Mathematics E-Book

Christian Hermenau

• Herausgeber: neobooks
• Kategorie: Wissenschaft und neue Technologien
• Sprache: Deutsch

Seitenzahl: 140

Veröffentlichungsjahr: 2022

Beschreibung

Mathematics is fascinating and undoubtedly one of the most amazing products of the human mind. It alone manages to develop an abstract, self-contained system of logic, which has universal validity through the always identical numbers or letters. This gives us a creepy whiff of infinity. If we could rewrite our world into a mathematical one, we would also have solved the answer to the question of where from and where to. That is why it seems so obvious to concentrate entirely on this path, as if we had no other choice. In the past, the existence of humans was proof that God must exist; today, not only humans but all life proves that mathematics, like a god, must exist. The physical laws of matter, indeed of the whole world, must all be subject to mathematics, because only it contains infinity and can claim a position of absoluteness. But just as we have given up on a personal, all-powerful, all-good and all-knowing individual God and believe instead in nature and evolution, so we must probably, with heavy hearts, rid ourselves of the divinity of mathematical formulae. The system of mathematics is good, how good we see in technology, in computers and our superiority in Everything on Earth. It catapults us to the pinnacle of creation, but it also makes us very lonely in this universe. It makes us something that may only exist once in a galaxy, indeed perhaps something unique in the whole universe. The probability of higher life arising is then so frighteningly small that the only way out for it to arise at all lies in the infinity of multiverses.

Leseprobe

Mathematics

Or

the ordering of the world

Christian Hermenau

Contents

Space and the equations of mathematics

Deep Thought and its Answer to Everything

It flows within us

The idea of the Big Bang

Matter and counter-matter

Storing and thinking

The proton mass

Gravity

Thinking matter, a horror for researchers

Is our brain big enough

The disregard of disorder

Can a chip generate consciousness?

The God Particle!

Or is it not?

Black holes and the emergence of life

Mathematics

Reference/Index

Space and the equations of mathematics

We have to get rid of the idea that space is something. It is not something that can be curved, nor does it make sense without the matter in it. Moreover, it cannot be infinitely fine or affect the masses. In this sense, both Newton's law of gravity and Einstein's general theory of relativity are only a mathematical model that describes reality well in general, but which is not universally valid or even reality itself. Without the reality of space, the idea of black holes as described in general relativity cannot be true either. But even the quantum foam theory is only a mathematical construct, more sophisticated than the infinitely fine space of relativity, it explains much additionally that is too simply laid out in relativity. It is an attempt to bring quantum mechanics into play, but we maintain that this theory is also only an interesting idea, but does not adequately describe reality. For example, the spectra of really distant quasars have been analysed in detail for dispersion, but nothing remarkable has been found. If there were tiny structures, if space were not homogeneous or if it were in any way more than just a void, this should have become apparent here at the latest. Light, no matter how old and long in transit, simply does not age. This should really make one think. Apparently the consequence of this, together with the knowledge that time stops at the speed of light and space disappears, is too outrageous. It is not the quanta that cannot be captured within the uncertainty or cannot decide on a particular slit, it is our idea of how the world should be that makes us fail to see the obvious. If we think about the universe, about the question of where everything comes from, why there is this abundance, then we are dealing with finiteness in an infinity - over and over again. Our world is limited, although for philosophical understanding this cannot actually be the case. We cannot imagine infinity, but a beginning and an end, or only a beginning without an end, until all eternity, makes even less sense and is even less imaginable. We live and we die, that is a beginning and an end. Everything in the universe is finite and fixed and yet the conclusion that follows is apparently fundamentally wrong. So, why introduce tiny quantum foam bubbles or vast numbers of universes as the answer to the question of whence. Does it always have to be more, more complicated? Can the equations of mathematics create the world, do they just have to be complicated enough?

Hardly. If we look at the universe, the many is always complex and structured. If we go into the deepest details, we actually find only the simple, seemingly always the same. We, too, shape our world from the simplest materials to highly developed buildings and devices. What is most amazing is that with only the principle of a switch, on or off, we have created a digital world with which we can apparently create almost anything. Time and space captured by bits and bytes. Films in razor-sharp quality stored in tiny components. Every little switch is nothing and yet all together they create the image and the sound. What then is reality, the little relays, on or off, or what we look at, this space held in time, again and again. Is matter at least the solid, the eternal, something we can hold on to, if space is not supposed to exist like that? Or does it also make us believe in something hard and eternal, but is only apparent, like a picture on a screen?

We see the filmmaker's world of thought and are emotionally moved. We are only interested in the story, the experience, not the dot matrix. We are in and live with this material reality, grasp the limits and the possibilities and shape reality, we do not question it. Physicists do not do this either. They only search for the regularities in this chaotic multifaceted world. It is also no wonder that order in it can best be established with mathematics. A theoretical, always correct system of order is used to discover the patterns of order, the recurring, always the same, and to take them as a basis. If something is fixed in the smallest, then that is the smallest reality. You don't have to question that. If there is a void between two particles, then that can be the space you introduce. In the world of physics, but also in our world, first of all something does not simply disappear, particles are always there: that is what we believed. Reluctantly, because it was not really necessary, we checked the particles and atoms and found something incomprehensible. For one thing, reality makes leaps in the smallest of things and for another, there is no order in when and how they leap, only a probability. People who are looking for regularities and structure, such as mathematicians and natural scientists, do not like this at all. In the worst case, it means that their knowledge is actually wrong in its basis. The macroscopic formulae are good and helpful, but the basic approach must still be wrong, because what our objects are made of is not interested in this order. In order to save their view of the world nevertheless, a probability is introduced and the principle non-apprehensibility of the world in the smallest is postulated. It is not the physics system that has errors, but nature that cannot be grasped with arbitrary precision. It is intrinsic, i.e. unpredictable from nature itself, and must be accepted pragmatically, like a law of nature. Then, at a certain point, everything can be grasped again and things pettily sorted into pigeonholes. The world is saved, thanks to the physicists.

Deep Thought and its Answer to Everything

We live and we die and all of our life is wondrous and magical, every moment, but thanks to quantum mechanics it becomes something that can be calculated again. Just an abstraction. Then we already know today what the result will be at some point, when quantum computers are ready, namely the number 42.

Let's go back to our space and the particles. The concept of space shows very well how everything can become out of nothing. In the beginning, it was only the void into which something could be filled. Today it is a continuum that you fill with everything that cannot be explained. Space, that is the electric and magnetic, but also gravitational fields. It accommodates both a scalar Higgs field and the many, energetic, virtual particles, the seething witch's cauldron below the uncertainty. Space is the dark energy within it that drives everything apart. It is infinitely transparent for some things and at the same time more solid for others than any known substance. Yes, space is perhaps the place where universes constantly come into being and pass away again. If string theory has its way, then we have not only three dimensions of space and one dimension of time, but eleven, in which case unused dimensions can also be found in a rolled-up state within it. It is traversed by strange branes that move through multi-dimensional space. If they collide with each other, as much energy is released as in the big bang. Besides the branes, it is full of tiny vibrating strings that attach themselves to the brane. Ring-shaped strings do not do this and could be the gravitons. In some ideas, the gravitational interaction particles may be connected to other universes via the graviton. But even without the ideas of the very exuberant string theory, space can be stretched and bent in physics today and it arose, like everything in this world, from nothing: from a singularity. Today it behaves kindly and obeys the laws of nature, but in the beginning it exploded exponentially, completely unphysically, in an inflation, within fractions of a second. Moreover, locally it can still bend in on itself, become a hole in the structure of the world. Either everything in it ends in a singularity or new universes are created. Some important physicists have calculated that space can also fold and that there are shortcuts to distant places in the universe. You just have to find these shortcuts. It is possible that on the other side of the event horizon there is a white hole from which everything flows out again, somewhere in a completely different part of the universe.

Space alters the movement of the masses, but is itself altered by a mysterious dark matter that only it can sense. A mystique that physicists have been searching for for almost 90 years now. It's almost the same with space as it was when the LHC was built at CERN. Many thousands of ideas were published about what else could be proven and found with this miracle machine. Nothing new was found except for a small peak that could be the Higgs boson with a certain coincidence. The problem afterwards, however, was not the many wrong ideas, but the accelerator, which is still not energetic enough. A much bigger one is needed, then we will surely finally find the answer to everything. The physicists don't know for sure either. They may just as well not even find a small new peak, or they may find a bewildering number of them, from which they would then develop entirely new models. Even more complicated, even less generally understandable. It's just their perplexity and their hope that more equals better. But is that really how it works? Is the essence of nature just hiding and has to be dragged out by force?

Should the approach be wrong in principle, will we still find the answers if we penetrate deeper and deeper into the structures? The problem is that we have not been penetrating deeper into the structures for a long time, but are chasing particles at each other with ever higher energies. We blindly smash matter and hope to find the beginning of a new path. It is like a young father or mother helplessly hitting their child harder and harder to finally get obedience and thus control back. But maybe we don't have to hit at all, maybe the child, the matter shows us in a much more relaxed way how living together works. Let us sit back and listen to what we are told voluntarily. Do we really just want to be in control of nature or do we want to understand it, enjoy it? Perhaps it could be much simpler. Maybe we really can't calculate and predict everything, but instead we get a feeling for the connections and an understanding for things that also exist; must exist, so that a world comes into being at all. So let space be as it is, let us not interpret anything into it that is not there. Even in its simple emptiness it is special enough. And let's not break down the elementary particles even further into smaller and smaller fragments. On the contrary, the less we have, the less we have to explain where it comes from. For example, let's make protons and electrons only two planes each, which are firmly opposite each other. The planes of the electron further away, those of the proton closer together. Fig. 1; Fig. 2

Two planes give us more scope for ideas than a sphere, and even more than a point-like quantity, as suggested by quantum mechanics. If anything is intrinsic, it is these two planes that belong together. They are supposed to be our reality, our foundation of it and the distance Re the basic space size for this universe. Not so much that space is so scattered, but more that if at all, only within this distance are things solid, the world automatically divides into multiples of it. If two particles stand opposite each other at a multiple distance of Re, then they have contact, otherwise not. Fig. 3

Such a thing seems almost impossible, or rather very rare, despite the multiplicity of particles, but let us not forget that every connection is remembered. We don't just let countless independent particles flow into an empty space and see what happens, but the particles are all ordered at first, then make contact and move away from each other in steps of multiples of Re. Fig. 4

Even if everything gets more and more mixed, the old contacts are not forgotten and the corresponding multiple distances remain. Mathematically, it is much easier to work with many point-like objects that are only subject to the conservation of energy and momentum than to pursue a system that forms a network from the beginning in which everything has its meaning. Network systems can also be treated statistically after some time, but we cannot generalise them in the same way as independent point particles. Point particles fit ideally into the ordering system of mathematics, networks do not. They have to be modelled and their logical connections are approximations, patterns and models. In it, formulas always apply only to areas, they are only auxiliary quantities. Not so with point-like objects: These can also function absolutely and generalised according to the equations. Significantly, we know very well how to deal with large networks. Here on earth, we would be helplessly lost if we wanted to calculate our environment with formulas in everyday life. If we want to learn how to hunt, we have to observe and practise, practise, practise. It must become second nature to us, then we can be successful. It is a matter of intuition. Intuitively, it is possible for us to grasp and process very many processes at the same time. We don't know exactly what is happening, so we don't control it, but we feel and sense what needs to be done. The result is a vague, imprecise picture, precisely because there is no exact solution either. Nevertheless, gigantic amounts of nonsensical solutions are ruled out at a stroke and only a large but manageable amount are allowed. We can never be sure of success, but if we are good, have tried a lot, have a lot of experience, then the chances of success are high.

In nature, this method has been good for ages, but for us modern people, and especially those in power and possession, it has never been good enough. They all want control. Preferably absolute control that can be calculated with mathematical precision, even if it is destructive to others and they themselves become ill from it. But maybe we are all just a plaything of the think tanks and there is no other way into modernity.

It flows within us

It flows into us, it flows through us: information, images, sounds, gravity, charge, energy. It flows out of the positive charges and flows into the negatives, incessantly: that is what the field concept means, isn't it? But what is flowing there and where does it come from, where does it go to, where does it all stay? What is actually different about gravitation, does the space-time field here only ever flow into matter: only into it, never out of it?

No, that's not how we should imagine it, because on the one hand and on the other... Sometimes a space is only curved without flowing, then again light spreads out at the speed of light because the field flows at the speed of light. The physicists do not want to commit themselves, in their pictures. The only thing that gives them support are the formulas. And these formulas are still partly piecemeal, not all connected with each other: So they say, and are firmly convinced that they will succeed in unifying them at some point. Almost like in Tolkien’s Lord of the Rings: One ring to rule them all, one ring to find them.

Yet we know that mathematics is a perfect system of order and that the formulas in it are always of infinite precision. However, this universe is by no means infinitely ordered, but is obviously of immense diversity and complexity. We can indeed grasp the general, the ordinary in it and write it down as formulae, but the formulae are not the world, not the important part of it. They create structure and order in the confusion, but nothing more. Physicists have no answer to what is actually exciting. Their answer is only as sober as that of the supercomputer "deep thought" from 'The Hitchhiker's Guide to the Galaxy', to the question of all questions, with the answer: 42.