only smart guys INVENT physics on terms they don’t understand.
Finally we get into the ∆-1 scale of electromagnetic quantum systems, and here again the equation is obvious Ei=H ƒ, so the quanta of space is H-Planck, the Universal constant, and the frequency of time, is ƒ, the frequency of the wave. So those are the 3 scales of physical systems. Its fundamental equations, time clocks and quanta of space.
All in the Universe is thus a mixture of space and time but both concepts are not the same bidimensional reality. We measure space with bidimensional quanta in each scale. They ARE the 3 most important Universal Constants of Physics, H-Planck, a bidimensional angular bijector, k-Boltzmann constant, the quanta of entropic space in the thermodynamic world, and c2, the quanta of constant space in the gravitational world (reason why we do NOT see it varying in speed-distances, as it IS the substance of which our gravitational light space-time is made):
In the graph you can see all the bidimensional planes of space of each scale, entropy, cc speed-distance and angular momentum (H-Planck).
So, your quanta of space=universal constants change, as you change scale of physical systems, in harmony with the change of ‘time clocks’ …
But the product of both, space quanta and time clocks, remain the same:
Sp x T ƒ = ∆ = Ei
This, physicists call it the principle of conservation of energy and information, clueless as they are about what ‘space’, ‘time’, ‘clock’, ‘energy’ and ‘information’, let alone the fractal space-time scales of the 5th dimension means.
But the concepts are easy to grasp, since the Universe is indeed as Einstein said simple and not malicious. So if we are still here, in a century or so, kids in a high school, will understand and find obvious what I just explained you – as now those kids find easy to understand Galileo’s equations. So let us go on with them.
Thus in the same manner there are infinite time frequencies and time cycles in nature – though we have found 3 parameters to measure them, frequency, speed and temperature, there are a lot of different ‘quanta of space’ around us, which we just defined, and so we can now tell you what that magic word, nobody knows in physics what it is, called, ENTROPY, means – merely the quanta of molecular space, which expands in gases, contracts in crystals. And DO NOT EXIST IN BLACK HOLES. OK? So now that we know, there is no room for nice smart guys to talk about what people ignored. My advice to Mr. hawking therefore is: find another theme nobody knows about to do speakeasy, and get your Ig prize to the worst scientist of the century.
The conservation of energy and information, lineal momentum≈space and cyclical time≈angular momentum.
But for you to grasp this, I will have to keep explaining the foundations of that fractal structure of space and time, long proved experimentally, and formalized with the metric equations of physics, in a more mathematical way. Don’t worry we will keep it simple, because as we said, the advantage on working with the proper time clocks, as in the case of the proper ‘heliocentric theory’ is that all becomes really much more simple. So Copernicus was much ore simple than Ptolemy.
Now in physics all is about Spatial, Lineal Motions (Lineal Momentum, which is similar to our spatial quanta) and angular Momentum, which is the minimal bit of our Temporal, cyclical clocks of Information.
So alas!, we have an immediate translation of the 2 ‘formal motions’ of which all is made; spatial, lineal quanta and angular, cyclical, informative cocks of time.
And this quanta of spaces of lineal momentum and cycles of times, angular momentum are the 2 formal motions conserved in reality.
But Physicists ‘integrate’ those concepts in the concept of Energy, which they divide into Kinetic energy (related to lineal momentum) and Potential Energy (related to the internal, angular momentum and form-position of the system)
As those are historic concepts, born of praxis – as all in physics, they are not ‘scientifically’ as wide as precise, as the concepts of space quanta and cyclical time clocks – the concepts of fractal time and space. Since physical concepts drag the mechanist errors and historic professions of physicists– as theory is always as secondary element to the worldly profession of physicists – to make machines, weapons and measure reality wit them.
But they are good enough, and by trial and error very slowly physicists have given us a lot of good mathematical stuff to define reality, so with a bit of ‘conceptual cleansing’, and repositioning we can easily get into a much richer and beautiful understanding of reality.
So just correcting those historic routines, and the conceptual errors dragged from them, the huge confusion of the present picture Physicists have of the Universe can be focused to see reality in all its astounding beauty and symmetry. So far we can save the essential concepts, we just expressed, writing them as follows:
Ei (Total Energy and Information of a system) = ∫ lineal and angular momentum = ∑ (Lineal Space motions x Temporal, angular frequencies) ≈ (abbreviated: ∑ Sp x Tƒ)
So now we have multiple time clocks and multiple space quanta, and while we might use different clocks (frequencies, speeds, temperatures) to measure time and different ‘constant of space quanta’ (H-Planck, k-Boltzmann, Mass) to match those time clocks, we do have that jewel of harmony in the Universe which is the conservation of energy and information (which of course, hawking’s musings break all over the place).
So we can write a very general equation for all the systems of reality made of vital spaces and time frequencies, including human systems, physical systems and biological systems:
Ei (Energy and Information, the quantities the Universe conserves) = ∑ Spaces x Time Frequencies
This simply tells us that the total energy and information of a system is the sum of all its vital spaces, each one with a different natural rhythm of time – measured by its time frequencies, which process and carry its information, in the cyclical forms and frequency of its cycles.
Since we do have 3 very simple equations that reflect the previous ‘5D metric’ that works for any scale, in each of the 3 scales of relative size of the Universe, worth to repeat to stress that simplicity and straightforwardness that shows truth in science, the so called Ockham’s principle:
∆-1 (quantum scale): E= h v;
∆ (thermodynamic scale): E= kT;
∆+1 (gravitational scale): E= c2 M
As shown in the above graphs.
Frequency of a quantum wave, temperature of a molecule, speed of a mass are the one-dimensional Clocks of Time that ‘change’ within a stable range in each scale.
H-angular momentum, K-entropy and Cc, are the bidimensional quanta of space that put together create the stable Ei, energy and information conserved in the 3 ∆±1 planes of physical systems that interact with the human being.
In 5d physics, we simply say the Universe conserves its quantity of ‘present space-time’. That simple statement includes all conservation principles of all sciences.
This canonical definition of H, K, and C, bidimensional angular momentum, entropy and Speed, the space quanta which of each scale means that entropy DOES not apply at ALL as a concept BEYOND the thermodynamic scale, roughly on the 0-10.000 temperature beyond which it breaks down, that is molecules cease to exist and become plasma ruled by electromagnetic flows, hence by the clocks of ‘frequency’.
Back to the beginning closing the cycle.
Now look at the second equation, E=kT.
if you substitute E for M its inverse then we write: M= k /T.
That is Mr. Hawking’s equation of a black hole evaporation, quoted at the beginning of the article, with the proper sign:
As temperature diminishes, Mass grows. So he black hole is born hot, follows the laws of thermodynamic entropy, diminishes temperature and eats up our world, till Temperature clocks come to zero, temperature disappears, the black hole reaches 0 entropy and perfect informative order, as experimental and theoretical facts, both in 4D Einstein’s EFE, equations and 5D Metric shows.
Why? Look at the next graph…
The dark world.
In the next graphs, when we cross scales of the 5th dimension, the simple Sp x Tƒ = E, lineal relationship and nice equations of conservation of energy and information ‘break’ and suddenly the equations do NOT work as we enter a ‘transitional region’ between two scales of space-time. Whereas the time frequency of motion no longer behaves lineally. It finds a limit and cannot grow more. And those barriers are met with the equations that Planck and Einstein discovered (and a few more for thermodynamic systems), which are no longer lineal but exponential equations, barriers where the system breaks, explodes and dies away, ‘crossing finally the barrier’ into the next world scale:
Now, the graphs, explain the other huge conundrum of physics: why in the ‘steady state’ regions of those relative planes of size and time speeds, all is lineal, but when we go to the borders, equations break, and in the ‘transitional region’ the whole thing becomes hyperbolic.
On the discontinuous verge between planes of space-time of the 5th dimension, the equations break and they are no longer lineal.
So they become hyperbolic geometries of exponential growth, unable to break the barrier of c-speed (relativity), temperature (violet catastrophe of radiation) and h-Planck quanta (uncertainty principle/limit).
Thus when you reach the limit between 5D planes, the region becomes catastrophic and you get the ‘barrier’ speed does no longer grows, but is absorbed as mass, temperature does no longer cools but it is converted in mass, frequency does no longer increases. And alas, once you cross the barrier you are again into a steady state region:
Simply stated, you MUST cross a discontinuous region between scales and things get rough, the previous parameters of time and space ‘are saturated’, you cannot longer increase your frequency, and speed, or you reach the inverse limit of 0 temperature, rest speed, and ‘cross between planes of 5D’ with NEW clocks and NEW time quanta. You exist in a Universe roughly divided in 3 fractal, scales=planes of space-time, which we shall call, ∆-1: quantum scale, ∆-Thermodynamic scale and ∆+1: gravitational scale.
When you change scale, YOUR CLOCKS of time=formal motions change. So you move from quantum frequency of radiation to thermodynamic temperature clocks, and then again to speed motions. But as you change clocks, obviously the ‘time tics’ are transformed, the previous time tick fades away and the new time tic grows. And those ‘discontinuous’ barriers in which we change of ‘parameters’ are signaled by a change in the lineal steady state graphs of mathematical physics that measure them.
So in the barrier between frequency and temperature you have the asymptotic ‘violet catastrophe’ of temperature≈radiation, which Planck found and made him postulate quantum theory; and on the other side, in the barrier between temperature clocks and speed, you have the c-barrier that made Einstein, discover Relativity theory, as the ‘simple equations of our thermodynamic world, where temperature is the clock of our activity (so hotter means faster in time, mammals vs. reptiles to put an example, solid vs. gas etc.) ‘break’. Therefore it is NOT meaningful to talk of ‘temperature and entropy’, once we are in the realm of Mass and the dark world with no temperature of dark matter, quarks and black holes.
A black hole is NOT an electromagnetic, expansive, thermal vortex, but the opposite, a gravitational implosive in-form-ative force vortex that ‘eats temperature’ and electromagnetic energy and converts it into ‘cold’ 0-temperature gravitational mass.
So black holes with 0-temperature when they grow fully into mass HAVE NO ENTROPY.
Now this dark world beyond c-speed and below 0-Temperature (or rather a world where c-speed and o-temperature break and have no meaning, as quanta of space and clocks of time), is NOT our world, our concern, it is beyond our parameters of survival and existence, it should not be explored by a kind of people who does not even know what temperature or speed is, just because they know they can do their science-fiction on that field and occupy their ‘free time’ and computers. Cogito?
All this is simple and beautiful and real.
Now, to close this introduction to the fractal paradigm, something you always wanted to know, why you live and die, as everything else in the Universe, including black holes, Mr. Hawking and me – though of course, it is stupid to do it, for no reason, no knowledge, just a machine… the FUNDAMENTAL CYCLE OF TIME OF THE UNIVERSE, THE WORLDCYCLE…
The worldcycles of nature.
Now, if you have gone so far, you probably understand that there are infinite time clocks, they are all cyclical paths, and they are all storing and processing information. So really what time is the different rhythms of processing information of beings, and that obviously changes. Consider yourself, you are born with a lot of lineal motion, and little information, you keep acquiring information till old age, and then you die and erase your information, ending your time life-cycle, back to the beginning of your process – the seminal dissolution of your cells.
The galaxy goes through an age of implosive creation of form, from vacuum space – so Einstein said that time curves space into mass, but then a quasar explodes the galaxy that throws information into space: E < = Mc2. Again we see a similar worldcycle Soon we will define those cycles with mathematical equations for different time cycles and quanta of space. But we are MORE interested in the qualitative nature of those processes.
What it is clear is that all systems perform those time cycles with the same pattern, going from an age of maximal lineal motion or youth into an old age of cyclical information and then back in the process of death to the dissolution of cyclical form into planar expansive motion – disaggregation of cells, of matter into energy etc.
So time is NOT a steady constant tic as the mechanical clock of humans in nature, time can accelerate, decelerate or move at steady speed for each system moving and this is one of the many deformed features of reality which Physicists have made canonical errors of our universal world view by putting ‘first his mechanisms’ over theory.
So what is the rhythm of time? Simply speaking, a series of worldcycles of life and death, of expansive and implosive motions, ordered in a natural manner in all systems of the Universe.
Now remember, I told you i was the chair of duality, expanding our understanding of the Universe with both arrows, entropy and information? So this is so far what I have tried to do now, but to fully complete the world cycle of a black hole we need the 3rd dimension of time. What can this be? If we have already entropy, disorder, the erasing of information? And we have information, order, the natural arrow of life towards an old informative age, in a fractal universe of infinite space-time beings?
Well, if we call youth, the past, with maximal Sp/Tƒ, density of energy (so you move a lot) and Tƒ/Sp, the old age of information, as we do in life, in this planet, in the galaxy moving towards the central informative black hole, as we move from the relative energetic past into the future informative maximal Tƒ age, we must cross through a central region where Sp=Tƒ, or present region. So we call:
Sp (spatial past) > ST (PreSenT) > Tƒ (Future Informative Time)
the equation of the 3 ages of a world cycle. Look how clever the symbols are s-p spatial past, Tƒ, Temporal Future. Ha, ha, it took me a decade to find them.
So what I did long long ago is to complete the model of the fractal Universe, adding the 3rd dimension of time, to the relative ‘entropic past’, the relative ‘future information’: its ‘relative present combinations’.
Further on, those 3 ‘time arrows’ are symmetric to the 3 dimensions of space – the 3 only topologies that exist in the universe:
- The lineal, toroid, past, spatial flat planes proper of limbs and fields that move you as the line is the shortest distance between two points.
- The hyperbolic present, body-waves that reproduce the form of beings: Sx T
- And the cyclical, spherical, informative particle/heads, as the sphere stores maximal information in lesser space.
In graph, the symmetry between the 3 ages/dimensions of time & space, which put together create all the forms and functions and ternary organisms of the fractal universe, a tapestry sum of them.
And this fully completes the work of Einstein and quantum physics, and fusions it with evolutionary theory, a theory of the evolution of information, and allow us to define, NOT the particle of God, but if we were so pedantic, the ‘Equation of God’, but as we are ‘normal people’, we call it the Generator Equation of the Fractal Universe of space-time:
Γ. Sp (past-lineal, toroid limbs-fields) ≤≥ ST (hyperbolic-planar body-waves) ≤≥ (spherical future particles-heads)
Whereas we introduce some basic symbols of 5D Metric, Γ, the G-enerator equation, which can be studied for each fractal space-time system in detail and its 3 parts: <, the arrow of expansive entropy, > the arrow of future information and ≈ =, the arrow of present balance, ST, that puts together, Sp: Spatial Limbs/fields and Tƒ-cyclical, temporal clocks in present beings.
So, if we see a system as Sp>ST>Tƒ constantly ‘informing’, > through time the system, we are in the 3 ages series, in a diachronic system, as ‘time bends space into masses’ (Einstein). But if we are:
Sp-limbs/fields > ST-body/waves <Tƒ-heads/particles, whereas the limbs/fields give energy to the body/wave and the heads-particles give it information, we are in a living organism in balance,in a relative present immortal state. And this is the ideal state of existence, since ‘The Universe conserves its present’.
Why then we die? Well if you see both equations together you will notice that adding up space and time states, there are in the time series two >> arrows unbalanced, as information grows excessively since the ‘head’ is selfish and the particle absorbs energy into information and finally exhausts energy, all converted into information, so at the end there is a reversal of time arrows, and we need 2 << fast explosive erasing of information, to restore the balance and maintain the whole reality as an eternal sum of dynamic present fluctuating between energy and information states, back and forth in the long arrow of life and the short arrow of death, since now in the reversal flow of death, << we jump over the present. So all death moments do not have present, are immediate closing of the world cycle in a big-bang death.
As a big-bang is not the birth of anything but the physical, instantaneous death in 0-time, of the system. So you die in a second and the Universe if there is cosmic big-bangs, the galaxy in a quasar, the black hole in a nova will kill you in a fraction of time, to restore the balance on ‘this lost rock in a corner of the cosmos where a mush called mankind’ (Schopenhauer) is busy busy killing all other forms of life.
This quantum physicists understand a bit better, specially in Feynman diagrams, when they say that relative past to future and future to past (informative and entropy motions) are possible. But they are ONLY possible, because the Universe is fractal, broken into infinite relative systems, which acquire more information as time goes forward with the arrow of life, and loose their information as time goes backward with the arrow of death. So Feynman wrote the antiparticle ‘moment’ of death as a past arrow. And indeed, the particle is the life, informative arrow, the antiparticle the past arrow, which last only the moment of death, and then the present light space-time is restored as a wave. And that is the reason why we see less antiparticles, as we see less corpses. They last far less, with no present, and that is the wisdom of the mind of the Universe, which makes death only a moment and time-future-life a much larger experience, yet, the sum of both is a zero sum that makes reality immortal.
IV. BIOLOGICAL SCALES
So I found long ago an equation to define those world cycles (which physicists still call worldlines):
Young-lineal age of maximal spatial motions: Sp < ST (wave-like reproductive age) > Tƒ (Informative old age). And then death, an entropic big-bang explosion of the fractal system of space-time that erases your information.
This worldcycle is truly the ultimate clock of time of the universe, of far more importance to understand the meaning of it all that the mechanical clock that has been hidding it for 400 years with its steady tic.
So paradoxically precisely when humans were able to observe for the first time with some detail thanks to telescopes and microscopes the multiple scales of space and speeds of time of the fractal universe, the straightjacket of mechanical clocks prevented them for 4 centuries to understand them their frequencies, finite rhythms and worldcycles including the worldcycle of life and death of all systems, which are born in at fast time speed (young age) and as they grow in size, diminish the speed of its time clocks, in all scales of the universe, till reaching maturity and finally stopping its clocks in the moment of death.
In the graph, the fundamental ‘development’ of the Metric equation of space and Time of the 5th dimension, which streamlines all the main principles of science, its conservation of energy, lineal and angular momentum, and the principle of relativity between motion and form, from the proper perspective of the multiple space-time cycles of the Universe – that is, THE SPACE-TIME BEINGS OF REALITY INCLUDING YOU, AS WE ARE ALL SPACE-TIME CYCLES AND EXISTENCE IS JUST A TRAVEL ON THE 5TH DIMENSION.
We have written above each graphic image the aforementioned Generator, which now we can complete with the moment of birth and death, as we are born in a lower scale of the 5th dimension as small fast moving beings, ∆-1: seeds of information, and we return in the moment of death back to the ∆-1 scale in the big-bang, closing the cycle;:
∆-1: seminal birth: ∑< ∆: Sp (spatial, relative past, lineal young limb/fields) < ST-reproductive, present bodywave> Tƒ (old particle/head age) << ∆-1: death.
Where the new symbol ∑ means the massive reproduction and reorganisation of the seminal death as it feeds on energy, in the black hole birth, our energy, to emerge in the upper scale.
And as you can see looking at the form of each of those beings, including the 3 artistic styles of civilisations, there is a beautiful symmetry between its 3 organs perceived in simultaneous space:
Sp (Lineal limb/field) <ST (Hyperbolic iterative body-wave)>Tƒ (informative particle/head)
And the 3 ages of existence, as they merely mean that in your young age the limb/field dominates the physical biological system, in the adult age, the body-wave iterates the system ensure the immortality of reality beyond death, and in the old age, the particle/head of information dominates.
Now this is only the very surface of the fractal paradigm, and its r=evolution in the way we will understand science in the XXI century – the details of that world cycle is the entire Universe, which can only be understood through the interaction of its 3 arrows of time, both in the largest generality and its details.
Consider for example the late studies on death at genetic level. As we explained the equation of death comes because the informative Tƒ element exhausts the energy system which dries itself So scientists have found that ageing is indeed caused by the loss of activity of the two ± energetic cell systems: the positive mitochondria that produces the energy of the cells, corrupted by its informative DNA and the negative, leukocyte system of immunologic cells, the T-cells which become old and loose capacity to control.
But this process starts, after the adolescence when the resources of the system move to the reproductive phase and stop producing new T-cells.
The why of science: the topological, fractal paradigm.
All what you see can be reduced to numbers, because numbers are ‘social groups’. In the 3rd paradigm of metric measure those social groups were described merely in its external properties. System sciences analyses its internal, topological structures, as societies of Non-Euclidean Points (points with form and motion), whose exchanges of ‘—motions’ and information create complex networks of self-similar beings. Can we reduce all those topologies and organic functions of network spaces to a few postulates as the previous Euclidean Geometry did?
Yes, we can, but for that we must complete the work started by Riemann and Lobachevski, who discovered the 5th postulate of Non-Euclidean geometry and affirmed that through a point infinite parallels could cross. For a century and a half no mathematician seemed to have realized that if the 5th postulate has changed, we had to adapt the other 4 postulates to the new definition of a ‘point with breadth’, through which parallels cross. This point is the fractal point, which grows in size and scale, becoming a topologic network of smaller points, as we come closer to it. The Universe is indeed absolutely relative because ‘each point is a world in itself’ (Leibniz).
Yet geometric restrictions that allow only 3 types of topological forms in a 4-dimensional Universe -the informative, toroid topology, the energetic, planer sphere, and the cyclical reproductive hyperbolic -reduces all the internal parts of a fractal point to 3+1 functions or arrows of time, ‘—motions’, information, reproduction and social evolution that conform the ‘program’ or why of the Universe explained in detail in the twin lecture of this work1.
Those 3 functions become the functions of 3 specialized fractal networks of points that construct the systems of reality, from your organism, made of 3 physiological networks (the energetic, digestive network, the reproductive, blood network and the informative nervous network), to the galaxy, organized by a network of electromagnetic ‘—motions’, gravitational information, and a series of herds of stars, non-Euclidean points that reproduce the atoms of the galaxy.
The principle of transformation of ‘—motions’ into form: ‘‘—motions’ never dies but transforms back and forth into information; Exi=K, Sp<=>Tƒ’ represents the two parts of ‘—motions’ and form of those non-Euclidean point, the new mathematical unit of the 4th paradigm, where points become ‘topological balls’, and the Universe a geometry of multiple fractal scales of space-time, which grow in size and information when we come closer to them. Each of those points have a different rotational clock, rhythm or ‘speed of time’ and a different size, which in each scale is used by those particles to gauge information and measure distances and energies and motions, as each of those points interact with other points of its relative space-time world.
Thus the key to understand the structure of organisms are the 4 new postulates of non-Euclidean geometry based in the concept of a fractal point. Since we have also to account for the other key property of the spaces we see around us: each of them when observed in detail is made of multiple, smaller self-similar parts, we call generically ‘cells’. So even the smallest point, when seen in detail, becomes a fractal point with multiple parts -a non-Euclidean point in which the parts assembly themselves into wholes by connecting themselves through networks, sharing flows of ‘—motions’ and information, and then become parts of even bigger wholes (so particles become parts of atoms parts of molecules parts of cells and planets parts of organisms and galaxies, parts of societies and Universe, in biological and physical spaces). Yet those networks leave dark spaces between their connections where other networks can occupy a place. So thanks to those dark spaces, we find that the system mixes two types of networks – toroid informative networks and energetic, planar or spherical networks (as a sphere has in small surfaces the properties of a plane).
Reality is constructed with 3 levels of increasing complexity: In the first level any trajectory that returns to a point creates a closed form or time cycle, a clock, the unit or minimal event of Reality. Then many time cycles, chained to each other with certain synchronicities create a knot of time cycles that fills a vital space and becomes an entity of reality. We will describe those knots of time cycles as Non-Euclidean points, whose topological parts and isomorphisms become the mathematical foundation of Multiple Spaces and Times. Finally many knots of time cycles, exchanging flows of spatial ‘—motions’ and temporal information create complementary, social networks, which in its more complex forms are able to reproduce the system and create ‘super-organisms’, wholes made of parts that are wholes of an inferior scale of reality.
Since non-Euclidean Planes are networks with ‘dark spaces’ not perceived by its points that only see the flows of the network; those ‘holes’ allow the creation of complex systems with many networks, webbed within those dark spaces.
Thus the why of the Universe is organic, social: the Universe is made of complementary energetic and informative networks of ‘Non-Euclidean points’ (points with form and motion) that evolve and combine together, creating reproductive networks. And such complex systems create, new bigger, fractal networks units of a larger plane of space-time, evolving reality in scales of size that follow the same organic isomorphisms – from particles that become atoms that become molecules, cells, organisms, societies, planets, galaxies and Universes.
‘Each point of the Universe is a world in itself ‘said Leibniz. What he meant was understood in the XX century when we discovered the fractal structure of the Universe. 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, repeated in all scales where those fractal points display the same logic behavior.
The Universe is a fractal of Temporal, informative cycles that are constantly generated and imprinted in reality. It is a fractal of 4 self-repetitive motions, ‘—motions’, 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 åctions 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 ‘—motions’, reproducing them and self-organizing them in 2 parallel, complementary networks, one of ‘—motions’ 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 space-times, the one of ‘—motions’ and information, have different Universal Constants which are ratios, e/I and o/e and Sp X Tƒ, which define the arrows of ‘—motions’, information and vectorial reproduction of any organic dual space/time plane of the Universe. Where the space-network of ‘—motions’ 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.
Thus, we shall now finish this first section dedicated to the ‘metaphysics’ 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 isomorphisms 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 ‘—motions’ 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 creation of a fractal networks. All what we see are fractal networks caused by those knots of time.
The Universe is a 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 ‘—motions’ 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 ‘—motions’ and information and the structures and isomorphisms 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 topological form – the same shapes of ‘—motions’ and information emerge and repeat themselves in all scales (though, and this is essential for the reader to learn how to compare them, they are topological forms, where the ‘distances’ and sizes are relative, so what is conserved is the overall ‘lineal, planar shape’ of energetic functions, such as lineal limbs, lineal weapons, planar membranes; the cyclical, hyperbolic shape of reproductive cycles, which combine ‘—motions’ and information to recreate a form, such as those of your body organs or the cycles of an assembly factory or a mitochondria, and finally the toroid, convex, warped, cyclical forms of informative organs, such as a brain, a camera or an eye or a black hole.)
Those 3 invariances create a new ‘paradigm’ of science, no longer built on the belief of a single arrow of time, a single space-time 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 ‘—motions’ 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 terms.
Fractals are mathematical or organic forms, which 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: ->ΔTƒ
All fractals originated by a Generator Equation (mathematical jargon) or mother cell, (biologic jargon) iterate=reproduce a series of self-similar fractals, called a set in mathematics or a family in biology:
Mother/Generator Cell: ->Σ∆-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? 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 eddy) 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: a Mandelbrot fractal holds more information in its smaller scales, as we enlarge 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 ‘—motions’ 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 add 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 maximal 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 ‘—motions’, 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 ‘—motions’ 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 are better described with visual and logic/verbal languages. Those Biological theories of Time (Evolution theory, Theory of Organisms) include also the logic of survival that extinguishes the less fit – hence a relative past species – and reproduces the fittest, hence the future species; and it includes the visual languages that give movement to the forms of ‘—motions’ and information described by mathematics.
Nature’s fractals combine the arrow of ‘—motions’ and the arrow of information in an organic way.
They differ from geometric fractals in their dynamism and capacity to absorb ‘—motions’ 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 add to the informative arrow – whose isomorphisms we deduced from the study of mathematical fractals and informative seeds – the ‘—motions’ arrow of ‘—motions’ that thermodynamics has analyzed:
‘—motions’, young arrow: Sp> ∞ x Tƒ->0 X sp->0 x Tƒ->∞: Information, old arrow
For any Σ number of cycles: ΣSp x ΣTƒ = Organic fractal ΣSe<+>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 ‘—motions’ and ‘—motions’ 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 ‘—motions’ into mass, Sp=mc2) in terms of process of creation and destruction of information.
A single language cannot 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 Pythagorean, 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, humans ‘talk’ those arrows of time with logic, verbal, visual, and mathematical languages. 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 topological form (self-repetition of the ‘—motions’ and information shapes of reality. The 3 invariances define a Universe better described with the mathematical isomorphisms 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-’—motions’ and form, in-form-ation; and all of them are structured into networks, which share their ‘—motions’ and information. Those 3 elements: bites and bits of ‘—motions’ and information; networks and scales define the structure of all natural fractals, including the Universe.
They can be formalized with the Generator Equation we use to formalize the arrows of ‘—motions’, 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 chemical or mathematical 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 ‘—motions’ and bits of information. Those bits and bites are not static forms, but arrows that exchange ‘—motions’ 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:
∆: Fractal Cycle: Sp<=>Tƒ (dynamic state) + Sp X Tƒ (static, formal state)
– The networks or systems of ‘—motions’ and information that organize those cells into bigger structures.
How feed-back cycles of ‘—motions’ and information grow into complex organisms, made of many 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 ‘—motions’ and information to them. For example, in a human fractal, the nervous system delivers bits of information and the blood system delivers bites of ‘—motions’, control together its cellular units. In the Universe the same roles are played by the informative, attractive, gravitational force, and the electromagnetic ‘—motions’ forces.
-In Space through the organization of cellular networks that deliver ‘—motions’ and information to each cell-cycle. Those cell-cycles attach to the networks to process constantly new ‘—motions’ and information in their iterating cycles, creating bigger organic systems, made of multiple, similar forms.
When both iterative processes are combined, the fractal units of the Universe grow in ‘—motions’ 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.
The equation includes an Σ-term to signify the gathering of individual Sp X Tƒ units into networks and webs:
ΣTƒ: Fractal networks: Σ (Sp<=>Tƒ) or Σ (Sp X Tƒ).
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:
– ∆st: The relative st-scales or dimensions across which fractals extend its organization. We use for the 3 relative scales of size that define most Nature’s fractals, the symbol O for information.
In humans there are 3: the cellular, individual and social scales; as most entities do not exchange ‘—motions’ and information beyond its upper and lower organic level. For example, humans, as individuals belong to a relative st-scale, and are aware of social tasks (our ∆+1 plane of existence) and cellular sickness (our ∆-1 plane), but the events that affect the galaxy, the macrocosms to which our planet belongs (st+2) or affect our molecules, the lower microcosms that make up our cells (st-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= ΣΣ∆-1 Cycles > Σst-Cells->∆+1 Organism.
How many elements in space make up a fractal, social network? The most obvious structure is a ‘tetraktys’, already considered by Pythagoras to be the magic number of the most perfect social networks. The reason is that a tetraktys can be written as a system with 3×3+st elements. Imagine then such tetraktys as a triangle with 3 vortices, each with 3 elements that will perform the arrows of ‘—motions’, 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 st-scale. Thus a tetraktys 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 ‘—motions’ and information that organize those cellular units, and st-scales in which a self-similar but not equal fractal structure emerges, once and again with the same energetic and informative complementary forms.
Fractal Reproduction of information: Non-E points evolve into morphological organisms that keep its 3 functions.
In the graph, the informative egg, and energetic, larva phase of most animals translate the inner, informative center to the region and the external membrane to the ‘tail’, inverting their positions as the informative function of the egg is substituted by the energetic function of the larva
Yet morphology is flexible, adapting itself to the 3 possible, Sp, et, T environments:
– Max. T: The spiral or spherical ‘still’, cyclical form that packs and focuses the maximum information in minimal space is preferred in a 3-dimensional, homogeneous, ‘safe’ space or when the form is born as a ‘seed’ of genetic information. Those specialized, informative, still points have an external, spherical, rigid, still, symmetric membrane that can ‘focus’ information into an accurate, reduced image of the Universe.
On the other hand, since energy-information flows occur within the borders of the world, the informative singularity that orchestrates those flows, occupies the central axis with a dimension of height, moving linearly as it orders the inner world. Some examples are: a cell with DNA, or a spiral galaxy with a tall black hole and a Halo.
– Max. Sp: Lineal, spatial, energetic, moving forms are common in moving worlds with directionality. Then the energetic system occupies the ‘tail’; the intermediate organic elements, the center; and the informative senses occupy the top ‘ in the direction of movement to absorb and control the ‘future’, energetic and informative flows that come from the forthcoming region, which the organism will occupy in the future. Some examples are: a train wave with a singleton ‘, the glycine or a shark. All of them have s upfront, with their energy cells on its tail.
– SxT: In complex, space/times existing in the limiting surface between 2 discontinuous regions, the form mutates between energy and information morphologies in 2 different ages as in the graph, or depending on the environment and function it performs, as spirals do; or it becomes discontinuous with quantized triangular legs to process energy, hands to emit information, tails to control directionality, eyes and antennas to absorb information, etc.
It is the case of life beings that exist in discontinuous surfaces between the atmosphere and the ground or the water. Thus the morphology and relative position of the energy and information elements of a Non-E point adapt to the ecosystem in which it exists. Yet its 3 Non-E regions and its parallel energy, informative and reproductive functions are maintained.
A galaxy, a DNA molecule, a tornado, a shell and a sunflower have all a spiral form, the most efficient and hence commonest form of any space-time field, since it can easily mutate between a lineal and cyclical form, opening or closing its arms. The homology and similar structure in time and space of all Universal entities shows the existence of an impersonal design in all forms of reality that obey the quantic laws of space and time.
V. HUMAN SCALES.
Medicine & Physiology deal with the 3 networks of the human organism, whose functions connected to the senses enact our time arrows: The Digestive, Energetic System is attached to the senses of smell and taste; the hormonal, blood, reproductive system is attached to the senses of touch and the 6th, emotional sense and the Nervous, Informative System is attached to the higher senses of sight and sound.
In the graph we see how FUNCTION MATTERS MORE THAN FORM, and yet both are in symmetric symbiosis. The galaxy is a ‘homogenous’ organism with a black hole in the centre; the plant has also its 3 parts, and it has a root brain with maximal fractal branching to gather more atomic information, while ‘flat’ energy leaves absorb light as energy. Humans though have the inverse orientation as they use light to obtain information and take energy from plants. both predators and preys have inverse functions/forms.
Moreover it is evident that there is a symmetry between the 3 spatial dimensions and its functions,a s ‘height is always the dimension of information’ to perceive better, so we have our heads on top in the direction where information comes. Length on the other hand is the dimension of forward motion the most common, and finally, width is the parallel direction of social organization and reproduction.
Thus WE ARE BEINGS MADE OF DIMENSION OF ENERGY AND INFORMATION AND LIVE ACCORDING TO ITS LAWS, OF WHICH THE TERNARY MORPHOLOGY OF SYSTEMS AND ITS 3 AGES IN TIME, WERE THE MOST ASTOUNDIN, perfect symmetry and ‘deterministic law’ of the Universe.
There are thus ‘3 topologies that correspond to the ‘3 components’ in space of any physical or biological system:
– Max. Entropy: the entropic, ‘lineal’ limbs/fields, as the line is the shortest distance between two points that dominated the youth of a system.
– Max. information: the spherical, particle/heads of information, since the sphere is the geometry that stores more form in lesser space, that dominated the 3rd age of the system, as the passing of time increased the informative complexity of the system, exhausting its energy.
– And the intermediate, e x i , ‘conic’, ovoidal or wave-like ‘bodies’ of the system that reproduced them, and repeated its actions, making the system stable, and ‘immortal’, when an organism could be kept in such a state.