Author
Prof. Dr. med. Walter van Laack
Specialist for Orthopaedics and Orthopaedic Surgery, Physiotherapy, Sports Medicine, Chiropractic and Acupuncture.
Author of numerous books for existential and natural philosophy
Cover
Designed by my son Martin van Laack, M.Sc.
Master of Science in Architecture (RWTH-Aachen)
Translation
Based on recent books translated by Anneliese Wolstenholme,
Roetgen/Germany with various modifications by the author.
© May 11, 2017 by Prof. Dr. Walter van Laack, van Laack Book Publishers, Aachen (Germany)
www.vanLaack-Buch.de - www.van-Laack.de - www.vanLaack-Book.eu
All rights reserved. This publication may not be reproduced in whole or in part by printing, phono- or photomechanical reproduction, photo copying, microfilming, computer processing, transfer to the Internet and translation or any other means of recording and reproducing by existing and future media. Exceptions only with the prior written permission by the author.
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Dedicated to all my beloved ones
Numbers are one important piece of real existing information!
Already more than 2,500 years ago Greek philosopher and mathematician Pythagoras (approx. 580-496 B.C.) became convinced that numbers are of outstanding importance in the world.
He recognised, for example, that musical harmonies are based on a whole-number relationship of oscillations. He also established that all triangles whose three sides have a whole-number ratio of 3 : 4 : 5 or a multiple thereof are right-angled.
Everybody knows the Pythagorean theorem a2+b2 = c2. The Babylonians had already used these three "Pythagorean numbers" to determine hours, minutes and seconds. One hour has 60 minutes, which is the product of 3 x 4 x 5, one minute has 3 x 4 x 5 seconds and one hour 32 x 42 x 52. These time units have been in use for more than 3,000 years already. By-the-way this suggests that the calculation system of the Babylonians was based on 60.
The number sequence 3-4-5 is not a coincidental. It is the result of the subtraction of two obviously universal core values from one another, the "Golden Section" and that, what I call the "Limit of Feasibility" in the whole world. These interconnections will be explained in detail later.
The Pythagoreans were of the opinion that everything in the world was determined and organized by numbers. For them a number itself was already something divine and a mediator between the divine and the profane.
Plato (427-347 B.C.) a student of Socrates (469-399 B.C.), established the so-called "Theory of Ideas". According to that physical objects in the world are based on something immaterial – an "idea" which is purely spiritual. These ideas alone are the real, true beings according to Plato. This includes, of course, numbers and also geometric forms. Although circles and spheres exist in various sizes, the principle of "circle" or "sphere" and the idea behind each remains the same and is existing in reality. Our thoughts alone enable us to gain access to this world of really existing ideas.
Plato told us, that, although we may perceive the world with our senses we will never really be able to fathom its true nature. This can only be achieved by conceptual thinking which is less a matter of experience than rather a kind of recollection (anamnesis).
Solomon's Book of Wisdom (III, 11.20) in the Bible tells us: "You have set all things in order by measure and number and weight" and the Latin father of the church Aurelius Augustinus (354-430 A.D.) thought that numbers are "a form of God's wisdom present in the world and recognizable by humans".
I also believe that we must admit that numbers and certain basic geometric forms are not a human invention but we should consider them as being a rather useful discovery. But in nature, i.e. in the physical world, we never find circles or spheres in their ideal form.
The Danish author Peter Höeg (born 1957) wrote in his thriller "Miss Smilla's Feeling for Snow": "Geometry. Deep inside we have a kind of geometry. My teachers at university used to ask repeatedly what the reality of geometrical terms was. Where is, they asked, a perfect circle, a real symmetry, an absolute parallelism if we cannot construct it in this imperfect world? I gave no reply because they would not have understood the self-evidence of the answer and its incalculable consequences. Geometry is an innate phenomenon in our consciousness. The outside world will never produce a perfect snow crystal. Yet the glittering and immaculate knowledge of perfect ice is embodied in our consciousness."
If there are no exact realisations of circles, spheres or triangles and other geometrical forms anywhere in nature, where do they come from? How do we know of them? It seems they exist as exact guidelines or blueprints which in their manifested reality never reach perfection.
However, in the same way as an ice crystal or a snowflake is only almost as perfect as the basic geometrical pattern, so obviously seem also all great cosmic phenomena such as the so-called background radiation of the universe or the velocity of light.
Furthermore, if the really existing perfectionism, e.g. a perfect circle or a right-angled triangle, is only found in the spiritual world, then it must be as difficult for us humans as it is for nature to produce these forms in the same perfection by the physical means of our world. This is indeed the case as the old Greeks realized with perplexity: with our possibilities to describe, for example, a circle with numbers – we call this mathematics – we cannot achieve the same perfection of the spiritual archetype or the idea as Plato puts it.
For the circumference of the circle or its area there are no "even" values. We are always impeded by the infinite or irrational number π. The same applies to the surface area or the volume of a sphere or to the famous right-angled triangle. Here, the longest side, the hypotenuse, is always infinitely irrational when both other sides are of even lengths – unless they relate to one another in accordance with the Pythagorean numbers 3, 4 and 5.
Therefore, in the course of human history numbers and some basic geometrical patterns were often attributed symbolic powers since they have been repeatedly discovered in nature.
Countless generations of humans re-identified them as important pillars in world affairs. Over time they became interwoven in numerous legends and anecdotes and became thus imbued with a mystical background. This explains again why their significance as being the possible pillars of our earth is categorically rejected today and banished to the world of esoteric.
Three points form a triangle and three lines close it – this is how Plato pondered about the number 3 two and a half thousand years ago, and he saw the world constructed out of triangles.
In fact, three points of information clearly define the simplest geometrical figure, the circle. Three coordinates of its circular arc are the optimal information and logically the simplest. If one point on its arc is chosen in addition to its central point one further point of information is needed to see what is meant. Regardless of how we approach this, in any case it is sufficient to obtain a maximum of three points of non-finite, pure information.
Each small finite point, be it as small as it may, is in itself again an even smaller circle. At some point there must be a finite point, the smallest finite point or circle. In theory this game may be continued in infinity. Eventually the smallest points which still define a finite circle must be nothing but pure information.
There is then the interface between spirit and matter, between immaterial information and finite point, the circle.
The information points are coordinates; they are no longer finite and possess no space at all. We can consider them to be infinitely small. In the same way as numbers do not end, we can consider them to be innumerable. Information points are something purely spiritual. However, they are still as real as the smallest finite circle which they describe.
This example shows that there must be infiniteness as well as finiteness and that there must be an interface between the two. Infiniteness and finiteness are the two flipsides of one coin. The existence of the coin proves the existence of its two sides.
In the same way as at some time a finite circle is so small that only (infinite) information points are clearly defining it, any kind of finiteness has its infinite opposite side and vice versa. Everything has a polar symmetrical counterpart. Interface in this context does not mean that the natural laws of the two symmetrical but opposed "worlds" can be simply mixed. Finite objects can only exist in a finite number and they are only finitely small or big. Infinitely many or infinitely small finite objects do not exist.
By-the-way: If the smallest finite circle is created by pure information why should the universe and its (finite amount of) matter not also be created by pure information and even be constantly regenerated?
The Gospel according to St. John starts as with the following words (New Testament, 1.1-1.3): "In the beginning was the Word, and the Word was with God, and the Word was God. The same was in the beginning with God. All things were made by him(it) and without him(it) was not any thing made that was made."
If we replace the term "word" with the modern term "information" this concept fits exactly.
Infinity does indeed exist. Should you have difficulties in imagining this then you should do the following: place yourself between two mirrors which are exactly opposite one another and you will observe that you are (theoretically) reflected an infinite number of times.
Since everything in this world seems to have a finite and an infinite aspect we run the risk of mixing them up. However, we have two categorically separate worlds. They stand in opposition to one another (they are polar) and each is the mirror image of the other. Both exist side by side but are simultaneously completely separate from each other. Someone existing in one world has difficulties perceiving the other. The following little analogy may help: imagine you are a creature which can only crawl along a straight line. You are one-dimensional. Another, polar-opposite dimension stands perpendicular to this line on which you are living. It forms a right angle to your world and, of course, for you this perpendicular would not be recognizable as a line. If you notice it at all you would see it as a small point. Nevertheless, between these two "worlds made of lines" there is a connection: it is your interface.
Numbers are of course pure information.
If the smallest, no longer divisible finite circle is finally defined solely by information this would mean:
Information creates matter.
If pieces of information keep reappearing at key positions in the universe, e.g. in the form of certain numerical values, it can only mean that they are of vital importance.
This being so, we may assume that there is a mathematical construction plan and we may try to simulate it. Then the "spiritual principles" of such a construction plan, i.e. the numbers and forms on which it is based, must themselves be just as real existing as the matter created by them. Mathematicians themselves, by the way, observe that it seems much easier to practise mathematics than to philosophize about it. The American mathematician Reuben Hersch (Albuquerque, New Mexico) comments on this, very aptly in my opinion: "It is like salmon: they know how to swim upstream, but they do not know why!"
At first this sounds amazing, yet it is true: one and the same number may stand for completely different pieces of information – it depends on the calculation system in which it is used.
In a calculation system different from the decimal system (DS), for example the hexadecimal system (HDS), a system based on the number 16, the sum of 9+9 would be the HDS-number 12, while in the decimal system with which we are familiar the result is 18, of course.