- Quantum Computing since Democritus by Scott Aaronson
I suspect that I was sent this book by mistake; despite its title, it has nothing to do with ancient science, my field. If so, the editors can be excused: the book is hard to characterize, hence its charm. I am glad to have read it, and you should read it too. It is about computer science and quantum mechanics; it is purely mathematical and yet all about the physical world. It is neither a textbook nor a popularization. The nonexpert will enjoy the thrills of the chase, the author almost vanishing into the mist of incomprehensibility, reemerging a few equations later as lucid as ever, then disappearing again: a difficult, rewarding book. The secret to the telling of a mathematical proof is in its pacing: getting the next step just at the right moment, when the audience is most—or least—ready. Telling a proof is rather like telling a joke, and Aaronson is an expert at both. The book could be retitled Quantum Computing in the Catskills. These are Borscht Belt lectures, always trying to be funny, succeeding much more often than one initially fears.
I suppose the author is familiar with Democritus’s reputation as the laughing philosopher. Aaronson’s serious reason for referring to Democritus in the title was to signal that, ultimately, this is a philosophical work. One point emphasized is the claim—which I simplify here—that quantum mechanics is best understood not so much as a physical theory but as the probabilistic “operating system” for our theories of the physical world. The author emphasizes this point, however, at least to some extent, because doing so allows him to tell an extraordinary joke (that this claim of his was plagiarized in an ad featuring Australian fashion models; you can look it up online).
The book’s key philosophical claim, though, is that philosophers are transfixed by Gödel’s incompleteness theorem and by its implications for knowledge and the mind but that actual computations have to be carried out; it is not enough that they be possible in principle. Thus, to understand the mind and its knowledge, the relevant mathematical theory is not that of computability but that of complexity. In the end, however, the main reason to read this book is not just to learn about mathematical theories, important as they may be. Rather, it is to see [End Page 490] the world, for a few hours, the way scientists do: joyously surprising, riotously precise, worthy of Democritean laughter.
Reviel Netz, professor of ancient science in the Stanford University Department of Classics, is coauthor (with William Noel) of The Archimedes Codex, which has been translated into twenty languages and received the inaugural Neumann Prize of the British Society for the History of Mathematics. Coeditor (with Nigel Wilson) of a transcript and critical edition of the Archimedes Palimpsest for the British Academy, he is also the author of a three-volume translation of the works of Archimedes with commentary. Other publications include The Shaping of Deduction in Greek Mathematics, which received the Runciman Award of the Anglo-Hellenic League; Ludic Proof: Greek Mathematics and the Alexandrian Aesthetic; The Transformation of Early Mediterranean Mathematics; and Barbed Wire: An Ecology of Modernity.