Is Ockham's Razor getting a bit rusty? That's the question that Brian Greene's The Elegant Universe brings to mind. The subtitle of Greene's book adequately captures its subject matter: "Superstrings, hidden dimensions, and the quest for the ultimate theory". Greene is a physicist working in superstring theory, and this book is his attempt to explain, in non-mathematical terms, what superstring theory is all about.
Greene takes as his starting point the irreconciled differences between the two great theories of the last century: general relativity and quantum mechanics. General relativity holds great power in explaining the large-scale structure of the universe, while quantum mechanics has been a productive way to view the small-scale structure of the universe, but it's been very difficult to apply them both simultaneously. Superstring theory offers a mathematical structure, interpreted as the interactions of tiny loops of "string" in 11-dimensional space-time, the melds the two into one overarching "theory of everything".
Greene writes well, and the book is relatively easy to read (it helps, I suppose, if you've already been exposed to such concepts as quantum mechanics and Kaluza-Klein spaces). The attempt to cover this complex field without mathematics, though, must be judged a failure. Analogy and handwaving and assertions that we'd see something was true if we could follow the math only go so far. By the end of the book, analogies have been piled on analogies to the point where the intelligent reader will, I think, detect a certain cotton-candy feeling to the arguments. Everything Greene says could be true, but there's no way for the reader of this book to form an informed opinion on the likelihood that it is true.
Of course, if strings in 11-dimensional space-time really do explain everything, I doubt that any non-mathematical exposition will ever be clear.
What troubles me most about this book, though, is that if it's an adequate representation of the state of physics today there seems to me to be a disconnect between theory and experiment. Superstring theory as presented by Greene currently makes no verifiable predictions that the experimentalists can test. Instead, his argument for the truth of superstring theory seems to depend on a combination of Ockham's razor and the strong anthropic principle. If the mathematical intuitions of some superstring theorists are correct, it may be a theory with no free parameters (as compared to 19 in the "standard model" of particle physics) that will be shown to explain a universe whose structure supports life. In its strongest interpretation, I do not believe it is a mistake to say that the idea of superstring theory is that the logical truth and necessity of mathematics itself will prove to be the "theory of everything" that explains the universe.
These are deep and murky waters indeed. Whether one agrees with Greene's conclusions depends, I think, on whether one believes mathematics is discovered or invented. And even if one believes in a mathematical absolutism where math is eternal and discovered, does the simplest mathematics necessarily correspond to the structure of the physical universe? (And what does "simplest" mean, for that matter?) To take a crude analogy of my own: draw a parabola on the infinite plane. Choose two points of the parabola. The "simplest" curve that one can construct through those two points is a straight line, but that's not the curve that gave rise to the points in the first place. Superstring theory is a grandly complex curve that may pass through all of the points that the experimentalists have provided -- but what assurance does that give us that it is the same curve the points came from?
For me own part, I'm not convinced that Ockham was correct. While the multiplication of entities may not add explanatory power to a theory, I do not feel compelled to believe that the correct theory is the one with the least entities. But I certainly appreciate any book that provokes me to consider these issues.