Book Review The Beginning of Infinity: Explanations That Transform the World Reviewed by William G. Faris elements in the interior of an exploding supernova. The Beginning of Infinity: Explanations That Gold, among other elements, is created and then Transform the World distributed throughout the universe. A small David Deutsch fraction winds up on planets like Earth, where it can Viking Penguin, New York, 2011 be mined from rock. The other source is intelligent US$30.00, 496 pages beings who have an explanation of atomic and ISBN: 978-0-670-02275-5 nuclear matter and are able to transmute other metals into gold in a particle accelerator. So gold is created either in extraordinary violent stellar The Cosmic Scheme of Things explosions or through the application of scientific A number of recent popular scientific books treat insight. a wide range of scientific and philosophical topics, In the claim there is a potential ambiguity in the from quantum physics to evolution to the nature use of the word “people”. Deutsch characterizes of explanation. A previous book by the physicist them (p. 416) as “creative, universal explainers”. David Deutsch [2] touched on all these themes. His This might well include residents of other planets, new work, The Beginning of Infinity, is even more which leads to a related point. Most physical effects ambitious. The goal is to tie these topics together diminish with distance. However, Deutsch argues to form a unified world view. The central idea is (p. 275): the revolutionary impact of our ability to make There is only one known phenom- good scientific explanations. enon which, if it ever occurred, In books written by physicists one expects to find would have effects that did not fall awe of the universe and delight that we have come off with distance, and that is the to understand something about it. There might creation of a certain type of knowl- also be an implicit assumption that people are not edge, namely a beginning of infinity. particularly significant in the cosmic scheme of Indeed, knowledge can aim itself things. Deutsch makes the contrary claim (p. 45): at a target, travel vast distances People are significant in the cosmic having scarcely any effect, and then scheme of things. utterly transform the destination. He presents the following example. The atomic Deutsch is a physicist who believes that matter composition of the universe consists mainly of is strictly governed by the laws of physics. However, the light elements hydrogen and helium. Consider he is no reductionist. He believes that atoms are a heavy element such as gold. Where can it be real, but also that abstractions are real. One level found, and where did it come from? There are two of abstraction is knowledge, which he defines as very different sources. One is the transmutation of “information which, when it is physically embodied in a suitable environment, tends to cause itself to William G. Faris is professor of mathematics at the remain so” (p. 130). This includes both knowledge University of Arizona. His email address is faris@math. embedded in DNA and ideas in human brains. arizona.edu. Biological knowledge is nonexplanatory, but hu- DOI: http://dx.doi.org/10.1090/noti821 man knowledge includes explanations that solve 544 Notices of the AMS Volume 59, Number 4 unexpected problems. The gold example shows they are used in his sys- that an explanation can have physical effects just tem. Thus “instrumentalism” as real as those created by an exploding star. is defined as the “miscon- Deutsch’s book is also a manifesto in praise of ception that science cannot the notion of progress. His claim is that a new describe reality, only predict kind of progress began with the Enlightenment. outcomes of observations” In the best case the growth of knowledge may (p. 31). As is clear from this proceed indefinitely in the future without bound. example, definitions often This is the “beginning of infinity” of the title come with a judgment. and of the quotation above. The argument has Deutsch’s main work as a several threads. It begins with a definite position physicist has been on quan- on philosophy of science, centered on an argument tum computing, and it is that a notion of “good explanation” of reality is natural that he would test Reproduced with the permissionLibrary of of the the London School of Economics. the key to progress. It includes a theory of cultural his ideas in the framework Karl Popper: philosopher of evolution, which explains obstacles to progress of quantum theory. This “theory-laden” and the lucky circumstance that swept them away. leads to a problem. Quan- science. There is extensive discussion of the anomalous tum theory is the accepted status of quantum theory, which on some accounts framework for understand- is incompatible with a realistic world view. The ing properties of matter, viewed as consisting of argument connects views on topics as varied as constituents on the molecular, atomic, and sub- mathematical reality, voting systems, aesthetics, atomic scale. It explains such properties of matter and sustainability. The author rejects sustainability as density and strength and conductivity and color. as an aspiration or as a constraint on planning; It also underlies the deeper understanding of the he favors an open-ended journey of creation and chemical bond. It is so pervasive in fundamental exploration. physics that it is difficult to see how to make the smallest modification to it without destroying the Good Explanations whole edifice. The problem is that the formulation of quantum Deutsch attributes recent progress to the discov- theory is abstract and mathematical, and, as usually ery of how to create good explanations. A “good presented, it also has a peculiar dual character. explanation” is defined as an explanation “that There is a law of time evolution given by the is hard to vary while still accounting for what it Schrödinger equation: For every time interval there purports to account for” (p. 30). This philosophy is a transformation U obtained by solving this is inspired by the writings of Karl Popper. In his equation. It maps the initial state of a system to the influential works, Popper argued against empiri- final state of a system. (The notation U indicates a cism, the notion that we derive all our knowledge unitary linear transformation.) from sensory experience. There is no such thing There is another law of time evolution, a random as raw experience; scientific observation is always transformation R that determines the result of theory-laden. Furthermore, there is no principle the measurement. Various possibilities for this of inductive reasoning that says that patterns of transformation may occur, according to certain the past will be repeated in the future. In Popper’s calculated probabilities. The state change under view the path to scientific progress is to make this transformation is called reduction or collapse. conjectures and then test them. Deutsch insists The origin of the transformation R is that that even explanations that are testable are not it describes an intervention from the outside. enough; they should be good explanations in the The system is in a certain state. A physicist sense that he defines. sets up a measuring apparatus and performs the His version of philosophy of science has two experiment. The observed outcome occurs. The complementary strands. One is realism, the notion new state after the experiment is determined by the that there is a physical world about which it particular R that corresponds to the experimental is possible to obtain knowledge. The other is outcome. If the experiment is repeated under fallibilism, the doctrine that there is no sure path identical conditions, then the outcomes vary, but to justify the knowledge that has been obtained at the frequencies are predicted by the calculated any stage. These together support the metaphor probabilities. of a knowledge base of good explanations that is Such instrumentalist accounts have a long and increasing but bounded above by a reality that is complicated history. An early version is sometimes never fully knowable. referred to as the “Copenhagen interpretation”, One useful feature of the book is the explicit since it stems from ideas of Niels Bohr and his definitions of philosophical terms, explaining how school. (See [8] for a critical account.) Deutsch April 2012 Notices of the AMS 545 will have none of this. For him instrumentalism Deutsch contrasts two ways that a meme may is defeat; the only acceptable account is realistic. successfully replicate itself. A meme may survive Here is his explicit definition (or dismissal) of as a meme of conformity, because it is never ques- Bohr’s approach (p. 324): tioned. It relies on disabling the recipients’ critical Copenhagen interpretation facilities. When such memes dominate, the result is Niels Bohr’s combination of instru- a static society in which dangerous dysfunctional mentalism, anthropocentrism and memes are suppressed. The other possibility is studied ambiguity, used to avoid a dynamic society. In such a society memes are understanding quantum theory as replicated in a rapidly changing environment. This being about reality. can take place in a culture of criticism, because If the instrumentalist account is not acceptable, the memes embody new truths. then what are the alternatives? One is to develop The transition from a static society to a dynamic a theory that includes the deterministic U time society depends on an almost accidental shift in evolution but also has additional structure. This how meme transmission is employed. A meme structure should introduce randomness in some cannot be simply copied from behavior. There has way; perhaps the reduction transformation R will to be a mental capacity to infer the idea from the emerge as a consequence.