**SUMMARY: ****ß**

- 2 manifolds.
- Non-Æ:The 2nd Isomorphism
- The bidimensional forms of the 10 planes of reality.

The third line increases formal depth and experimental detail in our study of all the systems of reality, defined now by its fundamental ‘ternary isomorphisms’, ‘equal properties’ derived of the 4 elements of reality, scales of space and time and the minds that perceive them: ∆ST•.

So we describe: º… the ‘languages’ of ‘the mind’ and ‘its actions’… the S-patial, ‘bidimensional’, ‘ternary, constant’, ‘organic networks’ created with them… which live in T-ime, through ‘3±1 ages’ as ‘species’ ‘traveling=moving’… through ‘§scales’ and ‘planes’ of the fifth dimension of ‘Γœ∆’ the whole of wholes…

Each of those ternary sub-properties of the four elements of reality is then illustrated for the 10 scales of ‘stience’, from the smallest quantum forces, to the largest cosmic Universes, showing that indeed, all what exists is ∆•st of space-time, sharing the same properties of exi…st¡ence.

**I. 2 MANIFOLDS**

“Space of itself, and time of itself will sink into mere shadows, and only a kind of union between them shall survive.” Minkowsky

‘Logos=God is the game of a plurality that maintains its union despite the constant attempts to separation of all its individuals. Departing from this logos we can study the dualities’ Heraclitus

‘The game that can be named is not the eternal game: the constant combination of yin-form-ation and yang-energy, which give birth to the 10.000 beings’ Lao Tse

**The perennial philosophy on the game of existence.**

I am often told the texts of GST come ‘from another planet’ by well intentioned scholar friends (-; but they don’t as they in fact plug in with the perennial philosophies of eastern cultures about the duality and ternary structure of the creative, reproductive, living universe.

So for a change I would like to show that there are in fact part of the perennial philosophy of the highest minds of mankind, which have always understood the Universe in terms of the duality between its spatial energy and temporal information, starting this post on Duality, with a reckoning of the work of the 2 ‘first’ philosophers of the west and east, which understood those principles fully, as the eclectic final ‘knots of thought’ of the earliest rational philosophies of the Universe, humans develop – Heraclitus, the last of the Milesian Masters, which discovered rational thought in the west, and Lao, the most important of the Chinese masters of dualism.

Both in Lao tse and Heraclitus, the final master of the first milesian school of rational thought talk on the divergence of logos, Tao, the game of existence in two opposites that come together yin and yang, become a harmonic peace in this substitution and permanent transformation of the contrary.

THE WAR AND PEACE sides of this duality is essential to both cultures, as it reflects reality. The divine in nature is life and death night and day, the peace between contraries its golden mean.

Ontology then becomes the study of the permanent unity in the plurality, the game of social love, the arrow of future of the 5th dimensions.

All things have this ontology of the being, the super organism.

But all is in continue transformation is and not is, as in anixamander. It is indeed the feedback opposition which allows through motion to transform one into the other. Contraries the low that rises and becomes high defines therefore the motions, which are medible, those actions that change beings of space and time in heraclitus is therefore dialectically living in motion.

BUT THE CONTRADICTORY ARE phases Not cataphases, life and death, loe and hate, FORGIVENESS AND KNOWLEDGE. harmonisation of contraries does not then become the same, but diverge when life crosses the darkness of death brings agains life as the Universe renews itself.

So those revolutions of beings, wordlcycles in our explanation, thesis that become antithesis through the motion and reproduction of the middle form, will then create the instant eternal logos limit that a finite universe makes things change.

**All yin has a drop of yang in its interior.**

What we perceive through senses is in perpetual change even if the logos or game of motions in invariable. He uses then the example of the fire, which is the same but constantly changes, as a reflection of the arje, the fire, the logos the process of dynamic separation of universals into individuals through the life and death ccle.

If we were to study the taoist in depth we could get so similar insights in the depth of the game of existence as the first greek philosophers, from the earlier Pythagoras and thales, anaximander and anaximenes, till closing with heraclitus.

All this is truly deformed, the logos is the limit that joins and separate, the universal constant that diverges in its two members to create the energy and information put to ether in logos broken in all the divergences of all unseal constants.

the logos allows to think when it sees the synchrony of the oposites, in this moment a still mind is creed, when dark and light form a simultaneous mapping of reality, so this still game of the mind of the synchronous which creates a thought allows the experience of the physical moving world, in this heraclitus is the mod profound, because chorines he says is only the perception of the returning cycles that are mapped in each simultaneous instant, and science a and philosophy and knowledge, which he fully realised to be in the instant of though.

His death in the refuge of artemis where he spent his last days, hidden in the moutons behind the temple isolated from all other humans, feeding on herbs, owning nobody among human was to rise so high in the perception of duality.

He was known for his hermitic ways. He searched silence to reach anthology in the darkness of the negative of the opposite to complete the cycle with both yin and yang, giving birth tot those still moments of deep reflections, where the change see the most evident and common, which is the essence of it all, the power of eusocial love in the joining of individuals into logos, unseals and its languages of perception in simultaneity, the harms of the buddha, the 3rd great man who understood it all.

la certain principle of creation is needed, the game is thus reflected in all, the chid is his example as that of child vishnu, the players who merely create virtual games as we are just all beings in logos in the game of the ∆dimension of parts that become Universals.

What there is then on top of this logic pyramid, which infuses all its parts of the same game?

** THE HOLOGRAPHIC PRINCIPLE**

**Space as a slice of time in the 5th dimension.**

The smallest Unit of reality is a space-time cycle, and for all of them there will be a relatively small particle with maximal time-motion-density-mass/charge which traces an external space-time cycle on a larger region with lesser time-motion-density mass or field.

This simple physical interaction responds to the basic duality of time, as faster moving cyclical, accelerated form and space, where with its excess of acceleration traces a lineal motion, a larger field of smaller energy-space, according to the metrics of the 5th dimension and its co-invariance between speeds in time and sizes in space.

Space is a derivative slice of time, thus space motions, which Physicists study is a small part of reality.

So first we must briefly enunciate this error corrected and how it changes our space-time compression:

Physicists define space-time continuum under the error of a single absolute newtonian space-time extended to the entire galaxy. The Universe though is a nested system of larger and smaller sub-systems, guided by different clocks ordered along size and speed with the co-invariant metrics of the 5th dimension, such as smaller systems turn faster clocks, and have higher attractive force (charges which are accelerated vortices of time space according to Einstein’s principle of correspondence between acceleration and forces, he applied to cosmological masses).

We see many cosmological vortices of mass with central heavy black holes and its gradient of increasing form, information at accelerated pace. Times are very varied, but all of them obey to a single cycle between birth and extinction. We shall study with Æ equations of existential algebra, of which the most important is the world cycle of life and death.

Time waves are also called world cycles, and they have 3 scales of ‘momentum, energy and time.

In physics time waves are studied among forms of maximal motion. We are more interested in the slow time waves with minimal motion in space, that evolve in longer times.

Of those waves and its time forces, physicists study only one the weak force. We can recognise a time wave of trans-formation and social evolution cross the 5th dimension, by studying its parity vs. chirality, since time waves are chiral, which mean traveling to the past (entropy arrow IS not the same that traveling towards the future.

Information don’t travel to the past said einstein (wires don’t travel to the past).

He was actually wrong, both energy and information ravel through time waves, and they do so constantly in worldcyles.

Physicists have simplified for centuries to ease measures the cyclical nature of time-clocks, of which there is an infinity in the Universe. First, Leibniz warned Newton against taking the artifact of measure, called absolute space-times as reality itself; then Einstein realized that in different parts of the Universe time clocks run at different speeds. Biologists and computer theorists found also that life and machines are run by cyclical clocks of information. Thus the next stage in science is the study of all those time cycles of the Universe, by reversing the concept and measure of duration (lineal time) by its inverse, cyclical time and frequency:

*T (lineal time duration) = 1/T≈ ∑ ƒ (frequency of time cycles) = ∑ Tƒ ≈ ∑Ti.*

We shall thus consider fundamental to the Universe, cyclical time, and its measure frequency, whereas duration is a simplification obtained by adding al the time cycles of a certain entity, from the beginning of its motion or life till its end.

For example, a wave motion, c is the product of its l, wave-length and frequency, the human motion is the product of our steps and frequency, a car motion is the product of the radius of its cyclical wheel and the frequency of revolutions per minute and so on. Those transformations of frequency into duration show that the original element is the cycle, and its frequency, and the simplified version, the lineal duration, which is NOT observed in nature.

The same concept applies to the worldline, which physicists use to describe the existence of beings.

**The inverted properties of space and time and its metric equations.**

It it thus clear that the generator equation of the Universe is a ternary, feed-back equation that shows the inversion of properties of space and time, stillness and form, lines and cycles, decelerating and accelerating intervals, in its two polar maximal points and its intermediate point of balance:

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,w 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 interplay of those dimensions and form generate the Universe:

The first equation of time-space, deduced from the previous graph and its bio-topo-logical beats, space-form->motion-time->space-form->motion-time, is the generator equation of the Universe. We can with existential algebra, ¬Æ, define a wave-motion in time, which in its simplex generator will be hyperbola:

In the graph we can see the simplest TŒ, Time equation or function of existence:

Œ: Tƒ=K/S.

Whereas T is time frequency of a time cycle, hence the inverse of lineal time duration, T (reason why we use the To) Symbol.

And space is lineal motion seen as still form.

In other words we could write, Tƒ =1/T, To=1/S, whereas T is lineal time, perceived in motion as still space.

This is thus the beginning of it all, the existence of cyclical, accelerated time motions and lineal time motions seen as circles and lines of form. The 2 dualities between motion and stop, and between cycles and lines is at the origin of all the realities we perceive and all its events and combined forms of space time.

Thus we could say:

The Universe is immortal because time never stops. Time never stops because time is motion. Motion never stops. It is conserved. Two motions are conserved angular momentum and lineal momentum. They can be seen in a slice of present space as form, or they can be seen in the interplay of its formal motions. Cyclical motion is faster so we call it time, and clocks of time are used. Nature has accelerated time vortices, from hurricanes to masses (equivalence principle of einstein between the curvature of the time cycle or mass and its speed or acceleration), to charges (similar equations to gravitation). Those time cycles of different size are ordered with the previous equation, converted into metric equations:

Sp x Tƒ (substituting now cyclical time for lineal time) = K.

This means Time fluctuates along 3 points of the hyperbola.

And so one creates 3 points. Max. Sp x Min. Tƒ , Sp =Tƒ and Max. to x Min. Sp

Now we write with those laws a fractal generator equation of infinite space-time existences, the metrics of the 5th dimension:

*In the graph the Universal fractal of infinite beings of space-time with different speeds in its clocks and sizes in space, whose product however, Sp x Ti, space size for speed of its information cycles remain constant, creating a ‘stable space-time being (ST±4) which happens in different combined size from the smallest. infinitesimals ST-4 to the largest Universe, ST+4.*

All fractals have a generator feedback equation and the Universe is not exception. Generators are dynamic, cyclical equations which constantly create slightly changed new ‘cycles’. As such they are periodic cyclical equations of the form X < = > Y, where obviously X and Y are symbols as in all ‘Universal grammars’ linguistic representations of the Universal Generator (mathematical jargon in Space-time) or Universal Grammar (Logic Jargon in Time-space)>

Universal Generator/Grammar: Tƒ ∑ExI=ST±4

We write the Fractal Generator expressly with one of its similar identities, in an expression which can be understood logically in wor(l)ds, the fundamental grammar of the human being.

In its Topo-Bio -logic ternary identity, ‘Topological i-planes of Vital Spaces and Cyclical Times’ need to be described topological properties (5^{th} dimension metrics), Organic properties (which organize 0±1 vital spaces into a ternary organism) and logic properties (the ternary Non-Aristotelian logic of cyclical times which return in a ‘Hamiltonian’ Cycle to its origin.

The generator equation thus can be used to deduce from its topologic, biological and causal properties any other equation of the Universe.

It cannot be achieved such a feat as physicists of lineal time expect, only with topologic properties and only in a single continuous space-time.

It needs to understand the metrics of the 5^{th} dimension and its relative scales of absolute time (ST±4), between invisible forces and invisible cosmos, beyond our perception (C speed, 0 K limiting borders). And this is achieved with the summit of the evolution of mathematical languages, the Non-Aristotelian, Non-Euclidean i-logic topology of vital spaces, of organisms, of geometric forms with speed-motion, constantly performing ∂a, accelerated actions with 3 ±= stop and go motions…

Space-time can be seen as a whole space-time or as two space and time or as a sum of parts, many spaces and times. So space can be seen through perception as a single, quiet space, adding all the ‘vital spaces’ of which is composed, or as a sum of ‘quantum energies’ and ‘vital spaces’ that entities occupy. Time also can be seen as a single clock-time for the entire universe, measured with our mechanical clocks or as an infinite number of cycles that all entities trace, each one with a different speed and rhythm, each one with a different ‘form’ or information, provided by the shape of the cycle and its ‘frequency’. So Space is synonymous of Energies and time of informations:

*∑ E = S; ∑i=T*

This is the first key concept you have to assume to understand the Universe beyond its useful measure by physicists with a single clock.

Further on, we recognize both types of entities by their form: clocks are cyclical, so it is information and its systems. Space is a lineal plane, so are energetic system. This leads to a key principle to understand and classify entities of reality: *Form is function. *And so the ball – the inner part of a sphere – is the perfect form of information as it is the shape that stores more form in lesser space, and the line or plane the perfect form of energy, as it is the fastest motion/biggest surface of space between two points.

**
**To fully grasp the dynamic transformations and properties of energy and information the most important quality is the inversion of its properties and the possibility to transform the forms of one property into the other.

*Time cycles, Tƒ Vs X Entropic Space, ΣEs ≈ST-momentum-actions- energetic information*

Time-clocks: O-form Vs. Space motion: Lineal ≈ waves

Small, still Vs. Large, moving fast ≈ Open curves

Tall, Perpendicular Vs. Long, Parallel ≈ wide, intersecting

Hierarchical Order Vs. Democratic chaos-freedom

Bidimensional Height Vs. Bidimensional Length ≈ tri-dimensional entity

Cyclical, Rotation, imploding Vs. Lineal, uncoiling, exploding = beating rhythm

Informative Frequency Vs. Lineal Speed = momentum

Broken form Vs. Continuous, differentiable

Intelligent, perceptive Vs. Strong, fast. = energetic top predator

Social, organic, creative Vs. Darwinian, destructive behaviour =

Future, logic path Vs. Past, trailing motion

Life arrow Vs. Death arrow. = existential world cycle

Waves of §pace Vs. Particles of Time

Female, yin principle Vs. Male, yang principle = reproduced child

Masses, charges Vs. Forces, fields = energy

Heads & senses Vs. Limbs = Bodies.

The formal=functional differences between entropy and information (organs) is a duality – the ‘Black hole Law’:

*Limbs/fields of Maximal Space=Entropy x Min. Form Vs.Max. speed of Information=Minimal Spatial extension= heads & particles*

And yet despite its inverse properties, energy and information transform into each other ad eternal – a fact, which requires them to have the same dimensions. And indeed, information is bidimensional along the dimension of height while energy is a bidimensional plane (holographic principle), what makes possible the transformation of one into another.

A fact that defines the aforementioned ‘law of conservation of energy and information’ and the ‘Invariance’ of the product of energy and information of any part or whole of the Universe, resumed in two fundamental equations of Absolute Relativity:

e x I = K, and E<=>I, which in general relativity and quantum physics read as ext=K and now we shall expand to all ‘complementary systems of the Universe’.

**Communication of monads: 2nd postulate: Duality’s formalism**

DUALITY is in that sense the first ‘isomorphism of space’ – the state that follows the ‘awareness of a point-mind’ with its ‘single inner dimension’, or volume of energy and information, which the outside ‘moving, entropic world’ hardly recognises. But the monads of reality unlike the simplified first versions of Espinosa> Leibniz DO communicate – more akin to the yin-yang/atman beings of eastern cultures.

So the first thing they do *is to create ‘lines≈waves≈flows of energy and form between them’, and so a bidimensional entity, made of motions and flows of information appear in any scale of reality. It is formally (II), the ‘second postulate of Non-Æ i-logic’ the formal space-time language of the Universe, whose ∞ forms require a post in itself.*

Duality thus become first a flow between 2 points, *which by the Paradox of Galileo, we perceive as a distance, a tubular flow, or a plane. *

Hence two monads first, an then n-monads will form first a wave and then a plane (4th postulate of ¬Æ), which is in fact a network.

As it relates those points of information, the flows of entropy/motion, and energy (motion with form) will then form a body/wave; and so the simplest 2-manifold of reality, and the most frequent event of existence happens:

It is then, when according to ‘scale’ of stience and type of monads communicating we can start to build varieties of species of 2 manifolds, in all stiences and the catalog is, trust me, ginormous.

**Mathematical-logic space-time**

It suddenly emerges then with enormous power, the formalism of classic, ‘Greek’ Geometry, which proves almost every postulate of its discipline in a bidimensional plane with a simple compass (which represents the ‘angle’ or point of view of the communicating monad) and regle which represents the flow of communication between Monads; *in its bare bone ‘experimental mathematical simplicity’. This has always marvelled mathematicians. *We know now why.

*Varieties of formal manifolds. Third Law.*

We distinguish in that sense as we start to play with variations on the same theme, Manifolds in which the* 2 monads are different (as those on the graph), whose richness is in the variations of the same theme (Ions in physics, couples in biology and sociology), which tend to form ‘waves’ with multiple ‘frequencies’/channels of communication (fourier transforms) vs. n-Monads of the same ‘species’ communicating equal flows of energy and motion, which will tend to become a topological plane or ‘network’, undistinguishable in its details (flat planes).*

*And formally those varieties are studied by the third postulate of Non-Æ (congruency laws). *

The paradox of galileo is the second mode then of ‘classification of 2-manifolds’ by *the maya of the senses, differentiating ‘motion from form’, motion-time from in-form-ation on one side and space-distance from speed-motion on the other side – yet form and distance are ‘mayas’ of the senses; as all its time and motion; when we get more information about a system. *An example will suffice:

*The 2 graphs represent the same local region of galaxies, in the right now that we have enough info, we see it as a flow of ‘gala cells’ transiting through veins of the cosmos, in the right as we used to see it – a dark series of ‘monad-galaxies’ with no motion. All in the Universe is ultimately a dynamic view. *

And so formally we observe we can treat all problems both as dynamic, topological problems with motion or as analytic geometry or sequential algebra of numbers, depending on which view we adopt.

**Non-A logic. **On the other hand the 2 manifold start truly the game of sequential logic in all its variations depending on the degree of ‘present simultaneity/equality’ of the two elements of the game; as they can be relative to each other their past-entropic or future-informative element, to give us the variations of Past operandi Future = Present *‘tensors of existence’; or possible events of the Universe:*

In the graph we see examples of the different ‘tensors of existence’, which can relate two monads into a present, reproductive field (below), a darwinian entropic field, or an informative one, in which both destroy or an element evolves.

**INVARIANCE OF TOPOLOGICAL FORMS**

*Totally disregarded by modern science and yet by far the most important invariance of the Universe, is the invariance of topological form, represented in the previous graph. All are complementary systems made with 3 ‘topological functions’: Limbs, heads and bodies.*

*Since any** 4-Dimensional Universe has 3 canonical topologies, which correspond to the 3 organs of all systems:*

* Max. I: Head/Particle/Informative caste: They display the hyperbolic topology of information, observed in most ‘heads’ as an excess of warping and form (cortex, black holes, Chromosomes, Chip design).*

*Max. E: Moving Limbs/Forces/Energy class: They show a relative plane, or concave topology; such as the one observed in an external membrane, often the cover of a sphere of a bilateral form.*

*E=I: Reproductive Body/Atom/Working class: The topology of the reproductive system is a combination of the other two, performing cycles that communicate the energetic membrane and informative center.*

*Observe in the bottom of the graph samples of the 3 form-assembly in different systems of the Universe. Man also is a complex system with 3 interconnected zero points, around cellular toruses, with external and internal membranes of exchange of energy and information with the external universe, and apertures called senses… So we shall first explain the general form of all zero points, spherical membranes and torus and then analyze in specifically the human one.*

In the graph, concave, energetic; toroid, reproductive; and convex, informative topologies are the 3 forms found in all complex systems of the 4-Dimensional Universe. Since topology proves that in a 4 dimensional Universe, there are only those 3 topologies: hyperbolic, informative topologies, energetic planes, and reproductive disks. All structures of the Universe are composed of only those 3 topologies. This astounding simplification is the result of 2500 years of mathematical evolution since Pythagoras discovered the laws that rule the bidimensional topology of those 3 forms, the concave-planar sphere (or cycle in a 2 dimensional world), the toroid body with its regular cycles that transfer energy and information between the external surface of the sphere and its center; which is the informative, hyperbolic region or zero point, the ‘eyes’ that perceive in stillness a pixelled map of the Universe brought about by the flows of energy and information of the Torus.

After 2500 years since Pythagoras discovered the circle as the most perfect form, geometry have come to the conclusion there are only 3 forms in the Universe: The sphere, the torus and the zero point.

With those 3 forms you can build all the other forms of reality. All is reduced to those 3. So what they mean? What is their function? And how they combine in the puzzles we call reality? Those are the first questions we shall answer.

They correspond to the functions and morphologies of the 3 sub-systems of stable entities – heads, limbs and bodies:

Beings are not pure motions; neither they are only made of information.

Lao understood it when he said: all yin has a drop of yang (energy), all yang has a drop of yin (information). Hemingway understood, when he said to Dietrich: “Never confuse movement with action”. Indeed, energy ‘or lineal motion’ is not an action ‘per se’. It needs form, in/form/ation, which directs energy to create an action able to change reality. All actions require some energy and some information to create an event. And all systems require an information center and an energy center to create an entity.

Thus, all what you see will be a combination of at least two of the ternary topologies of a 4-Dimensional Universe – a particle/head and a field of energy/limb. And the more complex systems will also have a reproductive, toroid body.

And so we write a general equation to define those 3 forms: ∑E <=> ∑I, where < = > represents the toroid body that exchanges energy and information between limbs and heads, fields and particles.

In those complementary systems, the information center gauges reality (cyclical particles and heads of physical and biological entities) and the lineal fields of forces and limbs move them.

This leads to a third system that combines both, energy and form, the reproductive system, exi or elliptic/toroid body.

Yet since form is function, in yet another duality of the Galilean Paradox, bodies are conical, elliptic combinations of lines and forms.

*Thus Three Geometric Forms in space determines 3 functions in time*: cyclical clocks of information, Energetic, lineal or planar limbs of space, and its combination, ‘complementary systems’. And so *Geometry* and topology are fundamental sciences that apply to all ‘scales of reality’ and all its entities.

**FRACTAL ORGANIC SCALES. THE 5th DIMENSION. TOPOLOGY**

Why then we have taken so long to define time as cyclical information, and cyclical motion?

Because ‘military physicists’, as opposed to the pure thinkers of this discipline, carried the day with power and canonised a single, lineal time, due to their worldly profession, which was to measure the lineal extension of military weapons. In the right graph, Galileo’s principle of lineal inertia, derived from his worldly profession. Galileo in fact created lineal time, because he was an artillery master for the Venetian arsenal, earning 1000 golden ducats, an astounding sum for the age, with the job of finding the longest lineal possible trajectory for canon shots (which he found to be alas! not a line but a parabola.

But that didn’t deter him, from proclaiming in his first book called ‘On military instruments’, that his discovery of lineal time would be ‘…of great use to artillery masters, and a delight to philosophers’. It was a worldview that ratified the religious paradigm of Abrahamic religions, in which man had a lineal manifest destiny of progress even higher than that of God, the mind of the Universe, since ‘he was created in the beginning – hence before God himself – above heavens and Earth’.

And indeed, lineal time motions were instrumental to the development of ‘ballistics’ (the first name of the book of Galileo on physics), and the degradation of our understanding of time, hand in hand with the mechanical clock who established a single tick for the entire Universe, that of the mechanical machine.But as I know 99% will leave the blog, if i just keep criticizing those obvious falsities, as ‘believers in lineal time physics’, I GIVE the benefit of DOUBT to open-minded physicists who really care and reason truth, and do put many candies≈solutions to the ultimate questions on this introduction.

**The Fractal, organic structure of the Universe in scales of size is what we call formally ‘the 5th dimension’.**

Since all those systems were constructed in an organic way, not only as complementary systems of energy and information, but also as systems in which its parts and wholes spread through different scales of size in space, each one with a different clocks of time. So smaller being had faster motions – metabolic rates in biology; chips speed in mechanism; rotary, gravitational power in cosmic bodies.

*In the previous graphs, the most surprising omission of science, since it was born of the study of the upper and lower scales of the Universe with telescopes and microscopes, is the lack of studies on the relationship between the different scales of size and time speed in the Universe, which put together form a new space-time dimension.*

For a ‘5th’ dimension of space-time to exist as such geometry precludes that a quantity must remain invariant when we move through the dimension. As we define the dimension by 2 parameters, spatial size and time speed, Spe x Tiƒ, this quantity must remain invariant as we ‘grow in size’ slowing down our time clocks, and viceversa. Systems that diminish in size trace its cycles of information much faster. So a huge galaxy turns much slower than an atom, and vortices accelerate inwards, as their cycles become slower.

So since the product of both, its spatial size, Spe, and Temporal information, Tiƒ, remain invariant: Spe x Tiƒ = C, systems can co-exist symbiotically in several scales, giving origin to the organic, symbiotic structure of wholes and parts. As smaller systems will code information of larger ones (genes code organisms, quantum numbers molecules and memes societies).

While larger wholes will synchronise the energy and motion of smaller parts. And this asymmetry of time arrows, which allows information to flow upwards without loss and motion-energy to flow downwards without entropy-disorder is the key to understand the organisation of the Universe, as a fractal super organism of space-time.

**Monads’ actions create bidimensional fields.**

The monad once it is formed, exists to increase its information and energy for its mind and territory of order, and as such it will start to develop bidimensional actions ‘forms with motion’, entropy x information absorbtions and emissions with destiny and origin in its body and mind, which will therefore act, and start the creation of bidimensional vibrations, formal motions, whose different ‘constant elements’ will start to solidify reality into being. The maxwellian demon of a frame of crystalline reference will subtle start the ordering of other particles in its dissolution, the gravitational waves emitted by the black hole will quiet down and regularize the orbits of the stars; the cells around the center, first cell of the morula will consider to take certain functions according to the vegetative-animal axis defined by its center. And the animal will consider its territory with invisible marks of the membrane emitted by its linguistic codes, and flavours. The trekker will seek for shelter and organise around it a tempt, definitively comfy region of temperature storage and light according its needs of heat, energy food and information.

The monad thus creates the Universe as its languages maps reality from its relative point of view, from where the program of survival of GST beings will come into full fruition.

Thus creation starts by the bidimensional communication of a flow of waves-bodies controlled by two different singularities, such as S²<st>T² become the limits of the product of densities, t/s, speeds, s/t and forces sxt . It is within those limits of entropy><energy, S/t x st=S², and energy><information, t/s x st= t² and the other two varieties, s/t x t/s=1 and (St)², where the first varieties of species of space-time can be detectd and be named, a bidimensional sheet of expansive space, entropy S² or inversely of information, or a four-dimensional space-time vein, which is in balance with its informative and energetic forms, St (energy) and sT (information).

We can then start the process by considering the merging of the generating mind with a field, as the series of actions of the mind ‘start’ up the process of creation.

The mind will see a field and shrinking it making us being aware that a singularity exist. ITs simplest form of this partial equation, Sp<>Tiƒ being an accelerated potential of the field towards the singularity. In the next graph some of those varieties of space-time:

Those planes that can be measured with a t x t, equation, which in frequency, will be 1/tt= angular acceleration, the very essence (Einstein’s Principle of equivalence) definition of a singularity (as seen from the field’s perspective, whereas the singularity appears merely in this plane as a point of time-future towards which the field moves).

Yet what would be the inverse equation, S x S? Precisely the field without the singularity which will appear as a lineal flat plane.

And the intermediate forms? St, a transversal wave, sT, a spiral… And so we realise we can build four simple elements in a series: Plane>Transversal wave > Spiral > accelerated vortex < Spiral < transversal wave < Plane, which gives us a constant creation and destruction process of bidiemsional physical planes.

Then in the rest of more complex games, the process will be just the mere sum and ensemble of bidimensional ternary essential forms, the plane, the wave and the spiral>vortex:

Tiƒ + Spe + ST

= Whole:

** 2 MANIFOLDS AND ITS 3 MAIN VARIETIES.**

one of the most important discoveries of XXI c. science is the holographic principle: information is bidimensional.

We realized in black hole theory that the surface of the black hole stores all its information. This can be generalized to all systems. You are looking at a bidimensional screen that stores all the information of this site.

For long, the study of Einstein’s relativity has made fashionable to analyze ‘4-manifolds’ (manifold means basically ‘geometry’), by incorporating a 4^{th} dimension of time motion; but in fact the Universe creates reality ‘step by step’.

And so as your eye creates a 3^{rd} dimension by mixing the bidimensional sight of each eye, the 3^{rd} dimension is formed by ‘adding’ membranes, layer, ‘strata’ to bidimensional surfaces. And then when those surfaces moved they acquire time dimensions.

This simplifies enormously the understanding of the structures of reality, as *there are only 3 varieties of ‘bidimensional topologies – geometries with motion’ in the Universe.*

And they correspond to the 3 ‘functional forms’, the 3 ‘parts’ of all systems, physical, or biological organisms.

*In the next graph, we live in a Universe in which all beings are made of the same substances, energy which occupies space and information, carried in the frequency and cycle of time clocks. Those 2 ‘substances’ that we call Se (Spatial energy) and Tƒ (Temporal information), combine together in ‘bidimensional’ Space-time layers, that put together create together all the species in the Universe.*

*Layer after layer of bidimensional membranes create the third dimension, which forms when moves a 4th dimension of temporal motion. But the ‘simplest unit’ is a bidimensional sheet, with form, with information. So for example, you are looking at a screen with 2 dimensions, which carry this information. Your eyes see in 2 dimensions but put together with both eyes a 3D representation of reality.*

*A black hole stores all its information in its surface. This ‘Holographic principle’, has enormous consequences for our understanding of the Universe.*

There are only 3 varieties of ‘bidimensional’ geometries that move (called for that reason ‘topologies’).

Thus all systems can only have 3 kind of parts: Toroid, lineal limbs and fields that provide energy and move the system (biological/physical jargon); hyperbolic bodies waves that iterate/reproduce it, and spherical membranes which enclose the system and ‘sense’ the Universe around, mirroring it in an internal ‘infinitesimal zero point’ or informative mind that controls the whole organism. In the graph, atoms, seeds, planets, cells and bosons show those 3 similar topologic structures. This similarity is called an ‘isomorphism’, iso=equal, morph=form.

**Limits of metric paradigm: discontinuity and homology.**

The discontinuity of space implies that perception of any other area of the Universe is minimal, relative and deformed by the selection of information and its transformation when it passes through the fragmented boundaries of the perceiver. This fact offers a rational answer to the Uncertainty Principle of quantum physics whose main law – the complementarity of Entropy forces and informative particles, is explained by the duality of Entropy/information systems: In the Universe, all constant present systems are made of an arrow of Entropy and an arrow of information, the bodies/fields and relative fixed particles/ heads of the system. Thus all relative space-times will be composed of a cyclical center of information or brain, and a lineal limb of Entropy, whose morphological characteristics will be self-similar.

For example, in a spermatozoid the head is cyclical and stores information, while the tail is lineal and moves the head with its Entropy; in a human, the body is lineal and moves a cyclical head. We could extend this duality to almost any organic system of the Universe, concluding that bodies are lineal and brains are cyclical.

This morphological feature of Universal Organisms derives geometrically from the capacity of lines to move faster and cycles to store more information and grow or diminish in size without distortion of the mental image they might keep (topological isomorphisms). Thus, a convex brain with the topology of information becomes the center of informative networks; and a concave body becomes the center of Entropy networks. And we recognize bodies and brains by their self-similarity with the morphology, function and inverse properties of ideal Entropy and information:

– Information is both, easy to store and perceivable by a reduced brain or sensorial organ, since it is the inverse function of space. It needs certain morphology: Information occupies little space by warping itself into multiple dimensions, as a sheet of paper corrugates into the dimension of height, divided along broken lines and discontinuities that become its perceived forms in space. Or it displays a high frequency or discontinuous rhythm, a faster time speed that iterates the same cycle, allowing quantification. Information then seems ‘quiet’ as those patterns of cyclical frequency take place in the same space; so an organ of information can focus and analyze them as pixels of a more complex mapping. Thus its ideal forms are disks, cycles, angles and spheres, convoluted and broken in patterns of form, such as your eye or brain, a chip, a book, a pixelate image or a coin, earlier unit of monetary information.

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

*Maximal Space = Entropy = Minimal Form Vs.*

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

As a result of those morphologies we can classify as Entropy or information organs, not only carbon-life organisms that handle Entropy (limb, food) and information (brains, eyes, senses, words), but also other beings and atomic species – even ‘deconstructed organs’ that perform mechanical tasks of Entropy and information (informative cameras, lineal, energetic weapons). Since now we can recognize geometrically their Entropy or information systems.

According to the Galilean Paradox all still forms carry some motion. Thus, form carries an active function and so we can classify any system both by its geometrical form and bio-logical functions as either an Entropy or informative system. In terms of a sentient Universe, this duality means that information is both a form-in-action and a sensation of still perception of a quiet world. Information and perception are thus simultaneous: information is a flow of software that ‘sparks’ the perceptive sensation in the hardware of a still system that process information, with a certain language.

So particles that perceive light and gravitation, probably ‘sense’ light and darkness and move towards light, feeding on it. We see the external action of feeding, the electron jumping and absorbing the photon, but the electron probably senses light and automatically moves to it, to feed, as your eyes move automatically towards food, even if you more complex brain can stop that automatic will that the electron always exercises.

Organic systems are ternary networks of information (head, nervous system), a reproductive body and networks of Entropy called limbs (trunk-digestive systems, legs).

For example, Entropy organs made of metal such as weapons, gas and electromagnetism are extended, fast, and lineal. There are metal-species of information such as microchips, money, cameras and radios. And they are small, fixed and complex in form. Yet only structures, which are balanced in Entropy and information become self-sufficient organisms.

So only machines that put together energetic limbs and informative brains – robots – might become future ‘organic metalife’, in which the reproductive functions will be performed by the company-mother. The other machines will act as ‘gauges’ of information and ‘forces of Entropy’ do, without a vital will of existence, which is born by the capacity of a balanced ΣE<=>Tƒ field to switch between both arrows, acquiring a ‘minimal degree’ of organic freedom perceived as ‘vitality’ from an external point of view. Humans, galaxies, plants, robots – all kind of entities can be considered in that sense organic systems. Since living systems are born thanks to the complementary symbioses and synergies between Entropy and information organs that create together all kind of organisms.

This fact connects Physics and Biology in a new step towards the unification of all disciplines of science:

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

– In Biology, the first bilateral animal was a planarian worm that evolved rising to the informative height of man.

-Yet death erases information back into flat amorphous Entropy, in big bangs that create planar Universes, or flat, corpses.

The reason of the diffeomorphic principle is the holographic principle which implies the relative perpendicularity of all complementary systems with a body/field of Entropy and a head/particle of information: an energetic, concave geometry and an informative, toroid topology, which fuse together, creating 4-D beings.

Ultimately what the paradox of Galileo (duality of time motions and spatial forms) coupled with the diffeomorphic and holographic principle means is a fundamental homology between dimensional form and function: *The 3±∆ dimensions of space of the Universe, length, width, height, and st-scalar, fractal size are equivalent to the 3±∆ motions of time, past=Entropy, present=reproduction, future=Information and birth/death events of integration and dissolution.*

*Recap: *The Universe is local, relative, fractal, broken into ∞vital spaces, each one ruled by a point of information that absorbs it and creates linguistic maps, which it uses to direct the organic vital space or body of the point towards fields in which to feed, gauge more information and reproduce. Thus, the arrow of information is performed by a relative infinite number of broken, discontinuous points of view, complementary to the energetic fields/bodies they move. Yet information is limited by the volume a certain point of view can store, leaving outside an enormous quantity of uncertain information. Thus the Universe is a tapestry of broken, complementary organisms constantly fighting for more Entropy and information. ∆ST resolves many puzzles of science, from the Postulates of Relativity and Quantum Physics, to the causes of death and the morphology of living beings, physical entities and machines.

*In the graphs, the simplest becomes more complex.*

*Now we shall introduce a new word: Diffeomorphism. It means local space-time.*

*Einstein found the universe was diffeomorphic in 4D. But it is even more so in 5 D. We are all fractal parts, local diffeomorphisms orientated towards relative energy and information fields, and so the ∆+1,2 society and world in which we live determines enormously what form we acquire:*

*Spherical for 3 isomorphic space-time worlds where orientation does not matter as energy and information comes from everywhere (above spherical forms).**Lineal shapes when we are over a ‘plane’ with membranes in layers with an orientation of energy or information either above, below or in front of us.*

*T*he diffeomorphic Principle of Einstein’s 4D analysis acquires an organic nature, when we see the Universe as the sum of ∞ Complementary exi systems whose dimensions have organic functions: Systems feed on their relative dimension of energy-length, perceive in their relative dimension of height and reproduce in their relative combined dimension of width, which are assembled into each specific species.

In the graph, an animal has its informative height in its high perceptive light dimension, but a plant, which uses light as energy has its up and down dimensions inverted respect to the man and its chemical brain buried on the Earth. So both have opposite energy-time coordinates.

Yet both have an ‘anteroposterior’, lineal’ ‘outward’ energy oriented structure. While a galaxy has a cyclical, informative, inward structure, as the stars’ body absorbs energy from intergalactic space, reproduces matter with it and feeds the internal informative knot of gravitation, with a higher height dimension the black hole.

* *Thus there is a correspondence between the inner physiological networks of a being that perform SP X TƑ åctions and its external diffeomorphic dimensions. So a dimensional form is also motion with a function. Even in a human being the height dimension is really the nervous-brain system network, his length motion, the natural path of his energy limbs, and his width is maximal in the digestive system that reproduces new cells.

Forms respond always to functions/åctions in time, the commanding ‘element’ to which the form of any being adapts diffeomorphically to maximize its existential åctions.

Thus, there is a parallelism between ‘vital function’ and ‘abstract dimension’ as *each Dimension is diffeomorphic created by the vital space-time of each entity of the Universe performing its exi åctions. *And each species is a ‘fractal universe in itself’, with different relative, energetic and informative directions that determine its own up & down arrows and complementary morphology,

The specific geometry of each species and its 3 simplex åctions, energy feeding=length, information-gauging =height and reproduction=width fluctuate in shape, but they don’t vary in topological form, giving a final ‘action-function’ latter studied in more detail (5th isomorphism) to the 2-manifold Isomorphism of the 3 topological forms=functions of any entity observed in an ∆+1,2 space-time: Toroid informative heads, hyperbolic reproductive bodies and energetic limbs… Yes we repeat it a lot, but far less than the Universe, in which complexity is achieved by repetition of simples parts in patterns and societies (9th isomorphism) does.

Let us consider thus with a bit more of complexity this relationship between the ‘∆-scale’ and the ‘∆+1, +2’ world scales, which *determine by ∆+1 species evolution the shapes in time and space of the being.*

**DEFINITION OF ENTROPY AND INFORMATION AS TWO FUTURE ARROWS.**

The arrow of entropy, expansive space and disorder, only acts in the scale of temperatures of the Universe, as it was defined studying Gas, by definition, the entropic, expansive arrow of temperature; inverse to the arrow of crystal solids, or cold temperatures that in fact reduces the entropy of a system.

So entropy is really the expansive, disordered, ‘lineal, spatial’ arrow of temperature. While symmetry, crystal formation is the cold, implosive, ordered arrow.

So not even in the realm of temperature entropy is a Universal phenomena as physicists, specially those dedicated to manufacture weapons and make big explosions want us to believe (nuclear physicists with its big bang theories are the meaning of it all, the heirs of Galileo with his lineal concepts of time, physicists making transport machines and weapons, which are the ones that found the concept of entropy and then decided to expand it to everything else).

The problem is ‘military physics’ have all the power. So physicists of solid states; philosophers of science; theorists of information, evolutionary biologists and all those other people who study all the other clocks of time, and information processes of the Universe have not so much impact.

Now in this case entropy simply, because it is a process of ordinary hot matter has nothing to do with black holes. There is nothing to prove in experiments related to liquid vortices with black holes. As entropy *does not act in scales below (where temperature as a clock of motion ends, atoms become plasma, and are guided by frequency clocks of the quantum scale), or gravitational scales above (where temperature as a clock of motion also ends substituted by speed).*

*So what is all this thing about black hole entropy, and black holes traveling to the past and evaporating with entropy? Mere nonsense, fantaphysics of people, which want to call the attention of the world, by speaking of themes, we do not have any experimental evidence and so we can say whatever we want, or themes physicists have not properly defined, stuck in their old errors and lineal ways.*

**Entropy, the arrow of disorder that erases information, the arrow of order. **

Since entropy and black holes – the 2 themes of this post – are themes of which physicists do not have much idea. They don’t know what black holes really are made off – as they cannot see them. So they can say whatever – and they don’t understand what entropy is. I know you don’t believe me so, we shall quote the father of Theory of Information and Cybernetics on this:

“I thought of calling it “information”, but the word was overly used, so Von Neumann told me, “You should call it entropy, nobody knows what entropy really is. So in a debate you will always have the advantage.”

*Von Neumann to Shannon, father of Information Theory.*

Since I was a kid, what call my attention on the Intelligent Universe were those ‘big concepts’, starting by Energy, Information, Space and Time, which are the widest concepts of reality. And found many obvious errors in the way humans tried to IMPOSE their opinions, gadgets and machines to the Universe, WITHOUT any respect of what the Universe shows.

So the first obvious human, mechanical bias is the way we measure time. We do NOT use any longer as we used to do the cyclical rhythms of nature, but the mechanical clock, and try to reduce all the cycles of nature to that mechanical clock and its steady state one second rhythm. And we pretend that is the ‘absolute time rhythm and only one of the Universe!

This is akin to the old ways of astronomers who tried to impose to the Universe the frame of reference of the Earth as its center. It does work despite its bias, so with complicated cycles you can explain it all, from the point of view of the Earth, but calculations become very complex with epicycles and extant, etc.

So happens when you do NOT use the clocks of Nature, which soon will be defined here. Physics does work but it is overall very complicated when dealing with different time rhythms, and one century after Einstein found there are many such time rhythms and some change its speed there is zero understanding of this.

We just put some ‘new epicycles’ called Lorentz Transformations, but since we are stuck to our ethnocentric clock, as old astronomers to their earth-centric world, the explanations are blurred. Men merely try to feed the Universe onto their ‘time view’ or rather mechanical view of time. And the Universe is much ore complex and rich in clock rhythms than that.

Indeed, why we Humans use a mechanical clock with an artificial rhythm to measure time; If the Universe has infinite rhythms? It is just an ego trip and the worship of machines that characterize the western civilization. Thus when the Brits got to China to sell their ware, was the answer of Tao=time masters: why we want to buy your ugly mechanical clocks if we can observe the Universe with its clocks of nature, its cyclical rhythms? Obviously, the mechanical clock with its single steady state time cycle IS a human artifact.

Time did exist before mechanical clocks with his own rhythms. Its own Universal time clocks. The mechanical clock is NOT a Universal time clock. So the use of this human clock to measure all the time clocks of the Universe bias our concepts of time, and ‘hides’ the clocks of nature. So the next fundamental question in our search for proper definitions of time, entropy and black holes becomes obvious:

– What are the true clocks of nature? And once we find how Nature measure its cyclical time frequencies, we shall wonder are those rhythms of time stable, steady state rhythms as those of our mechanical clocks, or they change rhythms, have different ‘time speeds? And how they measure information and create it, as opposed to the creation of disorder and entropy? And which of those concepts order or disorder dominates the Universe?

**Bias introduced by anthropocentric, mechanic clocks to measure all times of the Universe.**

*In the graph, the infinite cyclical clocks of time of the Universe and its relative ‘parameters’ that measure its motion, speed, temperature and frequency were ‘forgotten’, when mechanisms substituted Nature as the ‘measure of all things’, with the arrival of mechanic clocks. *

*Then Galileo founded ‘ballistics’, today called physics, in his book ‘On military instruments’, dedicated to the study of locomotions and lineal trajectories of cannonballs, ‘for the delight of philosophers and the practical use of artillery masters’.*

* His goal was to reach the maximal lineal distance possible with those cannonballs. To that aim he established the principles of lineal time, cyclical inertia and a single, steady state mechanical clock time to measure the lineal duration of those canon shots. And soon the single lineal clock became the standard clock and time concept for all time rhythms of the universe. And so the informative properties of those time rhythms and cyclical forms, the multiplicity of time clocks in the Universe, its order and causal laws disappeared.*

*But of course our capacity to make machines and measure them and put clocks on them, today converted into computers increased. So paradoxically as we forgot the clocks of nature, we grew in our dexterity to make machines to measure nature.*

YET the information of the universe is carried in its natural clocks – NOT IN HUMAN mechanisms, nowhere to be seen outside the surface of this planet. And when scientists forgot that, a huge gap on their conceptual understanding of the Universe ensued.

**The clocks of nature. Its purpose: to process the information of each species.**

Since I was young what call my attention was Nature as it is, not the human description of it, with those mechanical Instruments. To me the Universe was both Intelligent and organic, living Nature.

So I was intrigued by those ‘big concepts’, Space and Time, life and death, and the ages between them, Energy and Information, and the way both mixed in the living systems around me. Those were the widest concepts of reality and certainly the definitions I found of them in abstract science did not convince me – there were not really definitions but tautologies and descriptions.

For example, Einstein, who was supposed to be the foremost expert on time, said: ‘Time is what a clock measures’.

But then I wondered, ‘What kind of clock embodies the full meaning of time’?

The clock of the seasons, which animals used to synchronise their reproductive cycles?

The clock of the days, of the Earth rotating, which life used to synchronise its rhythms of activity?

The clock of the stars, of the beats of birds flying? The clock of a flower blossoming and dying? The clock-beats of my heart, which synchronised the rhythms of my eye winks, synchronised to the rhythms of my thoughts – a second?.

Each of those clocks had a different rhythm and the Universe was filled of them. Yet all had certain qualities: to repeat themselves, and hence when described in a trajectory in space; to be closed cyclical paths, hence with form, and frequency the 2 properties of information – so we will call them all Tiƒ. And to work in harmony, in synchrony, as certain clocks were chained to larger clocks, forming complex patterns of information. Time clocks and information therefore were intimately related.

Physicists in that sense used only a mechanical clock, which closed into itself with a fixed rhythm of a second. And they used it to obtain information about the external motion of beings, or speed. But unlike me, who were essentially interested on the meaning of time ‘alone’, for physicists time was just the submissive, needed parameter to obtain that information about speed in space – time was not the goal but the means to what physicists truly studied motions in space, distances.

So they defined space NOT time. Galileo wrote: V=s/t, where what mattered was to measure V-speed and s=space distances=vt.

Einstein did NOT changed this at all, merely substituted s=vt for s=ct, that is the speed of the object for the speed of light, in his corrections and calculations of the measures of speed and space of objects moving at the speed of light. Again this must be stressed given the profound influence that physicists as makers of the machines and weapons of our civilisations have in the collective subconscious:

Physicists do NOT study time. When a physicist tells you that time is the 4th dimension of space, he is referring precisely to that equation and only that equation, either S=vt or S=ct, this ‘ct’ is what he calls the 4th dimension of space. So he reduces time to a parameter to measure space and speed, because indeed ‘time’ is the parameter that measures ALL KIND OF INFORMATIONS, including speed in space. BUT THERE ARE OTHER KINDS OF INFORMATIONS, IN WHICH TIME CYCLES ARE THE PARAMETERS AND CARRIERS OF INFORMATION.

**Informative computer and life cycles.**

For example, computers process information and they are basically a series of time cycles, digital clocks. So both time and computers are measured by the speed of its time cycles, in frequency Herzs, Tiƒ. So we said that a computer is more intelligent when it has more ‘gigahertzs’, when his time cycles run faster, when its ‘speed of time is faster’.

What do then a computer time cycles have to do with space? Nothing. There time is still a measure of information, carried in the form of its logic circuits and the speed at which the algorithms of those logic circuits are traced. But now it is NOT measuring the information on the speed and distances of space.

Consider the evolutionary time rhythms discovered by Darwin. Evolutionary time measure the rhythms of change in the form, hence in the in-form-ation of beings. So the fittest species, those with more efficient forms and which act faster in time survive. Think of in-form-ation as ‘form-in-action’, because it is what time is. We perceive time cycles which are, forms in motion, changing forms, temporal forms, forms-in-actions, informations.

The problem though with physicists, as we have said is their megalomaniac, bully attitude; as their worldly profession has always been to make weapons (70% of them still work in the US as makers of weapons). So power corrupts, and their military power corrupts their attitude towards other scientists. So they think what they study is ALL what we must know. Their particles ARE essential. And all other forms of time, informations and beings IRRELEVANT to the ultimate nature of things. Alas, power imposes its view. So whenever you pretend to explain people, scientists and of course physicists, the much wider meaning of time, it is like if you were committing a blasphemy against the religion of time-physics: s=ct≈vt. And that’s all.

**The clocks of nature.**

So Physicists introduced two reductions of the whole concept of time in nature – to reduce it to study a single type of form in motion, in-form-ation – the translation in space of physical systems or ‘locomotion’. And to reduce and equalise all the clocks of nature, from orbital systems, to living systems and their world cycles, to evolutionary cycles, to mental cycles, and logic cycles, to a single clock tic – that of the clock. So they came with the infantile concept that time has a single tic, and that tic is like the clock, a steady tic. Yet it is evident as you have experienced with the growing speed of time of your computers and mobiles that even among mechanisms there are different speeds in their clocks, and this speed increases with the evolution of the clocks that keep processing ever more information.

And, so happens in nature, where new species are ever faster in their clocks of time. So mammals are faster than reptiles faster than plants. And the next ladder in the evolution, robotic machines are faster than men – and for that reason they are displacing us in all informative processes, as the new white collar pcs, blue collar workers and terminator soldiers, in fields of labor and war (cause of the present existential crisis of mankind, hidden by our financiers and economists working for corporations that make money with them).

So to me the first, most obvious error about Nature, was the way in which humans tried to IMPOSE their gadgets and machines of time measure over the Universe, WITHOUT any respect of the beauty the different rhythms of that Universe showed.

So I threw my mechanical clock, and never have worn one.

In the next graph we show you those concepts visually so you can realize that all is made of cycles of time (seen as information in still relative no motion) and planes of space (seen as kinetic lineal momentum, in its relative motion):

**The principle of relativity of motion and form. The holographic Principle.**

Next in the ‘awesome’ smartness of our geniuses talking on black holes, is the so called ‘theory of information of black holes’, which is so to speak the inverse to their theory of entropy of black holes. Here actually they got some smart results which they wonder and wonder because they don’t understand. Let us explain it to them. What they found is that the Information of a black hole could be stored in its bidimensional surface. From here, as they don’t understand what they talk about (remember Neumann) they deduced that the Universe could be a bidimensional holography. Ok. The first result as usual is good. Information is bidimensional, the second is a bit speakeasy Neumann style. Let us explain it properly.

To fully understand how spatial planes in motion and cyclical clocks can mess together to create the space-time beings we all are (we ARE NOT in a background space-time, we ARE made of vital spaces with rhythms of motion defined by its time frequencies in our human case mostly metabolic temperature regulated cycles), we need to make a further clarification, at the heart of Physics.

It is with the conservation of energy and information the most important law of physics, the principle of relativity, expressed by Galileo (e pur si muove, e pur no muove: the earth moves but doesn’t move – we do NOT see it moving), by Einstein and Poincare, the mathematician that found in parallel this principle: ‘we cannot distinguish motion from stillness, from ‘form’. Look around, all what you see are forms in motion, but we cannot distinguish clearly what part is ‘form’, ‘position’ and what part is ‘motion’. They are very mixed.

What this means is that our two parameters, quanta of space, and cycles of time, do have both, ‘motion’ and ‘form’. But space, does have a lineal, planar, ‘res extensa’ bidimensional shape. We talk fo ‘planes of space’, and clocks of time, are tall, cyclical, informative cycles – you look at information and its forms and cycles in tall broken cyclical forms, a s the screen of your computer.

So we do have certain clear ‘bidimensional properties’ of form and motion for space: Flat planes moving in lineal paths, and Time, tall cycles, moving in repetitive frequencies. And we know that the product of quanta of bidimensional space and time frequency cycles gives us the relative Energy of reality. And we have a very generic formula for it: Ei = ∑Sp x Tƒ.

Now this resolves a fundamental conundrum of modern physics – why information is bidimensional. Now it is easy: because it is the frequency and form of time cycles that now are bidimensional, tall and with a bit rhythm, a dimension of motion.

And so in the graph we can see the principle of the Holographic Universe, physicists are trying to define (10.000 papers only in the past decade about it) but have not yet grasped as they do NOT understand space, time, information and energy, (kinetic, potential, its integral, etc.).

We can then see that the holographic principle merely means that if you give to ‘time cycles’ the dimension of ‘height’, then you do have the 4 dimensions broken in 2 for spatial lineal, planar kinetic energy, width and length, and 2 for cyclical time clocks, beat, frequency-motion and height.

And alas, because only things with the same dimensions can transform into each other, now we can truly understand the holographic principle: Our 4 dimensional Universe is made of flat planes of spatial lineal kinetic energy, we shall call Spe and tall cyclical bits of information we shall call Tiƒ. When they combine they create a being of space-time, in 4 dimensions.

In the right we see the simplest one, a light beam clearly made of a tall, informative, electric field, perpendicular to a magnetic, energetic magnetic field, reproducing along the length of its c-speed.

Below we see humans and machines, which do have lineal, energetic, planar limbs//bodies, or as in weapons, lineal systems of release of kinetic energy, and cyclical, informative, eyes, brains, heads particles that gauge and process logically or mathematically information.

Below we further see how a black hole, the informative nucleus of the Galaxy, similar to the DNA-informative nucleus of a cell in a smaller scale, does have a tall high dimension and an enormous clock-like cyclical rhythm, the event horizon turning at c-speed. So if light is the quintessential plane of space, with both components but clearly dominant in flat, length, the black hole is the inverse, extreme case of an informative cyclical clock-like vortex of time.

Now entropy is generalized unnecessarily and without rigor by physicists to mean expansive, disorder, spatial motions. And what is absurd – expanded outside the realm of temperature to fit the entire Universe within a supposed absolute entropic arrow of time for all what exists – a huge leap of faith from the study of steam gas in vapor machines, where the concept first appeared.

What Hawking did, giving entropy to black holes, WHICH ARE EXACTLY THE INVERSE informative vortices of gravitation of the Universe, is just the last ‘leap of faith’ in the attempt to reduce all what exists to lineal cannonballs and lineal motions – the last step of the process started by Galileo.

The fact is the Universe is made of both lineal and cyclical motions, space and time, lineal and angular momentum, quanta of space and time clocks.

And the Universe is made of informative mass vortices, with gravitational information, as the galaxy we are in, reason why we are informative beings. Yet between galaxies, there are fractal planes of flat space with dark energy similar to the expansive entropy of gases. And both balance each other in the fractal universe.

Now because physicists; do not understand or want to accept despite amazing number of proofs, the fractal structure of the Universe, they do NOT realize that the expansive entropy of flat space between galaxies is balanced by the implosive conversion of that flat space into mass by cyclical clock-like tall vortices of information – black holes.

So they can go around with absurd concepts such as ‘the entropy of black holes’. And to make it possible, instead of describing black holes as systems that absorb in-form, with gravitation, the galaxy, inventing a motion to the past, changing its arrows of time as Hawking does and bringing its absurd time machines.

We see though that the arrow of information or arrow of evolution increases the dimensions of tall information, and so life evolved from flat worms into tall informative humans. So it does space, which time bends into cyclical vortices of mass. Or as Einstein said ‘time curves space into mass’. This is the Universe which Einstein said is ‘simple and not malicious’. And he put it in a simple equation E= M (c2), which explains how the Universe constantly transforms its kinetic energy/entropy (light, electromagnetic, thermal radiation) into informative masses, back and forth in big bangs and big crunches.

Now the graph clarifies the meaning of time – a tall cycle or clock, and its equivalent perception as still; information.

A simple proof of the holographic theorem: Fermat’s last theorem.

Now information is bidimensional as this computer ou are observing or any page of any book. Further on mathematics is the most realist of languages, since if we are made of time and space, logic algebra and spatial geometry and analysis (5 Dimensional integration of parts into wholes) are *both the 3 main branches of mathematics and the 3 components of the 5 Dimensional Universe of space-time beings.*

So a simple proof of the holographic principle comes from the fact that as Godel proved and Lobachevski said, mathematics is a realist science, which needs to be proved by the existence in the Universe of its theorems.

Mr. Fermat, my countryman, basque, amateur scientist (-; couldnt fit in the margin, a proof of his Ultimate theorem which states that no natural numbers x, y, and z exist such that x³ + y ³ = z³ (i.e., the sum of two cubes is not a cube). But we shall fit it (-:

This is the simplest proof of the bidimensional nature of time and space, as mathematics is the most realist of all languages, defining as Lobachevski thought despite the idealist Hilbert-Copenhagen school, the nature of reality through the proper understanding of its logic laws.

Numbers are social groups of equal entities and they organise by superposition into bidimensional planes, which are added to form the 3rd dimension, or multiplied perpendicularly to form space-time beings. So there are only single numbers, bidimensional complex numbers (where the imaginary axis is the axis of time, for reasons beyond the scope of this limited analysis of black holes) and quaternions for space-time complex beings, but NOT ternary numbers, NOT x³ + y ³ = z³ . You see, it fit in a margin (-; The proof found 400 years latter though required thousands of pages of computer thought, and this is the difference between good simple science and complicated work. The Universe is simple and not malicious. And mathematics is as lobachevski explained, an experimental science which needs as Godel proved, experimental proofs as the reflection of the structure of space and time. Space and time are bidimensional so we have only 1, 2, 4 dimensional numbers. Nobody has succeeded creating 3 dimensional scalars, or found a way in which to superpose cubes. So growth in the Universe happens as the sum or multiplication of bidimensional cycles of temporal information and bidimensional planes of space.

It is the study on how all of us through the frequency of our natural clocks, build systems along the height of our informative dimensions to go back to a flat, corpse or a flat big bang on the moment of death, what defines therefore the essence of existence…

In the graph, we see those parts and functions. Hence topological bidimensional physics *show indeed that black hole splay the role of information in black holes, as heads in human beings or roots in plants:*

It is the study on how all of us through the frequency of our natural clocks, build systems along the height of our informative dimensions to go back to a flat, corpse or a flat big bang on the moment of death, what defines therefore the essence of existence…

It shows the meaning of a generic quanta of space, a flat plane with lineal momentum or kinetic energy which is the lineal motion of a plane of space.

*In the previous graph we illustrate our ‘Space-time’ Essence: Time is measured with clocks, which are actually, one dimensional cycles. Information is the same than a time clock, a ‘form’ that we see static. Energy is made of quanta, which are lines, that group together into sheets of space. And to perceive them, we have ‘spheres’ made of multiple layers of cells, and cameras which are isomorphic. An to move through Space we have ‘lineal members’, which move us in toroid open and closed curves. And so happens to lineal weapons. And then fields of energy and information make together a light ray, which is really also a bidimensional surface.*

In the graph, the duality between moving time cycles and still information, captured by a mind, and moving vacuum energy and perception of still space by the mind is the essential feature of physical systems and its ‘relativity’ of motion. Since *Reproduction of Motion dominates perception of form***. **

The Universe is made of ‘Energy and Time’, ‘Lineal and Angular momentum’ Motion with form. But motion dominates form. Even if the mind thinks otherwise because of the Galilean Paradox – the duality of stillness and motion, as we perceive the Earth still but it is moving.

Yet this paradox is indeed the proof that form, information dominates motion, *because the mind prefers to see still information to blurred motion.*

The perception of time and space as a moving cycle or line or a fixed form or distance is obviously an effect of the mind. It is NOT there, it is the mind that stops time cycles and lineal spatial motions.

**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: Set<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.

**Topology: 2 manifolds**

We are all space-time isomorphisms. The best way to describe those st parallelisms between species, is by considering topology, the branch of mathematics which study forms with inner motion (deformation) and its varieties that put together creates the organisms and structures of the living universe.

This is possible since ‘pure space’ and ‘pure time’ dimensions are abstractions that do not correspond to ‘objective’ reality where space and time dimensions, ‘form’ and ‘motion’ come together. And so the branch that describes both, topology, is the fundamental branch of mathematics.

Further on, what we perceive, and what interacts with the external world is always a bidimensional membrane, not the whole 3 dimensional system, so the so called 3-varieties of a 2-manifold (bidimensional) surface become the 3 fundamental ‘parts’ of any system. And they correspond to the 3 ‘Bidimensional’ forms in motion of the Universe, which we call:

– Space-time Energy (expansive motion, toroid topography), combination of ‘length’ and an expansive, young state.

– Space-time Information (implosive motion, spherical topography), combination of ‘height’ and an inward, warping, old stage: Tƒ = Sh x Tƒ

– And its space-time combinations (repetitive motions, hyperbolic topography) combination of width and a present, iterative motion that seem not to change.

All what you see from the humblest chair or the smallest atom to the biggest galaxy or the most complex human being is an iteration of 3 unique topologies of a 2-dimensional space.

One of the most important problems of topology is the search for a classification of manifolds up to topological equivalence. Ideally, for each dimension ∆, one would like to produce a list of ∆-dimensional manifolds, and a theorem that says every ∆-dimensional manifold is homeomorphic to exactly one on the list.

The theorem would be even better if it came with a list of computable topological invariants that could be used to decide where on the list any given manifold belongs. To make the problem more tractable, it is common to restrict attention to compact manifolds, which can be thought of as those that are homeomorphic to closed and bounded subsets of some Euclidean space. Precisely such a classification theorem is known for 2-manifolds.

The first part of the theorem says that every compact 2-manifold is homeomorphic to one of the following: a sphere, or a doughnut surface with ∆ 1 holes, or a connected sum of ∆ 1 projective planes. The second part says that no two manifolds on this list are homeomorphic to each other. It means we need ‘surgery’ , tearing, ‘hurting’ the organism to break the variety of the manifold. And since this would upset the functions and health of the super organism, we are left with the 3 fundamental varieties of a bidimensional space, to construct the ‘wholes’ of all the systems of the Universe.

In the 2 previous graphs we can see the structure of all systems with an external, Max. Sp. toroid Limbs that move the system, an internal, Max.Tƒ, zero point and a hyperbolic, Sp=I, Max. ExI, organic, reproductive structure that puts together and maintains both, the membrane and limbs that move the body and the still, informative cyclical point that maps and gauges reality.

**The inverse properties of spatial entropy and temporal information**

*The Universe is made of two substances: spatial energy and informative time. We can see it with motion as energy and time or as fixed forms, as space and information. We can see it as a single reality, as space and time, or as a multiple quanta, as energy and information. We can differentiate them by form, as space and energy are lineal or planar surfaces and time and information are cyclical. And we can see it together into beings, the simplest of which is an action of light, ext=k. And this simple duality structures all beings of the Universe. So we are made of cyclical heads and lineal bodies. Weapons are lines that release energy. Informative machines are cyclical, and all physical systems are made of lineal forces and cyclical particles of information.*

**Topology: 2 manifolds**

We are all space-time isomorphisms. The best way to describe those st parallelisms between species, is by considering topology, the branch of mathematics which study forms with inner motion (deformation) and its varieties that put together creates the organisms and structures of the living universe.

This is possible since ‘pure space’ and ‘pure time’ dimensions are abstractions that do not correspond to ‘objective’ reality where space and time dimensions, ‘form’ and ‘motion’ come together. And so the branch that describes both, topology, is the fundamental branch of mathematics.

Further on, what we perceive, and what interacts with the external world is always a bidimensional membrane, not the whole 3 dimensional system, so the so called 3-varieties of a 2-manifold (bidimensional) surface become the 3 fundamental ‘parts’ of any system. And they correspond to the 3 ‘Bidimensional’ forms in motion of the Universe, which we call:

– Space-time Energy (expansive motion, hyperbolic topography), combination of ‘length’ and an expansive, young state.

– Space-time Information (implosive motion, spherical topography), combination of ‘height’ and an inward, warping, old stage: Tƒ = Sh x Tƒ

– And its space-time combinations (repetitive motions, toroid topography) combination of width and a present, iterative motion that seem not to change.

All what you see from the humblest chair or the smallest atom to the biggest galaxy or the most complex human being is an iteration of 3 unique topologies of a 2-dimensional space.

One of the most important problems of topology is the search for a classification of manifolds up to topological equivalence. Ideally, for each dimension ∆, one would like to produce a list of ∆-dimensional manifolds, and a theorem that says every ∆-dimensional manifold is homeomorphic to exactly one on the list.

The theorem would be even better if it came with a list of computable topological invariants that could be used to decide where on the list any given manifold belongs. To make the problem more tractable, it is common to restrict attention to compact manifolds, which can be thought of as those that are homeomorphic to closed and bounded subsets of some Euclidean space. Precisely such a classification theorem is known for 2-manifolds.

The first part of the theorem says that every compact 2-manifold is homeomorphic to one of the following: a sphere, or a doughnut surface with ∆ 1 holes, or a connected sum of ∆ 1 projective planes. The second part says that no two manifolds on this list are homeomorphic to each other. It means we need ‘surgery’ , tearing, ‘hurting’ the organism to break the variety of the manifold. And since this would upset the functions and health of the super organism, we are left with the 3 fundamental varieties of a bidimensional space, to construct the ‘wholes’ of all the systems of the Universe.

In the 2 previous graphs we can see the structure of all systems with an external, Max. Sp. hyperbolic Limbs that move the system, an internal, Max.Tƒ, zero point and a toroid, Sp=I, Max. ExI, organic, reproductive structure that puts together and maintains both, the membrane and limbs that move the body and the still, informative cyclical point that maps and gauges reality.

# II. FORMALISM

# **NON-E 2,4 POSTULATES**

The minimal Unit of the Universe is a 2-manifold, 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).

In the graph, minimal Units of the Universe are 2-manifolds, which if seen both static they appear as a bidimensional sheet or membrane, if seen as ST, dual motion-form dimensions they are Active Magnitudes that is Points with Motion or ‘Momentums’, and when seen as pure motion (two time dimensions), they are seen as acceleration or energy.

We call st combinations åctions: Sp x Tƒ = A.

The Unit of the Universe is a space-time action, which therefore requires at least a dimension of space≈form and a dimension of motion≈time. From this single Unit, the Universe builds itself. Hence the importance of bidimensional sheets (where the relative height dimension of information is minimal, as the system is extremely thin till it might reach the ‘infinitesimal indivisible’, ∆-1 quanta of the lower lawyer: X≈Z>>>Y.

It must be understood though that since the Principle of Relativity (Poincare) makes indistinguishable motion and form, any variety of the 3 motions of time and the 3 ∂till of space can give birth to a 2-manifold, and any analysis made in sequential, dynamic algebra can be explained in fixed form geometry. And so we must wear in mind when we study in detail many phenomena of nature that we shall find at least 2 possible, often 3 identical analysis: a geometrical, an algebraic and a parts & wholes infinitesimal (integral/derivative) analysis.

The duality of space≈form and motion≈time thus explains why we found soon two formalisms for quantum particles (Heisenberg formal matrices and Schrodinger’s wave equation), and then an integral formalism (Feynman’s sum over histories).

*It is in that regard essential to understand the underlying symmetries, dualities and ternary differentiations of fractal space-time Systems, Se<ST>Tƒ, so we can interpret the ‘many solutions’ to all problems of mathematical physics.*

Points which are knots of time cycles communicate through flows of energy and information, lines-waves that form networks which become finally social planes, energetic, informative and reproductive systems that collapse into super organisms, completing the creative processes of the Universe.

In the graph, the ever moving Universe of space-time is made of ‘Tƒ≈eS’ of existence. These ties or knots of space-time cycles and åctions are ‘fractal points’ Œ, crossed by infinite parallels. So departing from the first primary flows of time-space, lineal fields/limbs of entropic energy, hyperbolic body/waves and cyclical fields of information, fractal points create the first simplest Tƒ=es of existence.

Now the reader should notice that we use two ‘balls’ of different size to signify the relative energetic and information points (Max. Sp x Min. I vs. Max.Tƒ x Min. Sp), which communicate an intermediate ‘present hyperbolic wave/body network’ that ties them. This tie or flow of energy and information can be absorbed by the relative point-particles as they are ‘fractal points’ with parts, which become bigger as we come closer to them.

Now the mathematical purest expression of that basic ‘2nd postulate of Non-Euclidean geometry’, the communication of two points of energy and information would be in its pure Euclidean geometrical expression, the understanding of conics (ellipses, hyperbolas, parabolas, etc.) as the loci of communication between two points or one point and a line, which are at equal distance of both.

This ‘loci’ is the communicative membrane or ‘bidimensional space-time’ (if we consider all Non-E points by definition, one-dimensional), wave-body that we shall refer as the O x|= Ø-spacetime present region within each ties.

Now the previous graph shows the first operations of ∆-mathematics, of Non-AE, i-logic existential algebra. How do we such 2 points communicate its flows of existence.

While in Aristotelian Algebra/Logic whereas there is a single time logic arrow, A->B, upgraded to ternary logic in which any event can give 5 results or future outcomes, hence the sum of all the possible stories of an equation will be: A x B = A +B + AxB(parallel) + A/B (perpendicular) + B/A (perpendicular) variations of the first event. Hence we write A≤x≥B as the new operandi which expresses all the 5 variations of those space-time events in the pentadimensional logic of the 5th dimension of ∞ fractal space-times.

Thus we draw a full series of sub-events after any action of communication between 2 ∆-points of existence:

Thus the rules of engagement of non-Euclidean points differ but depart from the laws of classic geometry in which the inner region of the point, its ‘standard one dimension’ (which grows further when we see its internal parts). They make abstract Sp-geometry into a closer truth, similar to the vital ‘geometries’ of the Universe.

The next stage thus after the first ‘postulate of non-e points crossed by infinite parallels’, the second postulate of 2-manifolds born of the communication between 2-nonE points is the creation of non-Sp planes, which are networks made of flows of communication of energy and information exchanged by Non-E Points:

In the previous 3 posts, ‘time motions’, ‘still spaces’ and its combinations’, åctions of exchange of energy and information, we defined in a somewhat loose conceptual manner the fundamental elements of the Universe, its 3 motions of time, entropy, iterative vibrational motions and spherical gauging of information; its 3 symmetries of forms in space (toroid limbs/fields, hyperbolic body/waves and spherical heads/particles) and the combined space-time åctions those entities deploy in the outer World that acts as its ‘absolute space-time’, usually across several ∆±∆ planes of smaller and larger existences from where the system obtains its energy and information.

The answer is points, the eternal, fundamental unit of geometry and its algebraic equivalent, ‘numbers’. So to formalize with proper logic and mathematical languages the Universe of fractal space-time beings, we need to start from the beginnings of mathematics, and re-define properly geometry, and build up from geometry, with the more complex logic of 3 arrows of time, the architectonical structure of the ‘space-time planes’ of the Universe. And finally studying how those networks of points become planes of ‘existence’, we shall be able to define the ‘whole’ in time (the world cycle) and space (the super organism).

In that regard we talk of 3 scales of growing size and complexity that structure the Universe.

- The first level is that of the aforementioned ‘time motions’, which coupled with ‘still spaces’, become the åctions of points of timespace.

It is the understanding of those points of time-space as knots of external space-time’s cyclical åctions of exchange of energy and information, ±∆(ExI), which together evolve socially the system into stable space-time organisms: Exi=ST.

This existential stop and go, space-time action-oriented reality, however must found its formalism. And so when we integrate those space-time åctions together, into a ‘knot’, we define a Œ-point, an existential function, the minimal unit of the Universe in formal, logico-mathematical terms.

- Thus, the second level of understanding of the Universe is the next ‘scale’ of integration: Existential åctions are integrated into space-time knots-points, and those points then, enact further exchanges of energy and information with similar points, becoming ‘networks’ of waves of exchanges of energy and information – planes of existence.
- This brings us to the 3rd level of integration of the Universe, as networks of social points, distribute themselves in space, as energetic-digestive, informative-mental and reproductive-body waves, which messed together create a ‘super organism’ of space-time the fundamental unit and final ‘Universal’, to which all points aspire. And so in time, we can study the whole process of existence of a point of space-time from birth to emergence into the Universal ∆+1 scale, through its life and final death, when it becomes a 0-sums.

This 3rd level of integration which narrates the story of super organisms through its world cycles, completes therefore the ‘first line’ that resumes the Universe through its 3 integrative levels of complexity.

Of course the game is infinite and so we can take then each world cycle and super organism as a relative ‘point’ tracing motions in time, and performing space-time åctions in an ∆+1 higher world, and tell the tale of a new ‘game of existence’.

Thus in this post we start the ‘2^{nd} level’ of complex description of the Universe, that of its formalism of non-e points, forming waves, networks and super organisms. In this post we shall study the Œ-point and its spatial geometry of networks, till reaching the superorganism.

In the next post we shall study the same processes but with the tools of sequential algebra, the formalism of the 3 motions of time, and its complex logic laws, using the last posts of the line to describe the full game of super organisms tracing world cycle of life and death of existence and extinction (homonymous concepts that we prefer to eliminate the anthropomorphism that makes ‘life-death’ seem to be different to existence-extinction shared also by physical and mental species).

Thus, the unit of the bio-logic and mathematical, mental Universe, of infinite frames of reference, made of cyclical knots of timespace åctions, is the fractal point.

Thus once we have evolved our basic concepts of cyclical time, fractal space, dimensional motions, the arrows of time and its symmetries in the morphologies of space, we can reconstruct, r=evolve and advance our formal knowledge of the Universe, departing of its fractal units, non-Euclidean points with parts.

And the first fact we must establish are the postulates of this i-logic geometry that puts together the existential algebra, non-Æ, of sequential, logic chains of time motions, across bidimensional stop and go sheets of holographic space, acting, moving and reproducing Œ, functions of space-time existence.

**III. PHYSICAL SYSTEMS.**

**Samples of 2 manifolds in nature.**

2 manifolds thus are more than simple 2 manifold geometries; and if we want to interpret nature with mathematical realism, we must be aware always of the Poincare’s Relativity principle. For example, if we consider the minimal unit of the quantum world an action H of space-time, product of its energy and information and with the same parameters than angular momentum, we realize we already have ‘2 elements’ one of spatial energy and one of temporal information to measure it, and one is in motion and one is in form. So happens to the lineal momentum, where the active magnitude is a form in space and the motion is a translation in time.

Those are the simplest ‘2-manifolds’ of motion and form. And so layer upon layer of 2 manifolds of combined motions and forms, the next ‘dimensions’ of 3-depth, 4th-motion, 5th-depth appear by accumulation of those 2 manifolds, in the same manner a 3D printer works by accumulating 2-manifodl layers.

The external space-time Universe as a whole has in its absolute space-time 5 dimensions, but as we concentrate in a single space-time plane, and the inner space-time of beings, those dimensions are reduced. So we talk of 4 dimensions for a being in single space-time plane (Einstein’s 4D Metric of light space).

However in the fractal Universe we must reorder those 4 Dimensions according to a holographic principle in ‘bidimensional planes of ‘points with parts’, as systems organize in planes of similar point-particles (that grow in size as we come closer to them, from human head-particles to galactic points and atomic points).

Because *the amount of energy and information transferred across a single Universal Plane, U∆, is much larger given the ‘‡ parallelism’ of its elements that ‘smooth’ transfer and flow with no ‘singularity points’, than between hierarchical scales that transfer only information from U-1 to U and energy from U to U-1, it follows that the Universe is structure in Non-Euclidean planes which are layers, across which there is less transfer of energy and information.*

*In the next graph we see a simple well known example of liquids:*

*Speed is maximal in a liquid in which flows acquires a laminar form, yet when we introduce a ball which breaks the laminar natural structure of all systems, speed is slowed down by friction and eddies are produced in which particles are transferred in ‘cycles’ of formal height from the low laminar sheets to the upper ones:*

Those eddies, needless to say have a slower speed than the laminar flow and limit it, yet the flow naturally tries to acquire again a laminar plane from A to B after the ‘height disturbance appears’.

Thus what we call the 4 dimensions of space-time in classic physics is really the interaction of 2 bidimensional sheets with motion, in the relative perpendicular state, ‡, which follows the axioms of the ‘3^{rd} postulate of i-logic geometry’ (Darwinian, entropic behavior).

For that reason the Universe minimizes perpendicular, hierarchical exchanges and maximizes parallel exchanges, with the result that it is constructed in bidimensional layers. This is the case of all systems, which will have a membrane that surrounds it (surface), an inner series of networks of points with bidimensional topologies and finally a central zero-point, image of the external membrane , which itself is an image of the whole Universe.

Now the number of proofs of the 2-manifold layer structure of the Universe is enormous and we shall consider in all the articles some examples of it. Enough to say that one of the most fascinating proofs is that almost all the geometric theorems can be proved in pen and paper, in 2 dimensions, as the Greek already notice. And this 2-manifold nature of reality is the fundamental reason science is made in pen and paper, Cartesian graphs represent reality, computer screens and paper that carry information are bidimensional, so are your eyes, and all can be modeled in a screen just with one dimensional |s and bidimensional cycles.

The construction of the Universe in bidimensional layers is a bone for its understanding from parts to wholes. For example, when we study a shock wave in which the motion of the particle that disturbs the medium/field is faster, a simple law of speed sin a = v/u defines the form of the triangle formed by the particle and the wave.

This can be observed in 2 dimensions, in the surface waves of water as the ship advances. Its complex deduction in classic physics responds *as all laws of reality to simpler ∆ST laws: the point particle, in this case the ship is no longer creating a slow informative cyclical wave but a lineal speed-space geometry, which by definition is the ‘triangle or angle’ defined by the sin (max. S = min. sin= max. lineal shape of the triangle. Thus as speed increases the ‘O-form’ of the wave becomes an S– geometry. And the sin, S– geometry increases as the speed increases.*

*So without much mathematical elaboration the simplifying qualities of (∆ST) ^{2} µ (: isomorphic, invariant, scalar space-time theory 🙂 allow us to understand the shape of the shock wave. Now, when this shock wave happens in an entropic, more disordered, less laminar 3-D gaseous state (where chaos introduces an entropic 3-dimensional volume without clear laminar, hierarchical shapes), we just need to add a dimension of rotation to the angle-wave to create a cone which is the shape of the shock wave when the particle, the plane crosses the sound barrier.*

*In the graph, a shock wave: a classic Tƒ->Se, sphere to triangle geometric transformation of a wave form as the S speed-distance increases, reducing the form the system.*

*This reduction, sin a= vs/v expresses also the nature of the fundamental form of lineal space, a triangle which has the maximal perimeter for the minimal volume of form. .*

*From this example, we can deduce again 2 obvious laws of the construction of the Universe and its efficient functions of exi=st-ences:*

*– The layer bidimensional construction of reality works architectonically (as most events of ∆ST) first creating the lineal speed, then the triangular form, and finally the 3-dimensional cone.*

*– The Universe is NOT an ideal system, but imposes ‘ideal’ ∆ST laws because they are more efficient and work better and survive better. So a heated gas is truly a 3-D system, with very little if any bidimensional flows, when closed in a tridimensional volume, but for that reason it does have maximal entropy, chaos, heat, disorder which prevents it to do work. And for that reason ‘efficient’ systems, even gases tend to establish ‘gradients’, which are laminar hierarchical orders along an U combined ‘parameter’ (atmospheric layers in an open gaseous state). By definition this is what happens in nature which is always an open state in an infinite Universe. This has wide implications in a proper understanding of entropy (one of the less understood concepts of science), that we deal with in our section of physical systems.*

Enough to say in this introductory comment on 2-manifolds that ‘space-energy’ components will tend to be ‘faster-larger-longer’ in space and one-2 dimensionals and their ‘time-cyclical clocks’, will be 2-3 dimensional (by adding layers to the hollow sphere), and that is what the previous graphs of laminar flows show: in the upper graph, speed is faster and the system is a one-two dimensional flow of pure space-speed, in the lower graph an informative, temporal, cyclical sphere is added and this ‘brings’ according to 3^{rd} postulate ‡, parallel ‘imitative’ synchronic laws the creation of similar Eddie forms, which diminish the space-speed component of the system.

But those themes of ‘induction, imitation, repetition, creation of similar forms by a larger denser element – so when a particle appears a field of micro-similar particles is created, when a big man makes an action a child imitates it, when a clock has a frequency around it other clocks synchronize – are treated in other posts. So let us stick to the theme of this one: how 2-manifolds assembly wholes according to its 3 varieties.

This enormously simplifies our understanding of it. *As we can construct reality from bidimensional parts into wholes. And since there are only 3 varieties of 2-manifolds…*

**The 3 bidimensional parts of reality.**

…We thus affirm that all the internal space-times of all the exi=st-ences of the Universe are constructed

as ternary assemblies of 3 varieties of bidimensional parts:

Se: limbs/fields of toroid energy.

ST: hyperbolic reproductive wave/bodies.

Tƒ: And spherical heads/particles of information.

This post and its hyperlinks connects and explains the main topics of the study of spatial, topological isomorphisms in the Universe.

In that sense, the invariant equation or ‘metric of the 5th dimension’ is the departing point of the formalism of General Systems Sciences which describes wholes made of parts extended through several plane of relative time speed of information or I-scales of the 5th dimension.

However there is also an analysis of the ‘complementary systems’ of the Universe in space, in a relative present time, when both components, the fields of energy/limbs an the particle/head, act together exchanging motion/energy and form between them, through a 3rd element, called the body or wave in a stable system:

sp<ST>Tƒ, which becomes the essential structure of reality. This is the structure studied in this section.

**The frame of coordinates of the 3 parts of the Universe.**

The frame of coordinates are the ‘mind points’ that construct its inner world views. And they are 3-dimensional ad maximal, made of holographic 2-manifolds, of the 3 varieties (cylindrical, polar and planar coordinates), of which the most natural is contrary to belief, not the plane, but the spherical point.

Why there is not a 3-sphere in the form conceived by mathematicians and physicists, that is a 4-dimensional thing on which the sphere is its surface? This question requires the understanding of the existence of ‘only 3 motions in time’ and the corresponding 3 ‘static forms’ of space, which are in fact not new dimensions but the fractal division according to the ternary principle of a present time slice into 3 sub-spatial dimensions. And so we do not need to conceive 4D structures because the fractal Universe does create after 3 ‘fixed’ dimension, 3 fixed motions, which become static for 3 new fixed dimensions and so on.

So let us go back to the beginning, the beginning was the observer and the maximal number of dimensions he observed were 3, and then those 3 through infinite motions, became shrunk into its still mind made of two dimension, reflection of the whole Universe, as a mirror automatically reflects the whole in its small 2 dimensions.

**Needless to say, **the 3 organic 2-manifold parts of all systems have 3 natural coordinates, Cartesian > Cylindrical > Spherical coordinates, where we can better resolve the sub-åctions of each part in the inertial frame corresponding to the system.

And it is a characteristic of those 3 coordinates that to transform into the other, the ‘bridge’ coordinate is the cylindrical, hyperbolic system that connects both, the spherical and Cartesian, toroid (tending to infinities) coordinates.

An interesting element of analysis is thus the study of the 3 parts of a system as one of the 3 canonical coordinates of space-time and study their transformations as homomorphisms between those coordinates. Of special interest is the transform of elliptic, Riemannian spheres into the plane.

We can in this fashion study general laws of fluxes of energy and information as they move through the 3 parts of a given superorganism.

**IV. BIOLOGICAL SYSTEMS**.

**Network’s organisms.**

In topology however ‘geometries’ are defined as networks of points, and this is indeed the way to go with the systems of the universe. So instead of ‘3-bidimensional varieties’, a discontinuous analysis of those topologies will define systems as ‘3-fractal networks’, an energetic (digestive network) a reproductive (blood network) and an informative (nervous network). And we shall see how we can evolve further Non-Euclidean mathematics with the concept of Non-Euclidean fractal points and fractal networks which happen to have dimensions closer to ‘2’ to explain much closer to reality the 2nd isomorphism of the Universe:

In topology however ‘geometries’ are defined as networks of points, and this is indeed the way to go with the systems of the universe. So instead of ‘3-bidimensional varieties’, a discontinuous analysis of those topologies will define systems as ‘3-fractal networks’, an energetic (digestive network) a reproductive (blood network) and an informative (nervous network). And we shall see how we can evolve further Non-Euclidean mathematics with the concept of Non-Euclidean fractal points and fractal networks which happen to have dimensions closer to ‘2’ to explain much closer to reality the 2nd isomorphism of the Universe:

In the graph, the 3+3 >informative and <energetic dimensional åctions and its 3 topological invariances fusion into 3+3 >&< physiological networks, invariant in all Universal super-organisms, which display 3+1 elements extended in 3 ±∆-scales:

Cellular units, when we perceive the system in the ∆-1 scale.

Networks and organs that >-absorb or <-expel energy: external membranes, digestive tracts & limbs.

Networks and organs that >reproduce cells or wholes of energy and information or <communicate them externally.

Networks that input or output information – senses and ‘nervous’ networks – that give origin to:

∆+1 the whole ‘brain’ site of the ∆+1 consciousness.

Thus we define all systems of the Universe as quantic networks of spatial energy or/and temporal information, among which the most stable forms are those natural systems that combine both type of networks into a super-organism able to transfer energy and information with external networks and internal cells.

The key to understand those quantic networks is a proper definition of quantic spatial energy and temporal information, the 2 substances of which all forms of the Universe are made. Let us resume its opposite properties:

*|-Space =Max. Linearity= Max. Continuity= Max. Energy =Max. Movement=Min. Form= Field/limbs x*

*O-Time=Max.Cyclicality=Max.Quantification=Max.Information=Max.Stillness=Min.extension=*

*Ø-hyperbolic Wave whose cycles combine both*

Thus all systems are composed of 3 clear networks, which correspond in the fractal discontinuous ‘duality’ (remember the 1st isomorphism: ∑e=S, ∑o=T), to the 3 topologies of any 2-dimensional Non-Euclidean space-time:

* A**ll known scalar space-times being can be reduced to those 3 bidimensional networks/organ s.*

**A bit more detailed, complex analysis. Non Euclidean Topologies.**

Now we have summarized both, the ‘continuous’ and discontinuous vision of the 3 topologies of the Universe. We could also do an abstract analysis of it, with mathematical topologies. It would though be a bit complex and specialized. So we will try to introduce rigor with less abstraction. Consider the graph that started this post.

We drew the 3 ‘type’ of Non-Euclidean topologies which make up below the different species. It is those organic’ real species what matter to us. the parts above though guide us for the generalization of the isomorphism (hence the importance of formal sciences to ∆ST, and the postulates of non-Euclidean topology studied in sub posts attached to this one).

Enough to say that the toroid geometry is called by his authors Lobachevski and Belgrami, the hyperbolic goes by the name of Klein, and the spherical is called a ‘Riemann sphere’. They are the limbs/fields, bodies/waves and spheres (external membranes and central zero points) that make all of us.

In fact in embryology they are produced exactly by the 3 ‘ectoderm’, (the membrane and brain) endoderm (the guts that devour energy) and mesoderm (the muscles and body) parts of the fetus.

So the 2nd isomorphism is enormously important to understand all kind of systems of nature.

Indeed, the 3 topologies of a 2-dimensional space are the 3 zones of any being of the Universe*.*

The capacity to describe all space-times of our Universe that those 3 regions have is ‘absolute’ as Topology, a branch of mathematics that classifies all possible space-times, has discovered.

Since all possible forms of a 2-dimensional space can be reduced to those 3 zones that build the quantic geometry of any form of reality, whose inner parts can be transformed into the 3 bidimensional forms. The graph shows how any form becomes a bidimensional zone through topographic symmetries:

– A sphere or volume “without holes” becomes a Riemann’s external sphere or membrane connected to a zero-point of perception.

– A hyperbolic or any volume with a hole can be turned into an intermediate plane equivalent to the central Klein disk (if we cut it we have a cylinder that we develop into a plane).

-While a series of limbs attached to the membrane through multiple holes can be turned into a topology with negative curvature and a convex surface, homologous to the central hemisphere of Belgrami. And so our bidimensional Universe is indeed a sum of those 3 Non-E zones with clear geometrical forms and properties.

*The variety of real organic spaces that Non-E geometry explains is enormous. In the graph, an animal, an embryo, an electromagnetic flow, a black hole, a proton, a seed, a planet, a cell and a boson condensate: all of them can be described with the ternary structures of Non-E geometry.*

In the graph, Universal species are space-time fields, structured in 3 Non-E basic formal regions:

- A central, very quantized, evolved, ‘future’ zone, dominant on temporal
*information*. Which invaginates into ‘informative networks’ that spread throughout the other zones, connected to the external membrane that isolates the being and acts as the sensorial element which transfers without tear and deformation the information to its center. - A relative, simpler,
*energetic*, ‘past’ zone of lineal structures with little information and a lot of energy. Either and external field or attached dual limbs that move the system. - An inner,
*reproductive*region of mixed S-T quanta, which perform the 2 arrows of the universe of the system, mixing external energy coming from the membrane and internal information from the center to create new informative and energetic quanta, specific to the space-time field. It has often the topic hyperbolic ‘central tube’, as in all animals which derive from earlier hydras (in your case the tub that enters your mouth and exists your anus, which is formed already in the ‘blastocoel’ embryonic phase of development by ‘invagination’, an essential procedure of ‘topological surgery’ that allows to transform a topology in other variety in the dynamic Universe

As points evolve and develop specific structures, they become ‘*invaginated’ by energy and information networks* departing from the outer and inner regions of the point that spread through the intermediate zone to control the S-T quanta, creating in this manner the morphological varieties we observe in the Universe, which however can be reduced to the previous functional elements.

Those 3 zones are homologous in form and function to the 3 internal parts of most real fields, from the cell to the human organism, from an atom to a star to a galaxy, which have an informative center, an energetic membrane and an intermediate zone.

For example, the human being is a non Sp space-time with 3 inner networks-dimensions:

- The physiological networks of nervous information derived from the ectoderm membrane.
- The energetic gut, the digestive system of energy feeding with its toroid immense number of ex-vaginations which are in fact a kilometer long to absorb water from the ‘hole’ of the hyperbolic.
- The muscle and blood network and organs, the essential hyperbolic with the heart at its centers, another hyperbolic with tubes coming in and out. This are the blood and endocrine systems that combines energy and information, to which are attached a number of ‘space-time’ cellular quanta that reproduce all kind of glandular substances, creating together a human being.

While a nation is also a sum of human quanta, (its citizens), joined by networks of energy and information (legal, religious and cultural networks and economic systems).

In the graph we show the Non-E structure of Universal species according to those 3 quantic zones:

*– Tƒ: The singularity of max. quantic information:* the knot of quantic information ‘or brain’ of the system is located in the center or z-axis: it is the spin axis of atomic particles, the seed of fruits, the crystalline nucleus of a planet, the DNA spiral of cells, the height dimension where bosons condensate in matter, the spinal chord of the nervous system in living beings, the genetic nucleus of the embryo, the yolk in the egg, the axis of any electrical current, the vortex of the black hole in the galaxy, the nucleus of the atom…

*– Tƒ: The continuous membrane of max. sensorial perception that also displays great strength and* limits and isolates the system. The Non-E point reaches its max. extension, structural hardness and sphericity (that is, the maximal curvature of its cycles) in the inner zero point and external surface of the sphere, the skin that expels sweat energy waste and absorbs information in contact with the external organic territory of the point.

We use a small o for the zero-point a big O for the membrane.

This duality *of a zero point and a membrane of information proved unique by the Poincare Conjecture of topology (the sphere is the only variety that can sink without deformation, thus creating in the zero mind, crystal, brain, a mapping of the external Universe) is the MOST IMPORTANT PART OF REALITY IN ALL SYSTEMS. So we dedicate the 0(10th in the count) isomorphism to its study.*

Some examples of those membranes are the electron orbital in the atom, the skin of the tomato, the crust of the planet, the membrane in the cell, the placenta of the embryo or the halo of dark energy and matter in the galaxy.

- Spe; The limbs or cilia or fields of energy, toroid, made of multiple similar parts, external to the system, sometimes attached but often ‘rescindable’, the less important part in contact with the lower ∆-4 force that moves and accelerates and decelerates the system.

*– ST: *And between both limits, the intermediate space-time filled *with reproductive, cellular quanta* that combine energy bites and information, absorbed from the external world by the other 2 regions. They are the cells of the body, the stars of the galaxy, the carbohydrates of the cell, the planetary magma, the pulp of the seed or the electromagnetic forces that circulate within the atom.

And it has *a hole tube, an aperture, MOST LIKELY A POLAR one, which crosses through the system, and might bring food to the linen of energetic ‘cells’ ‘atoms’ (iron cores that absorb gravito-magnetic forces) or in more informative species, pixels of form to a central mind (crystals).*

And so we start to see also a fundamental *element of the 2 isomorphism, the patterns of differentiation and speciation along the ‘1st isomorphic Se<>Tƒ distinction’.*

Thus *all Non-E points are ‘inner worlds’ whose discontinuity defines an External Universe or* outer world from where the point obtains its energy and information. Since most points, despite being discontinuous, have in their external membrane several generic openings or ‘senses’ joined to the informative networks or ‘brains’ and energetic, ‘digestive networks’ of the superorganism:

*– Max. +Sp: A* ‘*mouth*‘ or opening that absorbs energy.

*-Max. -Sp: A* ‘*cloaca*‘, through which the cyclical body expels its temporal energy.

–*Max.+Tƒ: An* ‘*eye*‘ through which the informative center receives external information.

–*Max. -Tƒ: And an* ‘*antenna*‘, through which it emits information.

Those apertures vary in their number, location and size, depending on the form of the point. In the simplest, initial spherical ‘seeds’ of most species, they are mostly situated in 3 regions:

*– Max. Sp*: The Equator of the system, through which the membrane absorbs energy

*– Sp=T*: The Tropics, in systems that use the same opening to emit and absorb temporal energy.

*– Max.T*: The Poles or points of confluence between the membrane and its central informative region of height, which hits perpendicularly the membrane on those poles. North and South Poles orientate anti-symmetrically, acting as 2 relative, negative and positive apertures, communicated by the height dimension of the singularity or Belgrami hemisphere. Thus the Positive Pole absorbs temporal energy that crosses through the central singularity where it is absorbed and ejected to the intermediate region where it is re-elaborated before its emission through the negative Pole.

Some examples of those apertures are the senses, the sunspots, the magnetic poles of a planet or black hole*, *the spin or radius of a particle, etc.

Now we want to end this introduction with the study of another basic Se<Tƒ>Se Duality, the dynamic transformation of cyclical spherical systems into lineal ones, which keep the 3 parts. first a general case, then a specific one.

# IV. HUMAN SYSTEMS

**Diffeomorphism: fractal relativity. Each species has relative ternary dimensions.**

__ __

*In a Universe made of an infinite number of time arrows that gather together into ‘complementary knots’ of Entropy and information, each being is a relative fractal Universe, which we call a ‘world’ or ‘space-time being’ that deploys its particular ‘directions of height-information’, ‘length-Entropy’ and ‘width-reproduction’, different from those of other beings. All those fractal Universes interact through its particular, ‘local’=diffeomorphic coordinates, which departing from a central Non-Euclidean Point of view, or relative ‘self’, establish the 3 relative, perpendicular, minimal dimensions of any fractal world that signal its arrow of Entropy, information and reproduction.*

The first and most important emergence of properties of lower scales, is the emergence of the 3 axis through which the entity expresses departing from its point of view with ‘will’, the 3 arrows of informative perception, energetic motion and reproductive growth. The 4 arrow doesn’t need a four spatial dimension because it is the point of view, which uses an internal language and ‘algorithm’ of choice to alternate action in each of the 3 dimensions of spatial existence.

Thus there will be a point of view that directs the whole system, with the aim of achieving maximal reproduction, by switching between the arrow of informative perception and Entropy taking, in order to accumulate enough of it and reproduce more cells in the dimension of width/reproduction.

This happens in the two fundamental forms of the Universe:

- The radial form, with the informative point in the center; which corresponds to forms dominant in information and minimal motion.
- The bilateral, lineal form, with the head in the direction of motion, which corresponds to lineal energetic systems.
- Most often though species can switch between both forms and they do so in rhythms of Sp->O, from the Sp(day)>O(sleep), extended>coiled position, to the 3 ages of galaxies which evolve from extended nebulae to implosive spirals that end up in a 3
^{rd}globular age.

In the graph, 3 diffeomorphic beings and its relative arrows of Entropy and information: a galaxy with an inward arrow of gravitational information, pointing towards the central informative black hole; a tree and a man, whose informative/energetic dimensions are inverted. Since plants use light as Entropy and animals use it as information. So the informative direction of animals is up, towards the head that absorbs visual information from the sky, opposite to the informative arrow of plants, which is down, towards the roots that absorb chemical information.

Both have their space-time parameters inverted, as often happens between Entropy victims (in the graph, plants) and their anti-forms or predators (animals). Such Entropy/information, relative past/future inversions happen in all Universal systems. For example, they happen between a ‘particle’ and its ‘antiparticle’, which in a Feynman diagram have also inverted coordinates of space-time, as the antiparticle travels to the past. They also happen in mental, linguistic codes that represent that external reality. For example, eviL=death is the exact inverse word of Live. Since indeed, for a living human being, there is no bigger eviL than death.

Yet, death, a release of Entropy that kills is the inverse function of information, the arrow of life. So the linguistic, spatial inversion of words corresponds also to an inversion of time arrows – a fact that explains scientifically the biologic meaning of ethics. Since humanity, history and religion are a sociological space-time that obeys the same homological isomorphisms of Multiple Spaces-Times. Thus each species establishes its own up and down arrows; its relative Entropy and informative directions, departing from that central knot of information, which is gauging and perceiving.

What classic science denies and system sciences proves is the reality of an existential will in that perceptive Sp=I Informative knot, which controls the entire organism and directs its search for ‘åctions’ that provide Entropy and information to the being. It is precisely the infinite number of Discontinuous, Non-Euclidean Points of View, what creates a general arrow of Information in the Universe that constantly reproduces the form of those entities and balances the arrow of continuous entropy, Entropy motions and expanding space, which physicists dogmatically consider the only arrow of the Universe.

According to the Principle of Correspondence, any new theory has to include the previous theories within it and solve the questions unresolved by all those previous theories. Since the XX C. theory of space-time is Relativity, it is unavoidable, to explain the Principle of Local Relativity from the perspective of the Time Arrows of each species.

Relativity establishes that in any point of the Universe the coordinates of the entity (the up and down, right or left directions) are different from those of any other point of the Universe, as they only depend on what happens in that local region of space/time. This is only possible if space/times are fractal, discontinuous, broken into infinite points of view that gauge and map the information of reality from its own perspective.

Relativity thus is at the core of the structure of the fractal reality and must be considered the right step into the process that has taken the knowledge of multiple space-times from Leibniz’s analysis of relational space-time to this book, which generalizes all those findings to all disciplines and species.

According to Relativity what happens in a point of space-time doesn’t affect what happens in other isolated, discontinuous point. Each space-time fractal is a Relative Universe=World in itself. Thus the isomorphisms of space-time apply locally to each fractal ‘species, superorganism or world’ that will reflect those isomorphisms in its own structure. We are local, ‘diffeomorphic’ species; our time-space coordinates are relative. Time wrinkles our vital space in the process of aging with different speeds, depending on our content of Entropy and information.

Hence the diffeomorphic principle also establishes different informative cycles – the multiple ‘clocks’ of Nature that show different speeds and locations. Yet since space is synonymous of Entropy and time synonymous of information, we can establish the local coordinates of space-time of each being by establishing its relative informative and energetic arrows – its relative body and head – using the invariant Isomorphisms and dimensions of all spaces and times, *as long as we can localize the origin of those arrows; that is, the Non-Euclidean point of view, where the will of the Entity ‘exists’*.

Some geometrical tips about the location of those points in any superorganism or world should guide researchers:

– The point will be a relative ‘unmoved’ Aristotelian God, cause of the motions of all the other elements of the organism.

– The point has the max. density of information and the max. number of connections with all the parts of the organism.

– The point is either in the center or top of the organic system.

– The point is a spherical or convex, informative shape.

Thus in a human being the point of maximal will is in the eye-brain system, on top, with spherical (eye) and convex (brain form), which has the maximal connections with the rest of the body (nervous axons), the maximal density of information and it is the part of the organism which maintains more often a still position (balanced by the negative sensation of vertigo.)

In a historic organism, the point will be the capital, most likely in the zone of maximal communication of the nation – a coastal port, like London, Amsterdam, Rome or Athens or a central city like Madrid, Moscow, Mexico.

In a cell the point is in the center, with max. DNA information. In a galaxy, the point is in the center, where a swarm of black holes control from its unmoved position the motion of stars.

Indeed, according to the ‘Diffeomorphic Principle of Relativity’, every fractal space-time is independent of all the others; since it has different spatial and informative orientations. Yet we can recognize its informative and energetic organs in relationship to each other, since both will respond to the opposite dimensions and morphologies of Entropy and information.

Those isomorphisms of geometry also allow us to study ‘dual’ complementary entities of Entropy and information (Bodies/Brains, fields of forces/particles, energetic victims/ predators), which will create complementary entities that last in time (organisms) or are Darwinian events where the larger, energetic victim is prey of the smaller, informative point.

In the graph, in biological species animals use light as information and so they are ‘informative’, smaller and faster than plants, which use light as Entropy and are ‘big, slow’ beings.

Thus plants are the relative Entropy of animals. Further on, since what it is Entropy for plants is information for animals, both species have opposite Entropy-time coordinates: plants have their brain upside down in their roots that ‘feel’ chemistry; while animals have their brain on top, looking at the light they use as information. In the cosmological scale stars are big, slower than black holes, which rotate faster and have cyclical height.

And the space-time equations of black holes are inverted to those of electromagnetic stars. And so stars are the relative Entropy that feeds and reproduces black holes, which seem to behave as ‘gravitational animals’, species that perceive gravitation as information, which guides its precise movements through the galaxy, in the same way animals perceive light as information. While plants perceive light as Entropy in the same way stars absorb gravitational space-time as Entropy, deforming it with their masses.

That cosmological homology defies the anthropomorphic myth that only humans perceive the information they gauge. That religious myth, which denies the sentient, intelligent nature of the Universe, is today a dogma of ‘mechanist science’. So it will not be easily accepted by the self-centered ‘Galilean paradox’ of Humans, who always will think to be the center of the Universe. And since science is a human endeavor, ‘enlightenment’ and respect for the sentient Universe will not happen soon. Yet only a theory that affirms the existence of will in all knots of information that control from its unmoved position reality explains the role of black holes in the galactic ecosystem.

The discontinuity and minuscule size of informative points, due to its opposite properties to those of space, makes them difficult to localize by science, and our incapacity to ‘perceive’ the internal mind/world of the point makes easier to deny them. Indeed, all mountains have a single point of discontinuity in its informative height.

And so you have also two single points of will in your complex visual/verbal I=eye-world: the nervous point that connects both eye-visions which determines your rhythm of space and time (the size we perceive as normal given by the eye vision and the rhythm of our human time, a second per thought, equal to the rhythm of perception of the eye, which winks every second); and a yet unknown cell, probably a Purdinke cell in the limbic system that defines our emotional åctions, the will of our body.

Those points are stillness, as it is in your eye, to ‘focus’ and create a map of linguistic information, which will guide the åctions of the point. And so a basic beat of the Universe appears in all systems; a rhythm of:

*Stillness (perception) ->action(motion searching Entropy/form)*

For example, in Relativity, this dual beat explains the Michelson experiment, without the need for the *never proved postulate of a limit of c-light speed in the Universe, today clearly shown false by experimental evidence (non–local gravitation, quasars expelling matter at 10 C, dark Entropy flows, quantum tunneling, the spooky effect of entanglement, etc.). *In classic relativity this limit was needed because classic physicists considered that the electron was in motion when it emitted light, and so they had to add the speed of the electron and the speed of light. In fractal relativity the electron ‘stops’ when it emits information (the light frequency) then moves and so motions do not add since when the electron emits information is always in the particle/still/informative state.

And so the Postulate of a c-speed limit is not required. This dual stop and go process is also evident in film: the celluloid stops to let pass the light and create an image in the screen even if we perceive it in constant motion by adding all the stills, as we add from the human point of view, all the stops and goes of the electron that emits the light observed in the Michelson experiment in a single flow of motion.

The existence of an information arrow explains also the paradox of informative, evolving, life species in a Universe that seems in energetic expansion:

If we are external to a certain diffeomorphic space-times its directions do not affect us, but if we are inside a certain space-time, as in the case of the galaxy, then the direction of information or Entropy of that macro-being becomes the direction of Entropy or information of our ecosystem.

Indeed, there is more information in the center of the galaxy, and since the Earth moves towards that center, this planet increases its information towards the future in its relative discontinuous galactic space-time, regardless of what happens in the Universe as a whole, which seems to be ruled by the opposite arrow of big-bang expansion and entropy. This subtle change of paradigm caused by the discontinuity of space-time (from a world ruled by entropy to a galaxy ruled by information) has in fact enormous consequences to our daily life and explains the contradiction between the arrow of life and evolution, local to this planet, and the arrow of Entropy and entropy proper of the intergalactic space.

Since here in this galaxy space doesn’t expand but time-information contracts it through the ‘will’ of informative black holes of mass and in this planet, through the ‘will’ of living beings. As Woody Allen put it in Annie Hall: ‘Brooklyn is not expanding^{’.} I recall to ask Mr. Hawking in a conference at the Astronomy Institute of Madrid this same question, when at seventeen I was starting to doodle with the first principles of Multiple Spaces-Times Theory: ‘why space is not expanding between you and me?’ He wondered for a minute or so and responded ‘next question’.

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

*Recap*. There are ∞ fractal space/time fields that constantly adapt their organic, moving dimensions to the directions of their relative Entropy and temporal information, conditioning the existence of its micro-cells; and so the galaxy conditions the arrows of time of its cellular sun and human beings of maximal information; while plant which obtain only Entropy of the sun have inverted parameters to those of animals.