The Fate Of The Universe
The concept of matter in relation to the curved space-time and its geometry
Einstein’s general theory of relativity supports that gravity is not a force, but a curvature of space-time. The matter deforms (curves) the structure of space – time and the bigger the quantity of the matter is, the bigger is the curvature caused. According to Einstein’s special theory of relativity, the light has got mass (Ε=mc2). If we combine these two theories we approach the answer to the question about the fate of the universe. The total amount of matter influences the geometry of the universal space-time and gives the universe a specific “shape”. The fate of the universe depends on its “shape”.
Let’s examine the above in detail:
At the equations that describe the Universe, as the Belgian astrophysicist Αbbé Lemaitre proved, there is a factor symbolised with an (ε). This factor is called curvature factor and describes the type of the geometry of the Universe and its properties. Based on this factor:
A Euclidian space has got curvature ε = 0 and then the Universe is called flat.
A Lobatschewsky space has got constant negative curvature and then the Universe (for ε = -1) is hyperbolic (non Euclidian).
A Riemann space presents positive curvature (ε>0) and the Universe is spherical (non Euclidian).
It is interesting to point out that according to the theory of Relativity, the curvature of space and its formation into Lobatschewsky or Riemann space depends on the density of matter that is formed in its frames.
For different values of the curvature factor (ε), the Universe is reported as flat (ε=0), spherical (ε>0) or hyperbolic (ε<0). As understood, for (ε>0) or (ε<0), the spaces are not Euclidian, nor are the according shapes, irrespectively of the dimensions, sensed by us humans.
Well, which will be the fate of the universe? The total amount of matter is very close to the “borderline” that separates a closed (spherical) world from a flat or an open one. If the universe is closed, it is only closed. If the structure of space-time is either open, or closed, this means that there is a different fate for the universe.
If the universal space-time is “shaped” as a sphere, then the universe will begin to shrink gradually and it will reach a “point” of zero radius and infinite density: a black hole. A black hole is a part of space where the matter shrinks, due to the effect of gravity and becomes so dense that the space – time wraps in a “bottomless well”. In this situation not even the light can get away. The borderline, from which neither the light can get out, constitutes an absolute barrier for any information and is called event horizon. Through the event horizon of a black hole, any communication with the known world is excluded by the rules of physics themselves, since no signal sent from inside a black hole can escape the trap of gravity.
If the universal space – time continues to expand to the infinite, then the world will experience the consequences of the second thermodynamic law: the entropy. The whole cosmic order will gradually degenerate and will reach the state of the final balance (thermical death).
The question about the fate of the universe is a mystery.
The Geometry Of The Universe
When we refer to geometry, it goes without saying that there also exists a space where it develops and the properties that this geometry describes.
In maths, in the world of mathematics, the meaning of space is ideal – notional and has nothing at all in common with the material reality. Respectively, the geometric shapes that are formed inside the world of mathematics are ideal – notional and dematerialized and are not at all related to the material reality that our senses perceive. The shapes and the forms that are designed inside these mathematical spaces are identical to the 4 Platonic solids: the regular octahedron, the regular icosahedron, the regular tetrahedron and the regular cube or hexahedron.
The Dimensions
The physical man has got even a poor sense of these non material spaces and of the forms that are created inside him. He identified these non material spaces to the material shapes that were perceivable by the human senses. He named “three dimensional space” the material space that the human senses can perceive. Inside this three dimensional material space he identified the two dimensional space with every material level, for example, the surface of a table.
Likewise, he identified the single dimensional space with the section of two material levels, for example, the edge of a cube. In that way, the false impression that one three dimensional material space includes in itself infinite spaces of one or two dimensions was created. In the same way, a two dimensional space includes infinite spaces of a single dimension and a space of a single dimension includes infinite spaces of zero dimensions.
This identification, however, is false! Every spot around us, inside the material World, is described by three coordinates. This means that, according to the definition we gave above, the spot is not a space of zero dimension, since it can be described by three coordinates. However, as it is known, every material level or straight line, is a set of three dimensional spots and therefore they are described by three dimensions as well. Namely, they are three dimensional shapes that have nothing in common with the respective spaces of two and single dimensions. Inside a three dimensional material space we can distinguish curved surfaces as well, like the spherical, the parabolic or the hyperbolic one. So, these surfaces are three dimensional since they are consisted of three dimensional material spots.
The Non Perceptible Universe
If the dimensions of the universe are more than three, even if the geometry of the universe is Euclidean, humans cannot perceive the real nature of the four dimensional universe, nor the forms and shapes that are created inside it. Namely, everything that he perceives as real, even the whole universe, is nothing more than projections (depictions) of parts of the non Euclidean real and non perceivable universe, on a three dimensional Euclidean world which is constructed by the biology of the human senses. We scientifically name the World constructed by the biology of the brain pseudo – Eucledean Minkowski space.
As we mentioned above, the purely mathematical spaces, and the geometric shapes that are formed inside them, are ideal and non material and have nothing to do with the material reality. Mathematics study ideal spaces, “unreal” and non perceivable ones, while Physics studies the material, perceivable and measurable World. The connection was made by the well known Theory of Relativity by Einstein, who conceived the idea that the main composite of classic Physics, the material, is nothing more than curving of the main component of the World of Mathematics, the space that is.
The Space - Time Continuum
The only real thing inside the universe is the space - time continuum, which cannot be cut or divided. Namely, if we make a section on the space - time continuum, we have space and time, but neither the time, nor the space that is counted by the human describe the universal reality. Briefly, time as described and counted by clocks and space as described and measured by the units of measurement have nothing in common with the reality of the universal creation, nor do they describe it.
How Can Material Be Defined?
According to the Theory of Relativity, the material is a curved three dimensional space. However, the three dimensional space is a delusion; the material is the curve of a delusion.
When we talk about the curving of the Euclidian three dimensional universal space that is perceived by our senses, we simply mean a curvature of space in relation to the third dimension, the dimension of time. In fact, the perceivable material is a curved three dimensional space towards the dimension of time. That means that the material is perceivable if the value of the dimension of time is located between a minimum and a maximum.
The variation of the curvature of a region of a three dimensional space marks the birth, the evolution and the death of a material existence. If we consider stable the extent of a region of space, the amount of the curvature of space in relation to the dimension of time is the basic parameter that characterizes the evolution of a material existence. The Curvature of a region is equal to the density of the energy. This means that instead of saying that the material is the curving of space, we can say that the material is a region with a great density of energy. Namely, it is equally right to say that the evolution of a material existence depends on the changes in the density of its energy.
The Elusive Concept of Time
Time, before the advent of thetheory of relativity, had in fact a meaning. Now on, in the period after the theory of relativity, time has not got a single meaning any more, but a logical coupling of two meanings – these of space and of time as space - time. Namely, when we want to refer to the meaning of time, we say that time is inextricably connected with space, and vice versa, space is inextricably connected with time. The result of this forced coupling is catalytic because basically the meaning of time (and the meaning of space of course) is from now on defined by another meaning – that is, it is like understanding time through space (and vice versa).
In that way, however, both those two meanings, space and time, seem to be disembodied. As far as space is concerned, it can easily be understood, since its three dimensions have always been visible. But, what happens with time, whose indirect perception has always been problematic? Now, the only traces of time that are left are two: an outer (the fingers of the clock) and an inner one (the persistent feeling that we have concerning time). In other words, back in time there used to be a universal clock, which was perfectly tuned by God. But now on, time is tuned universally, but conventionally by Greenwich.
We have now reached the point where time has been transformed into a “ghost”. On the contrary, due to the degradation of time which we are talking about, space gains accretion, resulting in it being more flexible both in its meaning and in its content. For example, the scientists who study the above theory are talking about a transformation of space into something geometrical – curvature of space -. That is how the meaning of gravity has occurred. But, the phenomenological concept of space - time as a single entity gives accretion to the meaning of space against the meaning of time. We can show, for instance, in what way a clock located on the highest floor of a building is accelerating, while on the contrary a clock located on the lowest floor has got a lower speed. Another example can be a withe which seems to be smaller in length when its speed goes up concerning the observer.
We are showing, in fact, time as an elastic figure and a reality non stable and rigid. It seems, namely, that space and time are quantities that are being affected by bodies and forces. A body on the move and a force empowered have an effect in space and time and this transforms their curvature. This works vice versa as well, the curvature of space and time affects the way in which the bodies move and the way in which the forces act. Space and time not only affect, but are also affected by whatever takes place in the universe. The curvature of space - time leads to the perception of a universe finite and infinite at the same time.
Well, since time is relative and depends equally on the gravity field where the observation is taking place and on the speed of the body being observed, the only stable meaning that we can attribute to it, is its flexibility. But, in fact this flexibility is nothing else than the strain of space. Besides, when one part of a double (and reversible) being becomes relative as a size, the same thing happens directly versa to the size of the other part. Namely, as one part, time, becomes relative, the other one, space, becomes absolute. This is the condition or requirement in order the space - time can be a piece of information. Space is the piece of information, while time is its entropy when the symmetry of information is broken. We, as human creatures, move in its space - time.
Time, Entropy, Brain
In the frame of the universalspace-time continuum, time is relative and as a consequence space is absolute. How does this reverse ratio lie in the eyes of an observer? The answer can be divided into two parts:
a) The reverse ratio, in the eyes of an outer observer would seem like an expansion of space. b) On the other hand, a participatory observer would experience this expansion of space through the growing of his own age. Consequently, a conscious and self-aware observer would observe the expansion of the universe on the one hand, and on the other he would measure the decrease of his own time.
These parallel processes, if examined on the basis of their phenomenological intuition, are presented as relational: increase of the disorder (or uncertainty) degree, which is an entropy increase, both as a behavior of the universe (expansion) and as a behavior of the biological body towards its growing up. But, by eidetic reductions, we can draw other conclusions.
1) The expansion of the universe, namely the increase of its entropy, is not connected with the increase of the entropy of the material factor of human existence. This happens because growing up takes place due to a decrease in space - time – and consequently in the entropy of the material body, while in the case of the universe, the expansion takes place due to an increase of its space. So, poetically speaking, while in the sky there is an increase of the entropy, on Earth we can see a decrease of it, at least on the part in which the living bodies are concerned. As a matter of fact, the increase of the entropy in the expansion of the cosmic space - time is inversely proportional to the entropy on the earthly scale of space - time.
2) This consequents directly (and indirectly) to the independent behavior of the human brain, which –always in an earthly scale of space - time –slightly increases its entropy, even though the whole material body tends towards disorder. So, the brain is driven, through the increase of the energy of the rest of the biological body, to the creation of more and more information. It has to be seen that the entropy, namely the consumption of energy is itself inversely proportional to the information inside the earthly space - time: higher entropy, lower information and vice versa.
3) Well, it seems, that the brain, as a piece of information, is a part of the cosmic space, while as energy, it takes part in the increase of the entropy that is taking place in the earthly space - time. Maybe, in this way, harmonizing the earthy with the heavenly, the phenomenon of life is adjusted catalytically.
4) Finally, if the above indeed takes place, the participation of consciousness (in its broad meaning) in the expansion of the cosmic space, which as analyzed here is nothing else than the fluctuation of space - time from the illusion of time, i.e. the visible universe, towards the truth of timeless time, namely the invisible universe
Mathematics Of Imagination
“Logic will get you fromA to B imagination will take you everywhere” Einstein.
The genuine mathematics –as Kurt Gödel showed - can be classified in absolutely no Formal Axiomatic System, no matter how advanced that system is. They cannot be formal; they are by default informal (non typical). The logical assumption is then, that there cannot be a (formal) mathematical theory. Therefore, the nature of genuine mathematics is not objectively “mathematical”. Namely, it is not governed by the logic of set theory.
The logic of the set theory is governed by the principle of identity, the principle of non-contradiction, while the choice of their axioms is strictly poetical, that is “creative”. The choice of the axioms is not empirical, nor are they produced logically, because if it were so, they would not be axioms, they would be theorems of logic. So, mathematics is not a simple acceptance of logical principles and metamathematic rules. If there is no creation of new axioms, where there is a need of them, then mathematics stop developing. There is no restriction on the choice of the axioms, except for the non-contradiction and their sufficiency. However, those two principles are not enough for the creation of axioms. They are the negative terms that have to be abided for the axioms to be valid and acceptable. The mathematics of thought exceed the totals and deal with magmas. For example, all the pictures that we keep in our minds when we are thinking or dreaming do not form a set in mathematical terms. That is because a set consists of elements defined and distinguished from each other, which come either from the real world or from the notional imaginary world. Our pictures, however, do not consist of elements distinguished and defined. We cannot separate them; all elements are connected to each other and are defined mutually.
Only the linguistic expression of genuine mathematics is typical, since, as being a language, it is a human construction of symbolic/point patterns which express the earthly dimensional (Euclidean) space-time environment. These extreme spot symbols of mathematical expression are nothing else but the extreme sections of the net (intangible) mathematical universe. Namely, they are material thickenings that take place due to the function of the human brain (1). An example may analyze the above: as electromagnetism is material (electricity) and “power” (“something else”) altogether, the mathematical universe is language (material) and thought (“something else” – “energy”) together. The language should not be coincided with thought (2).
On the other hand, neither the thought should be coincided with the written language. Both the oral and the written language are nothing more than a form of the net structure of thought – logic. Logic in turn, should not be coincided with mathematics (neither as being a mathematical logic), because mathematics are an immaterial – invisible “language” which is expressed as a visible material through mathematical symbols – spots. Ultimately, Mathematics themselves cannot be categorized, as we showed, in rationalism or in empiricism (“sensualism”), or in intuitionism (“intuitive mathematics”) either. They refer directly to the queen of human capabilities in Communication, i.e. imagination (and the Imaginary).
“Imagination is more important than knowledge. For knowledge is limited to all we now know and understand, while imagination embraces the entire world, and all there ever will be to know and understand.” Einstein. As Hegel said, desire is the matrix of Thought. Man desires what he lacks and what he lacks is the “other”, the unseen and invisible world. Man imagines what he lacks and he creates it with imagination. “Nothing exists in thought if man has not imagined it” (Aristotle). Creativity, creative imagination (Kant) is the ability to create new ideas, forms and situations from void and nothing.
‘’Imagination is the queen of truth, and possibility is one of the regions of truth. She is positively akin to infinity’’. Charles Baudelaire
As Baudelaire said, imagination is the queen of the human capacities. Indeed, reality is unified with the imaginary and the image we create for something is more important than that thing itself. However, imagination does not only create images. It also creates wishes and provocative excesses. Unquestionably, both the greatest and the most awesome human accomplishments were born in his imagination in the first place. We need imagination in order to “touch” others and spread ideas strange or even annoying to them. Imagination is required in order to surprise, to satisfy and to move them. Imagination means communication and creation after all. Furthermore, communication is the creation of the imaginary; it is an address to the imagination. This explains why communication is creative in more than one ways.
Imagination, then, is necessary to Communication, because beside the creation of images, words, meanings, universe, wishes and dreams, it also results in offering the pleasure of knowledge or the knowledge of pleasure to the world… It offers that is, mathematical imagination itself!
1. According to the special Theory of Relativity, the material universal reality is nothing more than the projection, the image, the reflection of everything enclosed in the four dimensional non Euclidian and invisible universe. The fourth dimension is the projection to the four dimensional and Euclidian space that is created by the physiology of our senses.
2. The language must not be identified with the Thought nor must it be distinguished from it, as the visible world of the perceptible material is not identified nor is it distinguished from the invisible world of the super noticeable energy. Time is the rhythm that combines the opposites without identifying them.