1.1. From the Publisher.

A landmark volume in science writing by one of the great minds of our time, Stephen Hawking's book explores such profound questions as: How did the universe begin - and what made its start possible? Does time always flow forward? Is the universe unending - or are there boundaries? Are there other dimensions in space? What will happen when it all ends? Told in language we all can understand, A Brief History of Time plunges into the exotic realms of black holes and quarks, of antimatter and "arrows of time," of the big bang and a bigger God - where the possibilities are wondrous and unexpected. With exciting images and profound imagination, Stephen Hawking brings us closer to the ultimate secrets at the very heart of creation.

1.2. Review by: Leemon B McHenry.
The Review of Metaphysics 42 (3) (1989), 626-628.

Stephen Hawking is well known for his research on general relativity and black holes. The present work is his attempt to explain his re-research in a form intelligible to the non-specialist.

A Brief History of Time is a survey of cosmology from the ancient Greeks to the present. One of Hawking's central aims in this book is to communicate the threshold of what promises to be a major advance in physics - the consolidation of a cosmological theory that reconsider the partial theories of the twentieth century: electromagnetism, weak and strong nuclear forces, and general relativity. Grand Unification theories have attempted to unify the first three, namely, the forces that operate on a subatomic scale, but the link between the quantum world and the large-scale structure determined by gravity has been the most formidable. The key to the unification of all four forces as different aspects of a single force lies in a quantum theory of gravity.

With the discovery that light from distant galaxies is systematically shifted toward longer wavelengths (indicating galaxies receiving from us with velocities proportional to their distances), an expanding universe has firmly replaced the static model of Einstein's theory of general relativity. The dynamic, expanding model now implies a beginning of the universe that must be a singularity of infinite density and space-time curvature. As with the big bang, singularities are also thought to exist in the gravitational collapse of a star that forms a black hole. In both cases of the big bang singularity and those of black holes, there is a breakdown of all the known laws of physics since they cannot accommodate infinite quantities.

Hawking attempts to remedy this situation by using a quantum theory of gravity to discuss the very early stages of the universe. This unified theory includes two essential features: (i) Feynman's formulation of the quantum theory in terms of a sum-over-history approach, modified by Hawking's proposal of "imaginary time," where waves for particle histories are measured using imaginary numbers rather than real ones, and (ii) Einstein's idea of ​​a curved space-time as an accurate representation of the structure of the gravitational field. Feynman's sum-over-history applied to Einstein's theory of gravity results in a view of the history of particles in a Euclidean curved space-time that represents the history of the whole universe.

In a quantum theory of gravity, it is possible for the curved space-time manifold of the universe to be finite in extent yet without bounds in time or space. The expanding universe is thus represented in imaginary time by concentric circles growing outward from an ordinary point of space-time, where it expands to some maximum size, and then begins to contract where the concentric circles recede to a point. But at the points there are no edges or singularities much like the finite and unbounded surface of the Earth. In such a theory there would be no big bang singularity; the universe would have zero size at both points, but it would be unbounded and without beginning or end in time.

Why should a scientific theory that eliminates the singularity be preferred to a theory that does not, i.e., as in classical general relativism? In Hawking's view, the reason is that the laws of physics will hold everywhere, including the beginning of the cosmological expansion, and not just in limited regions of space-time. But as he himself admits, until the test of whether the theory makes predictions that agree with observation, it is put forth on the basis of metaphysical or aesthetic preferences. It is preferred for its comprehensive capabilities: (i) for its explanatory power once the partial theories have been modified for the Grand Unification, and (ii) for the benefits gained from having the ordinary laws of physics hold throughout the universe, without breakdowns at singularities.

Hawking maintains that there are "grounds for cautious optimism that we may now be near the end of the search for the ultimate laws of nature", and that a "complete understanding" of the universe is possible. At various points in this book, the epistemic claims are far too strong for a philosopher's taste. Hawking's optimism for complete understanding gained from a unified cosmological theory also appears overconfident in the face of shattering evidence from the history and philosophy of science. The claim that the end of the search for the laws of physics has been made by several zealots from now-overthrown scientific theories. They too argued that the accumulated knowledge of their time made their case different from their predecessors. But at the same time that Hawking espouses commitment to a unified theory, he also maintains that scientific theories are just mathematical models we create to describe our observations; The final analysis depends on "which is the more useful description".

This apparent inconsistency between what appears to be a realist view of science on the one hand, and an instrumentalist view on the other, is resolved once we see that, for Hawking, the discovery of a unified theory would not mean that we knew we had the correct one. At best we could be reasonably confident that it was the right one if the theory proved mathematically consistent and always gave pre-dictions that squared with observations. Hawking, therefore, seems to argue for a realist view, that an ultimate theory of the universe is possible by study of the early universe, but its mode of verification will remain problematic. In the process of clarifying this position, however, another problem arises. While Hawking is clearly aware of the fact that the logical structure of theory-testing makes proof of scientific theories impossible, he argues that an infinite sequence of more and more refined theories about ultimate particles is limited by gravity as we go to higher and higher energies. A particle with an energy above Planck energy (ten million million million GeV) would be so dense that it would form a little black hole. So the postulation of elementary particles beyond this energy level is impossible. The trouble with this argument is that it presupposes that the theory of gravity is essentially correct as a basis for determining the limit of elementary particle theories. Clearly if theories cannot be proven, as Hawking himself admits, one theory cannot serve as a foundation to prove something about the limits of other theories. The high theoretical content in the theory of gravity itself remains unverifiable and is therefore just as subject to revision as particle theory.

A Brief History of Time is fascinating for its imaginative leaps of high speculation and for the clarity gained from the overview of contemporary cosmological theory. But it just whets the appetite for what can only be accomplished in a more specialized and technical form.

1.3. Review by: Lee Loevinger.
Jurimetrics 29 (2) (1989), 245-253.

My own guess is that one major achievement of this book is to demolish the myth that you cannot explain or understand modern theories of physics without the ability to understand all of the mathematics that scientists rely on to formulate and test such theories. Hawking has provided an explanation of the most arcane and esoteric physical theories in purely verbal terms. Although the explanations may not always be entirely simple, that is because the concepts are complex, not because the verbal language system is inadequate. Indeed, purely mathematical expressions are inadequate to describe such concepts fully with-out the supplement of words at least to identify the symbols.

An important aspect of the writing is that Hawking, a mathematician, comprehensively eschews mathematics in his exposition. Indeed, he does not even use mathematical notation to express large numbers. Thus, he would write a million million million million million rather than 1024 (which is really quite explicable and easily understandable). He also writes with a pleasant light touch, using whimsical metaphors to illustrate a point. He not only analogises the Second Law of Thermodynamics to Murphy's Law, but suggests that the inevitable increase in entropy, which is a measure of disorder, is confirmed by the common experience that disorder will tend to increase if things are left to themselves, as anyone can see if they stop making repairs around the house. More seriously, he illustrates the difference in the behaviour of a particle at low and high energies by the example of a roulette ball on a roulette wheel. When the wheel is spun quickly, which corresponds to having high energy, the ball spins around with the wheel, but as the wheel slows the energy of the ball decreases and the ball eventually drops into one of the slots. The writing is consistently lucid and will amply repay the effort necessary to follow the argument by anyone who is really interested in learning the fundamental theories of contemporary science.

Many scientists rank Hawking as one of the greatest scientific minds since Einstein. He is too modest to make such a claim, but six pages following the text of his book suggest that he may not be entirely insensitive to that possibility. In brief sketches of two pages each, he gives a few salient facts about the lives of Galileo, Newton, and Einstein. These pages contain little of purely scientific significance and may be a subtle suggestion of the position Hawking envisions for himself. He may be right - only his friend will tell. However, he is in the tradition of many eminent scientists who have undertaken to present the recondite theories of basic science to the general public.

1.4. Review by: Monroe K Spears.
The Sewanee Review 99 (1) (1991), 113-121.

In the last decade or so there has been an outpouring of books purporting to explain, if not without tears at least without mathematics, the latest discoveries and theories in cosmology. Among these, Hawking's book deserves special attention, for it has been a phenomenal best-seller, leading the list in the U.S. for more than a year and still high on it as I write, and now repeating the performance in England and, in translation, in France, Germany, and eighteen other countries.

Part of the reason for this popularity is obvious: Hawking himself is a leading scientist, much admired for his work on black holes, and a Lucasian professor at Cambridge (the position held by Newton and Dirac); hence, he speaks with singular authority. Perhaps a more important factor is that the public has been made aware by the news media that he is a victim of motor neuron disease, confined to a wheelchair for more than 25 years, and unable to speak for the last several years. In spite of this fearful handicap, he has managed not only to carry on his work as a scientist and teacher but to have a full life as a husband and father. His book is thus an inspirational work simply by the fact of existing, and one suspects that many people buy it as a tribute to Hawking's courage and determination as a human being as well as to his eminence as a scientist. Buying the book may also be a kind of ritual, a pious gesture toward the mysteries of science, especially mathematics.

Hawking's has reached a wide audience through paperback publication and earlier appearances in periodicals. Hawking's book, however, is straight cosmology. The common reader may find it mercifully short; But can the "history of time," "the origin and fate of the universe," and such unimaginable phenomena as the big bang and black holes really be explained and discussed in 182 innocent pages of mathematics and diluted by many anecdotes and graphic illustrations?

Hawking's book is autobiographical only in sketching the development of his cosmological theories. He writes simply and without recourse to intimidating mathematics. A good example of the personal tone, with its reassuringly casual sprinkling of exclamation marks, is the beginning of the chapter, "Black Holes Ain't So Black": "Before 1970, my research on general relativity had concentrated mainly on the question of whether or not there had been a big bang singularity. However, one evening in November of that year, shortly after the birth of my daughter, Lucy, I started to think about black holes as I was getting into bed. My disability makes this rather a slow process, so I had plenty of time. ... I had already discussed with Roger Penrose the idea of ​​defining a black hole as the set of events from which it was not possible to escape to a large distance, which is now the generally accepted definition. ... It is a bit like running away from the police and just managing to keep one step ahead but not being able to get clear away! Suddenly I realised that the paths of these light rays could never approach one another. If they did, they must eventually run into one another. It would be like meeting someone else running away from the police in the opposite direction - you would both be caught! (Or, in this case, fall into a black hole.)"

Hawking and Penrose proved mathematically in 1970 that there must have been a big bang, though the discovery of uniform microwave radiation by Penzias and Wilson in 1965, together with other evidence, had already settled the question empirically. By 1981, however, Hawking had changed his mind, and he relates with some amusement that when he attended a conference in that year organised by the Jesuits in the Vatican, he was glad the pope "did not know the subject of the talk. I had just given at the conference the possibility that space-time was finite but had no boundary, which means that it had no beginning, no moment of creation." (He has explained earlier that the Catholic church as early as 1951 "seized on the big bang model and officially pronounce it to be in accordance with the Bible.") Later he comments that his paper was rather mathematical, "so its implications for the role of God in the creation of the universe were not generally recognised at the time (just as well for me)."

1.5. Review by: Frank C Mahncke.
Naval War College Review 43 (1) (1990), 131-133.

One of the magnificent characteristics of the human intellect is its ability to engage in an open-ended quest for understanding the universe not for gain but for knowledge alone. This is the life and work of Stephen Hawking, professor of mathematics at Cambridge University and inheritor of Isaac Newton's chair (this is appropriate, for Hawking is widely regarded as the most profound physicist of the 20th century).

Although Hawking's body is cruelly crippled by amyotrophic lateral sclerosis, his mind is at the very edge of human understanding of the physical origin of the universe. His research in fundamental physics is directed at that deceptively simple question: How did the universe form and why is it like it is? In this short but important book, his objective is to give the average reader a qualitative grasp of the physical ideas that hold the answer to that question.

Forswearing all equations save Einstein's - for his editor told him that each equation would halve the book's sales - Hawking leads us through the wondrous world of physics and ideas about the formation, state, and fate of the universe. He begins with the first-cause concept so central to the history of Western science: "Within the universe, you always explained one event as being caused by some earlier event, but the existence of the universe itself could be explained in this way only if it had some beginning." Thus the question becomes, What was the beginning?

In searching for the answer to that question, Hawking's intellect and the work of experimental physicists have pushed the edge of our knowledge back to the smallest fraction of time between the big bang and the formation of the laws of physics as we now understand them. From space and time, the universe, as we can imagine, is the domain of modern physics. It is filled with black holes, strings, virtual mass, quarks, and curved spaces, each of which leads Hawking to show us the most intriguing ideas.
...
Reading Hawking is like his search for the grand unified theory of physics: it requires great imagination, and a complete understanding seems near but always elusive. Along the way, one deals with the most extraordinary and challenging ideas and concepts. For these alone, the trip is worth the intellectual exercise.

1.6. Review by: Wayne P Hughes Jr.
Phalanx 22 (1) (1989), 29-30.

When I was young it was common coin that Einstein was too deep to be understood by mere mortals. Later when I taught at the Naval Academy I saw this to be wrong. No science is so arcane that it cannot be explained. It is true that there are levels of comprehension, and grasping the rudiments is not the same as having a facility to operate with the theory of relativity, much less having the genius to develop and know how to test it. I got my first understanding of relativity from George Gamow, who had the teacher's knack.

Now comes Stephen Hawking with the genius to teach the simple folk like me the qualitative aspects of modern physics. That talent is almost as valuable as Hawking's understanding of the quantitative outer limits of the subject, which he not only grasps in its full richness, but to which he has contributed as few as have mortals. Hawking set out to write a bestseller, and as I write this, his book has been at or near the top of the list for the past three months. It deserves to be, even though "Someone told me," he writes in the introduction, "that each equation I included in the book would halve the sales, ... I did put in one equation, Einstein's famous equation, $E = mc^{2}$.

Because the book is a clear interpretation of the latest physics (relativity is explained on page 29 and is old hat), his contribution is a wonderful service to mankind. It is a fusion of the macro breadths of time and space of astronomical dimensions and the micro depths of nuclear physics - indeed, subnuclear physics, if such a term is appropriate for the particle physics of one dimensional (!) string operating in an unheard of number of dimensions. It is this span of knowledge, theory, and hypotheses that Hawking deals with under the buzz-wordy but unifying title, A Brief History of Time: From the Big Bang to Black Holes.
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2.1. From the Publisher.

Readers worldwide know the work of Stephen Hawking through his phenomenal bestseller A Brief History of Time. In this collection of essays and other pieces - on subjects that range from warmly personal to the wholly scientific - he is revealed variously as the scientist, the man, the concerned world citizen, and - as always - the rigorous and imaginative thinker. Whether remembering his first experience of nursery school; puncturing the arrogance of those who think science can best be understood only by other scientists and should be left to them; exploring the origins and the future of the universe; or reflecting on the phenomenon of A Brief History of Time, Stephen's wit, directness of style and absence of pomp are vital characteristics at all times.

2.2. Review by: K K Theckedath.
Social Scientist 22 (7/8) (1994), 101-110.

Like his earlier book, A Brief History of Time, with its runaway sales that made it enter the Guinness Book of Records, the present book is also expected to reach a very large audience. This is one important reason why one should take a look at some of the weaknesses of Hawking's position set out in this book, which incidentally were also present in his earlier work.

The book contains fourteen essays written during the years 1976 to 1992. They range from autobiographical sketches through the philosophy of science to attempts to explain the excitement he feels about science and the universe. The volume concludes with the transcript of a program 'Desert Island Discs' in which he appeared on the BBC.

The essays are eminently readable, especially the ones about his childhood, his work at Oxford and Cambridge, and his experience with an incurable motor neuron disease (ALS). The mighty courage with which he faces his condition of ALS with the compounded problem of the complete loss of his voice following a tracheostomy operation in 1985 is seen in the following passage:

I am quite often asked: How do you feel about having ALS? The answer is, not a lot. I try to lead as normal a life as possible and do not think about my condition or regret the things it prevents me from doing, which are not that many.

What we are considering in this review is his philosophical position, which he derives mainly from the fields of quantum mechanics and relativity through an unconscious operation of the general positivist influence on him. He tries to forestall criticism from the philosophers by making an attack on them right at the beginning of his essay My Position, where he says, 'The people who ought to study and argue such questions, the philosophers, have mostly not had enough mathematical background to keep up with modern theoretical physics. There is a subspecies called philosophers of science who ought to be better equipped. But many of them are failed physicists who found it hard to invent new theories and so took to writing about the philosophy of physics instead. They are still arguing about the scientific theories of the early years of this century, like relativity and quantum mechanics. They are not in touch with the present frontier of physics.'

He further goes on to say: 'We have known for 25 years that Einstein's general theory of relativity predicts that time must have a beginning in a singularity 15 billion years ago. But the philosophers have not yet caught up with the idea. They are still worrying about the foundations of quantum mechanics that were laid down 65 years ago.'

Since this piece was written in 1992, he is referring to the 'foundations' of quantum mechanics that were laid down at the Solvay Conference in 1927 and to the so-called singularity theorems that were propounded by Roger Penrose and himself in 1977.

Though Hawking's criticism of the philosophers of science may be broadly correct, it must be stated that on the question of awareness of certain important developments in physics, the boot is apparently on the other leg. Hawking seems to be totally unaware of the large volume of work done after 1950, which finally proved that the so-called Copenhagen interpretation of quantum mechanics, the foundations of which were laid in 1927, is only one possible theory among others. With the help of Einstein himself, David Bohm had presented an alternative theory in 1952 entitled, in retrospect unfortunately, as the Theory of Hidden Variables, which disproved von Neumann's contention that the Copenhagen theory was the only possible quantum mechanics. The large number of papers on the subject of the foundations of quantum mechanics in the same internationally reputed journals that carried Hawking's work, such as the work of Louis de Broglie, Jean-Pierre Vigier, B J Hiley, C Dewdney, P R Holland, Kiprianidis, and of course the fundamental contributions of J S Bell are all considered by Hawking to be unworthy of even any reference.

Likewise, his reference to the general theory of relativity and the singularity theorems also reveals a lack of familiarity with the recent work, especially in the former Soviet Union, in relativistic gravitation theory. It is to be made clear that the singularity theorems, from which Hawking derives the conclusion that time had a beginning, do not follow directly from Einstein's relativity theory but require for their derivation additional assumptions called the 'energy conditions'. One look at his own technical book The Large Scale Structure of Space-Time written with Ellis will convince anyone that along with the field equations of general relativity, Hawking and Penrose are using energy conditions. It is by using these additional conditions that they derive the singularity theorems. This is also the basis for the conclusions about the existence of black holes.
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3.1. From the Publisher.

Einstein said that the most incomprehensible thing about the universe is that it is comprehensible. But was he right? Can the quantum theory of fields and Einstein's general theory of relativity, the two most accurate and successful theories in all of physics, be united into a single quantum theory of gravity? Can quantum and cosmos ever be combined? In The Nature of Space and Time, two of the world's most famous physicists - Stephen Hawking (A Brief History of Time) and Roger Penrose (The Road to Reality) - debate these questions. The authors outline how their positions have further diverged on a number of key issues, including the spatial geometry of the universe, inflationary versus cyclic theories of the cosmos, and the black-hole information-loss paradox. Though much progress has been made, Hawking and Penrose stress that physicists still have further to go in their quest for a quantum theory of gravity.

3.2. Review by: Robert M Wald.
Science, New Series 272 (5267) (1996), 1445.

The theory of general relativity was formulated in a mathematically complete form 80 years ago, and the basic principles of quantum theory were laid out about 70 years ago. Nevertheless, only within the past few decades have major efforts been made to merge these theories into a mathematically consistent and complete quantum theory of gravitation. Despite these efforts, research in quantum gravity remains highly speculative, with very few solidly established results and with wide disagreements among re-searchers not only about the best approach to take but even about what unresolved issues deserve the most attention.

Stephen Hawking and Roger Penrose are, without question, the leading developers of our modern view of the structure of space and time. In particular, their singularity theorems and their contributions to the theory of black holes have provided us with major new insights. Both Hawking and Penrose have given considerable thought to the relationship between quantum theory and gravitation. In view of the situation noted in the paragraph above, it is not surprising that they differ widely in their views.

This book is based on a series of public lectures by Hawking and Penrose and is described as a debate between them. This characterisation is accurate only if one understands the term "debate" in the sense used in American presidential campaigns. Both Hawking and Penrose do an excellent job of expanding their own views and perspectives on fundamental issues related to space-time structure and quantum theory. Although they make some criticisms of each other's views as well as some criticisms of other alternative approaches (including some "one-line zingers" on string theory), most of the criticisms and responses are of a "sound bite" nature; there is relatively little direct engagement at a deep level between them in the book.

The first two chapters (one each by Hawking and Penrose) discuss some key concepts and results in modern general relativity. Almost all of these results are solidly grounded, and there is little or no disagreement between Hawking and Penrose here. Chapter 3, by Hawking, describes his work on particle creation by black holes and some related (somewhat more speculative) ideas in Euclidean quantum gravity. Chapter 4, by Penrose, primarily introduces his concerns about quantum measurement theory. Chapter 5, by Hawking, presents his (much more speculative) views on quantum cosmology, while chapter 6, by Penrose, contains a very brief discussion of twistor theory and his views on how it may be related to quantum gravity. The final chapter, entitled "debate," contains some direct engagement between Hawking and Penrose on issues such as "Schrödinger's cat," Euclidean methods in quantum gravity, and the equivalence or inequivalence of black holes and white holes. All of the main ideas in the book have appeared in previous scientific writings by the authors (and, indeed, their views do not seem to have evolved significantly in the past decade or so), but the discussion here is much more lively and informal than can be found elsewhere.

Most of the details of the arguments given in the book are far too technical for a layperson to follow or even a physicist not specialising in general relativity or related areas. Nevertheless, even readers without much technical background should be able to enjoy the flavour of much of the discussion. This is an interesting book to read now, but it promises to become an even more interesting book for future generations of physicists, after it becomes more clear which present-day ideas lie on the path toward the development of a quantum theory of gravity.

3.3. Review by: Arlen Anderson.
American Scientist 85 (4) (1997), 377.

In the spring of 1994, the Newton Institute of Cambridge, England, attracted leading physicists and mathematicians to a workshop on geometry and gravity. The problem considered was one of the deepest and most long-standing in theoretical physics: how to combine general relativity and quantum mechanics into a theory of quantum gravity. The plan to share the excitement of this group with the general public and to communicate a sense of the issues and challenges they faced was highly commendable. The format of a public great debate, harking back to those held in the last century, seemed inspired. Here were two of the most original thinkers in general relativity and quantum gravity - Stephen Hawking and Roger Penrose - both experienced and popular expositors, ready to grapple in public with fundamental issues about the nature of space and time.

In a series of six lectures, followed by a debate, Hawking and Penrose presented their personal views on classical and quantum gravity. This book is an edited transcript of those lectures. The eagerness and anticipation of those who waited to attend the lectures is likely shared by those in-tending to read the book. Equally, as the lectures begin, readers will share with those in attendance a growing awareness of the magnitude of the task before them to keep up with what is being presented. For this is not a breezy popularisation; it is a frank and rather sophisticated tour of the major contributions Hawking and Penrose have made to the study of gravity.

The nature of this lecture-debate must have posed a dilemma to the participants. They were to describe their views on profound and slippery issues to a general audience, yet they needed to be sufficiently careful so that their positions could be defended from the expert criticism of one another and possibly the judgment of history. Hawking and Penrose made the conscious decision to give as faithful an account of their work as possible in the time available. Comparatively, few concessions are made to the uninitiated. Indeed, some may find it difficult to grasp the thread of motivation that ties the lectures together. Although the detail of a complete treatment is necessarily absent, Hawking and Penrose give verbal sketches of the major arguments of their work. Key equations stand as signs to mark the way for those who can read them. The result, although sometimes confusing to the general reader and unsatisfactory to the expert, is nevertheless a credible effort on a formidable task. The greatest value, which everyone will appreciate, is the personality that comes across, the sense of how these great men see their own work.

The order of the material in the lectures is sensible from an unarticulated perspective encompassing the full series but is perhaps not the best for capturing the reader's attention and interest. The first two lectures describe the classical singularity theorems.

These are very significant and essential for understanding the limits of classical general relativity, but dry and prone to pithy but intricate and jargon-laden reasoning. If one begins to lose interest here, it is best to skip ahead to the later lectures, which are rather less rigorous.

The third lecture, by Hawking, is a summary of (quantum) black-hole radiation and an introduction to the Euclidean path integral. Although the manipulations hinted at may seem mysterious, one comes away with a clear sense of the style of reasoning being used. The fourth lecture, by Penrose, focuses on the measurement problem in quantum mechanics, as exemplified by Schrödinger's cat, and presents his ideas on how gravity is involved in the collapse of the wave function. Here, the resolution may be controversial, but why there is a problem is clearly explained. The fifth lecture, again by Hawking, outlines in some detail the programme of Euclidean quantum cosmology and its relation to cosmological observation. The sixth lecture, by Penrose, is a brief sketch of the twistor program and its relation to quantum field theory. This is a bit technical, but it is thought-provoking because it is a concrete example of an utterly radical description of the world: The entire history of each light ray is denoted by a point, whereas spacetime points become finite-sized spheres consisting of intersecting light rays.

The final debate is a sharp and entertaining exchange as Hawking argues that Penrose's preoccupation with Schrödinger's cat is a nonissue, while being pressed to defend Euclidean methods against the charge of being unphysical.

There is also an extended exchange over the issue of phase-space loss and whether a white hole is simply a time-reversed black hole. Each makes a number of interesting points, even when they are arguing on the opposite sides of an issue.

In the end, the most lasting impression of these lectures is the personal insight they provide into the thinking of Hawking and Penrose. That the level of the lectures occasionally seems so high should not be held against them. Hawking and Penrose chose to treat the audience's intelligence with respect and to give them a sincere taste of "the real thing." One is reminded of Feynman's retort to a journalist asking him to explain in five minutes the work for which he had just won the Nobel Prize: "If I could, it wouldn't have been worth the Prize."

4.1. From the Publisher.

Stephen Hawking's A Brief History of Time was a publishing phenomenon and continues to captivate and inspire new readers every year. When it was first published in 1988 the ideas discussed in it were at the cutting edge of what was then known about the universe. In the intervening years there have been extraordinary advances in our understanding of the space and time. The technology for observing the micro- and macro-cosmic world has developed in leaps and bounds. During the same period cosmology and the theoretical sciences have entered a new golden age and Professor Stephen Hawking has been at the heart of this new scientific renaissance. Now, in The Universe in a Nutshell, beautifully illustrated with original artwork commissioned for this project, Stephen Hawking brings us fully up-to-date with the advances in scientific thinking. We are now nearer than we have ever been to a full understanding of the universe. In a fascinating and accessible discussion that ranges from quantum mechanics to time travel, black holes to uncertainty theory and the search for science's Holy Grail - unified field theory (or in layman's terms the 'theory of absolutely everything'), Professor Hawking once more takes us to the cutting edge of modern thinking.

4.2. Review by: Marc Kamionkowski.
Science, New Series 296 (5566) (2002), 267.

In the world of Newton and Galileo, space and time were the flat, featureless canvas on which were painted the then-known celestial objects. Einstein's canvas was curved and it had bumps and wiggles caused by the presence of matter. During the past few decades, it is the canvas itself that has increasingly become the focus of study, as the dimensionality, shape, and nature of space and time have become intertwined with subatomic particles, black holes, and superstrings in a unified quest by physicists and cosmologists to understand the laws of physics and how the Universe came to be.

This enterprise is the subject of Stephen Hawking's The Universe in a Nutshell. A theoretical physicist, Hawking first emerged in the 1960s with brilliant work that helped elucidate the mathematical structure of general relativity. His celebrity in physics was solidified by his 1974 discovery of "Hawking radiation," the quantum-mechanical emission of radiation from black holes. This work opened the attack on the merger of general relativity and quantum mechanics, the central focus of theoretical physics to this day. Since then, Hawking has weaved in and out of the mainstream as both a central figure and sometimes iconoclast in the world of physics. With the spectacular success of A Brief History of Time, he has also become science's biggest pop star since Einstein.

Thus, expectations for Universe are high. The book does not disappoint. With colourful illustrations besetting self-contained essays rather than a single story, this book discusses new developments in a way that will be even more accessible to a wide audience than his previous book.

Hawking reviews quantum mechanics, general relativity, the big bang, and black holes, and then goes on to tackle string theory, M theory, imaginary time, multiple histories, the information-loss paradox, the black-hole holographic principle, extra dimensions, and time travel, among other things. These topics are certainly as daunting as one might guess. Some are still developing ideas, and some are fairly challenging concepts, even for theoretical physicists (present company included). Hawking does not underestimate his audience; to his credit, he does not water down the physics nor does he filter out the most difficult ideas. Instead, he presents the topics fairly and honestly, though stripped of the mathematical language that physicists usually use.

Not every reader will necessarily understand every concept. Are we all really supposed to grasp what he means by imaginary time or cancellation of infinities in supersymmetry? Or why a black hole's entropy is related to the area of ​​its horizon? Perhaps not. But readers will become familiar with some of the more tantalising issues theoretical physicists are confronting and may even share the frustration we scientists sometimes face in our continued efforts to sort these all out.
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Hawking's spirited discussion is filled throughout with ambition, big ideas, plain talk, and humour. The excitement of exploration and discovery is evoked in every chapter, even if the explanations aren't crystal clear in every case. Although readers may not attain Hawking's depth of understanding, they will surely be infected by his curiosity.

4.3. Review by: Rocky Kolb.
American Scientist 90 (2) (2002), 182-183.

The Universe in a Nutshell is Stephen Hawking's second popular book. His first, A Brief History of Time, was more than a publishing phenomenon. It launched Hawking into the universe of cultural icons. Before the success of the book, no one could have imagined that a living scientist would share a television screen with the likes of Commander Data in an episode of "Star Trek" or Homer Simpson in an episode of "The Simpsons." Millions of people throughout the world have since come to recognise the synthesised voice of Hawking as the voice of scientific authority.

For years after A Brief History of Time was published, on airplanes, at cocktail parties, and in health clubs, the revelation that you were a cosmologist invariably led to questions about Hawking and his book. I was always amazed by the number of people who claimed to have bought it without reading it or to have read it without understanding it, and it was even more astounded that their admitted lack of comprehension did not in any way dampen their enthusiasm for the book. In fact, part of the popular cachet of the book seemed to be that it was beyond comprehension.

The Universe in a Nutshell is written with the same exuberance as A Brief History of Time. Few scientists would have the courage to take a lay audience across the entire sweep of modern relativism and theoretical particle physics in a 200-page book. The scope of the book is as vast as its subject, covering subjects such as p-branes, warped spacetime, black holes, closed time-like loops, curved spacetime, dualities, event horizons, Grassman dimensions, vacuum fluctuations, "hidden variable" theories, imaginary time, Gödel's theorem, inflation, the no-boundary condition, spacetime singularities, M-theory, and supersymmetry. It is not easy reading. Any one of those topics could easily be expanded to fill a book. To cover such an enormous area, Hawking usually employs a broad brush, but even with the absence of details, the reader is able to appreciate the grandeur of the landscape.

In A Brief History of Time, Hawking wrote that if scientists really understood the workings of the universe, then they should be able to explain it in sufficiently simple terms so that the broad principles and concepts would be understandable to everyone. The Universe in a Nutshell is the best effort to date to explain the principles and concepts of our present understanding of the universe. The book may not be understandable to everyone, but then, scientists don't really understand the universe.

5.1. From the Publisher.

Stephen Hawking's worldwide bestseller, A Brief History of Time, has been a landmark volume in scientific writing. Its author's engaging voice is one reason, and the compelling subjects he addresses is another: the nature of space and time, the role of God in creation, the history and future of the universe. But it is also true that in the years since its publication, readers have repeatedly told Professor Hawking of their great difficulty in understanding some of the book's most important concepts. This is the origin of and the reason for A Briefer History of Time: its author's wish to make its content accessible to readers - as well as to bring it up-to-date with the latest scientific observations and findings. Although this book is literally somewhat 'briefer', it actually expands on the great subjects of the original. Purely technical concepts, such as the mathematics of chaotic boundary conditions, are gone. Conversely, subjects of wide interest that were difficult to follow because they were interspersed throughout the book have now been given entire chapters of their own, including relativity, curved space, and quantum theory. This reorganisation has allowed the authors to expand areas of special interest and recent progress, from the latest developments in string theory to exciting developments in the search for a complete, unified theory of all the forces of physics. Like prior editions of the book-but even more so - A Briefer History of Time will guide nonscientists everywhere in the ongoing search for the tantalising secrets at the heart of time and space. Thirty-eight full-colour illustrations enhance the text and make A Briefer History of Time an exhilarating addition in its own right to the literature of science.

5.2. Review by: Michelle Press.
Scientific American 299 (2) (2008), 106.

"The title of this book," the authors write, "differs by only two letters from that of a book first published in 1988." That book was Stephen Hawking's A Brief History of Time, a publishing phenomenon that sold more than 10 million copies.

Despite its success, readers confessed to difficulty in grasping its more abstruse concepts. Hawking and Mlodinow (a physicist and writer) eliminated many of the technical explanations and clarified and expanded on the subjects of greatest interest - the creation of the universe, curved space, quantum gravity. They discuss developments during the past two decades in string theory and the discoveries of dark matter and dark energy. Clarity and conciseness do not have the almost mystical power of the original, but the book is a delight to read - and its new softcover makes it perfect for the proverbial summer day in the hammock.

6.1. From the Publisher.

When and how did the universe begin? Why are we here? Is the apparent 'grand design' of our universe evidence for a benevolent creator who set things in motion? Or does science offer another explanation? In The Grand Design, the most recent scientific thinking about the mysteries of the universe is presented in language marked by both brilliance and simplicity. Model dependent realism, the multiverse, the top-down theory of cosmology, and the unified M-theory - all are revealed here. This is the first major work in nearly a decade by one of the world's greatest thinkers. A succinct, startling and lavishly illustrated guide to discoveries that are altering our understanding and threatening some of our most cherished belief systems, The Grand Design is a book that will inform - and provoke - like no other.

6.2. Review by: Joseph Silk.
Science, New Series 330 (6001) (2010), 179-180.

In The Grand Design, Stephen Hawking, in collaboration with Leonard Mlodinow, addresses some of the biggest questions in the universe: When and how did it begin? Why is there something rather than nothing? Why are we here? And does the grand design of the universe provide evidence of a creator?

The core of the book describes an attempt to unify the fundamental forces of matter with the force of gravity. Quantum theory deals with the infinitely small, and gravity with the cosmically large. The quantum forces are strong, and gravity today is weak. Only at the beginning of the universe, in the Big Bang, was there an environment where the forces must have been comparable in strength. Attempts to unify gravity with quantum theory have attracted the brightest minds in physics, from Einstein onward.

The first serious attempts at unification in the physics of physics developed via string theory, which describes elementary particles in terms of one-dimensional vibrations, rather like infinitesimal pieces of string as opposed to points. There were competing string theories, and a breakthrough finally came when it was realised that all were manifestations of an underlying theory called M theory.

M theory predicts the existence of ten spatial dimensions. We observe three. This ought to be enough for any rational person to say M theory conflicts with nature. String theorists are clever, however, and saved the theory by arguing that seven of the dimensions are now tightly curled up in the low-energy limit. M theory succeeds in unifying gravity and quantum theories. It is the only current candidate for a complete theory of the universe, and Hawking sees it as the realisation of Einstein's dream. Unfortunately, M theory has hitherto made essentially no testable predictions in the limit of low-energy physics, apart from the possibility that particle collisions in the Large Hadron Collider will spawn infinitesimal black holes as relics of higher dimensions.

Some physicists might prefer to move onto other theories. Indeed, most do not even recall what the M means in M theory. This ought to provide an indication of the reality of the hyperspace inhabited by the theorists. To be fair, however, M theory does take one important step toward unification by removing the infinities that plagued earlier theories of quantum gravity. This is a compelling advance, and Hawking argues that its predictions must be taken seriously.
...

Hawking is led to a remarkable prediction that will raise the pulsebeat of many readers. Here is his logic: M theory unifies gravity with quantum theory. Gravity accounts for negative energy, whereas the mass of a star is undeniably positive. On large enough scales, once one counts all the black holes, stars, and empty space, the overall energy of the universe is close to zero (as measured). If the universe has zero energy, then it could have been spontaneously created from nothing by quantum fluctuations. So for God, substitute M theory: "It is not necessary to invoke God to light the blue touch paper and set the universe going."

For Hawking, M theory is the only candidate for a complete theory of the universe. He argues that it is the most general super-symmetric theory of gravity, and that super-symmetry is obligatory to avoid the infinities that plague all previous attempts to develop a theory of quantum gravity. Some humbleness would be welcome here. We are only a decade or two into M theory. A century or two hence, should we survive that long, I expect that M theory will seem as naïve to cosmologists of the future as we now find Pythagoras's cosmology of the harmony of the spheres, Ptolemy's cosmology of epicycles, or Kepler's cosmology of the five Platonic solids.

6.3. Review by: Chetan Datta Poduri.
Current Science 113 (2) (2017), 335-336.

Explaining science to the layman is a task in itself and is typically referred to as popular science. Stephen Hawking, a living legend of our times, 'reigns supreme' in the field of 'popular science', be it either through television shows or through authoring various books on science. Presented here is a review of one of his recent books The Grand Design, co-authored along with another expert of popular science Leonard Mlodinow. At this stage, one must keep in mind that one of the aims of metaphysics is to prove or disprove the existence of God, and thereby explain scientifically the origin of this Universe.
...
Stephen Hawking and Leonard Mlodinow (SHaLM) in their book, The Grand Design summarise the entire physics of the present day. And in this process, they bring out the positive side of the same, while highlighting the drawbacks in the current understanding of the Universe. One way, this book is best described as explaining science/summarising science to the layman. On the other hand, it is subtle metaphysics.
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In The Grand Design, SHaLM describes CMBR (cosmic microwave background radiation), theoretically suggesting that gesting/hunting at CMBR may serve as 'fingerprints of time' since the 'Big Bang' occurred. Presence of the same is a slight indication of the aftermath of the 'Big Bang', which is yet to settle down. Some more description of 'static' that is typically observed in attempts at contacting extraterrestrials would have made this book a bit more interesting.

Throughout the grand design, our SHaLM psychiatrists give the impression that they are the ones who'll eventually cure this world of the religion and God.
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... The Grand Design is one book that must be in the personal library of every literary person, as it offers a one-time snapshot of present-day physics. And SHaLM continue to reign supreme among all those scientists who successfully brought 'science' to the layman through 'the grand design'. This article would be incomplete without a salute to the cartoons and photographs that are included in the book. Some of them are 'simply brilliant', just as the book is ...

7.1. From the Publisher.

The world-famous cosmologist and #1 bestselling author of A Brief History of Time leaves us with his final thoughts on the universe's biggest questions in this brilliant posthumous work.

Is there a God?
How did it all begin?
Can we predict the future?
What is inside a black hole?
Is there other intelligent life in the universe?
Will artificial intelligence outsmart us?
How do we shape the future?
Will we survive on Earth?
Should we colonise space?
Is time travel possible?

Throughout his extraordinary career, Stephen Hawking expanded our understanding of the universe and unravelled some of its greatest mysteries. But even as his theoretical work on black holes, imaginary time and multiple histories took his mind to the furthest reaches of space, Hawking always believed that science could also be used to fix the problems on our planet. And now, as we face potentially catastrophic changes here on Earth - from climate change to dwindling natural resources to the threat of artificial super-intelligence - Stephen Hawking turns his attention to the most urgent issues for humankind. Wide-ranging, intellectually stimulating, passionately argued, and infused with his characteristic humour, Brief Answers to the Big Questions, the final book from one of the greatest minds in history, is a personal view on the challenges we face as a human race, and where we, as a planet, are heading next.

7.2. Review by: Andrew Robinson.
Science 362 (6416) (2018), 757.

The death of cosmologist Stephen Hawking earlier this year happened to fall on the birthday of Albert Einstein. This felt like an appropriate coincidence, given the centrality of Einstein's general theory of relativity in Hawking's much-celebrated life as a scientist.

Einstein is mentioned in Hawking's posthumously published book - Brief Answers to the Big Questions - which he left unfinished - far more frequently than any other scientist, past or present, including Isaac Newton, Hawking's illustrious predecessor as Lucasian professor of mathematics at the University of Cambridge. Indeed, the concluding "big question" of the 10 explored in 10 chapters, "How do we shape the future?" begins with Einstein. "Where did his ingenious ideas come from?" asks Hawking. He answers, "A blend of qualities, perhaps: intuition, originality, brilliance. Einstein had the ability to look beyond the surface to reveal the underlying structure. He was undaunted by common sense, the idea that things must be the way they seemed. He had the courage to pursue ideas that seemed absurd to others. And this set him free to be ingenious, a genius of his time and every other."

Was Hawking a genius, too? He never won a Nobel Prize, and the book gives no indication that Hawking regarded himself as a genius. On the other hand, he was one of the very few scientists since Einstein to become a household name. As his close collaborator, Nobel laureate Kip Thorne, remarked in his eulogy: "Newton gave us answers. Hawking gave us questions. And Hawking's questions themselves keep on giving, generating breakthrough decades later. When ultimately we master the quantum gravity laws, and comprehend fully the birth of our universe, it may largely be by standing on the shoulders of Hawking."

Hawking was well known for two additional reasons unrelated to his mind-boggling cosmological theories. The first was his 1988 book, A Brief History of Time, an international bestseller that sought to explain the physics of time to the general reader without using mathematical equations. The second was his courageous struggle with motor neuron disease, which rendered him wheelchair-bound and de-pendent on a computer screen and speech synthesiser to communicate. "As someone who at the age of twenty-one was told by their doctors that they had only five years to live, and who turned seventy-six in 2018, I am an expert on time in another sense, a much more personal one," he writes. "I am uncomfortably, acutely aware of the passage of time, and have lived much of my life with a sense that the time that I have been granted is, as they say, borrowed."

Some of Hawking's "big questions" and answers are firmly rooted in science - for example, "What is inside a black hole?" and "Is time travel possible?" - whereas others inherently cannot be, such as "Will we survive on Earth?" "Should we colonise space?" "Will artificial intelligence out-smart us?" and "Is there a God?" To the last question, he answers, "If you like, you can call the laws of science 'God,' but it wouldn't be a personal God that you would meet and put questions to. Although, if there were such a God, I would like to ask however did he think of anything as complicated as M-theory in eleven dimensions."
...
... the final testament of this unique scientist is well worth reading. One cannot help but be moved by Hawking's lifelong struggle to lead a creative life. "Remember to look up at the stars and not down at your feet," he sums up.

7.3. Review by: Robin Tatu.
ASEE Prism 28 (7) (2019), 42-44.

Stephen Hawking's latest - and last - book is a slender volume, with material familiar to readers of the renowned cosmologist's scholarly articles, popular science essays, and international bestseller, A Brief History of Time. His daughter, Lucy, writes in the afterword that he worked on Brief Answers to the Big Questions in the year before his March 2018 death at age 76 as a way "to bring his contemporary writings together into one volume." Readers will also sense a desire to reconcile a life's work - and a life - as well as to leave some final thoughts.

Several chapters distil issues from earlier works, including the origins of the universe, the Big Bang, time travel, and the question of God. One of the meatiest chapters, on the nature of black holes, delves into Hawking's research and views on a favourite topic as he continues to ponder the "information paradox" of these dense patches where even light can't escape their gravitational forces.

Other sections tackle more recent and pressing concerns, such as climate change, human genetic engineering, and artificial intelligence (AI) and people's relationship with it. Chapters 7 and 8 discuss whether further space travel is possible and desirable (a solid yes to both), and Chapter 10 closes with "How do we shape the future?"

Hawking declares that humans must leave Earth in order to survive as a species: "If we stay, we risk being annihilated." While the biggest threat to our planet may be an asteroid collision, "a more immediate danger is runaway climate change," he writes, citing "rising temperatures, reduction of the polar ice caps, deforestation, overpopulation, disease, war, famine, lack of water, and decimation of animal species." These are all solvable but unsolved, he cautions. "We have the technology. We just need the political will." If humans continue to behave with such "reckless indifference" toward Earth, then abandoning the planet may be our only choice.

Space is a violent, scary place, however, and exploration and colonisation may require hundreds, if not thousands, of years. Yet the scope of the challenge doesn't overwhelm Hawking - who beat the odds of survival by more than five decades after being diagnosed with amyotrophic lateral sclerosis (Lou Gehrig's disease) at age 21. Despite his dire predictions of ecological disaster, he remains optimistic that humans will find a way to persist and thrive, whether on or beyond Earth.

One key to that optimism may lie in AI. Although Hawking was among a group of scientists, engineers, and tech leaders to sign a 2015 resolution concerning the dangers of AI to humans, in 2016 he helped launch the Leverhulme Centre for the Future of Intelligence at Cambridge University. Its stated goal: "to ensure that we humans make the best of opportunities for artificial intelligence as it develops over the coming decades." In his book, Hawking declares himself convinced by the potential of technology to enhance and extend human bodily and brain capabilities. He also believes humans can work in harmony with robots if we remain alert and responsive to developing threats.

Throughout the book, Hawking reflects on the improbability of his life and career, most of which was spent at the University of Cambridge, where he received his Ph.D. and held Isaac Newton's post as Lucasian Professor of Mathematics from 1979 to 2009. Though strongly opinionated, he wasn't always right, and these chapters, completed posthumously by colleagues and friends, show he didn't mind continuing to push the envelope to test various hypotheses, including on black holes. He ends Brief Answers with the pronouncement that "we stand at a threshold of important discoveries in all areas of science," urging readers to keep striving to learn and improve their world and explore the benefits of technology. This thoughtful, provocative work is well worth the read.

7.4. Review by: Reg Naulty.
The Furrow 70 (7/8) (2019), 446-447.

Stephen Hawking was working on this book until the time of his death. It contains a valuable introduction by a friend and scientific collaborator, Kip Thorne, and a fond memoir by his daughter, Lucy.

It is impossible not to respect Stephen Hawking, as he achieved so much despite appalling disabilities. Nevertheless, he would not want criticism withheld on that account. What he writes about God is open to debate:

No one created the universe and no one directs our fate ... there is probably no heaven and afterlife either.

His ground for asserting that is as follows:

Everything can be explained by the laws of nature.

That is not science. That is ideology. And for all anyone knows, science may one day explain how someone made the universe.

Hawking writes that

... protons really can appear at random, stick around for a while and then vanish again, to reappear somewhere else.

He continues

The laws of nature themselves tell us that not only could the universe have popped into existence, like a proton, and have required nothing in terms of energy, but also that it is possible that nothing caused the Big Bang. Nothing.

A non-specialist cannot argue with Hawking about what is permitted by the laws of nature, but some claims about them strain belief:

A living being like you and me usually has two elements: a set of instructions that tell the system how to keep going and how to reproduce itself, and a mechanism to carry out the instructions.

Given that biological evolution is basically, as Hawking says, a "random walk," it is hard to see how it could come up with a set of instructions. Then there is the universe originating in "a single point of infinite density". How can something without volume have any density, let alone infinite density? Objects such as this, as with black holes, are known in physics as "singularities," i.e., regions in which the laws of physics do not hold. Who knows what mysteries may unfold there?

Despite his strictures, Hawking believes that people will always cling to religion because it gives comfort, and because they do not trust or understand science. With respect to the latter point, Hawking has forgotten a predecessor of his in the Lucasian Chair at Cambridge, Sir Arthur Stanley Eddington, OM FRS, who did understand science and was a theist.

There are other things of interest in the book. Hawking remarks that now we have mapped our DNA, we are in a position to make corrections. Then we can make improvements. Hawking believes that those venturing into space will be more capable than us because their genes will have been improved. He also thinks that self-designing, self-replicating computers are coming. He wisely remarks that we should build our values ​​into them.