The topology of the universe

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A way to unify the micro/macro world from the point
of view of the Philosophy of Existence

Tomáš Pfeiffer, Vladislav Šíma


Chapter 4

The macro world

4.1 The topology of the universe

As stated earlier, as a consequence of validity of the horizon of cognition, we are living in a self-similar, self-contained formation that is independent of any scale. Fractal geometry can help us approach an understanding of what such a formation is like. The terms “larger” and “smaller” are based only on the position (the apparent size) of the observer. And so, we have an infinite selfcontained chain of interconnected universes, all different yet all analogical.

There is nothing finite, solid or indivisible anywhere. We can view this in relation to the words of the Greek philosopher, mathematician, physicist, inventor and astronomer Archimedes of Syracuse: „Give me a firm spot on which to stand, and I shall move the Earth.“ [50]. There is in fact no firm spot in our world that is not dependent on the observer.

We know that we observe our world in three dimensions (3D).

However, in order to avoid any discontinuity of the permanent “decreasing/increasing in size” and for us to return back to our starting point, the world must necessarily be four dimensional (4D).

Only then can the topology of our 3D world be arranged so that we can return to our starting point without any discontinuity. Otherwise it is simply not possible.

We can also draw the conclusion, that the fact that we only see three dimensions (3D) and do not perceive the fourth one means that we exist as 3D beings in a 4D world.

We can use a simplified analogy of the relationship between the 3D and 2D space to help us understand the relationship between the 4D and 3D space. Imagine a Möbius strip, which is shown in Fig. 4.1. A hypothetical 2D being living on the strip would most likely be very surprised to end up back where he started if he walked all the way along the strip without changing direction, don’t you think? In our 3D/4D world, this does not only apply to motion in any direction but also to increases and decreases in size.

Möbius strip.

Figure 4.1: Möbius strip. A Möbius strip is created by taking a strip and turning one end 180 (twisting it half-way round) before gluing the ends together. The result is a strip with a single surface and a single edge. If we take a pen and draw a line along the strip, in one direction, we will eventually return to where we started without any discontinuity.

It is amazing that in the 4D view, which is usually inaccessible to us, all times and places of our three dimensions are observable at once (!). Let’s imagine an example with a simplified analogy of a two-dimensional drawing of a flower or a car. It would take a two-dimensional being a long time to move around the drawing in order to look at it and study it. Whereas a three-dimensional being can see the entire drawing of the flower or car at once.

But this example is a great simplification. Philosophical observations tell us that 4D can be regarded as a different kind of space and time. In 4D every dimension and every time is contained at once in all the infinitely many possibilities of their manifestations. A 4D view enables a simultaneous perception of everything at once – without any progression of time, space or causality.

There is thus more to it than just adding another axis to our Euclidean network! Since the fourth dimension contains all measurable intervals of the infinite reality at once, the starting point of an interval must change – the point becomes the surface of a dimensionless sphere1.

And so, logically, the fourth dimension makes it impossible to anchor more than four-dimensional spaces, which are shifted to becoming just descriptive mathematical model constructions2 - because infinity cannot be further divided.

Everything means everything, even in the area of multidimensional spaces (for example, the string theory [5] assumes that there are ten dimensions + time. Other “fractal” dimensions can be found in the infinite structure of force centres manifested in mass, the general theory of relativity [3] is the geometry of a non- Euklidean curved four-dimensional spacetime, etc.).

Since a 4D view contains all states, scales and possibilities at once, we can call it a “Superreality”.

And so, from a 4D perspective, the whole world is a static formation without time or development, everything in it exists simultaneously, at once. Only a 3D observer (who is also part of the 4D world) adds dynamics to this world through his observation. From his position, on one of the endless numbers of levels and possibilities, the observer perceives time, evolution, creation and extinction (causality).

The world is dual and exists in both states at once. While a 3D observer perceives the dynamics of the world and its seeming causality, from a 4D perspective the perception is static with all possibilities and states existing simultaneously.

If we take a train from place A to place B, the fact that we cannot see place A does not mean that it no longer exists. Similarly, if we decide that we shall never visit place B, that does not mean that place B does not exist.

The entire self-contained chain of sub- and super-universes has a structure that is analogical to that of the Möbius strip (otherwise we would observe a discontinuity when passing through the sub- and super-universes).

From the perspective of self-similar symmetry, it is also very likely that every sub- and super-universe has a structure analogical to that of a Möbius strip when seen in 4D (a 3D observer can go through the entire infinite universe yet never find its end).

Yet even in our 3D observation there is a duality that is analogical to the duality of particles in the micro world:

While an observer “within” the universe, regardless of his position, observes an infinite non-localisable formation without an end or a border (the apparent border is given only by the horizon of cognition), an observer from a superuniverse can observe it as a real, finite and tangible formation, e.g. as a grain of sand. Yet both observers are observing the same thing.

The topological distortion of all universes also prevents them from folding back to the starting point “O”. The universes are all interconnected (anchored) by singularities, which we know by the name “black holes”.

1 See also note 11 in Abstract. The term “dimensionless sphere” cannot be described or explained using current mathematics, where the only dimensionless formation is a point. We are now approaching the relation between “0” and “infinity”, where the two terms merge. A hypothetical observer in 4D becomes all possible projections of all possible levels of existence and also time. “Causality” does not apply here, the dynamic of development exists only in its static form, everything “is and exists”, literally simultaneously, here and now. We can also see this as a widened state of mind, which can only be achieved (for a human being) if we overcome the evolutional limitations of our human brain, i.e. if our mind leaves our brain. We claim, in all seriousness, that the mind can exist fully autonomously, independent of matter (!). One example that proves this are, for instance, the palm leaf records in India. The records were written thousands of years ago and contain exact descriptions of the fates of many people who lived or will live in the future. Unfortunately, these records do not attract any attention from current science.

2 Philosophy observes and explains, that our world is a 4D formation. It can certainly also be described using a mathematical model that works with other multidimensional spaces (5D, 6D etc.) Such a description (although it may be functional in certain limited areas) will always remain a mere thought construction, i.e. something which does not reflect the true reality of our world.



Tomáš Pfeiffer, Vladislav Šíma - THE HORIZON OF COGNITIONTomáš Pfeiffer, Vladislav Šíma – THE HORIZON OF COGNITION
Translated from the Czech original „Horizont poznání“
Published by © Tomáš Pfeiffer – Dimenze 2+2 Praha  Soukenická 21, 110 00 Praha 1  Czech Republic, 30. 3. 2020, www.dub.cz/en/,
ISBN 978-80-85238-27-3

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Graphic design including fractal geometry images,  visual works © Tomáš Pfeiffer, Vladislav Šíma

© Tomáš Pfeiffer, Vladislav Šíma, 2020


© Tomáš Pfeiffer. All rights reserved.