Customer Reviews

Descartes's Secret Notebook: A True Tale of Mathematics, Mysticism, and the Quest to Understand the Universe

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I had read Amir Aczel's book on Fermat's Last Theorem, and I felt the same way, more confused than enlightened. The problem is that Mr. Aczel has a less than interesting style: the reading goes by very quickly and it just does not feel like one is gaining a lot of facts when one is gaining some facts. I thought Simon Singh did a better job with Fermat and I can't help but think that someone else can do a better job with this material.

It seems like Mr. Aczel has better things to do and more things to say at the end of the book, so he rushes to get to the good stuff only to reveal that there is very little good stuff.

Rene Descarte has always been a very interesting person to me. I had read a rather extensive biography of the man many years ago as an undergrad, so what Mr. Aczel had to bring to the story is interesting but not surprising. He does a pedantic job of relating the basics with some interesting tidbits thrown in, yet his style makes the interesting seem superficial.

The entire time, Mr. Aczel is moving towards the big mysterious reveal, the reason for yet another Descarte biography. He keeps hinting at a great earthshattering surprise, yet when it does come, the surprise is hardly surprising. The ingenious work that Descarte did in defiance of the church authorities of his day is indeed impressive but Mr. Aczel does not do the revelation justice. He never fully engages the reader in the development of the discovery and he fails to explain the difficulty of the mathematic is ignored altogether.

It is a good short treatment of Descarte's life, but there is no heft, very little mathematical detail, and nonexistent mystery in what is promised as a mysterious and revelatory book.

James Frey has taught us that it's OK to call a work of non-fiction that isn't entirely true a memoir. So maybe this is book is also a memoir?

Aczel has received a number of positive reviews on this book, for example from a Boston newspaper and from two of Amazon's "Top Reviewers." But none of these people are actually competent to judge the contents of the book. All they can really do is summarize what's there and say that they enjoyed reading it.

As is well documented by other reviewers, this book is mostly just a biography and actually has very little about the secret notebook. Aczel does a reasonably good job of summarizing these secondary sources, but almost nothing else he says is true. For example, he says that Descartes invented the ruler and compass construction of the square root and says that the Greeks didn't know how to do this. If any real historian of science had looked over his manuscript, this boner never would have appeared in print. The publisher should be ashamed for propagating such misinformation. If they'd spent a little time and a couple of bucks having a real historian of mathematics review the manuscript, this sort of pathetic error could have been corrected. But the publisher and the author apparently have such contempt for the reading public that they don't care if they publish falsehoods. Or maybe they just didn't want to delay a pre-Christmas release date?

This isn't an isolated example. The book is loaded with nonsense, from matheamtical facts to dates to what the fifth element represented in Plato's cosmology. And the really pathetic thing is that almost none of these sophomoric errors has anything to do with the biography of Descartes or with the secret notebook. Aczel seems to have included them as window dressing or page padding or perhaps just a desire to appear learned. It's an old problem: the conceit that any semi-retired mathematician can "deduce" the history of mathematics the way he deduces a theorem, and he doesn't actually have to do any research.

Shame on Aczel and on Broadway publishers. Let the buyer beware!

To look at a portrait of Descartes, one would consider him somewhat of a fop. And if one were to strictly consider Descartes' contributions to mathematics and philosophy, then he might be seen as a nerdish fop. But this portrait couldn't be farther from the reality that was Descartes' life. He was a world traveler and adventurer in addition to being one of the most brilliant minds the world has produced - before or since.

But you wouldn't know it from reading current biographies of Descartes. They are in the main turgidly written tomes; the only excitement they instill in the reader is wondering when they will end. I began to despair of there ever coming into print a biography of Descartes that captures both the thought and details of his fascinating life. Until now.

Amir Aczel combines the life and thought of Descartes in a slim breezy volume with an enthusiasm for his subject rarely seen in this sort of biography. His talent for explaining mathematical ideas and formulas that might seem daunting to the lay reader only adds to our enjoyment and deepens our appreciation for this most prolific philosopher-scientist.

To say Descartes led an interesting life is an understatement, and perhaps the most interesting thing about was the aura of intrigue and mystery in which it was enveloped. Aczel uses this as his starting point, investigating the mystery of Descartes' secret notebook which survived his death and part of which was copied by Leibniz, who easily broke the code in which it was written.

What was in this notebook that was so dangerous that Descartes felt compelled to write it in code? Aczel rightly decides to view the work in context of Descartes' life and thought, examining the charges heard in Descartes' day that he was a Rosicrucian, that he was writing heresy, and embracing the banned theories of Copernicus. Descartes, for his part, feared the Inquisition, especially after learning the fate of Galileo. He sought refuge in Holland, only to become once again embroiled in controversy. He reluctantly accepted an invitation from Queen Christina of Sweden as her personal tutor, thinking perhaps he could leave his detractors behind. But even his death in Sweden a short time later would become controversial. Did he die of natural causes, or did his enemies in the Queen's court, fearing his influence on the Queen, poison him?

And why was Leibniz so interested in copying the notebook? And why were his notes only fully understood in the late Twentieth century? Aczel tackles these issues and offers reasoned explanations based on the facts at hand. All this makes the reader want to know more about the life and thought of Descartes and his times, and that makes Aczel's book a success.

I generally enjoyed the biography of the young Descartes in the first few dozen pages of this book. But soon I started reading things about the history of mathematics which I know to be incorrect. So I have to conclude that the book is at least somewhat untrustworthy.

When discussing the duplication of the cube, Aczel says that Eratosthenes was a contemporary of Eudoxus in Plato's Academy, whereas he actually lived more than a century later. Elsewhere on this webpage, Dr. Amir Bernstein dismisses this as "a mere hundred years" and says that "dates of Greek mathematicians/philosophers are known only approximately." Actually, we can date Eudoxus and Eratosthenes quite accurately because Aristotle wrote about Eudoxus' astronomical theories in his _Metaphysics_ and Archimedes dedicated his book _The Method_ to Eratosthenes. Not only did they live more than 130 years apart, but they belonged to completely different mathematical cultures. In between their two lives, there was a philosophical revolution (Aristotle proposed the axiomatic method), a mathematical revolution (Euclid's Elements standardized the practice of geometry) and a social revolution (Alexander's multicultural "cosmopolis" became a reality in Alexandria).

Even such a simple fact such as the year in which Euler first went to St. Petersburg is wrong: it's given as 1730 instead of 1727. Aczel also claims that Euler visited Hanover on this journey. Thiele (1982) gives a very complete chronicle of the journey, based on Euler's own notebook, in his German-language biography, but he makes no mention of Hanover. Tellingly, Aczel gives no citation for his claim, which he uses to bolster his questionable theory that Euler somehow learned his theorem that F+V=E+2 from Descartes' lost notebook.

The biggest error is this claim on page 164: after telling us that Descartes gave a ruler-and-compass construction for square roots, he says "this was one of his greatest achievements in mathematics ... which would have stunned the ancient Greeks since they could construct only much simpler things." Unfortunately, it was not Descartes' discovery, because the construction was, in fact, known to the Greeks. What Descartes presents is just a special case of Proposition 14 from Book II of Euclid's Elements. You need only look at the diagram in Descartes' Geometry (p.4 of the Dover edition) and the one in Euclid's Elements (vol. 1, p. 409, also in Dover) to see this. Yes, one is the mirror image of the other and the letters are different. But the construction is the same. And here's why it works. In II.14, Euclid tells you how to construct a square with an area equal to a given rectangle. If the rectangle has sides of length a and b then its area is ab. Since the area of the square is also ab, the length of each side of the square is the square root of (ab). The Greeks called this the "geometric mean" of a and b, where "mean" is a word we still use today for average. Now what Descartes does is the case b=1, so what he gets is the square root of a. It may seem paradoxical to some, but by constructing a square, Euclid gets a square root along its side.

I think Aczel also gives Cardano too little credit and Tartaglia too much in his story about the solution of the cubic equation, but I'll just refer readers to Boyer & Merzbach (1991, p. 282-286) and Katz (1998, p. 358-364) to make up their own minds.

Previous person wonders why so many reviewers hype this book. Isn't it obvious? At least half the reviews here were written by the author himself! Check 'em out: no Real Name (tm) attribution, no other reviews written by the same person, and Google searches turn up no real person by that name in that city. And they all write in that same quirky, fawning style. Check out his other books on Amazon: it happens there, too. I guess he does it to counter negative reviews and to pump up his ratings. The funniest one here is "Michael Bernstein," who claims to have a Ph.D. in the history of science. Sorry, history of science is a small world and there are no Michael Bersteins in it.

This book is essentially a weak summary of the life of Descartes with a short chapter at the end about the "secret notebook". Most of the material appears to be rehashed from previous (and better) biographies with little new insight. The secret notebook? Well, just skim the last chapters for that. It is not really that interesting.

When one reads a book titled "Descartes's Secret Notebook," one expects a few things: a) information about Descartes, b) information about the secret notebook. But Aczel does a slipshod job of presenting both to us.

First, information about Descartes. What biographical information we can find within this book we can find on the internet in greater abundance and depth. I see no reason to buy this book if a) there are many points of inaccuracy with regard to facts in this book, b) what can be found here can already be found on the net.

Second, the secret notebook. We expect to see the links between Rosicrucian teachings and Descartes's notebook, but what we find is the links between Descartes' life and Rosicrucian teachings, and that between Leibniz's beliefs and Descartes' notebook. So Aczel does not offer us what he promises when he claims a connection between the notebook and Rosicrucian teachings.

Besides, why should I buy this book when it is a poor summary of a 1987 article by Pierre Costabel? Aczel should be ashamed.

And if the Wikiproduct report at the bottom of this page is true (and evidence suggests that this is so), then Aczel should be as ashamed of his lack of integrity as he should be at his lack of scholarship.

The book has many weaknesses. Descartes' mysticism is not well documented. He suggests that Descartes' work on polyhedrals is motivated by biblical numerology (p. 215), but then a few pages later reverses his claim, and says that Descartes didn't have numerological motivations afterall(pg. 219). He has some interesting information on Descartes and Rosicrucianism, but the question is not throughly explored.

Also the book doesn't document its sources well. Its not a scholarly book for that reason. Much of the information/dialogue is based on Aczel's reading of biographer/hagiographer Adrien Baillet. There is reason to question Baillet as a source mainly because he wrote the biography 43 years after Descartes' death. Someone like Rodis-Lewis or Gaukroger wouldn't use Baillet so casually as a source.

This book is a well-written popular biography of Descartes. It is worth reading because Descartes lead such a fascinating life. However, I found it disappointing in a couple of respects.

First, Aczel's treatment of Descartes mathematical ideas is too superficial. Because Aczel was trained as a mathematician and has written books on complex mathematical topics such a Fermat's Last Theorem, I expected to learn much more about Descartes mathematical discoveries than I did in this book. There was some interesting discussion of the "Delian Problem" (about how to double the volume of a cube), but not much else. Mostly Aczel gives us a narrative account of Descartes travels and activities. This could have been written by any competent journalist who consulted the secondary sources used by Aczel. Unlike the best popular science writers, Aczel fails to use his expertise to give us any deeper understanding of Descartes significance in the history of mathematics.

Second, as other reviewers have noted, the title is misleading. The title should have been, "Life of Descartes." Calling the book "Descartes' Secret Notebook" is an advertising gimmick and a false promise. Of course, the story of these notebooks is intriguing. Descartes kept them secret and wrote them in code because he was worried that the church would persecute him for adopting the heliocentric theory of the universe and perhaps for being a Rosicrucian. In these secret notebooks, Descartes derived an important mathematical formula that he never got credit for (now it is called Euler's formula after another mathematician who rediscovered it in the 18th century).

But Aczel is telling us nothing new here. He is just repeating what the Descartes scholar, Pierre Costabel, figured out in an article published back in 1987. Aczel's summary of Costabel would have made a good 10-15 page article in a popular science magazine, but there is not enough here to make this the subject of a book. Some might argue that the "secret notebook" is a good framing device for a routine biography of Descartes, but it is a false promise in my eyes. The title and introduction imply that the notebooks have some kind of special significance that will radically transform our understanding of Descartes -- but they don't. They are just another interesting incident in a routine popular biography.

My only beef with this book is that the title is misleading. The first 200+ (out of 245 or so) are about Descartes' life and not really about the "secret notebook". At the end, finally, the subject is this secret notebook. I did enjoy the book, mostly because I didn't know much about Descartes' life, but if anyone is familiar with Descartes they will be disappointed with this book.