Home » -0points » 1st ¬Æ Postulate: Fractal Points

1st ¬Æ Postulate: Fractal Points

±∞ ¬∆@ST:

‘A point holds a world in itself’ Leibniz, father of relational space-time.

Abstract. The first and fifth postulates of non-Æ geometry seems similar, as the first defines a point with inner parts and the fifth, the only one so far known to present science defines a point as crossed by ∞ parallels. But a closer look at its Euclidean equivalents show that they have ‘2 different perspectives’. The first axiom of Euclid focuses on the non-existence of parts to define a ‘self-evident’ point so its equivalent  In Non-AE will focus on the INNER parts of the Point, which we shall call a fractal point.

The fifth however focus on its outer parts, the parallels, waves of communication or fractal networks (2nd postulate) to which they are attached.

Or in other terms, the 0-1 palingenetic sphere describes the 1st fractal points and ITS PARTS.

The fifth 1-∞ mind point looking at the outer entropic world describes the 5th Postulate.

So we shall call the definition of the fifth postulate a mind.

Both of course are connected. The flows of information of the outer world focus in the inner linguistic still structure of the mind. But a more subtle difference is this: a mind is concerned with mapping the outer plane of reality or ∆+1 ‘world’. While the fractal point is connected to its physiological networks, which intersect in the mind and explores through them the ∆-1 scales of its physiological existence.

So the Non-Æ point or T.œ, ∆º, has an ‘outer mind’ defined by the fifth postulate, which focuses in the ∆+1 world; while its fractal inner self focuses in the 3 physiological networks that connect it to its ∆-1 cells.

This post studies them as fractal points with inner parts connected to its physiological networks and ∆-1 planes.



The proper way to convert mathematics in what it is – the best mirror image of the properties of the fractal Universe – is to start with the laws of Non-Euclidean geometry, and then build up through the next layers of its reality:

  • S=T; the vital geometry of points with parts; parallel to the theory of numbers, in sequential scales; that move through:
  • ∆T(st): Analysis, that study its Dimotions and reproductions that form lines that are waves and networks, which become…
  • ¬∆@S≤≥T Algebraic Organic structures, self-centered in points of view (mental frames of reference), whose variations form ‘group species’, tracing worldcycles of existence through its Dimotions.

It is then obvious that we shall start such adventure with the study of the…

1-5th Non-Æ Postulates of Fractal points.

The Universe always starts with an asymmetric being, which can go both ways: towards a social evolutionary symmetry that lasts in time and implies a mirror parallelism, or an antisymmetric destructive, perpendicular event in which one part punctures and absorbs the energy of the other. It is the topo-biological ternary principle of non-Euclidean, Non-Aristotelian I-logic geometry that puts together both the biological and mathematical properties of reality.  The concepts of symmetry=parallelism, antisymmetry=perpendicularity and asymmetry are mirrored by the 4th Non-E Postulate of similarity. But we can extend the concept of asymmetries also to asymmetries of time, between the young age of locomotion and the old age of information, of actions=Dimotions between the step and stop similar actions, and the entropy and social evolution actions, which bring us the final asymmetry of scales between the upper arrow of whole with more spatial size and the lower arrow of parts with more information. When those dualities: step-motion/stop-perception and scale up (5D: social evolution), scale down (4D: entropic dissolution) are put together we obtain the most complex balancing dimotion, reproduction, and when they are all added up in the existence of a being, we get its world cycle.

In the graph, a ¬Æ point is a one-dimensional ‘form with parts’, as it has ‘inner energy and information’. As such it corresponds both to the first Dimotion of generation and the 5th Dimotion of non-Euclidean points that perceive a larger world. Why then 2 postulates? Because the 1st postulate is akin to the first dimotion when the memorial information of the seed WANTS TO GROW outwards and order a territory emerging as a larger whole, while in the final phase, in the 3rd age and entropic death the point is inwards looking, and finally disintegrating in an explosion of energy.

What is then a fractal point? All what exists.

It is both the beginning and the end. The point first perceives, then moves, And so itbecomes then a bidimensional wave of points exchanging flows of energy and information, as points with parts become cycles.

While a plane becomes a 4-dimensional ‘holographic topography’ with temporal height and movement, a quantic network of social points put together by n-flows of temporal energy. with ‘dark spaces’ in the holes of the network, and energy and information ‘dimensions’ to absorb energy and information.

Since a dimension is a flow (dynamic version) or network (static version) of energy and information around which quantic, cellular points gather into bidimensional waves and 4-dimensional space-time fields. Even the smallest points gather in waves which are lines of points that scientists call strings with 3×3 inner dimensions. Those lines then gather in herds called planes. And planes gather in topographic, relative, ecosystems, in which those organic points communicate energy forces and informative bits, showing in this manner their systemic nature.

For example, each human is made of many quantic points of space-time, that in the specific case of a human being we call cells, gathered around informative, nervous networks and energetic, digestive and blood networks that give 4-dimensional volume to the human space-time field.

But there are many types of points with parts gathering about networks of temporal energy: atoms in a molecule, stars in a galaxy, strings in a microcosmic piece of vacuum, etc.
In fact, once we have clarified that the Universe is made of points filled with temporal energy, it becomes clear that the fundamental mathematical property of those points-beings is its social nature. Since a number – the social unit of algebra – is a social set. While a plane – the social unit of geometry – is a social herd. Thus, the fact that all beings have mathematical properties means they associate in herds called numbers and planes, which are quantic networks made of Non-E points with a certain content of spatial energy and information.

And the sum of all those herds of points that aggregate in a series of systems and structures with discontinuous parts (humans made of cells, made of atoms, etc.) is the fractal Non-E space-times we call reality. Even the Universal vacuum, which seen from a macroscopic point of view seems a continuous, static emptiness, when observed in its microscopic scale becomes a ‘foam’ of space/time quantic energy, moving and fluctuating constantly.

In terms of size, the biggest of those space-times is the Einsteinian gravitational space-time, in which the luminous quantic space/time network seems to ‘float’ as a net in the water, occupying a mere 4% of it. Then we find ‘floating’ within that light-space a huge number of smaller, discontinuous masses and charges, or physical space-times points, some of which organize in complex, social networks which form the organic space-time of living beings like us.

   The 5 Postulates of Non-Euclidean, i-logic Geometry.

In the next graph we resume all the elements of the 5 postulates of Non-E=i geometry:


According to the Correspondence Principle a new scientific Theory has to include all previous ones. So happens with Multiple Time space Theory, which includes as specific cases all other simpler geometries of space-times, by completing the 5 Non-Euclidean postulates of geometry and adding the concept of a fractal point developed in XX C. fractal geometry. The result is a geometry that includes all other geometries; since the incomplete non-Euclidean geometry discovered in the XIX c. (5th postulate: a point can include many parallels) already included the previous Euclidean postulates based in points through which only one parallel can be traced.

Those new postulates describe with more accuracy all type of space-times belonging to all kind of sciences, from the physical space/time of atoms (described by quantum Physics) to that of galaxies (which Einstein described in his General Theory, using the 5thNon-E postulate); from the organic space/time of cells and species to the historic space-times of nations.

Thus, according to the Correspondence Principle, we establish a hierarchy of completeness among all those geometries that stretches from the simplest Euclidean Postulates to the i-logic geometry of fractal space-time, which includes all others as particular cases; and it is in itself a partial image of the total information about space-time we call reality – always bigger than any ‘linguistic’ image we made of it with the languages of the mind that reduce the total information of reality to fit it in the brain:

Euclidean Mathematics (Light- Space)> Classic Non-Euclidean geometry> (Gravitational Plane) > Fractal space-times (all scales) > Total Reality 2

We consider Euclidean geometry, the natural geometry of a single, continuous space-time, made by the ‘eye’ only perception of light-space and its 3 perpendicular dimensions (height/electric field, width/ magnetic field, and length/c-speed). But that space is not all the spaces of reality.

It misses at least a second fractal scale, gravitational scale and all the complex, vital spaces of organisms of information and matter. In Non-Euclidean mathematics, the new unit of ‘fractal space-time’ is the 3-dimensional Fractal Point of view, whose main property is to have in/form/ation – an inner content, which in a Universe made of multiple scales of size, we perceive as we come closer to the point and observe it in detail. Those fractal points with volume are described by the 5 Postulates of Non-Euclidean Geometry, which adapt to fractal, discontinuous space and cyclical time, the classic 5 Euclidean postulates.

The first postulate explains a fractal point, as a point with parts. In a more detailed analysis those parts turn out to be self-similar in geometrical terms, in all systems, due to the specific lineal vs. cyclical, concave vs. convex geometries of energy and information and its ‘planar combinations’.

In its more complex versions those geometries are defined by the three canonical topologies of a four-dimensional Universe, which describe the informative ‘head’, reproductive ‘body’ and energetic limbs and membranes of all the superorganisms of the Universe.

The 2nd, the interaction between two points connected by a wave of communication or ‘line’, the 3rd, the type of ‘biological’ interactions between 2 points according to their relative equality, and finally the 4th, the complex structure of a system of points across multiple organic space-time planes, such as those who create a human being.

Thus, the more evolved Fractal, i-logic Geometry of space/times includes all previous geometries as simplified cases of the more complex structure of the Universe in multiple scales. We call it a fractal, i-logic Geometry because some postulates can be interpreted in geometric terms, as the definition of the essential elements of any geometry of space/time (the point, 1st postulate; the line, 2nd postulate and the plane, 4th postulates) and some in logic terms, as the description of the different causal chain of events that can happen when st-points enter in communication -3rd, 5th and 4th postulates:

Further on, according to the duality between geometric form and logical function, those postulates of fractal i-logic geometry define also the basic arrows= cycles/dimensions of the Universe: the 1st and 5th postulate define a point as a system whose inner parts are able to transform and emit energy and information, e>o<e; the 2nd postulate defines an exi wave of communication that reproduces energy and form between 2 fractal points; and the 4thpostulate defines the social evolution of a herd that creates a fractal plane, a network with dark spaces; and the 5thpostulate explains a point in its iterative actions as it absorbs energy and transforms it into information through its small apertures to the Universe. Since even a minimal quark of mass, as Einstein affirms should be crossed by ∞ parallels.

The importance of the ‘linguistic laws’ of i-logic geometry resides in the fact that all systems of the Universe follow in space the laws of geometry and in time, the laws of logic, so the enhanced linguistic mind of science obtained with those laws can be used, as this author has done in multiple works to resolve long-standing questions in all sciences, which can further be ordered in a pyramid of increasing information and diminishing energy:

The best coordinates to represent a Function of Existence are cylindrical coordinates, where a point is defined by 3 different parameters:

Screen Shot 2015-10-12 at 20.33.51

Now the simplest part of the Universe is a continuous surface of space, whose parts are so small that seem non-differentiable continuous from the upper perspective of the system.

These systems, are idealized with the mathematical concept of a point with parts that shares flows of energy and information with other points and forms across different scales from past to future relative topological webs of existence.

Physics studies the simplest forms with maximal energies. But if we consider the 2nd arrow of ‘creation’ of reality, that of form, of information, the summits of science are biology, which studies the most complex forms of information (life) and Sociology/Religion, which goes a step further into the analysis on how the arrow of eusocial love creates Human Societies according to the Organic laws of the Universe (eastern religions).

To be able to consider biologic behavior (social evolution) and ‘mental perception’ (informative gauging), as factors dependent on geometrical qualities is an astounding break-through for science, which will be developed in its details in this work, to show an enormous number of experimental proofs.

Indeed, fractal, i-logic Geometry achieves a long-sought goal, which Plato, Spinoza and Leibniz tried to realize, but failed, with the use of simpler Euclidean geometry: to unify the logic and mathematical principles of the Universe. Since the 3rd and 5th Non-Euclidean postulates are logic, the 1st and 2nd are geometric and the 4th, the nature of a topological plane or network of non-E points is both logic and geometrical, as it defines the fundamental logic-geometric structure of the Universe: the superorganism.

The logical and mathematical conclusions we shall arrive in this chapter are the same we achieved in the previous one with a more descriptive, less formal analysis: the Universe’s final goal is to create ‘topological, organic planes, super-organisms’ – the 4th, more complex ‘geometrical postulate/form of reality’ – departing from simpler forms, points and cycles. We shall try to get to that conclusion step by step, first by describing the geometrical postulates, then by uniting hem with fractal mathematics and finally by studying the most fascinating of all of them, the 3rd postulate, which proves that behavior among the points of the Universe is based in the degree of equality or self-similarity between their inner form that determines if those forms communicate symbiotically or destroy each other, thus defining the duality of eusocial evolution as a group of a number of self-similar beings or destructive extinction.

Some, first-hand consequences of those postulates are:

– 1st Postulate: We correct Euclidean geometry, increasing and relativizing the dimensions of a point that fits inner energy and information. Since all points have either 1 motion, a time dimension, when we consider them from the perspective of the upper ∆+1 Plane for which they are in the limit of invisibility (what quantum scientists call a point-particle) but still has a motion or ‘function’ in that upper ecosystem, ∆+1 in which it exists; and 3 dimensions/networks/functions when we consider them from the inner perspective of the point.

This is the case even in the smallest planes of theoretical strings, made of points with parts, with volume – since we require 3×3+i theoretical inner dimensions to describe them – a paradox that can only be resolved if we consider the to be ‘strings’ of fractal points with inner, fractal dimensions.

– 2nd postulate: When we observe a one-dimensional line as a form with inner parts it becomes then a 4-dimensional wave made of cyclical points with motion. Hence in quantum theory we say that any particle in motion has associated a wave.

Thus the 2nd postulate resolves the wave/particle duality, as all lines are now waves traced by a point with inner volume. Further on, since all lines have volume, they carry information and so all forces can in fact act both as a source of energy and as a language of information – as physical experiments prove. Since when we observe a ray of light in detail it becomes a 4-dimensional wave with electric height and magnetic width, often exchanging flows of energy and information in action-reaction processes of communication between bigger points.

– 3rd Postulate: Equality is no longer only external, shown in the spatial perimeter of any geometrical form (3rdEuclidean Postulate) but also internal and further on it is never absolute but relative, since we cannot perceive the entire inner form of a point – hence the strategies of behavior such as camouflage. Forms are self-similar to each other, which defines different relationships between organic points, according to their degree of self-similarity. The 3rd postulate is thus the key to explain the behavior of particles as the degree of self-similarity increases the degree of communication between beings. Some of the most common behaviors and ‘events derived from this postulate are:

1) Reproductive functions in case of maximal self-similarity or complementarity in energy and form Max Sp x min. Tƒ (male)= Min. Sp x Max Tƒ (female).

2) Social evolution, when points share a common language of information, Tƒ=Tƒ -> 2Tƒ.

3) Darwinian devolution when forms are so different that cannot understand each other’s information and feed into each other: Tƒ¹ o. In such cases if those 2 entities meet they will start a process of ‘struggle for existence’, trying to absorb each other’s energy (when E=E) or simply will not communicate (when E¹E, since then there is neither a common information to evolve socially nor a common energy to feed on). Yet because any point absorbs only a relative quantity of information from reality, self-similarity is relative and it can be faked for purposes of hunting, allowing biological games, such as camouflage and capture, or sociological memes that invent racial differences, allowing the exploitation of a group by another.

The geometric complexity of the 3rd Postulate is caused by the topological forms created by any event that entangles Multiple Spaces-Times. Since it describes the paths and forms of dual systems, which connect points: Self-similarity implies parallel motions in herds; since equal entities will maintain a parallel distance to allow informative communication without interfering with the reproductive body of each point.

Darwinian behavior implies perpendicular confrontations, to penetrate and absorb the energy of the other point. Finally, absolute, inner and outer self-similarity brings boson states, which happen more often to simpler species like quarks and particles that can form a boson condensate as they do in black holes, where the proximity of the points is maximized. And indeed, the same phenomenon between cells with the same inner information /DNA originates the ‘collapse’ of waves into tighter organisms.

The 3rd Non-Euclidean postulate is implicit in the work of Lobachevski and Riemann who defined spaces with the properties of self-similarity (Riemann’s homogeneity), which determines its closeness (Lobachevski’s adjacency).

– 4th postulate: Now because a plane has an inner volume – that of its points – it is a cellular, organic topography, a network of self-similar points. And because networks of points of energy and information are complementary, often we find systems with 2 complementary networks that form ever more complex geometries – based in the geometrical dualities of lineal energy and cyclical information – with the results we observe in nature: the creation of an enormous number of complementary systems which are, as we shall see latter, all of them self-similar in its geometries and functions.

Thus, the types of Non-Euclidean planes of space-time range from the simplest Euclidean planes to the more complex organisms with a volume given by the relative point/beings that form its space-time networks.

Thus, a plane becomes a real topography made of points with volume, extended as a cellular surface.

We can observe its surface as a bidimensional membrane of information (for example your skin, or the screen of a computer made of pixels, or the sheet of this work). Or we can consider the 3-dimensional inner structure of its points and then it becomes a network with inner motions, as those points will form a lattice in which they communicate lineal flows of energy and information that maintain the lattice pegged. Often 2 topological planes of energy and form combine to create a 4-dimensional organism. Such is the most common structure of the Universe, a 4-dimensional World, which is a Universe in itself, made of self-similar cells or networks of points that constantly exchanges energy and information within the ecosystem in which it exists.

– 5th postulate: It defines points as informative knots or linguistic eyes – minds of information that absorb a flux of forces used by the point to perceive a relative world. A non-Euclidean point corresponds then to our concept of a relative mind that gauges the information reality with a certain force, similar to the concept of a monad in Leibniz relativistic space-time. In words of Einstein: a point of space is a fixed frame of reference.

Thus, Non-Euclidean mathematics fuses the logic and geometry of the fractal Universe, greatly improving our understanding of Reality even in terms of mechanist measure. Since mathematical solutions to problems with several points of view are impossible to find in continuous space (i.e. 3-body problem in gravitation), given the fact that a network of infinite points of view is local and relative and each point is a focal knot that acts from its perspective.

Thus, the absolute truth of a system is the sum of all its points of view, which influence each other. Yet even if we cannot calculate precisely with mathematics, systems with more than 2 bodies, since those systems are organic, hierarchical, made of networks with attractor points, fractal structures and self-similar paths, the new mathematics of attractors, fractals, scales and Non-Euclidean systems, refine greatly our analysis. In essence, indeed, we observe that ‘networks’ integrate parts/points into wholes, which then ‘act’ as a single point. So in the complex models of i-logic geometry we can tackle many problems by defining sets of points as ‘wholes’ of a ‘higher space-time’.

But the most rewarding consequence of the new language of the mind is the ‘deep’ understanding of the meaning of many experimental facts about the species of the Universe till now merely explained as hows. For example, the previous principle of local measure, where each point is a relative center of the Universe, is called in relativity the diffeomorphic principle, which now becomes explained as a partial case of the wider law we called the ‘Galilean paradox’; the duality particle of information/wave of energy becomes a specific case of the application to physics of the duality of energy and information found in all systems and so on.

The expansion of the laws of quantum theory (complementarity principle) and Relativity (relativity of scale, local measure, etc.) to other sciences and the organic principles of the 3rd and 4th postulate to physical particles is therefore the consequence of those postulates.

Yet it requires the understanding of the new, i-logic, organic laws of the Universe and its networks, because E-mathematics has clear limits to extract all the information of the Universe, given the fact that it syntax includes a priori errors and simplifying postulates (single space-time continuum of points without parts, etc.).

Thus, when the event described is complex, performed by a great number of points/variables you enter into non-lineal systems, which require topological descriptions (chaotic attractors, fractal non-differentiable equations and Non-Euclidean mathematics), and the i-logic laws of organic networks and systems – a better syntax in which to fit experimental evidence, especially in phenomena of informative nature (since only formless energy is continuous and resembles the models built with a single arrow of energy and a single plane of space-time).

So while classic physical systems calculate accurately the energetic, continuous properties of the Universe an overview on how multiple points of view emerge into wholes requires organic laws. Of course, this search of whys also applies to the understanding of mathematics. For example, the previous postulates resolve the long-standing question of what is the nature of the 3rd and 5th postulates that seemed redundant (as the 5th describes also properties of a point like the first does, and the 3rd seem to describe a non-geometrical property). They are no longer redundant, but they are more concerned with causal logic and time than spatial geometry in its purest forms (points, lines and planes.)

There is also self-similarity between the fractal postulates of i-logic geometry (since the 5th is geometrically self-similar to the 1st, as both are concerned with points) and the 4 dimensional time paths/arrows of the universe. This is not casual since all languages of space-times depict in self-similar ways the 4D Universe.

Thus if the 1st and 5th postulates define a gauging point of information as the fundamental unit of the Universe, the 2nd postulate defines a line or flow of communication of energy and information between 2 points, which reproduces part of the information of the ‘generator’ point across a surface of space; the 3rd postulate defines those points, which are not similar as energetic substances that will be absorbed by the points. Yet if those points are self-similar they will gather through the arrow of eusocial love, creating according to the 4th postulate a network of space/time, a new organic plane of existence. So the 4 arrows of space-time are explained by the 4 postulates of i-logic geometry.

Recap. The study of the geometric paths of Time Arrows with the tools of mathematics, explains the whys of mathematical laws:  Geometry and topology acquire now its ‘why’: topology explains in detail the 3 canonical parts of all Points of view, while the i-logic postulates of geometry explain the universal structures that those points of view create.

We use the symbol @ similar to ae, if you imagine the form as a whole larger e, as the alternative symbol for the mind, as @ it is also topologically meaningful with the 3 parts of the whole self-centred in the subjective •mind fractal point of view.

It is though part of the fun of the paradoxical mind, that the mind is limited and diminishes dimensions so it becomes aristotelian and Euclidean, self-centred and subjective, despite existing in a larger, non-æ point of view. So the 5th non-euclidean postulate paradoxically defines the functioning of the Aristotelian Euclidean mind, a point of view with an arrow of time, directed towards itself – of survival and growth of its own being (even if the non-se external Universe will suck in its energy and information to make it less infinite in its infinitesimal ego.

So the mind is topologically, memetically and conceptually meaningful of what a mind is. In terms of location the mind is at the point of maximal information of the system.

Yet the mind is Aristoteian and Euclidean, in relationship with the complete Universe. And that is essentially the difference between the non-Ae universe, much more complex hardly perceived by the subjective ae reduced mind. So we express this simple AE mind, with the symbols Æ or @ (as you can easily imagine the whole symbol to be an e with the central a-mind enlarged).

Thus the ultimate tension between the world and the Universe, the mind and the subjective point of view, and the whole and the objective point of view in terms of complexity happens between the simplex, Ae minds and the wider œ,  (ab. organic universe), such as Œ>æ, and ∑æ=œ.

The mind is thus the existence of the language itself in its pure form expressing a game called existence, and we do know this is the case through philosophy of science since Kant made his distinction – we are not indeed talking of anything material when we talk of the game of will and existence that moves the Universe, but a short of logic circuitry of biological actions that ensures a good knot of space-time cycles to have an inner mirror that will reflect properly its flows of energy and information trying to imbalance the external Universe in its favor.

As such the mind is pure language, something we know by observing the two minds of the human being, inside, the mind of the ‘cogito ergo sum’, ‘and the word god became man and inhabited among us’ and other mystical understandings.

While in the ∆+1 scale of super organisms of history the mind-government is the verbal-legal and financial-digital informative linguistic classes that control the languages of the social organism. So the mind is modular, made of neuronal people-castes on top of societies with linguistic control and we shall see that in all scales this is the case. The mind of cells are informative DNA-rich cell centres, which codify in its mirror-crystal like form, a holographic genetic code.

In the next graph we see the hardware and software of the human mind and its superoganic mind – which in physical systems would be the quarks of the atom, the crystals of solid matter, the black holes, bosons of top quarks in galaxies, always the system that combines the sensorial external membrane probes and the central point of view flux of all those motions which bring to it pixels of information, transformed by the mind languages into a still images of less-dimensional æ-simplex but meaningful and efficient, logic circuit-images of the whole, it will territorially manage to preserve its self:



In the graph, the old mystical representation of the mind,  with its o-black ball at the center, as the central black hole of the triangle of a tetraktys, with its 3 corners of 3 x 3 elements acting as active organs of energy  information and reproduction – as such the symbolism of the tetraktys both in terms of ‘scalar, social, topological, mental and even temporal parameters’ is remarkably accurate.

We prefer though a single letter symbolism, @. The @-mind is the AE, simple logic, world written in a limited language, which stores the logic knots that tie up in mental, time-configuration the @tions, the beings must expess in the external, universe, ‘

The symbol thus abbreviates for ae, the logic of the mind and ac, the active site of the will, and o, the central o-point of the mind, and its memetic meaning today ‘at’, the relative position of a virtual human mind in digital space.

Its equation is obvious:

O-mind (knot of the tips of a few of)… x ….. ∞ Universe of space-time cycles =Linguisitc mapping mirror.

The mind is thus the infinitesimal  mirror, © being also a symbol I often used for it, with the c-urved cyclical mirror in the center, a good symbol for the mind as a knot of time cycles.

The mind is a fractal point of view’ (mathematical interpretation) or zero point, in which maximal flows of information converge, both from the external and the internal regions of the being, where the will of the ‘4 actions’ resides. As such @ represents the topology of the whole

The Mind is the ‘point of view’, site of the will, that perceives each element, each part.

It is the i-centered dimension, in the sense that it is the most ‘connected’ point, in the centre of the system, which ‘reflects’ upon the existence of the whole.

In mystique terms it is in a way the soul, the atman. It is the central number of maximal communication in the tetrarkys that Pythagoras rightly considered the perfect number, illustrated in the Kabala graph above.

In Physico-mathematical terms it is the final black hole, non-euclidean point of view of the system. It is the 10th or 11th dimension of Time on the string formalism, etc.

In biological systems it is the nervous, ’10th system’ that integrates the other 3×3, energy/reproductive/informative physiological systems of the human being.

Depending on which ‘human jargon’ with more or less errors – lacking the iST formalism and GST philosophy – we talk of, it will be ‘named’ with different forms.

I often use the term the 5th Dimension, of all i-scales of the being, to represent the ‘whole’. And so we have termed it also as the 5th ‘invariance’ or ‘isomorphism’ that all beings share, since the mind-self, the centered dimension of all scales, the 5 isomorphism of nature, the point of view, the soul is the most important dimension of all beings.

It wraps up all the other dimensions, isomorphisms and scales.

And it is therefore the centre of its 3×3 i±4 scales, its 3 topological space organs, and its 3 time ages (the being is at its maximal force, in the ExI (e=i) steady state mature, adult age of balance, STd, age of maximal duration.

In man obviously is the brain, expression of the ‘Whole’ or ‘Soul’, which perceives internally the system through its ∑3×3 networks (our sensations of the energy, digestive system, the reproductive, endocrine system, and the mind thoughts and emotions) and externally through the senses. But in many other systems is a very different site.

So perhaps the best definition is that of Non-E mathematics: the ‘point of view’, the part of the fractal point that gauges maximal information. 

Minds are still: Information can only be obtained with a fixed point of view.

Why we need a fixed point of view? Easy, because to measure and perceive we need to focus and be still to observe details. If you take a picture of a fast moving object is blurry. If you try to perceive the details of a fast moving object you will not be able to do it. This happens because knowledge gathers information and in-form-ation is ‘form’. But form is the opposite of motion. In the Universe all what you see around is form with motions.

This is very important to grasp. Look around. What you perceive is only 2 things often combined: Forms of information and energy motions. And actions of beings that combine motion and form.

And both things have opposite properties. The less motion the more form you observe, the higher motion the less form you observe. But knowledge is form, information. So to create knowledge you must depart from a relative, fixed point of view.

And so that is why you do not see the Earth moving but fixed. This is how nature has given you a capacity to observe with your mind reality as still, with form.

You need a pov to create a certain  scientific truth. But the larger the p.o.v. the bigger the truth. So the center has moved but each new age of science have kept a relative still point of view. You must create a still center to measure, because perception happens in stillness, as opposed to energy, which expresses itself with motion. Information focuses form and it must be still as Buddha was in the tree of knowledge.

So when Galileo came the earth moved and the new still p.o.v. Was the sun.

And when Darwin came the idea that man had not evolved, changed but had always been still, the same form created by God per in secula seculorum moved and now the new ‘still p.o.v.’ of biology where the immutable laws of evolution.

Now this allows you to understand the limits of Einstein’s paradigm. Since what Einstein did is to create a new still point of view that could not be changed. It was no longer the Earth, it was not the sun. It was not even man or evolution. What was the new still point of view from where Einstein would take his rods of measure?


Einstein defined a Universe with a new point of view, the speed of light, which would remain constant from any perspective.

But why light?

Light seems an esoteric center. What makes light so essential to our view of the Universe, as to permit ‘measures’ that seem to be more accurate to our mind?

We must now give you the first upgrade on Einstein’s work by affirming that light IS the substance of the space we perceive with our eyes. And that is why from the perspective of our mind, which is what you are truly observing – not the full Universe and its exact objective measures, but the peculiar rod of your eyes and any other electronic mechanical device that absorbs light  – light IS space.

Indeed, you do not see reality in its totality, but light and so what you call space is light-space. And when you use an instrument, made to the image and likeness of our mind, you see light-space too.

But if you were a dog smelling the Universe, your mind mapping and distances would be different.

We are though an I=eye and for that reason our mathematical mind and light-space has 3 Euclidean perpendicular dimensions (the so called electric, magnetic and ray directions of light, which are perpendicular), which are the same dimensions of your perceived space.

Thus, what really Einstein did was to consider a larger point of view that the sun, the entire space of the Universe.

The center now had moved to every point of the Universe, and this allowed Einstein to say that all motions and points of view were relative, only space-light was a fixed background that didn’t change.

But he still established as a rod of measure of the other variable, time, the human clock; and so here, there were no advances on the objectivity of the point of view. ‘Time is what a clock measures’ he said.

Einstein did NOT change the point of view of the human clock, reason why Landau laughed at him saying that with his system he just had to ‘look at his watch to eliminate the uncertainty of time’ .

And so it IS in his understanding of time, where Einstein as most physicists before, had failed to expand the point of view. And it is where the 5th dimension will open up our objective view of the Universe, by defining in a more complex manner the meaning of time clock and consider the existence of many of them in the Universe.

In essence, what we want now to consider is the isomorphism between the 2 main time clocks of the Universe, according to the relative scales of the 5th dimension: the time clocks of the quantum scales, ‘charges’, and the time clocks of the cosmological scales ‘masses’.

Between them, of course there is a 3rd type of time clocks ‘thermodynamic molecules’, whose temperature define the variations of speed of those time clocks, but being the thermodynamic ∆o scale, the human scale, we do have a lot of information about those time clocks, so physicists are sophisticated enough to understand them. They do NOT understand however masses and charges, reason why they have been for 100 years trying to unify them the wrong way – without understanding they are TIME CLOCKS of different scales, of different ‘curvature’ and speed, and so they need the metric of the 5th dimension to unify their parameters.

So simple and so mysterious for a century because we lacked the proper ‘heliocentric’ perspective – an essential dimension of reality. Then once we enter into that larger reality (which physical systems do but humans obviously can’t), we are in…

Now it is obvious that as we grow in size we curve from our perspective reality and so we get less information as things slow down and part of the information disappears from our perspective, and vice versa, as we look downwards the universe become hyperbolic and grows in detail of information and so we get different entropies up and down. This is shown in the symbol of the 5th dimension, ∆, which as you can see have two motions up and down one thinner and the other thicker, and this asymmetry is important to explain many things – genetic for example, going upwards perfect in information, body motions for example perfectly going downwards when the whole wants to move. Wholes are very good with motions smallish things with information. Havent you notice how energetic and powerful are big guys, how smart are small ones? (-;

SPATIAL ANALYSIS: The mind-brain together as a space-time center of communication.

The simpler way to understand the concept of the mind is therefore that of a ‘point of maximal information and internal communication, with al the other parts of the system’. And the easiest example is the simplest, most successful ‘pythagorean’ tetraktys:

In the graph, the commonest system of the Universe is a decametre collection of points organised into a tetraktys. The relative point 5 has the maximal communication with all other points (if you trace a line between 5 and 1, 7 and 10 corners, the flow of information can also be transferred between those 2 points without interference).

The study of the tetrarkys as a topological game that represents the whole as the analysis of music with its dualist treble bass and pentagonal scales, is one of the highest degrees of spirituality of the game. The point five is in this case the mind-point of view, which we see communicates direct with 2,3,4,6,8 and 9. Yet if we consider those points entering flows of energy and information that converge in 5 in pairs, they will create an outer flow that connects straight-forward in a twice long path, 5 with 1, 7 and 10. So 2 and 4 mouths flow on 5, merge and change its angle  135 degrees to converge in 10, 3 and 6 converge into 7 and 8 and 9 into 1.  In this manner a 5 point can perfectly flow back and forth energy and information with the sides acquiring a convex form and the 1 7 10 vortices a longer distance, forming a hyperbolic geometry, and inversely, the form would then deform if the inward flows come from 1, 7 and 10, forming a sphere, and so the triangle also can be considered a hyperbolic form that can be transformed as spirals do into a hyperbolic line or sphere.

Also by rotation, the triangle can be transformed and by adjacency can grow socially into planes or geodesic spheres. It is this vital topological geometry what defines the efficiency of ∆ St@ beings.

Thus the mind of this system will be at 5, in as much as it can organise the communication of all other points, while the 1-2-3 will become the ‘informative, Tiƒ system, if that is the direction of motion or ‘head’ of the tetraktys, while the other 2 corners, 4-7-8 and 6-9-10 might become according to the fields in which the system moves, the energetic side and reproductive side of the system. For example if that form turns around a vortex of forces, the internal side with maximal gradient of force (6-9-10) will absorb energy and the other outsider side will expel a reproductive seed.

YET THE SYSTEM besides the 3 x 3 Spe<ST>Tiƒ elements defined by the Generator equation will still need a ‘central, internal communicative point of view’, which realises the whole exists, controls it and directs it by shrewdly handling the energy and information the corners absorb. This is the concept of the mind, which is slightly different from the head. Or in terms of physiology is the ‘part behind the head’, inside, in the center, where the survival consciousness exist. In humans and animals the deeper layer of the brain, where the emotional, survival hypothalamus resides.

Diffeomorphic minds: the relative location of minds depends on the flux of information.

Of course as we study the complex details of fractal systems, the Universe becomes more creative with form, as FUNCTION MATTERS MORE, and diffeomorphic geometry adapts each brain-mind to the system’s topology:


In the graph, the mind-head system is different in position in a galaxy (black hole in the center), plant (chemical roots) or animal (eye-head system).

It is thus clear that while the Tiƒ informative head system is physical and easy to study in depth, the concept of the mind or consciousness of the whole is far more ‘metaphysical’, and ‘mystical’, or ‘time-related’, as it implies the ‘existence’ of a continuity on time, through the entire world cycle of the being which feels ‘to exist as a whole’.

SCALAR ANALYSIS: Back to the tetraktys – the mind as the 10th unit which ’emerges’ into a new scale.

But the mind does have a physical place – the black ball of the triangle of pool (something understood subconsciously as you loose the game if you pocket the black ball), the hypothalamus in the animal, and generally speaking the 10th nervous system of the 10 systems of a human being (which is one of the strongest anthropomorphic proofs we have of our Nature as a space-time system. Indeed in the section dedicated to medicine, we shall study a human being and its 10 physiological systems; 3 related to the blood reproductive system; 3 related to the energetic digestive system and 3 to the sensorial system, all of them put together by the ‘brain’ or 10th system).

So besides the 3 x 3 systems we do have a final 10th system, which internally organises the whole and externally expresses the program of survival of the system, providing the leif motif for its space-time actions.

And for that reason we add this new symbol Œ, where 0 Symbolizes the mind and E the body moving with its limbs… It is thus an expression of the ‘whole’, guided by the O-head. How to write this Œ inside the generator equation varies. I propose:

Œ= ∆-1: |-Spe < ∆: Ø-S≈T > ∆+1: O-Tiƒ

Now, we have introduced the mind from a temporal, spatial and scalar point of view. This is the ternary method of knowledge that exhausts the analysis of ∆±iST beings. It is interesting if you come to read often to structure your own mind into this new form of knowledge. Think always when you study something on the spatial, temporal and scalar perspectives of the being, and then on the whole, because all do exist in those ternary simple structural terms and the ‘ternary method’ does ‘extract the best possible information of the being. We shall do so here with minds, and if we don’t is because I am unfortunately a disordered mind despite having this ‘deep insights on the minds of the Universe’ – hopefully though those who follow the path of ∆ST will be a bit more ‘professional in his ‘Manual Chicago style’ of writing papers (-;

The act of creation through languages.

The act of creation starts in the mind of information, not in the energy of the being.

What i am to state now might surprise the reader: the mind not the physical Universe, time not space, action not form starts reality. The first ‘action of existence’ is the perception by a mind of an external Universe. This is also truth if we consider the simplest possible forms of reality, the fractal minds-points of view of the fundamental particles, quarks and charges, which re minds of gravitation and electromagnetism. It is the act of perception of a field, ‘gauge’ in the abstract parlance of quantum physics, what makes an image of the Universe real.

In that sense the mind is a cartesian world that crafts reality by the act of perceiving it, ‘bending the field of entropic energy’ into a vortex. Fields create particles say physicists observing only one arrow. In reality in the Dialectic Universe, fields and particles in space, which are minds in time, create a flux of that transforms the lineal energy of the field into the curved form of information, knotted into the particle, a ‘quantum knot’, which becomes a geometrical still simultaneous mapping or mind.

This process is the essence of a mind in any system of reality:

All starts in the zero mind. This might surprise the reader but the first act of creation was perception of a virtual world by a mind. And as such we might consider that all worlds are virtual thoughts of a ‘higher mind’.

Perception is the first action, but perception is never perception of the being in ‘its self’, in ‘itself’, as it is a mirror who sees reality transmited by a ‘force’, ∑ E x I different system.

oIn the graph, one of my oldest paintings of ‘conceptual cubism’, my style of painting, which ‘draws’ with the tools of i-logic several non-Æ systems mimicking in 2 dimensions the act of 5D creation – as such the height of paintings represent the informative coordinates of an event. The conceptual comprehension is on the right. We symbolise it with the Å and å symbols for ‘Time ages’ which are the sum of space-time actions that shows the will of survival of the system:


In that regard, the first action of all systems is the awareness of existence as a whole, provided by the subconscious ‘chemical’ mind of the system, which organises an internal territory, establishes a ‘boundary’, and breaks into a fractal space-time system a form, starting the evolution of an organic system. 

So life is considered to start when a DNA mind controlled a territory by establishing a protein lineal boundary, and so the 3 parts of the being co-existing together formed. And as Feynman proved, all the laws of an electromagnetic field system created by a charge can be deduced of he existence of the charge and the circulatory closed loop that acts as its boundary. A mind-black hole establishes an area around itself with an event horizon, and at galactic level, when it creates a ‘likely’ strangelet halo. A living organism establishes a skin, a seed, a hard thin crust cover, so does the Earth, SO DOES A CRYSTAL and so on and so on.

BUT IN ALL SYSTEMS the first ‘action’ is the creation of a knot of maximal Information, Max. Tiƒ≈Œ, which will then create the whole. Those mind-points are thus the fundamental ‘missed’ element of the physical continuous, external view of the Universe, as they do establish indeed the fractal, discontinuous closed structure of all the organic systems of reality.

The first of those events was in that sense one of informative perception of a sheet of motion as form:

∆i: perception of information by a mind or fractal point of view.

There are two ‘wills’ of feeding and gauging common to all points, which we can measure objectively, externally by the fact that when energy appears, particle move towards energy (so electrons jump and feed on light) and when other particles appear they gauge their distances. We observe this property in all systems when they form a focus, which emerges as the point of maximal order in which the network of the system integrates its information.

Then the system becomes more stable: A crystal grows faster when the network creates a central point.

A hurricane can be destroyed when the central, still point where all the flows converge is disturbed. A life being becomes erratic in its motions when it becomes blind. A galaxy acquires order when a black hole, which probably gauges gravitational information, appears in its center.

The existence of an infinite number of such points is undeniable objectively and adds an enormous amount of order to the Universe, which mechanist science does not account for. Stillness to focus information into a pixelate map of the Universe, and the existence of a network that fluxes in that point through which ‘infinite parallels’ can cross, are the two conditions of formation of gauging points.

Then we can establish the birth of a complementary network of energy and information, an exi=stential point: exi=k; where k represents a ‘mapping of reality’ in the informative language that the waves of communication of the point with the external universe have created. This means that the models of metric measure developed by mechanist science merely creates a ‘space-time world’ self-similar to the mind of man in our machines, which does not exhaust all the measures of the Universe and its possible mappings.

 We cannot construct if we want to account for all the cycles of time, dark spaces and events of reality, a theory based only in a continuum, mechanical, light-space and its Euclidean coordinates of light-measure. The limits of that model have been reached, as the limits of precision of the Ptolemy’s model of astronomy were reached in the Renaissance.

Those limits of an Euclidean, continuum space-time were proved by Riemann, Poincare, Mandelbrot and this author, expanding and completing the Euclidean definitions. Einstein applied part of those new models and created Relativity Theory. This work applies the rest of those discoveries to create a model of Multiple Space-times, which includes the concept of absolute relativity, where measure – the gauging and mapping of the external universe by a non-Euclidean point, is relative to the observer and the rods of measure it uses.

What mathematicians did was rather a runaway path. Because once geometers realized that multiple lines can cross a point, they could not use any longer the Euclidean definitions.

Now points, lines, planes and equality could no longer hold under the definitions of Euclid (points, lines and planes with no breadth), they remained undefined, when Hilbert, the father of modern mathematics affirmed ‘I imagine lines, points, planes…’.

Instead the proper solution was to redefine them in terms of their ‘inner parts’ as fractal points that grew in size when we observed them with a more detailed ‘hyperbolic geometrical view’, as that unveiled by non-E mathematics.

So T.œ redefines points, planes and line-waves and their relative laws of equality (also called congruence) and continuity (which no longer holds), to refound mathematics on the basis of a far more realist view of its laws as ‘experimental laws’ that reflect the geometry of the 5th dimension and the complex casualty of a world with multiple time motions. And consider that those points with volume form social ‘numbers’, whose laws are therefore related to the laws of the 5th dimension that brings parts into social wholes.

Recap: All entities of the Universe gauge information and act-react to the external world. Thus we consider all entities to have a mind – an internal, linguistic mapping of reality made with those forces.

Fractal MINDS: the fundamental particle

Thus we must observe the Universe to prove mathematical statements and reduce mathematics as we do with all experimental sciences to those equations which ‘are real’.

T.Πdoes show by regressing a step back in the scaffolding of mathematics and defining those terms, as the Postulates of i-logic geometry, based in the structure of cyclical time, fractal space and the 5th dimension where:

1) A fractal point grows in size when we come closer to it, so it has parts, its O-mind and its E-field flows of energy or limbs. Hence we define it as Œ, an existential point.

What they perceive will depend on the Lobachevski/Gauss Constant of Time-Radius/Space-length, r2/L2 (Tƒ/Sp parameter), which defines its geometric view as hyperbolic (for smaller planes), Euclidean (for the human H/c2 plane of informative spin time cycles and light space-rods).

Let us elaborate a bit more on this essential component of the Human World – NOT the only worldview on space-time there is.

Now in the post on astronomy we explain ‘why’, light is a c-constant rod of space, and hence c² the factor of Lobachevski/Gauss definition of the form of the geometry. It follows that because H-planck, the constant of spin or minimal quanta of information of the human Universe is exceedingly small, and the ‘degree’ of Euclidean nature of a world depends on r²/L², in this case h/c² to be infinitely small so the ‘radius’ of a circle and the ‘angle of perception’ of a triangle becomes pi, and 180/3, we humans see an Euclidean light space-time.

But a bigger radius of perception (smelling minds with atomic pixels, i.e. insects) will be hyperbolic; or a larger rod of measure (action at distance in gravitation), will be elliptic (quark/black hole? perception).

Now of course, a ‘science’ as the human ego-centered science, which is fully unaware of its ego-centered paradox, and confuses the world of its mind with the entire Universe will ignore organic and perceptive explanations of reality, but they are THE ONLY ones that explain the whys of reality.

Lobachevski’s pangeometry. Where is the 5th dimension: ¬ æ ALGEBRA, AND I-LOGIC GEOMETRY

The universe is made of dimensions of space and time, which are opposite but equal in number and merge lineal and cyclical motions into bidimentional, 4-dimensional and 6 dimensional super organisms.

The six motions of time of Aristotle, and we have grouped two, dissolution and aggregation, a dimension usually studied by Analysis, as the generic name of the 5th dimension. As the arrows of present space or 4 dimension, ct, or vt, the immersion of past and future form a 6 dimensional structure. This would be the part of ‘¬Ae not treated here.

Let us now consider the 3 branches of mathematics, which are 5 Dimensional analysis, algebras of time worldcycles, and spatial geometry of space quanta.

They study obviously the 6 Aristotelian motions of space-time, and as analysis is a branch of algebra, we divide our upgrading into i-logic Geometry (after the Non-Euclidean), and ¬æ, Non-Aristotelian, Non Euclidean algebra, which studies not in terms of continuous world-minds as geometry does the ‘Maya of the senses’, but the whole of the discontinuous Universe of infinite worlds of the 5th dimension.

Thus algebra (and analysis specifically concerned with the processes of social numbers that sum and emerge or rest, and divide and plunge down the scales of eusocial love of the 5th dimension), is a larger subject, still not fully developed by the only human world-point, which as Boylai on the view of non-E spaces, can only exclaim ‘I have discovered (not invented, as he said, the ever arrogant human ego) a new strange world – and not out of nothing as he said, but out of everything’).

Now, it will surprise the reader to know that the Universe is not a continuum, but as all fractals it is discontinuum. This of course, the ‘axiomatic Hilbert-like’ arrogant humans do not like. So a guy called Dedekind found a continuity axiom, affirming that the holes between the points of a line are filled by real numbers, which are ratios between quantities such as π or √2, which happen NOT to exist as exact numbers, and more over represent an infinite number compared to those which do exist.

Further on, when XX c. geometers went further than Non-Euclidean Riemannian geometries into absolute geometries it turns out that the most absolute of all geometries, didn’t need the continuity postulate.

This geometry, which is the ultimate absolute plane geometry that included all others (and now further clarified by 5D i-logic geometry), reflected the absolute architecture of the planes of Existence of the Universe. It was discovered by a German adequately named Bach-mann, for its musical architectonical rigor.

It is the Goldberg variations of the theme. And it was discovered the year the chip homoctonos was found, ending all evolution of human thought, which now is busy-busy translating itself to the new species, with ever more powerful metal-minds and smaller human minds, receding into a hyperbolic state of stasis, thinking what the machines that are making them savant idiots discover belongs to their ego-trip paradox.

In terms of geometry is merely the ‘realization’ of the 3 canonical geometries, we have used to define a system in space, perceived from a given point of view across the scales of size of the Universe, taking into account that our ‘rod’ of measure is light speed-space.

Indeed, we see reality through light’s 3 Euclidean dimensions and colors, which entangle the stop measures of electrons.

Yet light-space and any relative size of space of the Universe must be analyzed with the pan-geometry of the 5th dimension, first explained by Lobachevski, as we see smaller beings with a hyperbolic geometry, which multiplies its ‘fractal forms’, and larger ones with an elliptic geometry which converges them into single, spherical ones. Hence the hyperbolic geometry of quantum planes, the elliptic geometry of gravitational galaxies, and the middle Euclidean geometry of light space-time, in which the Lobachevski’s constant of time and space is minimal, since our quanta of information H-Planck is minimal compared to our quanta of space-light speed.



TEMPORAL ANALYSIS: The mind – temporal concept vs. the brain – spatial concept.

But as we progress on General Systems Theory AND the description of its Generators of Space-Time (both ab. GST), we shall see that the mind, a TEMPORAL CONCEPT that relates to the existence in finite time of a world cycle of a being, more than its spatial organic place in which the super organism process its information, might not be even into the being.


And as we shall see sometimes the super organism or system we study might be mindless, either because there is no mind on it – as a part of a whole; or it is a ‘slave’ system hypnotised, somatized or controlled by other system. I.e: a virus becomes the mind of a leukaemia infected cell in the ∆-1 level of beings (human self-centred scale); a cockroach becomes controlled by a wasp, who injects soma and eggs to eat it inside out human becomes controlled by a social network or idol-ogy, in the ∆+1 level, acting under orders… a star becomes controlled by a black hole gravitational field which will devour it.

SO to start with mind, Œ, is a time concept, brain is a space concept, both are related to the Max. tif point of the being, and while the brain or Tiƒ point is always within the system, the mind might be external to it, as if often happens to all other parts of the being, and to beings enslaved by a more powerful mind.


In all systems, the To point of view organises an EXI territory of energy and information separated by a membrane from the field of energy in which it preys. Thus the mind-point of view is the will of the function of existence, and we write synoptically:

To< exi (st), as the ternary symmetry of a head/particle of information, To, which absorbs energy and information and controls a body-wave ixe, which preys on a field of space-time, St, of a lower scale.

A focal mind or point of view tries to order the Universe as a mirror image of its self, by maximising its action of existence,  Max. e xi (s=t).

We deduce the function of existence, as the maximisation of the actions of absorption, emission and reproduction of energy and information, which happens, when Max. E x I at the point in which the function is e=i.

We can then define a will point, which will carry those actions according to its best linguistic judgement to a logic conclusion, constantly trying to achieve the reproduction of presents, ExI (s=t), in the point of balance So the Universe is basically a game of present repetition enacted by future points of view of information that tilt slightly the function towards two sub-functions:

Max. E x I (s=t), body-waves of hyperbolic reproduction and…

Max. I (head-particle), the mirror point of view, which unaware perhaps, or selfishly increases its intake of information to form its mirrors, and so a deficit happens always through life in the:

Max. Spe, point of past entropy or field-limbs, which constantly step by step of the sum of actions is absorbed by the self-centred point of view or monadic mind:

This simple equation of the Mind as a knot of time cycles, or ‘fractal non-Euclidean point-world’ or ‘Monad’, defines a sentient Universe of infinite different ‘points of view’, with local ‘diffeomorphic’ space-time perspective and mirror-languages, according to the ‘pixels’ the mind uses to gauge information – atoms in smelling minds, h-quanta in light minds, words in human ones.

But why we see reality still if all is moving in time?  Because those mind-mirrors move step by step of ‘space’, as they complete their ‘world cycles’ of existence between birth and extinction.

Each of those ‘quanta of time’ is what we call space: ∂t=s/v, as the formula physics uses to measure ‘space’ distances shows.

The mind is a stop and go process, as that of a ‘digital metal-mind’ in a tv-screen. So Galileo said: the earth moves but doesn’t moves.

The mind stops ‘energy in motion’, Spe, into ‘still mental space’, Sp…

Tƒ fit more informative images, which are still pictures of Time cycles that mirror the larger moving universe.

So Energy, Spe, is space, Sp, in motion, and information, Tiƒ, is the still form of a time cycle in motion, Tƒ.

Mathematically the discontinuity of space-time and hence the existence of infinite fractal space-time motions in the Universe is proved by that fundamental theorem of topology (Lobachevski) and knot theory (Jordan): a closed cycle divides the Universe in an inner and outer space, breaking it.

So we see around us ‘fractal spaces, enclosed by time cycles, which carry their information’. The Earth is one of such vital spaces with energy and motion enclosed by a thin membrane, where the human beings act as the informative collective subconscious of the planet. The event horizon encloses the information of the black hole. All around you are broken space-times.

But what about the cycles of life and death, the rhythms of nature, the geological rhythms, the cycles of matter from gas to liquid to solid, to gas… the cycles of history, the cycles of evolution?

Now each science studied its cycles without even knowing they were cycles, as they were then elongated in lineal time, so when they found that alas, the same phenomena repeated, with a frequency ƒ, they didn’t care to study the meaning of those frequency and repetitive events.

Further on, because we were comparing the rhythms of all beings with the mechanical clock uncoiled into a time duration, suddenly the fact that we had internal clocks of time, that we were made of space-time cycles, of clocks of time that occupied a vital space in their cycles (cell cycles, physiological cycles, reproductive cycles, feeding cycles, thought cycles each second, heart cycles each second too) disappeared. The only time was now external, the graph of carte sin coordinates. And so the very obvious fact that we are made of a vital space, a volume of space-time cycles, with our own clocks of time, that we ARE timespace, also disappeared. An absolute background space-time mathematical artefact, the cartesian coordinates became outside of us, the only meaning of time.

From then on of course, nobody understood much. Physicists kept studying with lineal time the motions of beings, and concluded that if they used time to measure motion in space, V=S/T, time was a parameter of space and speed in space: T= S/V.

Hence the expression that time is the 4 Dimension of space, as either in Galileo or Einstein’s formula as we are MEASURING ONLY A TIME-RHYTHM, translation in space, yes, in that formula time is a parameter of space. Physicists did well as their job really was about measuring motions. The science of motion’ was then called.

In this manner they could express the total motion of those cannonballs, or the displacement of a ball along a plane, such as the space crossed by the ball was equal to the number of times the ball cycled: S= frequency x radius of the wheel, or in terms of the frequency of a wave:  S= λ (length of the wave)  frequency of waves.

A time clock or time cycle breaks (knot theory, topology) space into an inner and outer region. So we must also talk of infinite broken spaces, fractal parts of space with ‘motion’ or ‘energy’ that a time cycle surrounds and controls: The unit of the Universe is a space-time cycle; and all beings of Nature are made of such ‘fundamental particles’, the cyclical, fractal space-time born of enlarging, each ‘point’ of lineal time into a ‘cycle’.

Thus the existence of cyclical time clocks implies that space is fractal and enclosed by time clocks, which manage those spaces as their vital, inner spaces, the ‘internal substances’ of which vital space-time beings are made.

Indeed if time is cyclical some other immediate true properties of reality can be deduced logically from it. We shall put them together into 3 great ‘fields’: Cyclical time, Fractal space and the Metrics of the 5th dimension that orders them all.

Indeed, we can easily deduce all those elements and fundamental properties of reality from a simple fact proved ad nauseam by experience, the fact that time clocks are cyclical:

– The cyclical properties of time clocks, were simplified in the western tradition, to facilitate measure with the concept of a single mechanical time clock, extended into a lineal time duration, which equalizes all other clocks of nature, facilitating its measure, but looses some of its properties:

– The causal repetition of events, which are indeed cyclical origin of most laws of science.

– The different time speeds in the clocks of species, which vary according to size – from faster smaller to slower larger organisms, a fact ignored by physical theories.

– The fact that beings are NOT positioned in an abstract lineal, absolute, infinite Newtonian time, now reduced to a linguistic artifact or Cartesian plane no where to be seen in nature. So Beings are NOT in time, they are made of space-time cycles, which have motion=entropy+energy and information, form.

All starts in the will of survival of a mapping of the Universe, in a still fractal point of view a mathematico-biological focus of the function of existence, which will try to maximise, Max. E x I(s=t) along a physical vital space-time.

Such will oriented description of super organisms, comes from 0 the point of view monad or mind which does interact with flows of lineal and cyclical, wave-like ternary strategies:


The Universe is made of fractal super organisms of space-time , which can be easily mathematized departing from a generator fractal equation of 3 symmetries of space-time, the symmetry of size, the symmetry of form and the symmetry of motion: ∆ST. Each ∆ST being thus co-exists in three ±planes of bidimensional space-time cycles, which add in the holographic universe its flat and cyclical moving dimensions to become networks of organisms.

10 set of simple laws deduced from the meaning and parameters of any fractal super organism allow us to define all the laws and species of the Universe.

Now all starts with a simple statement: the Universe both conserves its present Spe=†iƒ, presents of existence, and at the same time as Max (Sp x Tiƒ), happens at Sp=Tiƒ, maximises its balance between time and space quanta.
That is there is a constant st, s=t=s=t=s, beating in the Universe, the beating of present closed motion-actions of conservative energy and information, an iteration a fractal spirit, a fractal form, giving in-form-ation and erasing it in 0-closed cycles which equals two arrows of motion, entropy and cyclical order into presents of existence.

To exist is to close world cycles in which the 7 motions of time as we know them today, generation, evolution, growth, locomotion, reproduction, decay and extinction do happen i a sequential time, itself a sum of a finitesmal number of open actions which somehow will mess u to create a cycle in which the ±∆e, i exchanges of energy and information remain also al together a conservative, energy-information S=T cycle. How by magic all the actions of an instant a derivative of the total time energy of the being, become modulated in such a manner as to close a world cycle is as mysterious and magic once understood in its discontinuous docile cycle, of stop and go motions in completion of its accelerations, feedings, informations, reproductions and social evolution – the 5 motions considered in genetic terms here, as short actions, giving to the evolutionary cycle a longer span and to decay a negative symbol to social evolution.

3±∆E, I are thus the 6 actions of space time, growth or diminution in time space and the 5th dimension.

And so travels through space time and the 5th dimension is all what we need to build all the motions and actions of the Universe. The way this happens is what the set of isomorphic laws that describe the whole game of fractal super organisms does with some experiential order.

But in the meanwhile, players have fun travelling through 5 dimensions as they trace those space-time cyclical actions of existence:



The Universe moves through symmetries of ∆st. The combined number of symmetries using 3 elements were already considered in OLD taoism the engine of existence. we call ‘real symmetries’ to those symmetries which do create in effect a ‘spatial form’ similar to the original one, albeit transformed through the symmetry, appearing in other region of space-time, or with other form, or size, as ‘changed by the symmetry’. We call the imaginary part of the symmetry, the temporal flow, often an iterative wave motion, or seed emerging into a larger plane of space-time, the in-between stable spatial forms flow that rises and trans-form one being into its symmetry of existence. The mathematical operations that describe those symmetries are ‘fixed forms of the mind’, to which we have to add the ‘imaginary motion’. If we are to study in such terms the space and time equations of mathematics we have in fact many times found a real and imaginary part corresponding to the spatial and temporal motion…

This must be understood from the beginning, the ultimate reality is motion not form, time moves and space moves. They just move in different shapes. And then minds, lock those motions into a simultaneous, ‘informative’, ‘dimensional’ shape because it sees those motions in ‘slow camera’. The arrival of filming makes this easier to understand. Stillness is just the perception of very fast cyclical motions, as when we see a turning wheel as a fixed form.

This is the fundamental principle of physics, called the principle of relativity:

“We cannot distinguish a motion from a still dimension (form or distance).’ Poincare.

So often we see motion as distance – we cannot distinguish motions from dimensions of form (this is the meaning of relativity, the relativity of all motions).

The duality of motion-distance is similar to the way we see a car moving in a night picture as a fixed line, or the stop and go duality of a film projector, which is perceived as motion. And it has deep implications, which help to resolve many uncertainties of physics. The next graph illustrates this and other dual paradoxes of endophysics –motion vs. stillness; continuity vs. discontinuity, single space vs. fractal scales, all of which depend on the detail of the observation – hence the quantity of information we have on the object we study:


In the graph, Saturn’s rings, first observed by Galileo, seem continuous, still and bidimensional from far away; but observed in detail they become discontinuous in motion and made of 4D spherical particles.

Moreover, what appears as a single space-time continuum in detail becomes at least 3 scales: that of the rings with cyclical motion, of its particles, the rocks that turn within them and the not seen but known scale of atoms that create the solid networks of those rocks.

The ‘present’ state of science deals mainly with the single space-time continuum of the more ‘obvious’ human scale studied in terms of ‘present’=differential motions, ∂t, with minimal latitude of time. The 5th and sixth dimensions deal with a longer duration from the absolute past (birth of the entity) to its absolute future (its death), when evolutions of form, frequencies of multiple actions and cycles of creation and extinction happen.

The Paradox of Galileo – ‘why if the Earth moves, we see it still?’ – is the key question to understand the meaning of dimensions, which can be generalized to all forms: ‘why we see reality still, if all what we study in the quantum scale has motion?’

The answer-  given by quantum physics that we expand to all scales – is the law of complementarity: ‘all what exists is still and has motion at the same time; all is a ‘fixed particle’ and a ‘moving wave’, but we perceive a limited quantity of information about reality – either state, but not both dual, complementary states, a motion state and a still state, together.

Next, once it is clear that there are different mathematical frames of reference, of different sizes; that mind reduce in scale reality – the Universe into worlds, and that dimension and motion are indistinguishable – absolute features of reality, which will be formalized soon with the proper understanding of the ‘undefined terms of mathematics’ (fractal points, lineal waves, and networks≈planes – we need to fully grasp the unit of the Universe, a ‘point with volume’, or fractal point, hence a time cycle.

Now there is much deeper question related to the duality of motion and form, which we shall studying the 2nd part of this treatise, when we study the formalism of 5D physics in more detail and consider a Universe, in which all is motion and form, AT THE SAME TIME, because motion is reproduction of form, resolving the paradox of Achilles and the Turtle (-;

Thus the second isomorphism of the Universe the duality of motion vs. form, time vs. space, will translate in fractal organic terms as a ‘reproduction of form’ in adjacent regions of space.

This allow us to understand the creation of new dimensions as a process of laying down new ‘regions’ of form, one over other, as in 3D printing, which accumulates 2 layers of points into depth, creating a 3rd dimension, and the constant switch between motion and form that converts space into time into space dimensions, to reach the classic 4 dimensions of human physics.

The cyclical nature of time and its simplification 

If you are schooled in the quantitative school of mathematical physics this reality more likely will escape you. Of course the fractal Universe can be as precise as mathematical physics – which is fully enclosed within it, according to the Correspondence Principle. But it does not discharge the ambivalences of the Universe and the role the human perception plays on it. Consider the first of those ambivalences, the ‘Galilean paradox’. Stience started when Copernicus and then Galileo calculated Earth’s motion. But we see the Earth still, because the mind eliminates motions of most beings in space to focus on their topological forms. ∑e=S.

Thus we add into a still continuity of ‘space’, the discontinuous, infinite motions of space (which we shall call with different names, as degrees of ‘—motions’, or energy quanta or ‘—motions’, and use the geometric and conceptual symbols | and e for them). This gave origin to unending arguments at the time. Since Vatican astronomers reasoned the Earth is still to our senses and a mathematical complex calculus could obtain the same results that Copernicus with the Earth still. Who was right? Both. Einstein’s relativity was about that: any point in the Universe can be considered a still frame of reference.  On the other hand, Quantum theorists advanced a step further on discontinuity, showing that in detail, the Universe was made of motions, which carried ‘energy’, another ambivalent word used for everything in physics.

With this argument we want to make you ‘think’, because ‘calculations’ are not ‘enough’ to understand the complex logic, multiple nature of the Universe. In the age of computers is easy to make a calculus, get a picture and think that is all what there is to ‘knowledge’. It is not. Stience then settled with the concept that the earth moved. And then plotted that motion in a pen and paper graph, where for simplicity’s sake the time cycles of earth’s motion (its rotation and orbit around the Sun) were made into a lineal infinite time coordinates. So it was easier to calculate that motion with a simple formula, V=S/T.

Alas! When the origin of the formula was forgotten, suddenly every physicist thought that time was a line, which ‘covered’ the entire Universe. And absolute lineal time was born. There was though infinite time cycles, orbits of planets, of electrons, rotary motions of masses and charges, closed magnetic loops, animals that feed with a daily frequency, or an hourly frequency, actions of reproduction which came every year in cycles. And specially life and death cycles.

Suddenly nothing of that matter anymore, because time was defined by a formula, V=S/T, graphed in a paper, as a line of space. This is the famous ‘4th dimension of space’, a mere property of all the time cycles of the Universe, which provoke its changes and motions, without explaining its cause – the change in the motion of beings, or translation. Fact is even that translation is cyclical in detail. So the motion of a wave is: V=λ ƒ. That is its speed is equal to the length of a single wave, alpha, multiplied by a number of cycles per second, ƒ.

Your motion is also cyclical, that is, your speed is the number of steps you make (or frequency, the main quantitative parameter of cyclical time) multiplied by the length of your steps. So people with longer steps (enduring long distance runners) or faster frequency (explosive short distance runners like Mr. Bolt) have higher speeds. Even a car actually moves in cycles, which are the cycles of the wheels, measured through the engine, ‘revolutions per minute’. And of course all clocks are cyclical.

BUT WHAT MATTERS TRULY IS THE INTERPLAY BETWEEN THE EXTERNAL membrane of angular momentum and its central still singularity in qualitative terms:


A key element of a physical system is the singularity ‘membrain’, which includes as in any key system of nature, a center that processes information and a membrane that encloses and breaks the system into an inner region, the T.œ and an outer region, the Universe. This dual system IS the COVER AND CENTER of a topological open ball, which is the vital energy enclosed by the system, which DOES NOT EXIST as a full T.œ unless those 2 elements are formed.  Consider the case of ‘Mass’. Energy contributes to ‘mass’, but if we do NOT have an enclosure we cannot measure mass, as energy is moving around and there is nothing to ‘weight’. Yet as soon as we close the membrane, the mass parameter will exist, as measured externally by the membrane.

Further on, as the membrane is CLOSING the inner region, which we normally do NOT access, or else we will have to tear the membrane and then mass might escape and a continuity equation will have to be applied to assess the flow of mass in and out, we cannot truly measure the mass.

It is then obvious that the ‘parameter’ of ‘density-weight-charge-angular momentum-rotational speed’ etc, tends to accumulate in each scale in the external region, where the ‘mass-force’ is maximal; while in the inner singularity center, it reaches ‘zero value’, and that point is the mind-still singularity, where motion stops, and so in black hole equations time moves to zero in the singularity, in the vortex of an Eddie.

The dimensional question: 1D singularities + 2D membranes (holographic information) = 3D vital energy.

Now it is obvious that the eye of the hurricane and the eye of the black hole has maximal height as it is indeed the informative center of the system, in fact ‘infinite height’ in the axis of a black hole, which means that ‘motion stops’ in the perpendicular plane but shuts off as a yet of dark entropy and matter through the axis of superluminal speed according to the Kerr equations of a rotating black hole.

Relative time travels.

How this works is simple, by accepting that fields are past and so it is possible a local travel to the pst, when we observe, Spe>>tiƒ, from the causal origin in tiƒ: Tiƒ<<Spe. So we affirm that a system Tiƒ can travel to its past, when it devolves into a field. 

And distinguish in this process of entropic devolution of a being into its ∆-1 ‘limbs/field scale’, two degrees of entropic motion, locomotion tiƒ<Spe, and entropic death – a fast dissolution of form and expansion in space, Tiƒ<<Spe.

In the graph sample we see how those local time loops play in a field around the black hole, where in the equations we see how time signs change in complex and various ways, depending on the models of equations we use, as physicists ignore the ¬Æ logic of ternary time. So weird interpretations like the one of the graph (Hawking’s black hole evaporation to the past, never found experimentally seem possible; as he affirms a man could fall into a black hole and come out in the past and kill the father). Not so as relative future to past motions are logic motions which affect only the time-space arrows of the ‘ternary system; singularity-body-field, through its world cycle of life and death. It is precisely the exploration of those three timespace arrows the content of ¬Ælgebra, which gives origin to a 3 x 3+ 0 10 dimensional description of the supœrganisms of the Universe.


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