Saturday, November 21, 2009

The Power of Limits

I checked this out from the library thinking that I would probably just skim it, but I got so engrossed in it that I read the whole thing. The topic is one of perpetual fascination to me, perhaps bordering on a minor obsession: the pervasiveness of certain geometric patterns and harmonious mathematical relationships all throughout the created order, and most specifically, the relationship known as the golden ratio, or .618…. This unique and remarkable ratio manifests itself virtually everywhere one turns, in created works of both Divine and human origin: spiral galaxies, hurricanes, sunflowers, the chambered nautilus, the human hand and ear, notable works of architecture and graphic design, ancient Greek pottery, paintings by the likes of DaVinci and Seurat, musical harmonies, and a Boeing 747, all just for starters.

No book could possibly be said to cover the topic exhaustively, but this is one of the more thorough treatments I’ve encountered on the subject. It explores numerous examples of this sort of thing which I had never even begun to consider. There are really fine illustrations and diagrams (many of them quite intricate, detailed and beautiful) on every page. So, in terms of a surface-level analysis of the phenomena, this book is superb.

What I find much less satisfying, however, are the author's attempts, interwoven with increasing emphasis as the chapters progress, to discover what this all means on a deeper, spiritual level. Though he never articulates such a position explicitly, it seems that he would probably be on good terms with what has since become the Intelligent Design movement. (This book was originally published in 1981.) As a Christian however, I am firmly convinced that the doctrine of a personal, Trinitarian Deity is the most obvious point of convergence for all the universally imbedded testimonies to intertwined unity and diversity which this book is dedicated to exploring. Though not really surprising, it is nonetheless disappointing to see this conclusion ignored by the author in favor of an unsatisfying and impersonal hodgepodge of eastern dualism, mysticism, and vaguely beneficent evolutionary principles. (That last point is especially a very interesting notion, one which I think would be most difficult to harmonize with Darwin’s theory of natural selection.) At any rate, had the author been able to rise above all this, I might have given the book at least four (out of five) stars.


  1. Without knowing anything else about it, that repetition of number/ratio thing sounds scarily like a signature!

  2. My intro to the golden ratio (phi) came through James Nickel's book Mathematics: Is God Silent?. Somewhat minor, but what I found most interesting was the fact that phi - 1 = 1 / phi. Given this, though, some people call the number "1.618..." phi, as opposed to the number which is one less that, which you indicated in your post.

    Go to Wolfram Alpha, and type in "golden ratio", and they'll also give you an equation that links phi to the number of the beast (which is pretty befuddling): phi = -2sin(666).

  3. Brent, I think you are right in saying that the correct value for phi is actually 1.618, as opposed to .618 as I have it referenced in the post above. I suppose that the correspondence between the two numbers is the essence of what makes the golden ratio so fascinating and, at the same time, so elusively perplexing. (At least for non-mathematicians like myself!) Anyway, thanks for pointing that out.