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by David Deutsch

Available to purchase from
Allen Lane, The Penguin Press, 1997
Reviewed by
Bryce DeWitt, Center for Relativity, Department of Physics, The University of Texas at Austin, Austin, Texas 78712-1081, USA

January 1998: This book is aimed principally at philosophers: persons who find word descriptions of the laws of physics easier to deal with than the mathematical description, but who quibble over the precision with which the words are used. Nevertheless, with patience, practicing scientists can gain something from it.

The author stresses the role of explanation as the true methodology of science, whether in quantum physics, biology (evolution), computer theory, or epistemology (how knowledge is acquired). The author calls these four disciplines The Four Strands, of which our current understanding of the fabric of reality is composed. The aim of the book is to show that each of the four strands illuminates the others in indispensable ways and that together they provide the necessary and sufficient framework for a Theory of Everything (not to be confused with the particle physicist's parochial goal of a single all-embracing high-energy physics theory).

In his Preface the author writes “Our best theories are not only truer than common sense, they make more sense than common sense...” This reviewer agrees with him insofar as quantum mechanics is concerned and is ready to accept “best-theory” status for Darwinian evolution as elaborated by Dawkins, but is less willing to place the “Turing Principle” and the author's cosmogony in the “best” category.

The following quotes embody some of the most important recurrent themes: “The truly privileged theories are not the ones referring to any particular scale of size or complexity, nor the ones situated at any particular level of the predictive hierarchy--but the ones that contain the deepest explanations.” “The overwhelming majority of theories are rejected because they contain bad explanations, not because they fail experimental tests.” “[The] most valuable attribute [of a theory] is that it explains the fabric of reality itself.” “One of the most valuable attributes of human thought... is its ability to reveal and explain the fabric of reality.” Already in his first chapter the author uses these assertions to dispose of positivism and instrumentalism (an old story) and, after analyzing emergent phenomena such as life, thought and computation, to dispose of reductionism as an explanatory philosophy.

The second chapter plunges straightaway into the many-worlds interpretation of quantum mechanics. Because the book is not aimed at physicists there are no equations. There is, instead, a new, fresh, and even audacious description of the many-worlds theory, based on the simultaneous phenomena of interference and discrete photons. Deutsch uses the word multiverse to refer to the reality described by the quantum theory and has these words to say about it: “The quantum theory of parallel universes is not the problem, it is the solution. It is not some troublesome, optional interpretation emerging from arcane theoretical considerations. It is the explanation--the only one that is tenable--of a remarkable and counter-intuitive reality.” This reviewer agrees completely with this statement and only regrets that Deutsch limits his discussion essentially to the setting dealt with by Hugh Everett in 1957, hence missing the understanding provided by the more recent consistent-histories theory of complex quantum systems, which explains not only the emergence of the classical world, and hence why we can perform good interference experiments in the first place, but also the fact that the generation of multiple worlds is far more common than the results of interference experiments would suggest.

Chapter 3 presents science (in the largest sense) as a problem-solving process and follows Karl Popper in regarding the birth and death of theories as analogous to the birth and death of species in biological evolution, with variation and selection playing key roles. Chapter 4 seeks criteria for selecting theories and hence criteria for reality itself. Deutsch notes the science-friendly, and indeed mathematics-friendly, property of reality. “Reality contains not only evidence, but also the means (such as our minds, and our artefacts) of understanding it. There are mathematical symbols in physical reality. The fact that it is we who put them there does not make them any less physical.” And he adds “The reliability of scientific reasoning... is a... fact about reality itself... The evidence will be the same regardless of who reveals it.” These words need special emphasis today.

Chapter 5 is the first in which computers, including brains, are brought into the discussion, initially as virtual-reality generators. Deutsch notes that computers can in principle be used to compute not only physical and abstract quantities but, at least to some extent, the behavior of human beings. This possibility he regards as part of a self-similarity property of physical reality. Chapter 6, entitled Universality and the Limits of Computation, is the first in which Deutsch begins to skate on thin ice. Consider the following sequence of statements: 1. “If the laws of physics... are to be comprehensible, they must be capable of being embodied in another physical object--the knower.” 2. “The laws of physics... make it physically possible for those same laws to become known to physical objects... [They] mandate their own comprehensibility.” 3. “A physically possible process [is defined] as one that actually occurs somewhere in the multiverse.” 4. “It is possible to build a virtual-reality generator whose repertoire includes every possible environment.” 5. “Since building a universal virtual-reality generator is physically possible, it must actually be built in some universes.” To this reviewer these statements seem increasingly teleological. They have all the earmarks of hypotheses masquerading as theorems. Deutsch calls the fourth The Turing Principle and makes extensive use of it later to bind the other three strands together.

Chapter 7 plays no essential role in the book. It consists of an imaginary dialogue aimed at refuting crypto-inductivism and seems to be included mainly to give other philosophers a more complete picture of Deutsch's views.

Chapter 8, entitled The Significance of Life, provides a sketch of Darwinian evolution as amplified by Dawkins (who places genes, rather than species, at the center of the adaptive process) and then uses the many-worlds theory to give a novel and stimulating cross-universe analysis of the stability and robustness of genes. This analysis permits an abstract distinction between true genetic material and junk DNA. A similar analysis can be applied to the robustness of knowledge itself. The following quotes summarize the author's conclusions: “The direct connection between the theory of evolution and quantum theory is... one of the most striking and unexpected of the many connections between the four strands.” “Knowledge is a fundamental physical quantity... and... life is only slightly less so.” “Life is the means... by which the effects referred to in the Turing principle have been implemented in nature.” “It is simply not true that life is insignificant in its physical effects [on the astrophysical scale], nor is it theoretically derivative [from other fundamental phenomena].”

Chapter 9 gives an excellent account of the infant science of quantum computers. “Quantum computation is... a distinctively new way of harnessing nature... It will be the first technology that allows useful tasks to be performed in collaboration between parallel universes.” Deutsch defines quantum computers in a very general way, not merely in terms of currently proposed devices, and he describes some of the marvelous computations they will be able to perform. When the technology reaches maturity the “other worlds” will unquestionably be as real as atoms to computer technicians.

Deutsch prefaces Chapter 10 (The Nature of Mathematics) with the statement “The next chapter is likely to provoke many mathematicians. This can't be helped. Mathematics is not what they think it is.” Here is where a ghost that haunts the whole book becomes clearly visible. Infinity--more precisely the axiom of infinity--stalks every page. This axiom says that the collection of all natural numbers exists as a set, on a par with all other sets. It is a very convenient axiom, and almost no practicing mathematician hesitates to use it. But it is not indispensable, as Kronecker and Brouwer, the fathers of intuitionism, correctly saw. The so-called constructivists (who are the modern intuitionists and who generally wear the mantle only part time) have effectively shown that all modern mathematics, including measure theory (!) (but not logic itself) can be reconstructed without its aid. Therefore it is wrong for Deutsch to make heavy use of Gödel's theorem (which depends on the axiom of infinity) to reach such conclusions as “Mathematicians [have made the mistake of thinking] that mathematical knowledge is more certain than other forms of knowledge.” “Mathematical knowledge may, just like our scientific knowledge, be deep and broad, it may be subtle and wonderfully explanatory, it may be uncontroversially accepted; but it cannot be certain.” The fact is that Gödel's examples of true theorems that cannot be proved within the framework of the standard axioms (or extensions thereof) always differ in fundamental ways from the bulk of the theorems that excite mathematicians' interest.

Despite all this, Chapter 10 is one of the best in the book. It gives space to the views of Roger Penrose, whom the author clearly admires, but with whom he chooses to differ. Deutsch convincingly shows that mathematical truths, despite being as real as the multiverse itself (in the objective sense of Platonic forms), are products of life and intelligence. He thus touches on one of the deepest mysteries of all: The multiverse cannot exist without mathematics, and mathematics cannot exist without the multiverse.

One welcomes Deutsch's assertion “Necessary truth is merely the subject-matter of mathematics, not the reward we get for doing mathematics. The object of mathematics is not, and cannot be, mathematical certainty. It is not even mathematical truth, certain or otherwise. It is, and must be, mathematical explanation.” This explanatory endeavor will always be open-ended. But complexity theory suffices to prove this. Deutsch's mistake is to feel compelled, for the proof, to use the diagonal argument of Gödel's theorem both here and in his earlier argument that the repertoire of a computer can never be as large as logic alone would allow.

Chapters 11 and 12 deal with Time. Time, in the modern sense, cannot be understood outside the framework of Special Relativity. Indeed, Deutsch correctly places Time within the framework of Einstein's general theory of relativity, in its quantum form. Quantum gravity does not yet exist as a fully coherent discipline, but enough is understood about it to enable one to say that Time, like Probability, is a phenomenological (i.e., emergent) concept. It requires all four strands. In Chapter 12 the many-worlds picture is broadened to include ideas found in old science-fiction stories, and Deutsch gives a lively and accurate description of time-travel within the framework of the multiverse. But the chapter adds little to his overall viewpoint. As he himself says “All four strands play essential roles in the explanation of time travel. Time travel may be achieved one day, or it may not. But if it is, it should not require any fundamental change in world-view, at least for those who broadly share the world view I am presenting in this book.”

Chapter 13 is a superb summing-up. It begins with an attack on Thomas Kuhn's book The Structure of Scientific Revolutions and on the sociologists and philosophers who have swallowed it whole. “Kuhn's theory suffers from a fatal flaw. It explains the succession from one paradigm to another in sociological or psychological terms, rather than as having primarily to do with the objective merit of the rival explanations. Yet unless one understands science as a quest for explanations, the fact that it does find successive explanations, each objectively better than the last, is inexplicable.” Deutsch gives a lovely description of the way scientists (physicists at least) really interact with each other, in seminars as well as socially.

He also provides a lovely and rather gentle trashing of the “Copenhagen” interpretation of quantum mechanics. He devotes space to the story of Hugh Everett as a Princeton graduate student, and afterward. It is this reviewer's fault (for keeping silent about it) that Deutsch does not get the story of Everett's interaction with John Wheeler quite right. Everett originally wrote a much clearer and more complete account of his ideas, which did not appear in Reviews of Modern Physics. The published article was basically written by Wheeler: He sat down with Everett and told him precisely what to omit from the larger work. (Various conclusions can be drawn from this.) It is also not true that Everett left scientific research because the many-worlds view failed to receive wide recognition. Everett always had a detached and amused view of other physicists. He devoted the rest of his tragically short life to the study of computer algorithms (for the Defense Department) and artificial intelligence (in which he had a passionate interest). He and Deutsch would have got along wonderfully together, and he would almost certainly have accepted Deutsch's demonstration of the reality of free will near the end of Chapter 13, which invokes the cross-universe robustness of decision-making.

Despite its grand theme, Chapter 14, entitled The Ends of the Universe, is a mistake. In this final chapter, Deutsch skates on very thin ice indeed. He turns the relationship between hypothesis and theorem completely upside down. The chapter should have been omitted. Deutsch's views stand more firmly without it (although one suspects that at least some of the rave reviews the book has received were induced by its inclusion). The first nine paragraphs of the chapter could usefully have been placed in Chapter 13, but in the tenth paragraph Deutsch hitches a ride on the omega-point theory of Teilhard de Chardin (which he incorrectly ascribes to Frank Tipler) and everything goes downhill from there, all the way to the final Big Crunch. Although disagreeing with Tipler's blatantly religious views, Deutsch is fascinated by what life (intelligence) will be like at the end of time and has quasi-religious views of his own.

It is curious how naked many physicists' prejudices become when they confront cosmogony. The espousal years ago, by Bondi and Hoyle, of the steady-state theory of the universe was almost certainly motivated by anti-religious denial of an act of creation. The even more enthusiastic reception of the Big Bang model was conditioned by opposite sentiments. Hawking's fierce championing of the “no-boundary” boundary condition represents a swing back toward Bondi and Hoyle. There is also a clear division between those who believe the universe is compact (i.e. finite) and those who are agnostic. For the former, among whom Deutsch is numbered, the belief is an act of faith, Deutsch's arguments notwithstanding. When not based on mere hypotheses like the Turing principle, these arguments are based on faulty physics, of which the following are examples: 1. Although it is true that the universe must be compact and must recollapse (according to Einstein's theory) if it contains more than a certain critical amount of matter, it is not true that it must be noncompact (i.e. infinite) if it contains less. Mathematicians have known for years of the existence of compact 3-manifolds of constant negative curvature, any one of which could serve as a model for a nonrecollapsing universe. 2. As for the recollapsing models, the argument for infinite memory capacity and an infinite energy source at the end of time is based on the well-known infinite oscillatory mixmaster behavior of these models. But this behavior holds only in classical general relativity and will almost certainly fail, or become meaningless, in quantum gravity. 3. It is not necessarily true, as Deutsch asserts, that there are no universes in which the charge on an electron differs from what it is in our universe. There are perfectly plausible scenarios in which the constants of nature are dynamically determined and differ from one universe to another. Furthermore, the commonly investigated cosmological models are far too bland to be believable. Much more fun is the infinite universe proposed by Andrei Linde in which mini-universes (our own, for example) are continually being born and recollapsing, with different physical constants and boundary conditions in each.

In the end, Deutsch's wistful memory of himself as a child who wanted to understand everything, with which he opens the book, does not differ much from Tipler's wistful longing to believe in an afterlife.

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