Rating: 
Summary: Not quite from alpha to omega
Review: There is a good book in this book somewhere, but it is trapped inside of a fair book that promises a lot more than it actually delivers. There is an initial problem that the book fails to make the case as to why particular constants are important. When discussing the fine structure constant (which is really the only constant that is given any significant coverage), the author tells us that it is made up of a combination of the electron charge, the speed of light, and Plank's constant. One might ask why these three particular values and that would be a fair question. The author tells us that if these three values changed but the fine structure constant remained the same, the resulting universe would be indistinguishable from our own. And then he leaves it there. What does that mean? Why is this the case? The author skips over this and moves on to other topics. He also makes a claim for "natural units" without being clear about what he means and why they are particularly natural. In chapter six the author discusses some curious coincidences surrounding Eddington's number. But after having debunked some other coincidental numbers he seems to leave himself open to claims that he is simply invoking meaningless coincidences. For example, he lays claim to an odd coincidence between the number of protons in the Universe and the ratio of the strengths of the electromagnetic and gravitational forces between two protons. Why these particular numbers? There are some interesting twists and turns in the book but there are also enough things that seem rather shaky that I began to doubt how much of the book was truly reliable. As one reviewer has already pointed out, what does one say when a book is so careless as to claim that solar eclipses are caused by the Earth's shadow falling on the Sun? I am sure the author doesn't believe that to be the case but it shows a certain amount of carelessness that worries me about the remainder of the book. There are some good parts to the book that I should mention. The discussion of the Anthropic Principle was clear and concise. His explanation of why intelligent life could not evolve unless there were exactly three spatial dimensions and one time dimension was convincing although I would have liked him to expand on this in more depth. Chapter eleven's discussion of natural nuclear reactors was also quite interesting. Overall there are some good parts in here but I didn't find the book as a whole delivered on its promise.
Rating: 
Summary: The new Pythagorean quest
Review: This very interesting book continues a quest that had its origin more than two thousand years ago. Let me explain.
Pythagoras is mainly remembered today for the famous theorem on right triangles named after him. But he accomplished much more. He was the founder of a school whose ultimate goal was to logically explain the world in terms of natural numbers. The Pythagoreans failed of course. What crippled their attempt most was their discovery that certain quantities (e.g., the diagonal of a unit square) could not be expressed as whole numbers, or even as common fractions. Over two thousand years had to go by before this was satisfactorily resolved. This required the development and acceptance of "irrational numbers." But the dream of the Pythagoreans has never been fully given up.
This book explains six related direction that the new quest has taken: 1) to discover the "natural" (non-anthropomorphic) physical units of measurement, 2) to find the largest and smallest numbers that have physical meaning, 3) to discover what is unique about three and four dimensional spaces (3D and 4D), 5) whether the physical "constants" are in fact time-varying, and 6) ultimately to explain all physical constants in terms of simple, mathematically meaningful constants (not necessarily "rational"). Thus although the book is a summary of fairly recent scientific research, its roots lie in wonderful mysticism.
The author, John Barrow (whose surname happens to be the same as that of Newton's teacher) has adopted a "Scientific American style" in which mathematical equations are kept to a minimum and at a simple level. While it is understandable that he does not want to scare off readers, perhaps he has overdone it. By not including, at the very least, a mathematical appendix, he has made some of his arguments very unclear. For example, on pages 215-216 he discusses the volumes and surface areas of n-dimensional spheres. He states that the "numerical factors grow to be enormously different from 1." This makes it appear that as the dimension increases the volume becomes enormously large. Actually the opposite is true, as shown (correctly) in Figure 10.10 (page 216). Perhaps what Mr. Barrows really meant to say is that the denominator of the numerical factor grows much faster than the numerator. As a result, these factors become vanishingly small for very large dimensions (as shown in Figure 10.10).
But wait a minute - that is not all. These same graphs show maximal values around dimension 6, before trailing down to zero. Since part of the book's objective is to explain the uniqueness of three and four dimensions, perhaps a discussion on what appears to be contrary evidence would be in order. ("Lucy! You've got some `splaining to do!")
I found Mr. Barrow's discussion of George Johnstone Stoney's work especially satisfying. I had never heard of this scientist before, and was surprised to learn of his significant contributions. On the other hand, I feel the book does not give Paul Dirac sufficient credit. All in all, a wonderful and stimulating book.
Rating: 
Summary: Hunting for Constancy
Review: We couldn't expect, inhabitants of any other world to know what a meter is. But we could expect them to know pi, or the ratio of the weight of a proton compared to an electron; that's a number, about 1836, without any meters or grams behind it, and it is considered one of the "constants of nature." There are other such constants, and they form the subject of _The Constants of Nature: From Alpha to Omega - The Numbers That Encode the Deepest Secrets of the Universe_ (Pantheon Books) by John D. Barrow. The book, which is the sort to be enjoyed by anyone who liked puzzling through such works as _A Brief History of Time_, paradoxically has a main topic about the constants: What if they are not constant? If, for instance, the proton / electron ratio were all of a sudden a little different, atoms might fly apart instead of maintaining their tiny orbital systems on which matter as we know it depends. There are other important numbers that we think are constant, like Planck's constant, the charge on the electron, and the speed of light. These three are linked within another constant, the fine structure constant. All these constants seem to have turned out just right for humans to have evolved to be investigating their physics. They all seem to be surprisingly bio-friendly. As surely as some insist that a conscious designer made the wonderfully baroque varieties of living things on our planet, others (who may admit that evolution rather than a conscious designer was at work) will say some godly entity picked the constants. But Barrow explains many alternatives, universes with the constants possibly turning out in some other way, and also explains ways that these universes might have come into being. If there are lots of universes out there, with lots of different constant combinations, it is no longer surprising that we are in one of them with the constants tuned just right to produce life, and intelligent life at that. But in our own universe, are the constants constant? There have been some very interesting and comforting confirmations of constancy which are reported here. Barrow himself, however, has been a member of a team using a different technique to spot a shift, over a longer period of time, and, well, a shift seems to be there. There is not much you can count on in this strange universe; whether our strange universe is more strange or less for having produced us is not a question that science can answer. There are plenty of others pending; this engrossing and clearly-written book brings lots of them up. Are our constants linked to an expansive universe? Do they evolve or cycle? Are there plenty of other universes out there already, in a multiverse of possible worlds? The current view of cosmology is clearly presented here, although it is very peculiar; and the answers to these questions will be more peculiar still.
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