Customer Reviews

Euclids Window (Penguin Press Science)

5 star:		(28)
4 star:		(14)
3 star:		(10)
2 star:		(3)
1 star:		(5)

 

 

Mlodinow ('M' below) writes entertainingly, as most of the other reviews here testify. It's good that the general public get a taste of the excitement of discovery/invention in these fields. He should just correct, in a subsequent edition, the serious distortions that IAS Professor Langlands (Notices of the American Mathematical Society, vol. 49, number 5, p. 554 - referred to as 'L' below) has pointed out; then the book could be a useful, reliable introduction to whet the appetite of people who might want to study the subjects in more depth. Here are a few of Langlands' criticisms:

1. M's portrayals of Proclus, Kant, Kronecker and Gauss' father are unfair caricatures. L provides evidence in their defense.

2. M strives for sensationalism, not fact. E.g., M speculates that Thales traded in leather dildos. Veracity is sacrificed to effect.

3. M missed the main point of Riemann's great 1854 habilitation lecture. L wrote: "I could hardly believe my eyes, but it seems [M] is persuaded that the introduction of elliptic geometry was the principal achievement of the lecture."

Since M acknowledges on p.205 that Einstein's general theory of relativity was based on Riemann's work, M owes the reader much more explanation of Riemann's new ideas, expanding on his p. 207 discussion, not dismissing Riemann by saying his work "wasn't pretty."

4. L criticizes M's account of Einstein's early years, saying: "...to represent Einstein as an academically narrow, misunderstood or mistreated high-school dropout is a cruel disservice to any young reader or to any educator who swallows such falsehoods."

5. L concludes that M's book is "thoroughly dishonest ... simply because the author shrinks from nothing in his desperation to be readable and entertaining."

I didn't dislike the book as much as L did. It would be a significant achievement to make great breakthroughs in mathematics and physics somewhat comprehensible to lay people in an entertaining way and to do so with integrity.

Even L concedes "There would be little point in reviewing the book, were it not that the germ of an excellent monograph is there."

As a teacher of geometry, I always keep an eye out for books that offer coherent explanations of the importance of this most intriguing and ancient branch of mathematics. This books offers that in spades. In fact, it is one of the best basic overviews of the field I have ever come across.

Mlodinow divides the history of the development of geometry into five major "revolutions." Starting first with Euclid and his Greek contemporaries, Mlodinow traces the field through Descartes and the development of analytic geometry, Gauss and the development of "non-Euclidean" geometries, Einstein and the physical application of these geometries, to Witten and the development of string theory--the attempt to understand the universe as a consequence of geometry. In high school we teach the basics of plane and analytic geometry but few people are aware of how the field has matured since then. This book takes us on that journey.

And it is a wonderful one. Along the way he gives insight not only into the mathematics but also into the personalities that created it. We too often forget that it is people who created this magnificent structure and that it was not just handed down to us perfectly formed. Even more, we need to be reminded that the development continues and people are still contributing to it.

The real achievement of this book, however, is its acessiblity. Despite the fact that most people will only have experience with the material from the first two sections of the book (Euclid and Descartes), Mlodinow's writing is understandable by anyone who has successfully navigated a course in high school geometry. In my view, he offers one of the most lucid explanations of Einstein's work and string theory that I have ever read. His style is engaging and very readable. The ability to bring the importance of mathematics to a general audience is a great gift that Mlodinow seems to have. I hope he continues to exploit it.

If I have a complaint about this book, it is that it could have used a few more diagrams to help the less mathematically minded visualize his explanations. This is a minor point, however. Overall, this book is a great piece of work.

I found Euclid's Window charming and profound. Though Mlodinow's topic is ambitious, his ability to explain with incredible clarity some of the world's most abstruse thinking reminded me of Jim Gleick's work on Chaos. Mlodinow's storytelling seemed something altogether different--a lot more fun than Gleick.

Building on historical anecdote, Mlodinow has stitched together a history of human thought for me in a way no one else has, explaining how millenia of physical observation have translated into conceptual thought. I worried that this might be heavy going, but Mlodinow glories in the fine line of tale and humor;it spills over in his prose with such ease that it appears unconscious. I suspect this may become something of a classic.

This is by and large the worst popular science book I've ever come across (and being an astronomer and translator of popular science, I've read quite a number of them). Mlodinow violates almost all rules of scientific method and conduct, and even some of rules governing the plain civility in writing. There are literally hundreds of examples of such violations, so let me mention just a few of them. Mlodinow engages in hero-worship to an unprecedented degree: he does not shy away from pronouncing Witten "the most influential physicist and mathematician in the world" (p.253), as if such a grandeloquent statement can ever be proven or even properly supported. He enjoys judging long-dead people without proper history knowledge: he finds Cantor genius and Kronecker "a crab", he outrageously states that medieval Arabs didn't contribute anything original to mathematics (perhaps he should have taken some *history* courses from Witten, who knows better for certain!) and then, a dozen or so pages later, contradicts himself by citing some important results of two Arab mathematicians; he finds geometry and calculus more cognitively important than algebra (a dubious statement and quite improper for a popular work); he censores ancient Romans for their decadent ways (while simultaneously celebrating Athenian often quite promiscuous "symposia"); he does not know that Sirius is the brightest star which can be seen from Greece; he calls Aristotle just a meteorologist (p. 56). In addition, Mlodinow heavily indulges in what serious historians call "Whiggish interpretation of history", i.e. judging of the past by its present utility. Thus, he repeats at least 10 times that middle ages were "dark ages" or "barbaric", or that everything similar to the obnoxious US system of tenuring academic scientists belongs to the best of all possible worlds.

Quite amusing are Mlodinow's factual mistakes: in calculating Kaluza's salary, he errs only for a factor of 5 (p. 233). He expresses Planck's constant in wrong units (p. 226). He confuses arithmetics and number theory (p. 149). Funnily enough, for all this slopiness, he excels in a strange field: telepathy and spiritism. Namely, we are almost at each page treated with something which "Einstein thought" or which "seemed to Euclid", or such. This is the history of science at its nadir.

Finally, a word should be said about underlying ideology of this disappointing book. It serves as a sort of rousing manifesto for a particular branch of physics (theoretical particle physics) and one single theory (string/brane theory). Since it is written and marketed as intended for general public, it is thus dangerously misleading in suggesting that this one narrow field, and this one particular narrow theory within this field is everything that exists, or at least everything that is important, beautiful or profound in modern physics. This is megaparsecs distant from the truth. There is no meaningful sense in which string theorists are "closer to God" and eternal truths than are solid-state physicists, or astrophysicists, or geophysicists, or quantum opticians, etc. They are certainly not funnier or more literate than the rest of us. Mlodinow, unwittingly, proved this exactly with this pitiful book.

Mlodinow's book does the nearly impossible, translating key moments in mathematical understanding into the stuff of gripping drama. The fact that he's written extensively helps; but his choice of subjects, his vision and understanding, takes us away. It's the kind of book to read--and recommend. We live in a world of points, and lines, and space...but Mlodinow shows how understanding..conquering that world...was a real intellectual adventure. Oh, and it is--amazingly--a page turner of the highest order!

I thoroughly loved this book. I found myself reading late into the night when I should have been sleeping! Mlodinow's style is lighthearted and very entertaining. He successfully pulls the reader into the progression of geometric knowledge from Euclid through modern string theory. Mlodinow's book clarifies how mathematics helps to describe the universe and is a great read whether you are mathematically inclined or not.

Euclid's Window is an astounding book. It takes you on a ride through History, where you explore the origins of Geometry & Mathematics. From the early Babylonians to the Egyptians who used Geometry & Mathematics, but didn't ask the deeper questions which the Greeks did. With the Greeks came Thales, Pythagoras, and Euclid (Not necessarily in that order) who changed our view of the world by developing Geometry as we know it today in High School books. Than came the Dark Ages, and Europe plummeted into more than 1000 years of intellectual silence.

The book than talks about the revolutions led by Galileo, Descartes, Gauss, and Riemann. Finally the Author describes the later developments in physics. The revolution that Einstein made with the Special Theory or Relativity and the General Theory of Relativity. From then on we knew that mass curves space creating gravity, that nothing can travel at the speed of light, and that time is a privet matter rather than universal. Than the Revolution of Quantum Physics which, was developed in particular by Heisenberg and Schrodinger. Leonard Mlodinow explains the conflicts that arise when quantum physics and the General Theory of Relativity are combined, they fail. Quantum Mechanics works perfectly on the small scale, General Relativity works fine on the large scale, yet there is no way physicist and mathematicians could combine the two.

And then came the birth of the String Theory, rather five different String theories that turn out to be approximations to the much larger M-Theory, the theory that would be able to describe everything in the Universe, from subatomic particles to distant galaxies in the Universe. There is only one problem nobody knows what it looks like, and mathematicians and physicist can only calculate approximations of the theory. Leonard Mlodinow takes the reader on a fascinating ride through the history of Mathematics and Physics, the book is enlightening, even to me who constantly tries to keep up with new developments in Physics.

A must read for anybody interested in Mathematics & Science, or just plain old History, this book is essential.

I loved this book. This book provides an understanding of the importance of the Greeks in the history of human thought that goes far beyond a mere historical description of what they did. I've known for more than thirty years that the Greeks were the fathers of rational and scientific thought (and answered exam questions with a suitably expanded discourse on that theme). But I now have a concrete appreciation for what that means. Mlodinow not only reveals the content of what they thought but also connects their discoveries and theories to later events. He shows how the foundation is connected to the top story (still under construction). Mlodinow is especially adept at presenting theoretical constructs in a way that is accessible to the non-scientist. His portrayal of the individuals who were responsible for the major steps along the way is characterized by a wry outlook that is effective and that contributes to the story he is telling. This is popular science at its best. A specialist might debate a point or two, but the story that is told here is clear and compelling. tThe author's frequent humorous touches add a note of grace to the subject. Simply put, it's fun to read this book.

I highly recommend the book. I think it would be particularly useful as a text for a course in the history of Western thought.

As a teacher, student, and geometry enthusiast who's always interested in the people and the experiences behind the theory, I really wanted to love this book. And for a couple of chapters, I did: though I've had plenty of exposure to the history of mathematics, I still learned new things about Pythagorus (most notably, that others considered him to be the son of God, and referred to his mother as 'the virgin'!), and I still shake my head every time I read of the extent to which politics and religion stunted even mathematical developments. _Euclid's Window_ is at its most enjoyable when Mlodinow sticks to describing the way that discoveries and formalizations of geometry were motivated.

Unfortunately, as the book progresses, it veers more and more from expositions of this kind. Mlodinow's writing style, humourous in small doses, is unrelenting. Perhaps there are those who find chapter titles such as "Particles, Schmarticles" and "Ten Things I Hate About Your Theory" to be amusing; after the twentieth such one, I just found them to be irritating. In the later chapters, the author uses his sons as examples to illustrate concepts; seldom does this device actually serve to clarify. Soon I felt as though I was reading the essays of a class clown trying half-heartedly to mask his ignorance of the subject with humour: the analogies he employed were long-winded, and I found myself trudging through paragraphs of attempted whimsy and stories about his ubiquitous sons, Alexei and Nicolai while thinking (and, on one occasion, muttering out loud), "Get to the point, already."

More seriously, though, Mlodinow later strays from pure geometry into theoretical physics, and here he finds himself far out of his element. The two subjects, of course, are inextricably related; just as the issues that affected Greeks in their day-to-day lives impacted (and was impacted by) the development of geometry, so too do modern physics and modern geometry play off one another. The author can certainly be forgiven (and, in fact, commended) for his (largely successful) attempts to make string theory and M-theory accessible to non-specialists. However, those who were looking for a "story of geometry" will likely find themselves dissapointed to see that this one omits any mention of topology, or - my favourite - projective geometry in favour of this "applied geometry". Furthermore, the author treats physics and geometry as though they are governed by the same rules, and here he goes seriously wrong. Experimental evidence showing that space is curved is presented as proof (or, at least, indication) that "there was something wrong with Euclid"; alas, it is no such thing. Euclidean geometry is inadequate as a model for the physical world, yes, but no amount of experimentation can /disprove/ an /axiomatic system/.

_Euclid's Window_ is entertaining, and a nonspecialist interested in a broad, accessible survey of the interactions among geometry, physics, politics, and civil life will find it useful if they can stomach the writing style. However, the actual content ought to be taken with a grain (or a block) of salt.

This witty rendition of those long-misplaced facts from schooldays about the fathers of mathetmatics allows one to put it all together once and for all. Mlodinow has a knack for integrating what could be heavy material, in a witty, understandable way as he tells juicy stories about each character. One feels the accomplishment of having reconstructed the development of mathematics by the end of the book, yet it goes down as easy as People Magazine. A great, valuable read.