Customer Reviews

Descartes' Dream: The World According to Mathematics

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THIS IS A well-intentioned but hardly satisfying book. From various angles it shows the increasing mathematization of our lives - but more importantly it questions the wisdom of placing our faith in this type of orderly, rationalized world.

We have become more mathematically inclined than you probably realize. It has become a given that those fields having a solid mathematical underpinning (e.g. physics and chemistry) have more validity than those that don't (e.g. psychology and sociology). The implications of this belief stretch far and wide. Mathematics has now reached into everything from biology, medicine, astrophysics, and economics to linguistics, musical composition, choreography, and art. The more math a field employs, it is believed, the more valid it must be.

The belief that guides much of modern society is that anything in the physical world can become the subject of a mathematical theory. This was French philosopher Rene Descartes' dream. In 1637 he published his revolutionary "Discourse on Method" which was a methodology for science based on the deductive logic of mathematical reasoning. This meant that since one plus one equals two, and this is a truth that cannot be challenged, then anything that can be put into a mathematical framework would also be true. This view also leads to the belief (as it did for Descartes) that animals - and perhaps humans - are merely complex machines; after all, life itself exists in the physical world.

But where does one draw the line? Certainly some things must be kept outside of the mathematical/computerized realm. Hopefully, emotions, attitudes, literature and the like will never make a successful transition into a computer program.

The authors attempt to create a "heightened awareness of the relationship between humans and the mathematics they have created!" An awareness, they say, "is necessary to shield us from the effects of the revolutionary waves of symbols that are about to wash over us."

However, the approach the authors take in developing this idea is less than satisfying. It pokes and jabs at various aspects of our math-inflicted society but the ideas do not always flow easily into the central theme. This is due to the book's construction, a loosely compiled collection of articles, addresses and taped interviews. Indeed, the authors suggest that readers should "browse at random and read whatever catches their fancy." At 306 pages, it's a good idea; but the result of this, however, is a book that has many interesting parts that often do not add up to any sort of unified whole.

Some of the essays lure you in with an interesting premise but then drown you in page after page of difficult math. By the time you've gotten to the end of the essay you've really forgotten what the point was or where it fits in with the rest of the book.

The message of this volume - that we "are being mathematized at an increasing rate ... and it may not be good for us" - is one that more people should hear.

Davis and Hersh write interesting, accessible overviews of pertinent social-mathematical topics and provide a respectable bibliography of reference materials. Topics covered include meta thinking, meaning of computation, and mathematical abstraction. If you are looking for information about Descartes, however, as I was, you will find very little of that in this volume.

My favorite part of this book was the interview with CS. As a programmer, it was gratifying to read such a sensible articulation of the profession.

I read this book over 20 yrs. ago, recommended by a friend who's a first rate mathematician, J. Palmore. I recall 2 things. First, that 'fairness' is not uniquely defined. Nice examples are given. Second, the 5 methods of mathematical proof: (i) proof by reference to the literature, (ii) proof by intimidation ("It's obvious!"), etc. Also recommended: to read in Descartes' memoirs the description of how he came on the idea to invent analytic geometry and derivatives of simple curves.

This book is supposed to cover how math is applied to real world problems, or at least that is what I expected when I got it. Alas, while it tries to address this agenda, there is very little of substance here beyond some rather simplistic assertions of how and why this was done. Sure, math has creeped into most academic disciplines, from hard to social sciences, but that doesn't mean it shouldn't be questioned, which the authors fail to do. As such, what you get is a series of exmaples, none of which I can even remember, some assertions of philosophical relevance, and then not much more than simple convenstional views.

For example, even the title attests to the authors' superficial treatment: Descartes is portrayed as the source of much of the revolution of the physical and other sciences, folllowing his "vision" of unifying the sciences while lieing in an oven to keep warm. Well, I think even that view can be challenged: many scientists I know, while acknowledging his contribution to math with coordinate geometry, would argue that Descartes philosophical writings in fact had little impact on the direction of science - one even told me that it was the French intelligensia that hoped to claim responsibility for the sci revolution then underway. (In this view, the real hero would be Newton.) THe authors' probe none of that. Nor do they question the usefulness of what I see as an overapplication of math to many disciplines, such as political science and even economics in some cases, which may be revealed as little more than academic fashions in the future.

That makes this book the conventional view, over lightly. Not recommended. Mathematicians may like it, but critics of math will not.