Customer Reviews

Five Equations That Changed the World: The Power and Poetry of Mathematics

5 star:		(23)
4 star:		(5)
3 star:		(5)
2 star:		(8)
1 star:		(3)

 

 

You might characterize this book along the lines of "an opera book for people who think they don't like opera." The author, Dr. Michael Guillen, sets himself the formidable task of instilling into non-mathematicians an appreciation of the beauty and glory of mathematical equations. His approach is to take five historical figures, give a brief biography of each, select an equation best encapsulating their accomplishments, and explain this equation's relevance for contemporary society. The figures selected are Isaac Newton, Daniel Bernoulli, Michael Faraday, Rudolph Clausius, and Albert Einstein.

Is his format a good choice? Yes, perhaps among the best. Are the historical figures good choices? Yes again; but here one might quibble a bit: all the figures selected are male physicists who lived during the approximately 300-year time-span, 1640-1950. Were there no important equations prior to this? What about the Pythagorean theorem? Euclid's proof of the infinity of primes? Archimedes's formula for pi? The delFerro-Tartaglia-Cardano equations for the cubic? What about women?

Is his approach successful? Generally speaking, yes. It is not clear what readership Guillen has in mind. At first I though it might be your typical Scientific American reader. But the biographies tend toward a Horatio-Alger style, suggesting a younger audience.

Dr. Guillen's unique talent is his understanding of the relationship between religion and science. Although he treats the subject only briefly, I have never seen a better exposition in readily accessible material. As Guillen points out, this relationship has not always been favorable to religion. A comparison with the proverbial ingrate camel comes to mind: having inveigled its nose into the tent, the camel proceeds to evict the original tenants. This process began with Plato's plea that science be allowed to investigate the celestial realm (at that time considered the province of the gods), and ended with Laplace's claim he had no need of the "God hypothesis."

Although I liked the book as a whole and applaud Dr. Guillan's effort, the book is unfortunately marred by some careless and misleading passages. I cite some in the hope these might be corrected in a future edition.

Page 58: "...a giant titanium bullet" - the Apollo capsule was made mainly of aluminum, not titanium.

Page 61: "As the rocket thundered its way to the clouds it began to spin like a bullet" - not so! Small rockets are sometimes "spin stabilized," but never large rockets like Apollo.

Page 61: "... the spaceship started to speed up ...the astronaut's had reached the point at which the moon's gravity was stronger than the earth's" - because the moon is a moving target, the minimum spacecraft speed along the trajectory does not occur at the point where the two gravities cancel.

Page 137: "He discovered that the force between [two magnets] diminished with the square of their separation" - Magnets always have two poles, so the force between them is complicated. For large separations the force diminished with the fourth-power of the separation.

Page 259: " ... letting out a hundred billion times more energy than one could ever get from ordinary, old-fashioned combustion" - the ratio is more like ten million.

Michael Guillen has chosen five famous mathematician to describe. The theme for discussing the particular person is that he discovered an equation that changed the world. Each deals with a result in Physics. One could argue that others could be added to the list but there is no question that these are certainly all contenders for the top five. Guillen is a science editor for ABC and is a professor of physics and methematics. This combination makes him well suited to choose the equations and to describe the results and the men behind them to a layman. The five equations and their authors are 1) F=GxMxm/d^2 Newton and the Law of Universal Gravitation, 2) P+rhox 1/2 nu^2 =CONSTANT, Daniel Bernoulli and the Law of Hydrodynamic Pressure, 3)DelXE=-dB/dt, Michael Faraday and the law of electromagnetic induction, 4) Delta S universe > 0, Rudoph Clausius and the second law of thermodynamics and 5) E=mxC^2, Einstein and the special theory of relativity. I am sure we all expected 1 and 5 and depending on your knowledge of physics, the others may or may not be a bit of a surprise. Guillen spends a lot of pages describing the nature of the equation, the character of the inventor and the impact of the results on society (sometimes centuries later). Newton's laws were instrumental in developing guidance and tracking systems for artificial satellites, space shuttles and other objects launched into space in the 20th Century. Our landing on the moon would not have been possible without Newton's laws. This makes for interesting reading for anyone interested in mathematics or science. A good book for teenagers to read to develop motivation to study math and science and to aspire for a career as a scientist.

Delightfully written, easy to follow, Guillen describes the personal situations and scientific context of Newton's Law of Gravitation, Bernoulli's Law of Hydrodynamic Pressure, Faraday's Law of Electromagnetic Induction, Clausius's Second Law of Thermodynamics, and Einstein's Theory of Special Relativity (the equivalence of mass and energy).

As is the recent custom outside of textbooks, Guillen has given an exceptional amount of personal detail, letting us be amazed once more about how much these five scientists achieved despite personal situations that varied from ordinary to awful. Furthermore, the resistance from other scientists of their times is still surprising to some of us, while the resistance of the Catholic Church is not.

Guillen's efforts to provide clear explanations for the discoveries mostly succeed, least well for Clausius's Second Law of Thermodynamics, in my opinion. Many clever similes are used. A better explanation of the inverted delta in Clerk-Maxwell's equation on Faraday's Law of Electromagnetic Induction is needed. Guillen defines it as "the amount of" (p158), while "the rate of change" might be better. The math does not go beyond high school algebra, with that one exception, so the mathematically challenged such as this reviewer need not fear.

What is very disappointing is the number of errors:

1. On p27 globes are said to 2-dimensional, when they are actually 3-dimensional; circles are 2-dimensional.

2. On p36 et seq planetary motion around the sun is said to follow oval paths, when the paths are actually elliptical. These are different shapes.

3. On p137 the Leyden jar was said to be the forerunner of the modern battery. In fact is was the ancestor of the modern capacitor.

4. On p139 Volta's piles were said to provide more current the higher the pile, meaning the more plates). In fact, more plates gave more voltage, not more current. The two terms are not interchangeable. The piles were said to be the ancestor of today's storage batteries, while, in fact, they were the precursor of today's "dry" cells, which are not rechargeable.

5. On p158 the general term "electricity" was used instead of the proper term "voltage" (E).

6. On p162 a perpetual motion machine seems to be described inadvertently by the supposed possibility of using an electric motor to spin a dynamo that, in turn, powers the motor. This is not possible, of course.

7. On p163 the term "current" is used instead of "voltage"; these have never been interchangeable. The current is the number of electrons passing a certain point per second, while voltage is the unit of electrical pressure.

8. On p163 the term "heat" is used instead of "temperature". Thermometers measure temperature; calorimeters measure heat.

9. On p187 there seems to be total confusion between heat capacity and conduction. The apple filling in a pie is mostly water which has high heat capacity and good conduction, so it is easy to be burned on hot filling. The crust is mostly carbohydrate with air pockets, almost a foam, and the combination of low heat content at a given temperature and poor conduction makes it harder to be burned by the hot crust.

10. On p246 the speed of light was said to be constant. This should have been qualified from the start as being in a vacuum, as was done from p248 et seq.

11. The gross structure of the atom was worked out by Ernest Rutherford et al. in 1911 by bombarding gold foil with a beam of alpha particles from radium, not in the 1930s with "atom smashers" (particle accelerators), p258.

12. Einstein's 1921 Nobel Prize in Physics was for his discovery of the photoelectric effect, not for quantum mechanics (p259), which Einstein never even accepted!

Other Amazon.com reviewers found other mistakes as well.

I consider Guillen's selection of his five main equations in physical sciences to be ingenious. His book should be an inspiration to us all, including the young generation which will discover in the amazing story of Faraday that an "uneducated" inventive genius was able to change the world of physics and electricity forever and immeasurably. The story of the Bernoulli family is insightful for all scientists, including philosophers of science, and illustrates exceptionally well the importance of tolerance and not letting success go to one's head and spoil one's open mindedness. The numerous applications of the Bernoullis to different fields are inspiring. The chapter on entropy is fascinating and should be read by everyone, although Guillen might have remarked that entropy is far from settled - especially since there are many different kinds of entropy and different theories of entropy and their deeper analysis and comparison is still far from complete. Newton and Einstein are indispensable for all physical scientists, and probably for all scientists for that matter. There are still many interesting questions about both Newton and Einstein that should provide much material for study by historians, psychologists, philosophers of science, and even social scientists. For example, why did Newton really wait so long to publish? Why did Leibniz' publications impel him to publish his own work? Why was Einstein so opposed to quantum theory, and why did quantum theorists fail to establish a peaceful dialogue with Einstein? The questions go on and on. I might remark here that Clarke et. al in their recent volume on nonsmooth analysis have shown that equations become inequalities and subset relationships in the disconnected and discontinuous/sharply bending curve worlds, which makes understanding of equations even more important than ever, including their roles and origins and where they are and are not applicable.

It is difficult for me to review this book. "Five Equations That Changed The World" suffers from a racist, anti-German stereotype the author invokes in the chapter about Einstein that I simply cannot get out of my mind. Sadly, whenever I think of this book that ugly comment is all I will think about. Except for that comment I would have given it four stars.

Aside from that, I rather liked "Five Equations That Changed The World" and would generally recommend it to the non-technical reader. Michael Guillen's choice of the five equations combines the obvious (Newton and Einstein) with the interesting, more obscure choices of Michael Faraday and Rudolph Clausius.

I especially like the way author Guillen describes the scientific and philosophical worldview into which each of his five geniuses was born. This is critical - because this is not a book about five men; it is a book about five Earth-shattering ideas that changed the way science (and eventually society) looks at the universe.

Extremely interesting is the chapter about Clausius and his formulation of the concept of entropy.

Less interesting to me was the details of each man's life. The author attributes too much importance to incidents in the lives of his subjects that have little bearing on the ideas they developed. It is evident that author Guillen holds to a strongly Judeo-Christian religious point of view. It is important to note that Guillen's religious views appear to have something to do with his selection of subjects and intrudes often in his telling of their lives. The passionate Protestant religious convictions of Faraday and Clausius is something I did not realize. I also never knew that Einstein was an ardent Zionist.

I highly recommend this book to a high school student who has to write an essay about Newton, Bernoulli, Faraday, Clausius, or Einstein. I also recommend it to adults with an interest in the historical evolution of the modern scientific worldview.

Any avid reader knows the experience. After weeding through countless uninspired (and uninspiring) novels, or grueling non-fiction that could only be improved by a couple of bald-faced lies, you somehow come across that ONE book that completely captures your imagination, and you simply can't read it fast enough. I would bet that anyone reading this knows the feeling exactly; it's the kind of experience that keeps one going back to the libraries and bookstores.

I'm pleased to report that Michael Guillen's "Five Equations that Changed the World" falls into this category with ease. The subject matter may not initially attract those for whom "mathematics" is synonymous with "inferiority complex", but speaking as an "almost pure" non-mathematician, this book will appeal to anyone with an interest in history, in the processes of scientific method, or who simply enjoys an absorbing human drama. Additionally, even the most mathematically challenged may finally have their first experience of truly understanding intricate numerical concepts, as well as the thought, experience and effort which go into their creation.

The book details the lives of five historically prominent individuals, from Sir Issac Newton to Einstein, with the central focus of each story being a mathematical principle (and resulting equation) that proved to be their defining and enduring achievement. Guillen doesn't shy away from presenting the numerical concepts in their pure form, or try to take refuge in "layman's terms", but instead allows you to see some of the thought that went into the development of each equation, and in this way ensures that you will understand the concepts that led to the numbers. This process allows the reader to clearly see mathematics as a language that can be used to elegantly summarize complex ideas.

Ultimately though, what is truly astonishing about the book doesn't lie in the five equations, but in the details of the lives of these remarkable men. Each story is filled with the passion, competition, family drama, ill feelings, jealousy, hard work and sheer will that underlies most human endeavours, science not the least. On finishing the book, I found myself wondering for days where people like these are today, people for whom "genius" seems a small and confining definition. There obviously is not space here to provide any details, so I will can only encourage anyone who finds this even mildly intriguing to do themselves a favour and go to the source as soon as possible.

Guillen manages to find that extremely rare balance where, even as you're reading the book, you're marvelling at his ability to maintain an almost perfect mixture of enlightenment and entertainment. This book is one of those rare items (fiction or non-fiction) that is so absorbing that I found myself checking the number of the last page, not because (as so often happens) I wanted to know how much more I had to wade through, but because I just didn't want it to end too quickly. Be warned, though: this book will almost certainly disrupt your life for whatever time period it takes to finish it! Mr. Guillen, I thank you.

Robert Haaf

Our discussion group has just finished reading this, and the verdict is unanimous: Five Stars! For me, a Registered Nurse, the book brought to life what were once merely dry, colorless historic characters; I can picture them now, thanks to Dr. Guillen's brillant writing.

I've also just finished reading the other reviews recorded here and am glad to see that most others also heartily endorse this fabulous book. But frankly, I'm surprised and shocked at the nastiness of one or two of the other reviews. Literary criticism is one thing; viciousness is another.

Regarding the lack of a bibliography or footnotes, I say: who cares? This book was obviously written for the average, albeit intelligent non scientist like me, it wasn't meant to be a PhD thesis. If you want footnotes, subscribe to the professional journal of the American Mathematics Association, and good luck.

Regarding Dr. Guillen assigning thoughts and emotions to the principals, that's pretty obvious, and hardly sinister. Only an incredibly simple minded person would assume that Dr. Guillen was somehow trying to trick the reader into believing he knew with certainty what was going through the scientists' minds. It was a no brainer to me that Dr. Guillen, with Phd's in Mathematics and Theoretical Physics, would be careful to weave these so effectively in his book only on the basis of his extensive research. Even though there's no bibliography, one can get a sense of the depth and breadth of his resources from the acknowledgements in the beginning of the book.

Regarding errors, who has ever written an error free book? Isn't that what errata sheets are for? In addition, what may seem to be an error may only be an honest difference of opinion about how a technical idea can best be explained to a lay audience. I believe that Dr. Guillen's amazing ability to demystify heady topics that for too long have been understood only by the high priests of science must necessarily involve simplifying things that some close-minded "know it alls", would brand as errors. For example, Dr. Guillen is critized for writing that a circle is a two-dimensional sphere. Well, during our meetings, one member of our group, an engineer, pointed out that a circle drawn on a sheet of paper does exist in a two-dimensional plane. And if you imagine spinning the circle around its diameter, you get a sphere, which is three dimensional.

Here's tha bottom line for me: Five Equations that Changed the World is a unique, fascinating book that taught me a lot about a subject I absolutely hated in school. Now that I've read it, I can see why it was picked Best Book of the Year by Publisher's Weekly. If You buy one book about mathmatics and mathematicians in your lifetime, this should be it! It could change your world too.

Throughout history, innovators in science have risen from obscurity to fame by virtue of some original inspiration. These are the tales of five such pilgrims and their journeys. They are facinating biographical sketches of young boys, some poor or frail, whose life's work brought into clearer focus some aspect of the world around us. In the course of the book the author coaxes us to a better understanding of the state of knowledge before and after these innovators. We learn about gravity through Isaac Newton, hydrodynamic pressure through Bernoulli, electromagnetics from Faraday, thermodynamics from Clausius, and special relativity from Einstein. Michael Guillen's book isn't about equations, or even math, as a quick flip through the pages will illustrate. But the general reader, whom Guilen knows well through his television work, will not be disappointed by the lack of mathmatical notation. Ultimately we come away believing that, understanding the five protagonists, we understand their contribution, ...if not the language of their legacies.

my husband (who is Stanford M.D.)and I(Beloit CollegeB.A.) were both impressed by this book. It shows how easily a great mind can make the jump from noticimg some common occurrence to realizing its application to a vast and important universal application.

Eleven of the 14 reviews give this book 4 and 5 stars. I also give it 5 stars. The book explains how these great men formulated their equations with reasoning and observations. These equations are normally in textbooks without any explanations of their derivations. This book explains their origins that will help students understand them better. Can you understand the derivation of the schrodinger equation when it is discussed in just one page of a chemistry book? I would like to comment on the criticisms of JAYBREY@CONCENTRIC.COM from San Francisco. (1) If you increase the volume of the water behind a damn, the height and the pressure of the water against the damn increases. From this point of view, volume does affect the pressure. (2) You are basically right about friction and the Carnot Cycle. However, if you actually measured the work from an engine, friction would be a factor. I am certain that Dr. Guillen is aware of these two points. Regardless of all complaints, he has our attention. Keep in mind that he is writing for the average layman. I want my grandchildren to read this book. I wish it were available when I started college.