The Big Small and the Human Mind

Current page: 1 (book has 12 pages in total)

Roger Penrose, Abner Shimoni, Nancy Cartwright, Stephen Hawking
Big, small and the human mind

Roger Penrose's original, bright and provocative ideas regarding the processes occurring in the gigantic world of the Universe, in the microworld of quantum physics and in the human brain, have more than once become the subject of heated controversy and discussion. Some of these ideas will already be familiar to readers from his previous books: The Emperor's New Mind("The New Mind of the King") and Shadows of the Mind("Shadows of the Mind"). In this book, Penrose summarizes and develops them further, and also gives an excellent overview of many unsolved problems of modern physics. Penrose's radical concepts provide new insights into how the brain works and the nature of human consciousness.

Three scientists associated with various scientific disciplines entered into controversy with the author in this book - famous experts in philosophy of science by Abner Shimoni and Nancy Cartwright, as well as the famous theoretical physicist and astrophysicist Stephen Hawking. In the last chapter of the book, Roger Penrose, continuing this extremely interesting discussion, responds to his opponents. The reader gets the opportunity to get acquainted with his own, very non-standard (sometimes even humorous) point of view of the largest theoretical physicist on the most important problems modern science.

Cambridge University Press owes much to the collaboration of the President and Fellows of Clare Hall, Cambridge, under whose auspices the 1995 Tenner Lectures on Human Values, which gave rise to this book, were held.

About the authors

ROGER PENROSE Roseball Professor 1
Note ed.

Professor of Mathematics at Oxford University

ABNER SHIMONI Professor Emeritus of Philosophy and Physics, Boston University NANCY CARTWRIGHT Professor of Philosophy, Logic and Science, London School of Economics and Politics (LSE)

STEPHEN HAWKING Lucasian Professor 1
Professors in departments established in honor of Rose Ball and Lucas. The honor of occupying “named” departments is given only to outstanding scientists. For example, Newton and Dirac were professors at the Lucasian Department. – Note ed.

Cambridge University

Borrowed drawings

The Emperor's New Mind, R. Penrose, 1989. Oxford: Oxford University Press. 1.6, 1.8, 1.11, 1.12, 1.13, 1.16(a), (b) and (c), 1.18, 1.19, 1.24, 1.25, 1.26, 1.28(a) and (b), 1.29, 1.30, 2.2, 2.5( a), 3.20.

Shadows of the Mind, R. Penrose, 1994. Oxford: Oxford University Press. 1.14, 2.3, 2.4, 2.5(b), 2.6, 2.7, 2.19, 2.20, 3.7, 3.8, 3.10, 3.11, 3.12,3.13,3.14,3.16,3.17,3.18.

High Energy Astrophysics, Volume 2, M. S. Longair, 1994. Cambridge: Cambridge University Press. 1.15, 1.22.

Translator's Preface

The complexity and variety of issues discussed in R. Penrose's book require us to preface its translation with at least very brief remarks. Firstly, as the author himself convincingly demonstrates, quantum mechanics is far from not only completeness, but also from a unified methodological approach. Over decades of debate about the principles of quantum physics, a huge amount of literature has accumulated on many of the issues under consideration (for example, entire libraries have already been written about Schrödinger’s famous cat). In this monstrous array of information, philosophical, methodological and scientific contradictions naturally long ago grew (or degenerated) into linguistic and terminological ones. The reader can get some idea about current state question on the article by M. B. Mensky “Quantum mechanics: new experiments, new applications and new formulations of old questions” (Uspekhi Fizicheskikh Nauk, Vol. 170, No. 6, 2000, p. 631) and the discussion it caused (UFN, 2001; t . 171, No. 4, pp. 437-462; UFN, 2001; vol. 171, No. 6, p.

Particular difficulties arise when translating sections related to the hypothesis proposed by R. Penrose about the quantum nature of human consciousness. Terms related to psychology (such as Russian soul, thought, consciousness, awareness or English mind, awareness, conscious), are not only poorly defined and vague (compared to physical ones), but also much less amenable to translation (for example, the concept widely used by Penrose intelligence has practically no unambiguous Russian interpretation).

These circumstances greatly complicate the translation of a small book, but the translator and editor still hope that they managed to preserve the original and free style of the author and accurately convey the complex course of his reasoning.

A. V. Khachoyan

Preface. Malcolm Longair

Over the past decade, many books have appeared in which outstanding scientists of our time try to explain to the general reader the essence and exceptional interest of their research in various fields of knowledge. The most famous of them were the famous “ Short story Time" by Stephen Hawking (which was such an amazing success that its publication became a notable phenomenon in the history of world popular science literature), James Gleick's book "Chaos" (which successfully showed that the most complex scientific research is sometimes like an exciting detective story) and " Dreams of a Final Theory" by Steven Weinberg, which made the latest advances in particle physics understandable and interesting.

Even among such famous works Roger Penrose's previous book, The New Mind of the King (1989), stands out for its originality. While other authors usually try to simply convey the meaning and significance of the achievements of modern science, Roger risked offering readers a completely new, at times stunning possibility of the existence of some kind of (not yet fully formulated) theory of fundamental processes that allows us to unite almost unrelated with a friend, theories related to a wide variety of sciences (physics, mathematics, biology, neurophysiology and even philosophy). It is not surprising that the book “The New Mind of the King” caused fierce controversy, as a result of which the author had to publish the book “Shadows of the Mind” in 1994, in which he tried not only to answer his many critics, but also to further develop the proposed ideas. In 1995, R. Penrose was invited to give the famous Tenner Lectures, where he presented a general overview of his concept and called for discussion of his most famous opponents, Abner Shimoni, Nancy Cartwright and Stephen Hawking. The three lectures of the cycle made up the first three chapters of the book offered to the reader, containing a brief introduction to the range of ideas developed in detail by the author in the books mentioned above. The next three chapters (4–6) contain the arguments of the discussed participants, and in the final chapter 7 Penrose comments on the comments received and summarizes the results of the discussion.

In fact, the sections written by Penrose are quite eloquent, and therefore my preface is intended only to prepare the reader for the discussion of some of the rather complex problems of modern science discussed below. R. Penrose is considered one of the most brilliant mathematicians of our time, but his research has always had a very strict physical justification. He gained international recognition and fame for his achievements in astrophysics and cosmology related to the relativistic theory of gravity, many of which were carried out jointly with Stephen Hawking. One of the theorems he formulated in this area proves that (in accordance with the classical relativistic theory of gravity) physical singularities of space-time arise inside the so-called black holes, i.e. at some points the curvature of space (or, accordingly, the density of matter) becomes infinitely large. The second "infinity" theorem states that the classical relativistic theory of gravity inevitably leads to singularities of this type in cosmological models associated with the Big Bang. These theorems show that the theories we use are still very far from complete, since such singularities should not arise in closed and mature physical constructions.

These works represent only part of R. Penrose's extensive contribution to various branches of physics and mathematics. Physicists are familiar with the Penrose process (in which particles absorb rotational energy in black holes), and they widely use the diagrams he created to describe the behavior of matter in the vicinity of black holes. The beautiful geometry (at times reminiscent of painting) of many such phenomena is clearly presented by the author himself in the first three chapters of the book. Some aspects of the problems under consideration are already widely known to the public from the “impossible” constructions and paintings of the famous artist Maurice Escher and the so-called “mosaics” of Penrose himself. It is interesting that M. Escher was inspired to create some of the engravings (namely those that attempt to depict the “impossible”) by one of the articles written by R. Penrose and his father L. S. Penrose. In ch. 1, Penrose’s hyperbolic geometric constructions are illustrated by the famous series of engravings by M. Escher “Limit Circles”. In this regard, one cannot fail to mention the “mosaics” or “tiles” created by Penrose himself, which make it possible to completely cover an infinite plane with a small number of varieties of simple geometric shapes of a given type. The main and most interesting mathematical side of the problem is that the pattern that allows us to solve this problem is non-repeating. This geometric problem appears unexpectedly in Chap. 3 books in connection with the ability to define rigorous computational operations for computers.

Penrose managed not only to develop a number of brilliant mathematical approaches, but also to successfully apply them to solve the most complex specific problems of modern physics. The issues he considers always turn out to be very important and interesting. Now physicists are confident that the Big Bang theory gives us a fairly accurate picture of the origin of the Universe, but it is still far from complete, and we do not yet know many of the fundamental laws that determine its main features from the age of one thousandth of a second after birth to the present day. To recreate full picture we have yet to determine the initial conditions, but all the laws of physics known to us apply only to a fairly “old” Universe, the age of which exceeds the mentioned limit of one thousandth of a second. Therefore, we still have to intelligently extrapolate the patterns we know. We already have a fairly good idea of the required initial conditions, but we know very little about the causes that give rise to them, and this problem remains central to all modern cosmology.

Usually in cosmology, a model of an inflating (inflationary) Universe is used, however, even in this model, to describe some features of the process, it is necessary to introduce parameters characteristic of the early, so-called Planck epoch of the development of the Universe (10 -43 s), when in this exceptionally short period happened major events, the consequences of which modern science is trying to describe.

Accepting the generally familiar picture of the Big Bang, Roger Penrose abandons the inflationary model and suggests that at a very early stage the development of the Universe was determined by physical laws still unknown to us associated with the quantum theory of gravity. He believes that numerous attempts to construct such a theory were unsuccessful precisely because the task was incorrectly formulated theoretically. His arguments are primarily related to the problem of determining the entropy of the Universe, considered as a single object. Since entropy (very simply the degree of disorder of a system) increases with time, the Universe must have emerged from a very ordered state with very low entropy. The probability of such a state occurring by chance is vanishingly small, as a result of which Penrose suggested that the problem could only be solved within the framework of an exact theory of quantum gravity.

In ch. 2 are being considered common problems quantization and quantum physics, which (together with its relativistic generalization - quantum field theory) has long been very successfully used to describe the properties of individual atoms and particles, as well as to explain experimental results in nuclear physics. However, only in last years we began to understand the deep physical meaning of this theory. Penrose was able to brilliantly demonstrate that its internal structure contains very complex (intuitively non-obvious) ideas that have no analogues in classical mechanics. For example, nonlocality means that when a particle-antiparticle pair arises, each of them retains a “memory” of the birth process in the sense that these particles cannot be considered completely independent of each other. Roger explains this by saying that “quantum entanglement of objects represents amazing phenomenon, lying somewhere between their separation and unification.” Quantum mechanics even allows us to obtain information about processes that did not occur, but could have been realized. The difference between classical and quantum mechanics is especially clearly manifested in the very unusual (from the usual point of view) problem of the so-called bomb test in the Elitzur-Vaidman experiment.

Intuitively unacceptable features are part and parcel of quantum mechanics, but it also poses deeper problems. Penrose is particularly interested in the question of how physics manages to connect quantum phenomena with the behavior of systems at the macroscopic level. In this highly controversial situation, many physicists use quantum mechanical rules simply as computational tricks to obtain surprisingly accurate solutions. This approach, despite its effectiveness (if you correctly apply some methods, you get absolutely correct answers), in essence only means a crude and graceless transition from the simple and linear world of quantum phenomena to the real world of the experimenter. The transition occurs through the so-called “collapse of the wave function” or “reduction of the vector of states.” Penrose is confident that with this standard quantum mechanical technique, a very significant part of the picture of the physical world is lost, and we need to develop a completely new theory that will somehow include the specified “objective reduction of wave functions.” Such a theory, with appropriate passages to the limit, will be reduced to ordinary quantum mechanics and quantum field theory, but it should also describe new physical phenomena(in particular, it should allow us to solve the problem of quantizing the gravitational field and give a description of the early period of the development of the Universe).

In ch. 3 Penrose attempts to identify commonalities shared by mathematics, physics, and human consciousness. If you think about it, it is truly amazing that in the most seemingly logical and abstract areas of physics and mathematics, it is not possible to create programs for the discrete computers we are familiar with (even for the most accurate and with the largest amount of memory). All computers practically cannot, for example, prove mathematical theorems, as ordinary human mathematicians do. All this, on the other hand, fits perfectly with one version of Gödel's famous theorem, which, as interpreted by Penrose, means that mathematical deductions (and, generally speaking, all processes associated with thinking and behavior) are carried out in an “incomputable” way. This conclusion seems very fruitful, if only because intuitively we ourselves feel that almost all of our acts of “conscious perception” cannot be reduced to computable operations. Much of Penrose's previous book, Shadows of the Mind, mentioned above, was devoted to precisely this interpretation of Gödel's theorem, which has special meaning for all logical constructions of the author.

Penrose unexpectedly sees many similarities between the fundamental problems of quantum mechanics and the processes of consciousness. For example, he believes that nonlocality and quantum coherence can explain to us the coherence of the human brain, and the “non-computational” nature of consciousness processes can be associated, in his opinion, with the objective collapse of the wave functions of macroscopic variables. Penrose not only formulates these very general principles of brain function, but also tries to directly identify structures in the brain that correspond to these physical processes.

Of course, the introduction to the book can only very weakly reflect the originality, richness and brilliance of the ideas and concepts proposed by the author, but I would like to once again draw the reader’s attention to the main directions that play an important role in understanding. The author is primarily struck by the remarkable ability of mathematics to realistically describe the fundamental processes of nature. Penrose is convinced that our physical world in a sense, it is a manifestation of the Platonic world of mathematical ideals. Nowadays, of course, no one tries to derive mathematics from attempts to describe the world around us or from fitting experimentally observed patterns to mathematical formulas. In fact, we are now trying to understand the structure of the Universe, based on some very general principles and from the laws of mathematics itself.

It is not surprising that such bold hypotheses proposed in the book became the subject of fierce controversy, in which scientists of various specialties and intellectual orientations were involved. Abner Shimoni agrees with Penrose in many respects (for example, he acknowledges the incompleteness of the usual formulation of quantum mechanics and agrees that some quantum mechanical concepts are quite suitable for describing the work of the brain), but he compares Roger Penrose to “a mountain climber who climbs the wrong mountain.” , and is ready to offer his own constructive approaches to solving these problems. Nancy Cartwright asks fundamental questions for philosophy about what sciences should form the basis for understanding the nature of consciousness and what the role of physics is in this. It also raises in the discussion a very sensitive topic of compatibility (or the possibility of reducing to each other) the laws of various scientific disciplines. The most critical section is written by Stephen Hawking, Penrose's old friend and colleague. In many ways, it is Hawking’s position that is closest to the point of view of the “average physicist.” He suggests that the author, first of all, develop a procedure for detailed reconstruction (reduction) of wave functions. However, Hawking does not believe that the opinion of physicists about the problems of consciousness has any special value. The appearance of such remarks is quite natural, and Penrose tries to refute them in his general response, which forms the final chapter of the book.

Penrose, of course, solved one of the tasks he set himself with brilliance - he created a kind of manifesto or program for the development of theoretical physics of the 21st century. In the first three chapters of the book, he managed to present a coherent picture of how a completely new physics should be “structured,” based on the general idea of the incomputability of some operations and the objective restoration of wave functions, which is the main idea of the book. The correctness of the proposed concepts will ultimately be determined by whether Penrose and his followers can actually create a new type of physical theory. In any case, even if work on this program does not lead to rapid success, its basic ideas, in my deep conviction, will have a fruitful influence on the future development of theoretical physics and mathematics.

Chapter 1. Space-time and cosmology

The book offered to the reader is called “Big, Small and human mind”, and therefore, in full accordance with the title, its first two chapters are devoted to the largest and smallest objects in the physical Universe surrounding us, which I depicted with the utmost schematicity and simplicity as a “sphere” in Fig. 1.1. I will not waste time on purely “botanical” descriptions of what and how happens in different parts Universe, but I will try to draw your attention to the analysis and understanding of the real laws governing its behavior. The main reason why I have divided physical laws into "large" and "small" parts is that the general laws of physical processes on the very large and very small scales appear to be quite different. The central theme of ch. 3, where we are talking about human consciousness, is precisely this striking difference between the laws of nature for phenomena of different scales. Since I will talk about the physical world in the language of the physical theories that describe it, I simply have to say at least something about another world - the world of Plato, the philosophical representation of the world of ideas, absolutes and mathematical truths. Of course, Plato's world contains other absolute concepts(such as Goodness and Beauty), but in this case I will only talk about mathematical principles and concepts. Some people find it difficult to imagine the existence of this world at all, and they prefer to consider mathematical concepts as simply some idealized forms of objects in our physical world, and in this case, of course, the “mathematical world” should be considered only as a creation of our physical world (Fig. 1.2).

Rice. 1.1.

Rice. 1.2.

I personally believe (and, it seems to me, most mathematicians and theoretical physicists adhere to approximately the same point of view) that mathematics has other, more serious foundations and represents a certain structure governed by its own timeless laws. Therefore, perhaps many physicists and mathematicians would prefer to consider the physical world to be a product of the “timeless” mathematical world of ideas. The corresponding picture (Fig. 1.3), for all its simplicity, is very important for the problems discussed in this book (this especially applies to the material in Chapter 3).

Rice. 1.3.

The most remarkable characteristic of the laws of nature is that they obey mathematical laws with extremely high precision. The deeper we understand the laws of nature, the more we feel that the physical world somehow disappears, “evaporates,” and we remain face to face with pure mathematics, that is, we are dealing only with the world of mathematical rules and concepts.

Before moving on to further consideration, we should evaluate the temporal and spatial scales of the Universe and somehow relate them to the place and role of man in big picture peace. I made an attempt to combine the scales of some well-known objects and processes into a single diagram (Fig. 1.4), where characteristic times are presented on the left, and characteristic sizes on the right. In the lower left corner of the figure, the minimum time scale that has some physical meaning is indicated. This time interval, equal to 10 -43 s, is called Planck time, or "chronon", and it is much shorter than the duration of all processes known to us, including the very short-lived processes of elementary particle physics (for example, the lifetime of the shortest-lived resonance particles is about 10 -23 s). The diagram above shows on a logarithmic scale the duration of some known processes, up to the age of the Universe.

Rice. 1.4. Characteristic time and sizes of some objects and processes of the Universe.

On the right side of the diagram are distances corresponding to certain time scales. Planck's time (chronon) corresponds to a fundamental unit called Planck length. These two quantities naturally arise in any attempt to combine physical theories that describe very large and very small objects (we are talking about Einstein’s general theory of relativity and quantum mechanics). With any combination of variants of these theories, length and Planck time act as fundamental units of measurement. The transition from the left scale of the diagram to the right is carried out by multiplying by the speed of light, which makes it easy to compare any period of time with the distance traveled by the light signal during this time.

The sizes of physical objects in the figure vary from 10 -15 m (the characteristic size of elementary particles) to 10 27 m (the radius of the observable Universe, approximately corresponding to its age, multiplied by the speed of light). It is interesting to evaluate the position we occupy on the diagram We, People.

On the size scale we are somewhere in the middle, being extremely large relative to the Planck length (and many orders of magnitude larger than the size of elementary particles), but very small on the scale of the entire Universe. On the other hand, on the time scale of processes, the duration of a human life looks quite good, and it can be compared with the age of the Universe! People (and especially poets) love to complain about ephemerality human existence, however, our place on the timeline is not at all pitiful or insignificant. Of course, we should remember that everything said refers to the “logarithmic scale”, but its use seems completely justified when considering such gigantic ranges of values. In other words, the number human lives, which fit into the age of the Universe, are much less than the number of Planck times (or even the lifetimes of elementary particles) that fit into the lifespan of a person. In essence, we are fairly stable structures of the Universe. As for spatial scales, we really are somewhere in the middle of the scale, as a result of which we are not given the opportunity to perceive in direct sensations either very large or very small objects of the physical world around us.

Let's look at what physical theories describe objects of such different sizes. In the diagram of Fig. 1.5 I tried to squeeze in all the existing physics. In doing so, I, of course, had to sacrifice many minor details (for example, simply throwing out all the equations and branches of science from the picture!), however, in my opinion, I preserved the fundamental theories.

Rice. 1.5.

The most significant fact is that physics uses two completely different approaches. To describe the behavior of micro-objects, we use quantum mechanics (I denoted it in the figure with the words “quantum level”), which is described in more detail in Chapter. 2. Most people believe that quantum mechanics is a strange, mysterious and non-deterministic theory, but this is not true. In fact, if you consider events at the quantum level, then quantum theory is completely precise and deterministic. Its most famous relation is the Schrödinger equation, which determines the behavior of the physical state of a quantum system (it is simply called quantum state) and is certainly completely accurate and deterministic. I use the letter U to denote all calculations or methods related to the quantum level of consideration. Uncertainty in quantum mechanics only arises when you make a so-called “measurement,” which requires a significant “zoom in” on the scale of the event to move from the quantum to the classical level. We will consider these problems in more detail in Chap. 2.

At large scales we use the concepts of classical physics, which is completely deterministic. It includes Newton's laws of mechanics, Maxwell's laws (allowing the introduction of the concepts of electricity, magnetism and light into physics), Einstein's two theories of relativity (special theory of relativity, which describes the movement of bodies at high speeds, and general theory of relativity for systems with powerful gravitational fields) , and all these laws are satisfied at large distances with exceptionally high accuracy.

I also note that in Fig. 1.5, I used the term “computability” to characterize both quantum and classical physics. In the first two chapters this concept is practically not used, but it has important for the problems discussed in Chap. 3, where we look at the problem of “computability” more closely.

This chapter is mainly devoted to Einstein's theory of relativity, its characteristic features, exceptional precision, and amazing grace and elegance. However, first it is necessary to talk at least very briefly about Newtonian physics. Soon after Einstein developed general relativity, Cartan showed that Newton's theory of gravity also allowed for the concept of a unified space-time. The physical picture in the mechanics of Galileo and Newton makes it possible to represent space-time by introducing a global (universal) time coordinate, after which the state of the system can be described simply by a set of sequential diagrams (Fig. 1.6), in which sections of four-dimensional space-time correspond to different moments of time. Each such spatial section (i.e., the plane in Fig. 1.6) corresponds to an ordinary Euclidean three-dimensional space. A characteristic feature of Newtonian space-time is that all spatial “sections” exist in it as if simultaneously.

Rice. 1.6. Unified space-time in Galileo-Newton mechanics. Straight lines correspond to uniformly moving particles.

Thus, for example, all events occurring at midnight on Monday lie in the lower horizontal plane of the diagram; everything that happens at midnight on Tuesday is on the next plane, etc. Time sections along the time axis simply give a sequence of Euclidean spaces in time. All observers (regardless of their method of movement in space-time) record the same events simultaneously, since they see the same “slices” or “sections” of a single space-time.

Things are completely different in Einstein's special theory of relativity, where time and, accordingly, the complete picture of space-time cease to be universal quantities, as in Newton's physics. To demonstrate the significant difference between these theories, we must first introduce one of the most important concepts of the theory of relativity - the so-called light cone.

What is a light cone? Imagine a flash of light at a given point in space and at a certain point in time (this is event in space-time), after which the waves begin to propagate at the speed of light, transmitting a signal about the event. In spatial coordinates, the propagation front has the form of a sphere expanding at the speed of light (Fig. 1.7, b), however, in the full coordinate system (space-time) we get a much more complex picture (Fig. 1.7, A), which will take into account horizontal displacements corresponding to the shifts in Fig. 1.6. Unfortunately, the image in Fig. 1.7, A is only two-dimensional (drawing plane), since we use only three dimensions to depict four-dimensional space-time. Therefore, we have to depict a flash of light as a point at the origin (event), and then as circles on horizontal sections, reflecting the actual movement of light rays (waves) through space. In this case, the movement of light rays forms a cone in space-time, the upper part of which describes the history of the “flash” by the movement of light rays into the future space-time. On the other hand, the lower part of the cone corresponds to the arrival of light rays from the past at the flash point (this part of the diagram is usually called the past light cone). The observer receives all the information from light rays propagating along the surface of the cone!

Roger Penrose's original, bright and provocative ideas regarding the processes occurring in the civilian world of the Universe, in the microcosm of quantum physics and in the human brain, have more than once become the subject of heated controversy and discussion. Some of these ideas are already familiar to readers from his previous books: The Emperor's New Mind and Shadows of the Mind. In this book, Penrose summarizes and develops them further, and also gives An excellent overview of many unsolved problems in modern physics.

Penrose's radical concepts provide new insights into how the brain works and the nature of human consciousness. Three scientists associated with various scientific disciplines entered into controversy with the author in this book - famous specialists in the philosophy of science Abner Shimoni and Nancy Cartwright, as well as the famous theoretical physicist and astrophysicist Stephen Hawking. In the last chapter of the book, Roger Penrose, continuing this extremely interesting discussion, responds to his opponents. The reader gets the opportunity to get acquainted with his own, very non-standard (sometimes even humorous) point of view of the largest theoretical physicist on the most important problems of modern science.

Over the past decade, many books have appeared in which outstanding scientists of our time try to explain to the general reader the essence and exceptional interest of their research in various fields of knowledge. The most famous of them were the famous “A Brief History of Time” by Stephen Hawking (which was such an amazing success that its publication became a notable phenomenon in the history of world popular science literature), James Gleick’s book “Chaos” (which successfully showed that the most complex scientific research sometimes resembles an exciting detective story) and “Dreams of a Final Theory” by Steven Weinberg, which made the latest achievements in particle physics understandable and interesting.

It is not surprising that the book “The New Mind of the King” caused fierce controversy, as a result of which the author had to publish the book “Shadows of the Mind” in 1994, in which he tried not only to answer his many critics, but also to further develop the proposed ideas. In 1995, R. Penrose was invited to give the famous Tenner Lectures, where he presented a general overview of his concept and called for discussion of his most famous opponents, Abner Shimoni, Nancy Cartwright and Stephen Hawking. The three lectures of the cycle made up the first three chapters of the book offered to the reader, containing a brief introduction to the range of ideas developed in detail by the author in the books mentioned above. The next three chapters (4-6) contain the arguments of the discussed participants, and in the final chapter 7 Penrose comments on the comments received and summarizes the results of the discussion.

The second "infinity" theorem states that the classical relativistic theory of gravity inevitably leads to singularities of this type in cosmological models associated with the Big Bang. These theorems show that the theories we use are still very far from complete, since such singularities should not arise in closed and mature physical constructions.

These works represent only part of R. Penrose's extensive contribution to various branches of physics and mathematics. Physicists are familiar with the Penrose process (in which particles absorb rotational energy in black holes), and they widely use the diagrams he created to describe the behavior of matter in the vicinity of black holes. The beautiful geometry (at times reminiscent of painting) of many such phenomena is clearly presented by the author himself in the first three chapters of the book. Some aspects of the problems under consideration are already widely known to the public from the “impossible” constructions and paintings of the famous artist Maurice Escher and the so-called “mosaics” of Penrose himself. It is interesting that M. Escher was inspired to create some of the engravings (namely those that attempt to depict the “impossible”) by one of the articles written by R. Penrose and his father L. S. Penrose. In ch. 1, Penrose’s hyperbolic geometric constructions are illustrated by the famous series of engravings by M. Escher “Limit Circles”. In this regard, one cannot fail to mention the “mosaics” or “tiles” created by Penrose himself, which allow
completely cover an infinite plane with a small number of varieties of simple geometric figures of a given type. The main and most interesting mathematical side of the problem is that the pattern that allows us to solve this problem is non-repeating. This geometric problem appears unexpectedly in Chap. 3 books in connection with the ability to define rigorous computational operations for computers.

Penrose managed not only to develop a number of brilliant mathematical approaches, but also to successfully apply them to solve the most complex specific problems of modern physics. The issues he considers always turn out to be very important and interesting. Now physicists are confident that the Big Bang theory gives us a fairly accurate picture of the origin of the Universe, but it is still far from complete, and we do not yet know many of the fundamental laws that determine its main features from the age of one thousandth of a second after birth to the present day. To reconstruct the complete picture, we still have to determine the initial conditions, but all the laws of physics known to us apply only to a fairly “old” Universe, the age of which exceeds the mentioned limit of one thousandth of a second. Therefore, we still have to intelligently extrapolate the patterns we know. We already have a fairly good idea of the required initial conditions, but we know very little about the causes that give rise to them, and this problem remains central to all modern cosmology.

Usually in cosmology, a model of an inflating (inflationary) Universe is used, however, even in this model, to describe some features of the process, it is necessary to introduce parameters characteristic of the early, so-called Planck epoch of the development of the Universe (10 "43 s), when the most important events occurred in this exceptionally short period. events, the consequences of which modern science is trying to describe.

The probability of such a state occurring by chance is vanishingly small, as a result of which Penrose suggested that the problem could only be solved within the framework of an exact theory of quantum gravity. In ch. 2 discusses the general problems of quantization and quantum physics, which (together with its relativistic generalization - quantum field theory) has long been very successfully used to describe the properties of individual atoms and particles, as well as to explain experimental results in nuclear physics. However, only in recent years have we begun to understand the deep physical meaning of this theory. Penrose was able to brilliantly demonstrate that its internal structure contains very complex (intuitively non-obvious) ideas that have no analogues in classical mechanics. For example, non-locality means that when a particle-antiparticle pair arises, each of them retains a “memory” of the birth process in the sense that these particles cannot be considered completely independent of each other. Roger explains this by saying that "quantum entanglement of objects is an amazing phenomenon that lies somewhere between their separation and unification." Quantum mechanics even allows us to obtain information about processes that did not occur, but could have been realized. The difference between classical and quantum mechanics is especially clearly manifested in the very unusual (from the usual point of view) problem of the so-called bomb test in the Elitzur-Vaidman experiment.

The transition occurs through the so-called “collapse of the wave function” or “reduction of the vector of states.” Penrose is confident that with this standard quantum mechanical technique, a very significant part of the picture of the physical world is lost, and we need to develop a completely new theory that will somehow include the specified “objective reduction of wave functions.” Such a theory, with appropriate transitions to the limit, will be reduced to ordinary quantum mechanics and quantum field theory, but it should also describe new physical phenomena (in particular, it should allow us to solve the problem of quantizing the gravitational field and describe the early period of the development of the Universe).

In ch. 3 Penrose attempts to identify commonalities shared by mathematics, physics, and human consciousness. If you think about it, it is truly amazing that in the most seemingly logical and abstract areas of physics and mathematics, it is not possible to create programs for the discrete computers we are familiar with (even for the most accurate and with the largest amount of memory). All computers practically cannot, for example, prove mathematical theorems, as ordinary human mathematicians do. All this, on the other hand, is in perfect agreement with one version of the famous Gödel theorem, which in Penrose's interpretation means that mathematical deductions (and, generally speaking, all processes associated with thinking and behavior) are carried out in an “incomputable” way. This conclusion seems very fruitful, if only because intuitively we ourselves feel that almost all of our acts of “conscious perception” cannot be reduced to computable operations. Most of Penrose's previous book, Shadows of the Mind, mentioned above, was devoted to precisely this interpretation of Gödel's theorem, which has special significance for all the author's logical constructions.

Penrose unexpectedly sees many similarities between the fundamental problems of quantum mechanics and the processes of consciousness. For example, he believes that non-locality and quantum coherence can explain knowledge that, in his opinion, can be associated with the objective collapse of the wave functions of macroscopic variables. Penrose not only formulates these very general principles of brain function, but also tries to directly identify structures in the brain that correspond to these physical processes.

Of course, the introduction to the book can only very weakly reflect the originality, richness and brilliance of the ideas and concepts proposed by the author, but I would like to once again draw the reader’s attention to the main directions that play an important role in understanding. The author is primarily struck by the remarkable ability of mathematics to realistically describe the fundamental processes of nature. Penrose is convinced that our physical world is in some sense a manifestation of Plato's world of mathematical ideals. Nowadays, of course, no one tries to derive mathematics from attempts to describe the world around us or from fitting experimentally observed patterns to mathematical formulas. In fact, we are now trying to understand the structure of the Universe, based on some very general principles and from the laws of mathematics itself.

It is not surprising that such bold hypotheses proposed in the book became the subject of fierce controversy, in which scientists of various specialties and intellectual orientations were involved. Abner Shimoni agrees with Penrose in many respects (for example, he acknowledges the incompleteness of the usual formulation of quantum mechanics and agrees that some quantum mechanical concepts are quite suitable for describing the work of the brain), but he compares Roger Penrose to “a mountain climber who climbs the wrong mountain.” , and is ready to offer his own constructive approaches to solving these problems. Nancy Cartwright asks fundamental questions for philosophy about what sciences should form the basis for understanding the nature of consciousness and what the role of physics is in this. She also raises in the discussion a very sensitive topic of compatibility (or the possibility of reducing to each other) the laws of various scientific
disciplines The most critical section is written by Stephen Hawking, Penrose's old friend and colleague. In many ways, it is Hawking’s position that is closest to the point of view of the “average physicist.” He suggests that the author, first of all, develop a procedure for detailed reconstruction (reduction) of wave functions. However, Hawking does not believe that the opinion of physicists about the problems of consciousness has any special value. The appearance of such remarks is quite natural, and Penrose tries to refute them in his general response, which forms the final chapter of the book.

Penrose, of course, solved one of the tasks he set himself with brilliance - he created a kind of manifesto or program for the development of theoretical physics of the 21st century. In the first three chapters of the book, he managed to present a coherent picture of how a completely new physics should be “structured,” based on the general idea of the non-computability of some operations and the objective restoration of wave functions, which is the main idea of the book. The correctness of the proposed concepts will ultimately be determined by whether Penrose and his followers can actually create a new type of physical theory. In any case, even if work on this program does not lead to rapid success, its basic ideas, in my deep conviction, will have a fruitful influence on the future development of theoretical physics and mathematics.

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Roger Penrose, Abner Shimoni, Nancy Cartwright, Stephen Hawking

Big, small and the human mind

Three scientists associated with various scientific disciplines entered into controversy with the author in this book - famous specialists in the philosophy of science Abner Shimoni and Nancy Cartwright, as well as the famous theoretical physicist and astrophysicist Stephen Hawking. In the last chapter of the book, Roger Penrose, continuing this extremely interesting discussion, responds to his opponents. The reader gets the opportunity to get acquainted with his own, very non-standard (sometimes even humorous) point of view of the largest theoretical physicist on the most important problems of modern science.

ROGER PENROSE Roseball Professor, Professor of Mathematics at the University of Oxford

ABNER SHIMONI Professor Emeritus of Philosophy and Physics, Boston University NANCY CARTWRIGHT Professor of Philosophy, Logic and Science, London School of Economics and Politics (LSE)

STEPHEN HAWKING Lucasian Professor at Cambridge University

Borrowed drawings

Shadows of the Mind, R. Penrose, 1994. Oxford: Oxford University Press. 1.14, 2.3, 2.4, 2.5(b), 2.6, 2.7, 2.19, 2.20, 3.7, 3.8, 3.10, 3.11, 3.12,3.13,3.14,3.16,3.17,3.18.

High Energy Astrophysics, Volume 2, M. S. Longair, 1994. Cambridge: Cambridge University Press. 1.15, 1.22.

Translator's Preface

The complexity and variety of issues discussed in R. Penrose's book require us to preface its translation with at least very brief remarks. Firstly, as the author himself convincingly demonstrates, quantum mechanics is far from not only completeness, but also from a unified methodological approach. Over decades of debate about the principles of quantum physics, a huge amount of literature has accumulated on many of the issues under consideration (for example, entire libraries have already been written about Schrödinger’s famous cat). In this monstrous array of information, philosophical, methodological and scientific contradictions naturally long ago grew (or degenerated) into linguistic and terminological ones. The reader can get some idea of the current state of the issue from the article by M. B. Mensky “Quantum mechanics: new experiments, new applications and new formulations of old questions” (Uspekhi Fizicheskikh Nauk, Vol. 170, No. 6, 2000, p. 631) and called its discussions (UFN, 2001; vol. 171, no. 4, pp. 437-462; UFN, 2001; vol. 171, no. 6, pp. 625-647).

A. V. Khachoyan

Preface. Malcolm Longair

Over the past decade, many books have appeared in which outstanding scientists of our time try to explain to the general reader the essence and exceptional interest of their research in various fields of knowledge. The most famous of them were the famous “A Brief History of Time” by Stephen Hawking (which was such an amazing success that its publication became a notable phenomenon in the history of world popular science literature), James Gleick’s book “Chaos” (which successfully showed that the most complex scientific research sometimes resembles an exciting detective story) and “Dreams of a Final Theory” by Steven Weinberg, which made the latest achievements in particle physics understandable and interesting.

Even among such well-known works, Roger Penrose's previous book, The New Mind of the King (1989), stands out for its originality. While other authors usually try to simply convey the meaning and significance of the achievements of modern science, Roger risked offering readers a completely new, at times stunning possibility of the existence of some kind of (not yet fully formulated) theory of fundamental processes that allows us to unite almost unrelated with a friend, theories related to a wide variety of sciences (physics, mathematics, biology, neurophysiology and even philosophy). It is not surprising that the book “The New Mind of the King” caused fierce controversy, as a result of which the author had to publish the book “Shadows of the Mind” in 1994, in which he tried not only to answer his many critics, but also to further develop the proposed ideas. In 1995, R. Penrose was invited to give the famous Tenner Lectures, where he presented a general overview of his concept and called for discussion of his most famous opponents, Abner Shimoni, Nancy Cartwright and Stephen Hawking. The three lectures of the cycle made up the first three chapters of the book offered to the reader, containing a brief introduction to the range of ideas developed in detail by the author in the books mentioned above. The next three chapters (4 - 6) contain the arguments of the discussed participants, and in the final chapter 7 Penrose comments on the comments received and summarizes the results of the discussion.

These works represent only part of R. Penrose's extensive contribution to various branches of physics and mathematics. Physicists are familiar with the Penrose process (in which particles absorb rotational energy in black holes), and they widely use the diagrams he created to describe the behavior of matter in the vicinity of black holes. The beautiful geometry (at times reminiscent of painting) of many such phenomena is clearly presented by the author himself in the first three chapters of the book. Some aspects of the problems under consideration are already widely known to the public from the “impossible” constructions and paintings of the famous artist Maurice Escher and the so-called “mosaics” of Penrose himself. It is interesting that M. Escher was inspired to create some of the engravings (namely those that attempt to depict the “impossible”) by one of the articles written by R. Penrose and his father L. S. Penrose. In ch. 1, Penrose’s hyperbolic geometric constructions are illustrated by the famous series of engravings by M. Escher “Limit Circles”. In this regard, one cannot fail to mention the “mosaics” or “tiles” created by Penrose himself, which make it possible to completely cover an infinite plane with a small number of varieties of simple geometric figures of a given type. The main and most interesting mathematical side of the problem is that the pattern that allows us to solve this problem is non-repeating. This geometric problem appears unexpectedly in Chap. 3 books in connection with the ability to define rigorous computational operations for computers.

The author of this work is not Stephen Hawking, but Roger Penrose. Stephen Hawking appears in the book as one of his fellow physicists, and Penrose himself is a mathematician and apologist for mathematics. And his main idea, which he seeks to convey to the reader, is that our world is subject to strict laws, which are very elegantly (from the point of view of a scientist familiar with higher mathematics and quantum theory first-hand) described by mathematical expressions. So elegantly that the author is inclined to believe that it is not we who describe our world in the language of mathematics, but our world is a reflection of a certain mathematical model, an absolute, an idea, onto physical matter. This is a very interesting assumption, especially if we remember that we don’t know a damn thing about the world around us! That is, nothing at all! We think that we live in a century of progress and technology, but in fact we are standing in the middle of a small clearing, like hedgehogs in the fog.
My idea about the projection of a mathematical model onto real world Penrose voices it at the beginning of the book, and all subsequent really difficult calculations in the language of quantum theory are designed to draw attention to specific things and examples.
Wu studied quantum physics at the university's physics department. Now I remember very little, but it is a fact that the book is not intended for a wide range of readers!
The rating is underestimated due to the fact that it was assessed from the point of view of an ordinary reader. The average reader will not understand beyond the first chapter :)

not popular, but highly specialized...

In my understanding, a popularizer is someone who brings complex things to the masses and explains them in accessible language.
You took the book and learned something for yourself, understood something. You understood, if not everything, but some grains of knowledge and understanding settled in your head. Hawking is presented as a popularizer of science. Lies.
Honestly, I didn’t understand a damn thing in this book. Yes, I am certainly a humanitarian, but this does not mean that this and that is not available to me. And if I set a goal, I will sit and painstakingly study everything. Did not work out.
This book is apparently for physicists, astrophysicists, those who have mastered quantum mechanics... For teachers, advanced students of these faculties, graduate students - but what is not for the general public is definitely...

Roger Penrose, Abner Shimoni, Nancy Cartwright, Stephen Hawking

Big, small and the human mind

ROGER PENROSE Roseball Professor, Professor of Mathematics, Oxford University

ABNER SHIMONI Professor Emeritus of Philosophy and Physics, Boston University NANCY CARTWRIGHT Professor of Philosophy, Logic and Science, London School of Economics and Politics (LSE)

STEPHEN HAWKING Lucasian Professor at Cambridge University

Borrowed drawings

Shadows of the Mind, R. Penrose, 1994. Oxford: Oxford University Press. 1.14, 2.3, 2.4, 2.5(b), 2.6, 2.7, 2.19, 2.20, 3.7, 3.8, 3.10, 3.11, 3.12,3.13,3.14,3.16,3.17,3.18.

High Energy Astrophysics, Volume 2, M. S. Longair, 1994. Cambridge: Cambridge University Press. 1.15, 1.22.

Translator's Preface

The complexity and variety of issues discussed in R. Penrose's book require us to preface its translation with at least very brief remarks. Firstly, as the author himself convincingly demonstrates, quantum mechanics is far from not only completeness, but also from a unified methodological approach. Over decades of debate about the principles of quantum physics, a huge amount of literature has accumulated on many of the issues under consideration (for example, entire libraries have already been written about Schrödinger’s famous cat). In this monstrous array of information, philosophical, methodological and scientific contradictions naturally long ago grew (or degenerated) into linguistic and terminological ones. The reader can get some idea of the current state of the issue from the article by M. B. Mensky “Quantum mechanics: new experiments, new applications and new formulations of old questions” (Uspekhi Fizicheskikh Nauk, Vol. 170, No. 6, 2000, p. 631) and called its discussions (UFN, 2001; vol. 171, no. 4, pp. 437-462; UFN, 2001; vol. 171, no. 6, pp. 625-647).

A. V. Khachoyan

Preface. Malcolm Longair

Over the past decade, many books have appeared in which outstanding scientists of our time try to explain to the general reader the essence and exceptional interest of their research in various fields of knowledge. The most famous of them were the famous “A Brief History of Time” by Stephen Hawking (which was such an amazing success that its publication became a notable phenomenon in the history of world popular science literature), James Gleick’s book “Chaos” (which successfully showed that the most complex scientific research sometimes resembles an exciting detective story) and “Dreams of a Final Theory” by Steven Weinberg, which made the latest achievements in particle physics understandable and interesting.

These works represent only part of R. Penrose's extensive contribution to various branches of physics and mathematics. Physicists are familiar with the Penrose process (in which particles absorb rotational energy in black holes), and they widely use the diagrams he created to describe the behavior of matter in the vicinity of black holes. The beautiful geometry (at times reminiscent of painting) of many such phenomena is clearly presented by the author himself in the first three chapters of the book. Some aspects of the problems under consideration are already widely known to the public from the “impossible” constructions and paintings of the famous artist Maurice Escher and the so-called “mosaics” of Penrose himself. It is interesting that M. Escher was inspired to create some of the engravings (namely those that attempt to depict the “impossible”) by one of the articles written by R. Penrose and his father L. S. Penrose. In ch. 1, Penrose’s hyperbolic geometric constructions are illustrated by the famous series of engravings by M. Escher “Limit Circles”. In this regard, one cannot fail to mention the “mosaics” or “tiles” created by Penrose himself, which make it possible to completely cover an infinite plane with a small number of varieties of simple geometric figures of a given type. The main and most interesting mathematical side of the problem is that the pattern that allows us to solve this problem is non-repeating. This geometric problem appears unexpectedly in Chap. 3 books in connection with the ability to define rigorous computational operations for computers.

Characteristics of men