Max Tegmark is our mathematical universe. Our mathematical universe. In search of the fundamental nature of reality. Life purified from subjectivity

The mathematical universe hypothesis (also known as the Finite Ensemble) - in physics and cosmology, one of the "theory of everything" hypotheses proposed by theoretical physicist Max Tegmark. According to the hypothesis, our external physical reality is a mathematical structure. That is, the physical world is mathematical in a certain sense. All mathematical structures that can be calculated exist. The hypothesis suggests that worlds corresponding to different sets of initial states, physical constants, or completely different equations can be considered equally real.

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Max Tegmark

This article by Max Tegmark puts forward a hypothesis about the structure of the proposed superuniverse, which theoretically includes four levels. However, in the next decade, scientists may have a real opportunity to obtain new data on the properties of outer space and, accordingly, confirm or refute this hypothesis.

Some scientists believe that our Universe is a giant computer simulation. Should we be worried about this? Are we real? What about me personally? Previously, only philosophers asked such questions. Scientists tried to understand what our world is like and explain its laws. But recent considerations regarding the structure of the Universe pose existential questions for science as well. Some physicists, cosmologists and artificial intelligence experts suspect that we are all living inside a giant computer simulation, mistaking the virtual world for reality.

As you know, Galileo declared that the Universe is a “great book” written in the language of mathematics. Why does our Universe seem so mathematical to us? What does it mean? The universe is not only described by mathematics, but it itself is mathematics in the sense that we are all elements of a gigantic mathematical object, which, in turn, is part of a multiverse - so gigantic that in comparison with it the rest of the multiverses, oh which have been talked about in recent years look small.

For life to arise, a basis is required. Our Universe synthesized atomic nuclei at the initial stage of its history. The nuclei trap electrons to form atoms. Clusters of atoms formed galaxies, stars and planets. Finally, living things had a place to call home. We take it for granted that the laws of physics allow such structures to appear, but things could be different.

Neil Tyson, Lawrence Krauss, Richard Gott

This is the fourteenth annual Isaac Asimov Scientific Conference. This time, its host, Neil deGrasse Tyson, is leading a lively discussion about the “Existence of Nothingness” with a group of physicists, philosophers and journalists. The concept of "Nothing" is as old as "Zero" itself, and this debate will cover everything humanity knows about it. They will pave the way from the ancient Greeks, the equation "God created the world from Nothing", inherited from Christian metaphysics to modern research in the field of quantum gravity.

Lawrence Krauss

Over the last century, since the discovery of the expanding universe, science has begun to sketch the structure of all of outer space, attempting to describe a hundred billion galaxies and the beginning of space and time itself. It's amazing how quickly we have learned to understand the basics of everything from the formation of stars to the emergence of galaxies and the universe. And now, thanks to the predictive power of quantum physics, theoretical physicists are beginning to move even further - towards new universes and new physics, towards contradictions that were previously discussed exclusively within the framework of theology and philosophy.

David Deutsch

The book by the famous American specialist in quantum theory and quantum computing, D. Deutsch, actually presents a new comprehensive point of view on the world, which is based on the four most profound scientific theories: quantum physics and its interpretation from the point of view of the plurality of worlds, Darwin's evolutionary theory, the theory of computation (in including quantum), theories of knowledge.

As you know, a person lives in 3 dimensions - length, width and height. Based on “string theory,” there are 10 dimensions in the Universe, the first six of which are interconnected. This video talks about all these dimensions, including the last 4, within the framework of ideas about the Universe.

Yuri Lebedev

Parallel, intersecting, branching and again coming together worlds. What is this - an invention of science fiction writers or a reality that has not yet been realized? The theme of many worlds, developed by philosophers since ancient times, became the subject of discussion among physicists in the mid-20th century. Based on the principle of interaction of the observer with quantum reality, a new interpretation of quantum mechanics emerged, called “Oxford”. Its author, the young physicist Hugh Everett, met with Niels Bohr, the founder of the then generally accepted “Copenhagen” interpretation of quantum mechanics. But they did not find a common language. Their worlds have diverged...

The world around us has always been a little strange and mysterious. Most of the time it is hidden from our consciousness. The study of the nature of reality took scientists far beyond the boundaries of understanding. Reality begins with the atom and reaches black holes, stretching to the boundaries of the Universe. But be careful. Once you enter their reality, you will never be able to look at the world with the same eyes.

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* * *

Dedicated to Meiya

Chapter 1. What is reality?

Trees are mostly made of air. Burning, they return to the air again, and in their fire the heat of the solar flame, which was bound during the transformation of air into wood, is released. And the small amount of remaining ash is the part that came not from the air, but from solid earth.

Richard Feynman

There is much in nature, friend Horatio, that our sages never dreamed of.

William Shakespeare

Not what it seems

A second later I died. I dropped the pedals and hit the brakes, but it was too late. Headlights. Radiator grille. Forty tons of steel, screaming like a modern dragon. I managed to see the driver's eyes. Time slowed down for me, life flashed before my eyes, and my last thought was: “I hope this is just a nightmare.” Alas, I felt in my gut that this was reality.

But how could I be sure that this was not a dream? What if, just before the impact, I saw something that is only possible in a dream - say, that my late teacher Ingrid, alive and well, sitting on the trunk of my bicycle? Or would suddenly, five seconds earlier, a pop-up window appear in the upper left corner of the field of view with the text: “Are you sure you should enter the intersection without looking to the right?”, and under it a pair of buttons: “Next” and “Cancel”? If I had seen enough of films like The Matrix and The Thirteenth Floor, I might have wondered if my whole life was a computer simulation and questioned my beliefs about the nature of reality. However, I did not experience anything like this and died with the firm belief that the problem was completely real. After all, what could be more solid and real than a forty-ton truck?

This mystery is the essence of quantum physics ( Ch. 7). But if I am made up of such particles, and they can be in two places at once, couldn’t the same happen to me? In fact, three seconds before the accident, I was subconsciously deciding: should I just look to the left, which is where I always turned on the way to Blakebergs Gymnasium, since there was never any traffic on the cross street - or should I look to the right, just in case? That morning in 1985, an ill-fated spontaneous decision brought me to the brink of death. It all depended on whether a single atom of calcium would hit a specific synapse in my prefrontal cortex, causing that particular neuron to fire and send an electrical signal that would set off a cascade of activity in other neurons that collectively coded the thought “Don’t worry.” So, if the calcium atom were initially in two slightly different positions at once, then half a second later my eyes would be looking in two directions at once, a couple of seconds later my bicycle would be in two places at the same time, and a little later I would be alive at the same time , and dead. The world's leading quantum physicists are emotionally debating whether something is really happening that is causing our world to split into parallel universes with different histories, or whether the Schrödinger equation, the fundamental quantum law of motion, really needs to be corrected. So did I really die? In this reality, this almost happened to me, but did I die in another universe, equally real, where this book remained unwritten? If I am both alive and dead, can we adjust our ideas of what reality is so that it all makes sense?

If you think that what I have written is absurd and that physicists are muddying the waters, I warn you: when I come to the story, how I perceived that moment, it will be even worse. If I am in two different places in two parallel universes, then one of my copies will survive. If you apply the same reasoning to all the other ways I could die in the future, then it seems there will always be at least one parallel universe in which I never die. Since my consciousness exists only where I am alive, does this mean that I am subjectively immortal? If so, will you also feel immortal? We will answer these questions in Chap. 8.

Are you surprised that physics reveals a reality far stranger than we could ever imagine? In fact, this is not so surprising if you take Darwin's theory of evolution seriously! Evolution has given us intuition only about those aspects of physics that mattered to the survival of our distant ancestors, such as the parabolic trajectories of flying rocks (which explains our interest in baseball). A prehistoric woman who thought too deeply about what matter was ultimately made of might not have noticed the approaching tiger and dropped out of the gene pool. Thus, Darwin's theory makes a testable prediction: whenever we use technology to look at reality beyond the human scale, our evolutionarily developed intuitions fail. We have tested this prediction many times, and the results unequivocally support Darwin. Einstein realized that time slows down at high speeds, and reproached the Nobel Committee, which considered this discovery too strange to award the author a prize specifically for the theory of relativity. At low temperatures, liquid helium can flow upward. At high temperatures, colliding particles change their identity. For me, an electron that, when colliding with a positron, turns into Z-boson seems about as natural as a pair of cars colliding into a cruise ship. At microscopic scales, particles are surprisingly able to be in two places at once, leading to the quantum conundrums described above. On an astronomically huge scale - what a surprise! – strange things appear again. If you intuitively understand all aspects of black holes, then I think you are one of a kind and you should immediately put down this book and publish your findings before someone snatches the Nobel Prize for quantum gravity out from under your nose. As we move to even larger scales, new oddities await us, since the reality is much grander than anything that can be seen with the best telescopes. The currently dominant theory about the beginning of the universe is cosmological inflation theory (Ch. 5), suggests that space is not just huge, but infinite and contains infinitely many exact copies of you and even more “almost copies” of you, living all possible versions of your life in parallel universes of two types. If this theory is confirmed to be correct, then even if there were something wrong with the argument from quantum physics (I gave it above when I talked about my copy on a bicycle that didn’t make it to school), there would still be an infinite number of other Maxes in solar systems somewhere in distant space that lived exactly the same lives right up to the same fateful moment and decided not to look to the right.

In other words, discoveries in physics have challenged some of our fundamental assumptions about reality both in the microcosm and in the macrocosm. Many ideas about reality are severely tested, even at intermediate scales commensurate with humans, when we use neuroscience to penetrate our brains ( Ch. eleven).

How about a mystery that needs to be solved? Answering this question is the main goal of this book. In ch. In Chapters 10–12, we'll look at the fascinating connections between computing, mathematics, physics, and consciousness. I will also share with you my (at first glance crazy) idea: our physical world is not only described mathematics, he and There is mathematics that makes us self-aware parts of a giant mathematical object. This brings us to a new, latest family of parallel universes, so vast and exotic that all the oddities mentioned above pale in comparison, and it forces us to throw away our deepest innate ideas about reality.

Rice. 1.1. Looking at reality through the lens of physics, we see that they describe patterns and patterns. But for me, mathematics is more than a window into the world. I intend to convince you that our physical world is not only described by mathematics, but is itself mathematics, or more precisely, a mathematical structure.

The most important question

Where did all this come from? How will it end? How big is all this? Probably all human cultures have asked these questions and arrived at answers in the form of myths, legends and religious doctrines. These issues are so complex that there is no global consensus on them ( rice. 1.2). Answers vary widely, and at least some of these differences appear to reflect differences in lifestyle. Thus, in the myths of the ancient Egyptians, who depended on the floods of the Nile, everything that exists in our world came from water. And Scandinavian mythology claims that life came from fire and ice.

Other big questions raised by ancient cultures are no less fundamental. What's real? Is there something more in reality than we can see?“Yes,” replied Plato. The ancient Greek philosopher compared people to prisoners who spend their whole lives in a cave, in chains. They look at a wall with shadows falling on it and become convinced that these shadows are reality. Plato argued that what we call reality is only a limited, distorted idea of it, and in order to get closer to understanding it, we must free ourselves from mental shackles.

Rice. 1.2. Many of the cosmological questions we touch on in this book have fascinated thinkers for centuries, but universal agreement has never been achieved. The classification shown in the figure is based on a presentation by MIT graduate student David Hernandez in my 2011 cosmology class. It should be borne in mind that simplified classifications are guaranteed to be inaccurate: many religious teachings have branches, and some fall into several categories at once. For example, Hinduism contains elements of all three concepts of creation: according to one legend, both the creator god Brahma and the Universe arose from an egg, which in turn arose from water.

Some answers to the question: “What is reality?”

If physics has taught me anything, it's that Plato is right. Modern physical science has made it abundantly clear that the nature of reality is not what it seems. But if so, what is reality? What is the connection between the inner reality of our consciousness and the outer reality? What does everything ultimately consist of? How does it all work? Why? Does everything have a meaning, and if so, what is it? And (to borrow a formula from Douglas Adams) what is the answer to “the ultimate question of life, the universe, and everything?”

Thinkers have offered an impressive range of answers to the question of what reality is, and some have even tried to dismiss the question as such.

This book (and indeed my scientific career) is a personal attempt to answer this question. Part of the reason for the polyphony is obviously that thinkers have interpreted it differently. The word "reality" has many connotations. I use it to refer to the fundamental nature of the external physical world of which we are a part, and am committed to seeking a better understanding of it. But what is my approach?

As a schoolboy, one evening I started reading Death on the Nile by Agatha Christie. Although I realized that the alarm was set for seven in the morning, I did not put the book down until the mystery was solved around four in the morning. Detective stories have attracted me since childhood, and when I was twelve years old, I opened a detective club with my classmates Andreas Bette, Matthias Bottner and Ula Hanson. We didn't catch a single criminal, but we were fascinated by the idea of solving riddles. For me, the question of what reality is is the ultimate detective story, and I am incredibly lucky to have the opportunity to spend time solving it. I will tell you about cases when curiosity forced me to sit until the morning, not having the strength to stop, until the riddle could be solved. Except I wasn’t reading a book, I was trying to derive mathematical equations that I knew could lead me to the answer.

I am a physicist and take a physical approach to the mysteries of reality. This means that I start from the great questions - how big is the Universe and what is everything made of? – and I work with them like a detective riddle: I combine successful observations with reasoning and check all versions.

The journey begins

Physical approach? Isn't this the best way to turn something exciting into something boring? When a fellow passenger on a plane asks me what I do, I have two options for answering. When I'm up for a chat, I say astronomy, and it always leads to an interesting conversation. 2
This conversation sometimes begins like this: “Oh, astrology! I'm a virgin". To put it more precisely: “Cosmology,” then I often hear: “Oh, cosmetology!” – and then follow questions about pencils and mascara.

If I’m not inclined to talk, then I answer that I’m studying physics, and in response I usually hear something like: “Oh, but for me this was the worst subject in school” - and they don’t bother me until the end of the flight.

In fact, physics was also my least favorite subject. I still remember my very first physics lesson. In a monotone voice, the teacher announced that we would study the concept of density. That density is mass divided by volume, and therefore, if the mass is such and such, and the volume is such and such, we can calculate the density. Everything that happened after that is remembered as if in a fog. Whenever the teacher’s experiment failed, he scolded the humidity and said: “Everything worked in the morning.” I also remember how my friends couldn’t understand why they couldn’t do anything until I admitted that I had put a magnet under their oscilloscope.

When the time came for higher education, I did not want to study physics and other technical disciplines, but opted for the Stockholm School of Economics and specialization in environmental issues. I wanted to make a modest contribution to making our planet a nicer place, and I felt that the main problem was not a lack of technical solutions, but that we were not using the technology we had available properly. I believed that the best way to influence people was through their wallets, and I was captivated by the idea of economic incentives that would put selfishness in the service of the public good. Alas, very soon my illusions were shattered and I came to the conclusion that economics is basically a form of intellectual prostitution: you get rewarded by telling the powers that be what they want to hear. Whatever a politician wants to do, there will always be an economic adviser who will justify why this is what needs to be done. Franklin Roosevelt wanted to increase government spending, so he listened to John Maynard Keynes, and Ronald Reagan wanted to reduce government spending and listened to Milton Friedman.

It was then that my classmate Johan Oldhoff gave me a book that became fateful for me - “Of course you’re joking, Mr. Feynman!” I never met Feynman, but it was thanks to him that my attention turned to physics. Although the book was, in general, not about physics (the author talks in more detail, for example, about how to pick a lock or pick up a girl), you could read between the lines that this man was in love with physics. This intrigued me. If you notice an average guy holding a stunning woman on his arm, you'll probably think you're missing something. Perhaps she sees his hidden virtues. Suddenly I felt the same way about physics: what did Feynman see in it that I missed at school?

I just had to figure it out. I took the first volume of the “Feynman Lectures on Physics” from my father’s bookcase and began to read: “If, as a result of some catastrophe, all accumulated scientific knowledge were lost and only one phrase were passed down to future generations of living beings, then what statement composed in the fewest words that would convey the most information?”

Wow! This guy absolutely doesn't look like my physics teacher! Feynman continued: “I believe that this is - atomic hypothesis: all bodies consist of atoms - small bodies that are in continuous motion, attracted at a short distance, but repel if one of them is pressed more closely to the other" 3
Quote by: Feynman, R., Layton, R., Sands, M. Feynman lectures on physics. Vol. 1. Modern science of nature. Laws of mechanics. M.: Mir, 1965. P. 23. – Note lane

It was like a light bulb went on in my head. I sat spellbound. I felt like I was having a religious experience. I finally got the hang of it! I had a revelation, and following Feynman, I realized: physics is the most exciting intellectual adventure that can be, a quest to understand the deepest mysteries of our Universe. Physics doesn't turn something exciting into something boring. Rather, it helps us see more clearly, making the world even more beautiful and full of wonder. When I ride my bike to work in the fall, I see the beauty of the trees in gold, orange, and red. But looking at these trees through the lens of physics reveals even greater beauty, which is wonderfully captured in the Feynman quote at the epigraph of this chapter. And the more closely I look, the more grace I notice: in ch. 3 we will discover that trees ultimately emerge from stars, and in Chap. 8 we will see that the study of the objects from which they are composed indicates the existence of parallel universes.

At the time I had a girlfriend who was studying physics at the Royal Institute of Technology, and I found her textbooks much more interesting than mine. Our relationship ended a long time ago, but my love for physics is still alive. Since higher education in Sweden was free, I enrolled at its university without even informing the administration of the Stockholm School of Economics about my double life. Thus officially began my detective investigation, and this book is a report written a quarter of a century later.

So what is reality? I have given this chapter such a bold title not to arrogantly impose a ready-made answer (although we will explore some very intriguing possibilities in the latter part of the book), but rather to invite you to join my own quest and share my thoughts and excitement about these expanding consciousness is a mystery. I think you, like me, will come to the conclusion that whatever reality is, it is radically different from what we thought it was. I hope you find, as I do, that it gives everyday hassles like parking tickets and sadness a different dimension, making it easier to move past them and fully enjoy the joys and mysteries of life.

When I discussed the idea for this book with John Brockman, who would later become my literary agent, he was very clear: “What I want is not a textbook, but your personal book.” So I wrote a kind of scientific autobiography. Although it is more about physics than about me, it is certainly not your typical popular science book, seeking to provide an objective overview of physics that reflects the established consensus and gives equal space to all other points of view. Rather, it is a personal exploration into the nature of reality, and I hope you enjoy seeing it through my eyes. Together we will examine the evidence that I consider most important and try to understand what it points to.

Rice. 1.3. If you've read a lot of modern popular science books and feel like you understand what curved space, the Big Bang, the cosmic microwave background, dark energy, quantum mechanics, etc. are, you might want to try skipping Chap. 2, 3, 4 and 7 by looking only at the “Summary” at the end of each. If you are a professional physicist, you can skip Ch. 5. However, many concepts that may seem familiar are surprisingly subtle, and if you cannot answer all questions 1–6 in Ch. 2, then I hope you will study the first chapters.

We begin the journey with how recent scientific discoveries have transformed the very context of the question of what reality is. Physics has shed light on external reality in the largest ( Ch. 2–6) and small ( Ch. 7–8) scale. In Part I, we'll look at the question of how big the universe is, and we'll get closer to the answer by moving to larger and larger cosmic scales. At the same time, we will study our cosmic cradle and two types of parallel universes, along the way discovering signs that space is essentially mathematical. In Part II we'll tackle the question of what everything is made of and dive into the subatomic microcosm. We will look at the third type of parallel universes and find that the fundamental "building blocks" of matter are also essentially mathematical. In Part III, let's take a step back and think about what this says about the fundamental nature of reality. Let us begin by arguing that our failures to understand consciousness do not prevent us from fully understanding external physical reality. Then let's tackle my most radical and controversial idea, that fundamental reality is purely mathematical; Let’s translate concepts such as “randomness,” “complexity,” and even “change” into the status of illusions and find signs of the existence of the fourth and final level of parallel universes. The journey will end in Chap. 13, when we return home and consider what this all means for the future of life in the Universe, for humans, and for you personally.

Current page: 1 (book has 34 pages total) [available reading passage: 23 pages]

Max Tegmark
Our mathematical universe. In search of the fundamental nature of reality

Publishing house CORPUS ®

* * *

Dedicated to Meiya

Chapter 1. What is reality?

Trees are mostly made of air. Burning, they return to the air again, and in their fire the heat of the solar flame, which was bound during the transformation of air into wood, is released. And the small amount of remaining ash is the part that came not from the air, but from solid earth.

Richard Feynman

There is much in nature, friend Horatio, that our sages never dreamed of.

William Shakespeare

Not what it seems

However, not everything is as it seems at first glance. This applies to both trucks and reality as such. This is not only discussed by philosophers and science fiction writers, but also evidenced by the results of physical experiments. Physicists have known for a century that solid steel is mostly empty space. Atomic nuclei, making up 99.95% of its mass, are tiny balls occupying about 0.0000000000001% of its volume, and this almost vacuum is perceived as solid only due to electrical forces that very reliably hold the nuclei in their places. Moreover, scientists have found that subatomic particles can apparently be in several places at the same time. This mystery is the essence of quantum physics ( Ch. 7). But if I am made up of such particles, and they can be in two places at once, couldn’t the same happen to me? In fact, three seconds before the accident, I was subconsciously deciding: should I just look to the left, which is where I always turned on the way to Blakebergs Gymnasium, since there was never any traffic on the cross street - or should I look to the right, just in case? That morning in 1985, an ill-fated spontaneous decision brought me to the brink of death. It all depended on whether a single atom of calcium would hit a specific synapse in my prefrontal cortex, causing that particular neuron to fire and send an electrical signal that would set off a cascade of activity in other neurons that collectively coded the thought “Don’t worry.” So, if the calcium atom were initially in two slightly different positions at once, then half a second later my eyes would be looking in two directions at once, a couple of seconds later my bicycle would be in two places at the same time, and a little later I would be alive at the same time , and dead. The world's leading quantum physicists are emotionally debating whether something is really happening that is causing our world to split into parallel universes with different histories, or whether the Schrödinger equation, the fundamental quantum law of motion, really needs to be corrected. So did I really die? In this reality, this almost happened to me, but did I die in another universe, equally real, where this book remained unwritten? If I am both alive and dead, can we adjust our ideas of what reality is so that it all makes sense?

The most important question

Some answers to the question: “What is reality?”

Thinkers have offered an impressive range of answers to the question of what reality is, and some have even tried to dismiss the question as such.

The journey begins

Whitehead once remarked that all modern philosophy is nothing more than commentary on Plato. American physicist and mathematician Max Tegmark goes even further and undertakes to prove that modern physics is, in fact, detailed notes to the views of the ancient sage. To do this, he needed 600 pages, 30 years of scientific creativity and... eternity as the unchanging basis of his universe. Mathematicians are like that; if anything exists in a fundamental sense, it is only their beloved numbers - uncreated, immovable, indestructible, being the cause and meaning of everything. And we are just a toy “in the hands” of the googolplex*.

But - jokes aside; Tegmark takes things seriously. In the first two parts of his book, he makes a large-scale, although in general already familiar to readers of modern science fiction, journey into the mega- and microworld - that is, to the levels of quantum matter and the multiverse. Yes, Tegmark is an ardent supporter of the idea of parallel universes, and there are as many as four nested levels of them. It directly follows from this idea that somewhere insanely far away, at googolplex distances, our countless doubles live, doing everything we do, having exactly our thoughts and feelings, with only one exception: what seems to us an accident : slipped on the street, won the lottery, undercooked the steak - there is only one of many options that all doubles implement: overcooked, did not win, or won, but not that. Well, just like in the joke: “not a car, but an apartment; and not in the lottery, but in poker; and didn’t win, but lost.”

By the middle of the third part, Tegmark finally gets to the long-awaited dessert - the mathematical Multiverse and deduces his “final theory of everything” (so far only in verbal form): “only mathematical structures exist; any consistent mathematical structure gives rise to a multiverse; to our limited mind these worlds appear physical.” Either I don’t understand anything about philosophy, or this is the reincarnation of the venerable idea of substance, or Tao, or “Buddha nature,” which is eternal, uncreated, unchanging, creates the illusion of the existence of “ten thousand things” and is understandable only by the mind! However, as Tegmark admits, he, unlike the ancient sages, has two tools: his mind and a computer, which gives him access to the world of googolplexes. Modern mathematicians are lucky that Plato did not have a computer, otherwise they would have no work left at all.

Tegmark's theory cannot be denied its elegance, even if it is just a mind game. Thus, it does not depend on initial conditions and physical parameters (such as meters or seconds) and represents exclusively the relationship of numbers and their functions. It answers the question: “why exactly these equations (the theory of relativity, quantum mechanics, etc.), and not some others?” in that it resolves any consistent equations and fundamental laws - it’s just that in some worlds there will be no one to formulate these laws, since life is impossible there. It even touches on many side, but very pressing problems: is our brain a quantum computer, are there limits to our knowledge, are we alone in the Universe, do we live in the “Matrix”? Tegmark is not afraid to explain time and consciousness, predict the future of life and civilization, deduce a diagram of all human knowledge and criticize the "herd mentality" of physicists. He does not answer only one question, simply ignoring it: “why does something exist at all, and not the other way around - nothing?” As you can see, a googolplex is much nicer to him than an empty zero.
______________________________
* Googolplex - one with a googol of zeros, Tegmark's favorite number.

Max Tegmark

Our mathematical universe. In search of the fundamental nature of reality

Publishing house CORPUS ®

* * *

Dedicated to Meiya

Chapter 1. What is reality?

Trees are mostly made of air. Burning, they return to the air again, and in their fire the heat of the solar flame, which was bound during the transformation of air into wood, is released. And the small amount of remaining ash is the part that came not from the air, but from solid earth.

Richard Feynman

There is much in nature, friend Horatio, that our sages never dreamed of.

William Shakespeare

Not what it seems

And last but not least: we know that mathematical equations open a window into the mechanics of nature, which is metaphorically illustrated in Fig. 1.1. But why does our physical world exhibit such exceptional mathematical orderliness that allowed Galileo, the superhero of astronomy, to declare nature a book “written in the language of mathematics”, and Nobel laureate Eugene Wigner to speak of the “incomprehensible effectiveness of mathematics in the natural sciences” as a mystery in need of solution? ? Answering this question is the main goal of this book. In ch. In Chapters 10–12, we'll look at the fascinating connections between computing, mathematics, physics, and consciousness. I will also share with you my (at first glance crazy) idea: our physical world is not only described mathematics, he and There is mathematics that makes us self-aware parts of a giant mathematical object. This brings us to a new, latest family of parallel universes, so vast and exotic that all the oddities mentioned above pale in comparison, and it forces us to throw away our deepest innate ideas about reality.