### ABSOLUTE RELATIVITY: THE 5TH DIMENSION.

*Luis Sancho*

#### Abstract

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General Systems is a theory of absolute relativity. Its aim is to describe all the isomorphisms, invariances and conservation laws of the Universe – 3 concepts that mean the same: an immortal reality that keeps reproducing self similar forms in space and self similar events/cycles in time.

Relativity showed all systems are invariant to motions in space. But physical invariance is only one of the 5 invariances of the Universe. When we widen the concept of invariance to ‘self-similarity’ - a more general term - the Universe remains invariant to motion but also becomes:

- Invariant to changes of ‘in/form/ation’ (topological invariance), shown in the existence of only 3 topologies in a 4-dimensional Universe, which correspond to the 3 formal functions of all systems, the energetic membrane or sphere, the toroid body that exchanges energy and information with the hyperbolic, informative, central zero point of the system.

And derived from the invariance of those essential parameters of reality, motion and form, its complex combinations:

- Invariance of the 4 actions that combine energy (e) and in/form/ation (i): energy feeding, information processing, reproduction of both (exi) and social evolution, of parts into wholes, origin of the 4^{th} invariance:

- Invariance of scale which define a 5^{th}, fractal, scalar dimension made of growing scales of size and self-organization that evolve reality from the smallest particles into the complex organisms and galaxies of the upper scales.

- And invariance of time frequencies, which determine the causality laws of the Universe and life-death cycles of all systems of the Universe, among them the invariance of 3 time ages of life and the parallel 3 states of matter in physical systems.

*Formalism of absolute relativity.*

Topology, Fractal, non-Euclidean Geometries, and ternary logic, further evolved by this author (definition of the first four non-Euclidean postulates and the paradoxical logic of information) become the formal tools to study those invariances represented by a feed-back, fractal generator equation.

The 5 invariances of the Universe, motion & energy (E), form or information (i), its combined actions, its cyclical time frequency or quantization, ∑E, ∏I, and their self-similarity through discontinuous space-time scales (i can be formalized with a feed-back equation, the Fractal Generator of the Universe - Max. ∑ Ei-1 ∏ Ti - which maximizes them, under the restrictions of the Non-Euclidean, Non- Aristotelian mathematical and logic laws that describe each invariance.

The fractal generator represents many things: the principle of conservation of energy and information; the complementary structure of all systems made of energy fields/bodies and informative heads/particles, the actions all systems enact to improve their chances of survival by maximizing their invariances; while* *its maximal points become the topological forms, ages and allowed states of all biological and physical systems: Max. E (sphere, energetic youth, gas); Max. ExI -> E=I, (toroid, reproductive age, liquid) and Max. I (zero point, 3^{rd} informative age, solid).

Since all stable systems are a combination of the 3 topologies that maximize the fractal generator and all existences a motion in time through its 3 maximal points, while all failed mutations and unstable particles are incomplete sets or ‘vibrational modes’ created around them.

Reason why I call the Fractal Generator, the Equation of Exi=stence - an algorithm, constantly run by the Universe that generates all its living and non-living systems in space and its ages/states of time and matter.

In this conference we introduce the 5 invariances and the fractal generator, showing how they create in its maximal points the species of all sciences across the 5^{th} dimension of fractal scales of space-time.

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