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It Must Be Beautiful: Great Equations of Modern Science
It Must Be Beautiful is a collection of 12 essays on the power and beauty of modern scientific equations by some of the world's foremost scientists and historians. Contributors include Steven Weinberg, Peter Galison, John Maynard Smith, and Frank Wilczek.
300 pages, Paperback
First published February 1, 2002
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About the author
Graham Farmelo
9 books89 followersGraham Farmelo is a senior research fellow at the Science Museum, London and associate professor of physics at Northeastern University, US.
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Displaying 1 - 15 of 15 reviews
February 22, 2010
"It must be beautiful : great equations of modern science"
I know, I know. If I tell you that this book is a collection of essays about a dozen or so equations that occupy a central role in 20th century science, most of you will start edging quietly towards the exits. We all know what to expect: no matter how good the intentions of the editor and contributors, the chances that it's intelligible to the general reader are infinitesimally small. Each author's goal was straightforward - to present his or her equation and to "explain" it to the nonspecialist reader. A "good" explanation should place it in its scientific context, which typically involves explaining its practical and theoretical implications and the reason it's considered important.
Four of the eleven essays achieve this goal admirably, providing a reasonably understandable account in lucid, well-written prose. Three more fell in the "honorable effort" category - though the authors weren't entirely successful in explaining the science, the essays were interesting nonetheless (authors in this group tended to distract the reader by focusing on the scientific personalities rather than the science; at least they managed to be reasonably entertaining). Of the remaining four essays, two were disappointingly murky - the authors seemed unable to write about the science in an accessible manner (it seems only fair to point out that some equations were undoubtedly intrinsically harder to explain than others, so the authors may not be completely to blame). The remaining two chapters had no business being in the book at all, in my opinion, as the "equations" they dealt with were essentially bogus (details below).
The central eleven chapters are flanked by an introduction by the editor, Graham Farmelo (who also contributed an essay on the Planck-Einstein equation for the energy of a quantum) and concluding remarks from Physics Nobel laureate Steven Weinberg. The dullness of Farmelo's introduction is more than compensated for by the lucidity and intelligence of Weinberg's contribution. One of the reasons Farmelo fails to impress is his insistence on trying to justify the book's title, despite its being a complete red herring. Even if we could agree on just what exactly constitutes "beauty" in an equation, it wouldn't apply to every equation in the book by any stretch of the imagination. Not that it matters - the equations are what they are, some appear elegantly simple, others are messy - whether or not they attain some ill-defined notion of beauty is highly debatable, but essentially unimportant.
So what do you get for your $16.95 (possibly less, as the book was first published in 2002)? Arranged in approximately descending order of quality:
"The Best Possible Time to be Alive" : Robert May's extraordinarily lucid account of the use of the logistic function to model the dynamics of animal populations, how some parameter values lead to a stable equilibrium, while others lead to chaos, is completely brilliant. I'd give my right arm to have written anything remotely as smart just once in my life.
"Understanding Information Bit by Bit" : Igor Aleksandr gives an excellent account of the two equations that form the basis of Shannon's Information theory - clear, succinct, and (I think) quite accessible to the general reader.
"Equations of Life" : John Maynard Smith on the mathematics of evolution (he offers a game theory formulation)
"The Rediscovery of Gravity" : Roger Penrose explains the Einstein Equation of General Relativity
Less successful, but still pretty good, were -
Peter Galison on the more famous Einstein equation: E = m c-squared
"Hidden Symmetry" : Christine Sutton on the Yang-Mills equation (which governs motion in the Yang-Mills field) - one can think of it roughly as an extension of Maxwell's electromagnetic equations to include the isospin of the relevant particles.
In "Erotica, Aesthetics, and Schrodinger's Wave Equation", Arthur I. Miller devotes far more time to discussing the (difficult) relationship between Schrodinger and Heisenberg than to exposition of the equation that bears their names.
Frank Wilcek's discussion of the Dirac equation can best be described as confusing, with occasional appeals to mysticism. I got the impression this might be unavoidable.
The first essay in the book, dealing with the Planck-Einstein equation for the energy off a quantum, was written by the book's editor, Graham Farmelo. It is, unfortunately, one of the weakest. Farmelo seems unable to give a clear exposition, so he falls back on the old standby of giving the reader lots of biographical tidbits from the lives of Einstein and Planck, respectively.
The book contains two other essays, neither of which has strong justification for being included. I'm guessing that their inclusion is probably a reflection of a certain kind of political stance shared by the majority of the contributors and the publisher, Granta. One of the pieces discusses the realization by chemists Mario Molina and Sherry Rowland that repeated use of chlorofluorocarbons (CFCs) was contributing to erosion of the ozone layer. Which is a fine and interesting topic, except that there is no relevant equation to describe or quantify it, so that there is no particular reason for it to be in this book. The "equation" in the remaining chapter, given over to a discussion of the search for extra-terrestrial intelligence (SETI) is not, strictly speaking an equation at all. Rather it is a formula, proposed by astronomer Frank Drake, to develop an estimate of the number of radio-emitting civilizations in the galaxy. Drake's suggestion was to take it as the product of a bunch of other factors (seven in all), many of which are also unknown and must be guessed at. Drake's equation may have appealed to the likes of Carl Sagan, but as an expression of any kind of scientific reality it has no validity whatsoever. I found its inclusion in the book just plain weird.
Despite my reservations, the four "good" essays in the book are so astonishingly good that I strongly recommend it.
I know, I know. If I tell you that this book is a collection of essays about a dozen or so equations that occupy a central role in 20th century science, most of you will start edging quietly towards the exits. We all know what to expect: no matter how good the intentions of the editor and contributors, the chances that it's intelligible to the general reader are infinitesimally small. Each author's goal was straightforward - to present his or her equation and to "explain" it to the nonspecialist reader. A "good" explanation should place it in its scientific context, which typically involves explaining its practical and theoretical implications and the reason it's considered important.
Four of the eleven essays achieve this goal admirably, providing a reasonably understandable account in lucid, well-written prose. Three more fell in the "honorable effort" category - though the authors weren't entirely successful in explaining the science, the essays were interesting nonetheless (authors in this group tended to distract the reader by focusing on the scientific personalities rather than the science; at least they managed to be reasonably entertaining). Of the remaining four essays, two were disappointingly murky - the authors seemed unable to write about the science in an accessible manner (it seems only fair to point out that some equations were undoubtedly intrinsically harder to explain than others, so the authors may not be completely to blame). The remaining two chapters had no business being in the book at all, in my opinion, as the "equations" they dealt with were essentially bogus (details below).
The central eleven chapters are flanked by an introduction by the editor, Graham Farmelo (who also contributed an essay on the Planck-Einstein equation for the energy of a quantum) and concluding remarks from Physics Nobel laureate Steven Weinberg. The dullness of Farmelo's introduction is more than compensated for by the lucidity and intelligence of Weinberg's contribution. One of the reasons Farmelo fails to impress is his insistence on trying to justify the book's title, despite its being a complete red herring. Even if we could agree on just what exactly constitutes "beauty" in an equation, it wouldn't apply to every equation in the book by any stretch of the imagination. Not that it matters - the equations are what they are, some appear elegantly simple, others are messy - whether or not they attain some ill-defined notion of beauty is highly debatable, but essentially unimportant.
So what do you get for your $16.95 (possibly less, as the book was first published in 2002)? Arranged in approximately descending order of quality:
"The Best Possible Time to be Alive" : Robert May's extraordinarily lucid account of the use of the logistic function to model the dynamics of animal populations, how some parameter values lead to a stable equilibrium, while others lead to chaos, is completely brilliant. I'd give my right arm to have written anything remotely as smart just once in my life.
"Understanding Information Bit by Bit" : Igor Aleksandr gives an excellent account of the two equations that form the basis of Shannon's Information theory - clear, succinct, and (I think) quite accessible to the general reader.
"Equations of Life" : John Maynard Smith on the mathematics of evolution (he offers a game theory formulation)
"The Rediscovery of Gravity" : Roger Penrose explains the Einstein Equation of General Relativity
Less successful, but still pretty good, were -
Peter Galison on the more famous Einstein equation: E = m c-squared
"Hidden Symmetry" : Christine Sutton on the Yang-Mills equation (which governs motion in the Yang-Mills field) - one can think of it roughly as an extension of Maxwell's electromagnetic equations to include the isospin of the relevant particles.
In "Erotica, Aesthetics, and Schrodinger's Wave Equation", Arthur I. Miller devotes far more time to discussing the (difficult) relationship between Schrodinger and Heisenberg than to exposition of the equation that bears their names.
Frank Wilcek's discussion of the Dirac equation can best be described as confusing, with occasional appeals to mysticism. I got the impression this might be unavoidable.
The first essay in the book, dealing with the Planck-Einstein equation for the energy off a quantum, was written by the book's editor, Graham Farmelo. It is, unfortunately, one of the weakest. Farmelo seems unable to give a clear exposition, so he falls back on the old standby of giving the reader lots of biographical tidbits from the lives of Einstein and Planck, respectively.
The book contains two other essays, neither of which has strong justification for being included. I'm guessing that their inclusion is probably a reflection of a certain kind of political stance shared by the majority of the contributors and the publisher, Granta. One of the pieces discusses the realization by chemists Mario Molina and Sherry Rowland that repeated use of chlorofluorocarbons (CFCs) was contributing to erosion of the ozone layer. Which is a fine and interesting topic, except that there is no relevant equation to describe or quantify it, so that there is no particular reason for it to be in this book. The "equation" in the remaining chapter, given over to a discussion of the search for extra-terrestrial intelligence (SETI) is not, strictly speaking an equation at all. Rather it is a formula, proposed by astronomer Frank Drake, to develop an estimate of the number of radio-emitting civilizations in the galaxy. Drake's suggestion was to take it as the product of a bunch of other factors (seven in all), many of which are also unknown and must be guessed at. Drake's equation may have appealed to the likes of Carl Sagan, but as an expression of any kind of scientific reality it has no validity whatsoever. I found its inclusion in the book just plain weird.
Despite my reservations, the four "good" essays in the book are so astonishingly good that I strongly recommend it.
July 17, 2022
I confess I did not grasp all or even much of this, but the work entertained me. Someone better than I am needs to review it.
July 9, 2011
By "modern science" Farmelo means the era since Maxwell's equations. He focuses primarily on the equations of physics, with a smattering of astronomy, biology/ecology, and chemistry.
As often happens, the book's title isn't paid off very well. The grand theme is really "A biography of the discovery of the major physics equations of the 20th Century." The concept of beauty and mathematical elegance is discussed, but not in any meaningful detail.
Was it Justice Stewart who said "I can't describe it, but I know it when I see it?" I get the feeling the author subscribes to that notion. There is a lot of room left for someone to compare equations and their derivations, and find principles of beauty and truth therein.
Perhaps if the editor had focused a bit more on pure mathematics branches and/or broadened his timeframe, he would have found more material from which to generalize. And since the essays didn't really deal with the beauty of the equations, his Foreward could have been much more substantial.
All that said, the book is a good one, well written and a lot of interesting sidebar info.
As often happens, the book's title isn't paid off very well. The grand theme is really "A biography of the discovery of the major physics equations of the 20th Century." The concept of beauty and mathematical elegance is discussed, but not in any meaningful detail.
Was it Justice Stewart who said "I can't describe it, but I know it when I see it?" I get the feeling the author subscribes to that notion. There is a lot of room left for someone to compare equations and their derivations, and find principles of beauty and truth therein.
Perhaps if the editor had focused a bit more on pure mathematics branches and/or broadened his timeframe, he would have found more material from which to generalize. And since the essays didn't really deal with the beauty of the equations, his Foreward could have been much more substantial.
All that said, the book is a good one, well written and a lot of interesting sidebar info.
August 6, 2015
Good, not great, or perhaps my math skills just aren't quite up to the level of this book as some of it was way beyond my abilities. I do love the title, and wish I was capable of writing a book like this. Mine would be titled It Must Be Elegant: Great Equations that are Beautiful and that I Understand!
February 17, 2023
Maravilloso libro que explica muy bien cuales son las ecuaciones que nos gobiernan hoy en muchos aspectos de la física, la biología, etc. Me hubiese gustado que abordase un poco el tema del comportamiento humano. Como lo hubiese disfrutado en la adolescencia un libro de este estilo.
November 20, 2023
This is a nice collection of essays about some beautiful equations, edited by the author of a biography of Dirac. Not every equation is fully explained, but there's great history and big-picture explanation. The authors are frequently major contributors to the fields.
July 7, 2018
Enjoyable overall, but unfortunately a little lighter on the math than I’d expect and hope from the title.
July 7, 2007
If you can make it through the first essay (a dense and difficult chapter by one of the great physicists of our time), you cannot help but appreciate the significance and beauty of modern science and its expression through mathematics. And, the piece on the equations behind the strong force is almost lyrically lovely.
July 2, 2011
The book is a collection of essays by different authors. Some of the essays are outstanding (deserving a high rating), a few are really dull, and the rest are mixed. One essay, that looked like it was going to be the most interesting finished with a few pages of philosophical musing that almost put me to sleep.
December 23, 2015
I am no scientist. I found the essays informative and educational. Almost all were well-written. I consider two essays weak: Schrodinger's equation and Dirac's equation. It is no critique of the equations, only the essayists.
I need to reread these again (maybe many times) to fully grasp the science.
I need to reread these again (maybe many times) to fully grasp the science.
August 7, 2010
Contains some excellent, thought-provoking essays by leading scientists. Tempted to start reading from the beginning again.
June 11, 2011
Stimulating introductions to important equations in different subjects clearly written by experts.
August 2, 2011
Occassionally authors go overboard in praise of the scientists who derived the equation. Good book otherwise.
May 7, 2015
Definitely interesting, but some of it went over my head, especially the physics. It's also about the people involved, so you don't have to understand all the technical details
June 2, 2019
elucidating. i read/bought the hard back. i don't think it's any different.
Displaying 1 - 15 of 15 reviews