Customer Reviews

The Universe and the Teacup: The Mathematics of Truth and Beauty

5 star:		(12)
4 star:		(4)
3 star:		(4)
2 star:		(8)
1 star:		(9)

 

 

Chapter two, second paragraph: "The Milky Way galaxy contains 200 billion stars..."
Chapter two, a few pages later: "Fifteen billion is also more or less the number of stars in the galaxy." Obviously, the number of stars in the galaxy is not precisely known, but we do know that 15 billion and 200 billion are two different things. One of the author's "truths" is self-evidently not true. Purveyors of "truth and beauty", whether scientists, gurus, philosophers, spiritual leaders, or journalists, often regard their subject and their audience far too casually. Here we have a case in point. Perhaps most books contain 'typos' and the miscues inherent to humanity, but here it seems that both the author and the editor were asleep at the wheel, something that needs to be addressed if the book achieves a second printing (and I don't see why that would happen).
The subject is truly fascinating; or at least it should be -- the relationship of aesthetics, mathematics, and logic. At the deepest levels of the human intellect's inquiries, the answers are all about a mysterious mathematical beauty. The reality of this escapes most people, which is why the "National Bestseller" heading on the cover of Cole's book intrigued me. Apparently the book has enjoyed a larger readership than most such popularizations. Unfortunately the superficial, disjoined 'newspaper style' of science serves the material poorly. The writing rambles almost aimlessly. The books of many mathematicians and physicists have examined the relationship of reality, reason, mathematics, and aesthetics. Devlin's 'The Language of Mathematics' is very good. Fairly recent works by Penrose, Davies, Rucker, Berlinski, Greene, and others come to mind. Some of these books are far better than others. This volume is one of the others.

Despite the title, not once in this book is an actual mathematical problem presented coherently. Instead, Cole drones on about the virtues of cooperation, the importance of minorities, and other left-wing philosophical themes. I'm a liberal and would tend to agree with her politically, but that ignores the central problem with this book: Cole's failure to make the distinction between mathematics itself and beliefs that just happen to be justified by statistics or quasi-mathematical reasoning.

Perhaps The Universe and the Teacup is best described as a meta-popularization, since virtually all of Cole's sources are themselves popularizations. She hypes such familiar staples of popular science writing as fuzzy logic, chaos and complexity theory ("all the rage these days" -- I thought that's what they said back in the 80's), and Godel's theorem (both "a shattering blow" AND "a staggering blow to our sense of certainty"), without showing that she understands any of these things on more than a superficial level. (I don't claim to be an expert on these topics, either, but then again I didn't write a book about them.)

For general readers interested in how mathematics relates to everyday life, I'd recommend John Allen Paulos "Innumeracy"; for a survey of modern mathematics, both "From Here To Infinity" by Ian Stewart and "Archimedes' Revenge" by Paul Hoffman succeed where "The Universe and the Teacup" fails.

I expected more from K.C. Cole; she's an excellent general science writer for the L.A. Times, but she comes up short in this book. This book is clearly trying to bring an appreciation of math to general readers, but she does no better than to say "Look at that over there; if you understand it, it's really neat" -- but without trying to give you any sense of what's neat.

By contrast, I highly recommend "The Language of Mathematics : Making the Invisible Visible" by Keith J. Devlin. Devlin not only points out what is interesting, but provides enough depth to give you a fleeting glimpse of the way mathematicians see math.

Should it be that easy to write a book? Collect all the bits and pieces from newspapers' weekend-supplements and almost scientific coffeetable-talk and toss in some currently fashionable phrases concerning physics and mathematics, stir until the lumps have disappeared and do not bother with the spices of explanation and insight. If you love math and physics, stay off !

It gives me no pleasure to agree with so many of the write-in comments to amazon.com and to disagree with the many published critics regarding Ms. Cole's book. I expect I'd like her in person and am sympathetic to her objectives in writing this book, but it reads like a book about music written by someone who writes well but is tone-deaf.

It's unfortunate none of her many friends in the technical fields seem to have been adequately critical in discussing her book before its publication.

Rather than either attempt a lengthy explanation or engage in unsubstantiated assertions, I'll give two simple examples of what's so troubling about the book.

Page 57 has a poorly reasoned and inadequate discussion of error bars. The example cited is one where person A scores 98 on an IQ test and person B scores 101, both with "error plus or minus 3". First, Cole says, this "tells you absolutely nothing", which is absolutely false. She goes on to explain what it's supposed to tell you: there's a .5 probability that the test scores are within 3 points of the actual IQs. Then she asserts "that means the person scoring 98 could be superior to the person scoring 101 by three points." Notice that superiority has been implicitly defined to be a matter of IQ, which is troubling. But what Cole is missing is that while it may be true that A may have an IQ 3 points higher than B's, it's also true A may have an IQ higher than B by 4, 5, or 6 points. Further, the relative scores are more likely not to be reversed in this manner, and B is likely to score higher on subsequent tests too. Of course, in making these assertions, I'm making lots of assumptions. In particular, that the error is something like a bell-shaped curve that doesn't drop off to zero at 4, 5, or 6. Or 17, for that matter. She doesn't describe this curve at all, so I have to make a reasonable guess. So, when she's right, she doesn't give a complete answer and is consequently not very informative. For an important discussion of testing and IQ, see Stephen Jay Gould's "Mismeasure of Man" (also see the comments in www.amazon.com about that book).

Page 197 cites an old riddle that has you traveling due south one mile, due east one mile, and then due north one mile and finding yourself where you started. Cole asserts you're at the north pole. You may be, but it's not necessarily the case. This is only one of infinitely many solutions to the problem. To see this, consider the latitudes sufficiently close to the south pole that a one mile walk due east puts you back where you started. Since you're willing to walk around the world more than once in that mile, there are lots of these lattitudes. Pick any point on any of them and move a mile due north. That point is also a solution to her riddle. The incompleteness of her solution is very unsatisfying to a mathematician. (Parenthetically, she seems not to have understood that mention of bears - the riddle asks what color are the bears you see - is supposed to rule out the south pole solutions, rather than merely "make the riddle more fun.")

I must admit, I was more disappointed in this book than any other I can remember reading. While Cole is working hard at the arguably noble pursuit of writing about math and science for the layperson, she does so at the cost of any sort of actual relevance to the world of science. By absolutely eliminating ALL mathematical rigor and substance from her writing, Cole leaves the reader with nothing but her own third-rate analogies, sappy philosophical bumblings, and less than shimmering prose. I will admit that I was unable to make my way to the end of the book due to my utter frustration with Cole's destruction of the beautiful world of logic and numbers, and so it is concievable that the book becomes better near the end. Unfortunately, anyone interested in learning or thinking about mathematics will likely be quickly repeled long before. List this book with Gary Zukav's "Dancing Wu Li Masters" as abominations of the world of pop-science.

I found "The Universe and the Teacup" an enjoyable book, conveying to the average reader the meaning of math and science in our everyday lives. I was, however, disappointed that the author chose to stray from being a serious science writer and instead attempt to use math and science to justify her own political views. Cole takes shots at the Reagan administration, the NRA, and the Republican Party. No attempt for balance is offered by presenting examples from the left side of the political spectrum. She, at times, seems to miss the point of her book, devoting more time and space to the glass ceiling battled by female mathematicians and scientists than she devotes to their work itself.

The other reviewers have it right: Other writers have assembled rambling connections to provide insight into the interrelations between arcane sciences and ordinary life. Few have done it worse than this. This book illustrates that intelligence and education do not always correlate with insight and depth. With so little going for it, I am surprised that this book found its way into print. Both you and Miss Cole must have better things to do with your/her time.

The Universe and the Teacup by K. C. Cole is a stunning book. I know I was stunned by it. Expecting a book on math and science, what Ms. Cole delivers is more a book of vagaries and liberal political polemics. Probably the chapter called "Lani Guinier Was Right" should have been a tipoff. Guinier the mathemetician? No, there is no such person. The chapter is about the rejected Clinton apointee who claims that we don't count our votes right. Ms. Coles assures us that "the one thing most parties agree on is that the present system is the worst." She doesn't identify which parties she's speaking of but at least one of those mathematicians she quotes says of changing our voting system, "it can get all tangled and awful." Without doing any math, I feel sure that it would!

This book is rife with politics and Ms. Cole hints that math supports her very liberal beliefs without showing us exactly how it does. Cigarette smoking causes lung cancer because of the strong correlation between the two, but the correlation between cancer and living close to high-voltage power lines proves nothing. Why, she never really explains. She quotes a mathematician who, after talking of how the economy improved under Ronald Reagan, says that under Reagan "everything from the interstate highway system to public education was neglected almost to the point of destruction." Of course she doesn't use any math to prove this assertion, probably because there isn't any.

The constant intrusion of politics into this book might be forgivable if there was a meaty core of math and science over which it was ladled, but there isn't. An index which contains Guinier and Rodney King has no entry for Gaston Julia or Benoit Mandelbrot. In fact, the word "fractal" doesn't even appear in this book even though these mathematical constructs are both incredibly beautiful and model real life structures much better than other approaches. The author discounts the various forms of chaos science in a one sentence footnote to the effect that some scientists have said that they have not turned out to be useful.

Something that does seem useful to Ms. Cole is a process for dividing things fairly called Adjusted Winner. This system is "generating excitement far beyond the mathematics community because it's simple and flexible enough to use in divorce settlements, international conflicts, and a host of other kinds of disputes," according to her. I found the system laughable. She gives the example of using it in a divorce case where one spouse wants the house and the other wants alimony. I won't go into the complex math here, but, using the adjusted winner technique, it can be decided to give the one spouse the house and the other alimony! Duh. To paraphrase Ms. Cole, the key to eliminating envy is to have different parties who want different things. Duh again. Isn't the cause of most conflict that the different parties want the same thing?

This book often belabors the obvious (yes, a sphere is very symmetrical, I get it) while glossing over things we would like to see explained in detail. Her discussion of the O. J. trial is a good example. Apparently, the odds of a DNA match are up in the air! They are the subject of "much ongoing debate" she says as she jumps from the trial to Fraunhofer lines in the sun to the discovery of the top quark to a discussion of the odds in coin flipping to... I give up! I have no idea what mathematics said about the O. J. trial from reading this book.

The Universe and the Teacup is an extremely flawed work. Somewhere along the line, it got "all tangled and awful".

I bought this book in 1999 and recently found it in a closet.

Even though the cover says this is a math book, I didn't find it to be so. Yes, there is some math in it but Ms. Cole is more of an observer. As a "non-scientist" I did not feel totally lost within the book, I felt as if I was being introduced to new concepts at a very high level, with some delving into details.

The book contains five parts which touch on mathematics, social issues and how they relate to one another. Some parts, in my case, needed to be re-read to understand - but that's the nature of many books especially on this subject.

Ms. Cole tries to keep the imagery of her examples clear and informal using current events (of 1999) as a stage. I think that the effort put forth in the book to explain complex thoughts in simple terms is commendable and admirable - even though sometimes it just doesn't "click".

This book is not meant for the mathematician, but for us layman who want to understand physics using an informal style while getting an insight of how those ideas affect us and our society in our daily lives.