In the publishing industry there is a general rule-of-thumb that every mathematical equation included in a book will cut the audience of science books written for a popular audience in half – presumably in a geometric progression. This typically means that including even a handful of equations will give you an effective readership of zero – something no author and certainly no editor or publisher wants.
I suspect that there is a corollary to this that every picture included in the text will help to increase your readership, though possibly not by as proportionally a large amount.
In any case, while reading Melanie Mitchell’s text Complexity: A Guided Tour [Cambridge University Press, 2009] this weekend, I noticed that, in what appears to be a concerted effort to include an equation without technically writing it into the text and to simultaneously increase readership by including a picture, she cleverly used a picture of Boltzmann’s tombstone in Vienna! Most fans of thermodynamics will immediately recognize Boltzmann’s equation for entropy, , which appears engraved on the tombstone over his bust.
Page 51 of Melanie Mitchell’s book “Complexity: A Guided Tour” featuring Boltzmann’s tombstone in Vienna.
I hope that future mathematicians, scientists, and engineers will keep this in mind and have their tombstones engraved with key formulae to assist future authors in doing the same – hopefully this will help to increase the amount of mathematics that is deemed “acceptable” by the general public.
Gregory Chaitin’s book Proving Darwin: Making Biology Mathematical combining biology, microbiology, mathematics, evolution and even information theory is directly in my wheelhouse. I had delayed reading it following a few initial poor reviews, and sadly I must confirm that I’m ultimately disappointed in the direct effort shown here, though there is some very significant value buried within. Unfortunately the full value is buried so deeply that very few, if any, will actually make the concerted effort to find it.
This effort does seem to make a more high-minded and noble attempt than what I would call the “Brian Greene method” in which an academic seemingly gives up on serious science to publish multiple texts on a popular topic to cash in on public interest in that topic through sales of books. In this respect Chaitin is closer to Neil deGrasse Tyson in his effort to expound an interesting theory to the broader public and improve the public discourse, though I would admit he’s probably a bit more (self-) interested in pushing his own theory and selling books (or giving him the benefit of the doubt, perhaps the publisher has pushed him to this).
Though there is a reasonable stab at providing some philosophical background to fit the topic into the broader fabric of science and theory in the later chapters, most of it is rather poorly motivated and is covered far better in other non-technical works. While it is nice to have some semblance of Chaitin’s philosophy and feelings, the inclusion of this type of material only tends to soften the blow of his theoretical work and makes the text read more like pseudo-science or simple base philosophy without any actual rigorous underpinning.
I’m assuming that his purpose in writing the book is to make the theories he’s come up with in his primary paper on the topic more accessible to the broader community of science as well as the public itself. It’s easy for a groundbreaking piece of work to be hidden in the broader scientific literature, but Chaitin seems to be taking his pedestal as a reasonably popular science writer to increase the visibility of his work here. He admittedly mentions that his effort stems from his hobby as his primary area is algorithmic information theory and computer science and not biology or evolution, though his meager references in the text do at least indicate some facility with some of the “right” sources in these latter areas.
Speaking from a broad public perspective, there is certainly interest in this general topic to warrant such a book, though based on the reviews of others via Amazon, Goodreads, etc. the book has sadly missed it’s mark. He unfortunately sticks too closely to the rule that inclusion of mathematical equations is detrimental to the sale of ones books. Sadly, his broader point is seemingly lost on the broader public as his ability to analogize his work isn’t as strong as that of Brian Greene with respect to theoretical physics (string theory).
From the a higher perspective of a researcher who does work in all of the relevant areas relating to the topic, I was even more underwhelmed with the present text aside from the single URL link to the original much more technical paper which Chaitin wrote in 2010. To me this was the most valuable part of the entire text though he did provide some small amount of reasonable detail in his appendix.
I can certainly appreciate Chaitin’s enthusiastic following of John von Neumann but I’m disappointed in his lack of acknowledgement of Norbert Weiner or Claude Shannon who all collaborated in the mid part of the 20th century. I’m sure Chaitin is more than well aware of the father of information theory, but I’ll be willing to bet that although he’s probably read his infamous master’s thesis and his highly influential Bell Labs article on “A/The Mathematical Theory of Communication”, he is, like most, shamefully and wholly unaware of Shannon’s MIT doctoral thesis.
Given Chaitin’s own personal aim to further the acceptance of his own theories and work and the goal of the publisher to sell more copies, I would mention a few recommendations for future potential editions:
The greater majority of his broader audience will have at least a passably reasonable understanding of biology and evolution, but very little, if any, understanding of algorithmic information theory. He would be better off expounding upon this subject to bring people up to speed to better understand his viewpoint and his subsequent proof. Though I understand the need to be relatively light in regard to the number of equations and technicalities included, Chaitin could follow some of his heroes of mathematical exposition and do a slightly better job of explaining what is going on here. He could also go a long way toward adding some significant material to the appendices to help the higher end general readers and the specifically the biologists understand more of the technicalities of algorithmic information theory to better follow his proof which should appear in intricate glory in the appendix as well. I might also recommend excising some of the more philosophical material which tends to undermine his scientific “weight.” Though I found it interesting that he gives a mathematical definition of “intelligent design”, I have a feeling its intricacies were lost on most of his readership — this point alone could go a long way towards solidifying the position of evolution amongst non-scientists, particularly in America, and win the support of heavyweights like Dawkins himself.
I’ll agree wholeheartedly with one reviewer who said that Chaitin tends to “state small ideas repeatedly, and every time at the same shallow level with astonishing amount of redundancy (mostly consisting of chit-chat and self congratulations)”. This certainly detracted from my enjoyment of the work. Chaitin also includes an awful lot of name dropping of significant scientific figures tangential to the subject at hand. This may have been more impressive if he included the results of his discussions with them about the subject, but I’m left with the impression that he simply said hello, shook their hands, and at best was simply inspired by his having met them. It’s nice that he’s had these experiences, but it doesn’t help me to believe or follow his own work.
Though I would certainly agree that we could use a mathematical proof of evolution, and that Chaitin has made a reasonable theoretical stab, this book sadly wasn’t the best one to motivate broader interest in such an effort. I’ll give him five stars for effort, three for general content, but in the end, for most it will have to be at most a 2 star work overall.
Overall James Gleick’s book The Information: a History, a Theory, a Flood is an excellent read. Given that it’s an area with which I’m intimately interested, I’m not too surprised that most of it is “review”, but I’d highly recommend it to the general public to know more about some of the excellent history, philosophy, and theory which Gleick so nicely summarizes throughout the book.
There are one or two references in the back which I’ll have to chase down and read and one or two, which after many years, seem like they may be worth a second revisiting after having completed this.
Even for the specialist, Gleick manages to tie together some disparate thoughts to create an excellent whole which makes it a very worthwhile read. I found towards the last several chapters, Gleick’s style becomes much more flowery and less concrete, but most of it is as a result of covering the “humanities” perspective of information as opposed to the earlier parts of the text which were more specific to history and the scientific theories he covered.
Proofiness: The Dark Arts of Mathematical Deception
Charles Seife
Mathematics, Popular Science
Penguin
September 23, 2010
Hardcover
320
The bestselling author of Zero shows how mathematical misinformation pervades-and shapes-our daily lives. According to MSNBC, having a child makes you stupid. You actually lose IQ points. Good Morning America has announced that natural blondes will be extinct within two hundred years. Pundits estimated that there were more than a million demonstrators at a tea party rally in Washington, D.C., even though roughly sixty thousand were there. Numbers have peculiar powers-they can disarm skeptics, befuddle journalists, and hoodwink the public into believing almost anything. "Proofiness," as Charles Seife explains in this eye-opening book, is the art of using pure mathematics for impure ends, and he reminds readers that bad mathematics has a dark side. It is used to bring down beloved government officials and to appoint undeserving ones (both Democratic and Republican), to convict the innocent and acquit the guilty, to ruin our economy, and to fix the outcomes of future elections. This penetrating look at the intersection of math and society will appeal to readers of Freakonomics and the books of Malcolm Gladwell.
Charles Seife doesn’t prove that mathematics is essential for a democracy, but he certainly shows how the lack of proper use of mathematics can fray heavily at the edges!
Proofiness was a great book to have read over a long Fourth of July holiday. Though many people may realize some of the broad general concepts in the book, it’s great to have a better structure for talking about concepts like Potemkin numbers, disestimation, fruit packing, cherry picking, apple polishing, comparing apples to oranges, causuistry, randnumbness, regression to the moon, tragedy of the commons, and moral hazard among others. If you didn’t think mathematics was important to daily life or our democratic society, this book will certainly change your mind.
Seife covers everything from polls, voting, politics, economics, marketing, law, and even health to show how numbers are misused in a modern world that can ill-afford to ignore what is really going on around us.
This is a fantastic book for nearly everyone in the general public, but I’d highly recommend it for high school students while taking civics.
Artin very wisely identifies these matrix groups as more fundamental–and they are. They come up much more in mathematics. Linear algebra is the central subject of mathematics. You cannot learn too much linear algebra. That’s the basic principle for all of you going on in mathematics.
Linear algebra is presented as sort of stupid stuff, [but] you cannot learn too much linear algebra.
Benedict Gross, Ph.D., George Vasmer Leverett Professor of Mathematics, Harvard University
in Abstract Algebra, Lecture 2 at 14:25 via Harvard Extension
Popular physics has enjoyed a new-found regard. Now comes a brave attempt to inject mathematics into an otherwise fashionable subject
This review of Brian Cox and Jeff Forshaw’s forthcoming book The Quantum Universe: Everything That Can Happen Does Happen sounds intriguing. I’m highly impressed that so much of the review focuses on the author’s decision to include a more mathematical treatment of their subject for what is supposed to be a popular science book. I always wish books like these at least had the temerity to include much more in the way of the mathematical underpinnings of their subjects; I’m glad that the popular press (or at least The Economist in this case) is willing to be asking for the mathematics as well. Hopefully it will mark a broader trend in popular books on scientific topics!
Fundamental physics
Big bang
Popular physics has enjoyed a new-found regard. Now comes a brave attempt to inject mathematics into an otherwise fashionable subject
PREVIOUSLY the preserve of dusty, tweed-jacketed academics, physics has enjoyed a surprising popular renaissance over the past few years. In America Michio Kaku, a string theorist, has penned several successful books and wowed television and radio audiences with his presentations on esoteric subjects such as the existence of wormholes and the possibility of alien life. In Britain Brian Cox, a former pop star whose music helped propel Tony Blair to power, has become the front man for physics, which recently regained its status as a popular subject in British classrooms, an effect many attribute to Mr Cox’s astonishing appeal.
Mr Cox, a particle physicist, is well-known as the presenter of two BBC television series that have attracted millions of viewers (a third series will be aired next year) and as a bestselling author and public speaker. His latest book, “The Quantum Universe”, which he co-wrote with Jeff Forshaw of the University of Manchester, breaks the rules of popular science-writing that were established over two decades ago by Stephen Hawking, who launched the modern genre with his famous book, “A Brief History of Time”.
Mr Hawking’s literary success was ascribed to his eschewing equations. One of his editors warned him that sales of the book would be halved by every equation he included; Mr Hawking inserted just one, E=mc2, and, even then, the volume acquired a sorry reputation for being bought but not read. By contrast, Mr Cox, whose previous book with Mr Forshaw investigated “Why does E=mc2?” (2009), has bravely sloshed a generous slug of mathematics throughout his texts.
The difficulties in explaining physics without using maths are longstanding. Einstein mused, “The eternal mystery of the world is its comprehensibility,” and “the fact that it is comprehensible is a miracle.” Yet the language in which the world is described is that of maths, a relatively sound grasp of which is needed to comprehend the difficulties that physicists are trying to resolve as well as the possible solutions. Mr Cox has secured a large fan base with his boyish good looks, his happy turns of phrase and his knack for presenting complex ideas using simple analogies. He also admirably shies away from dumbing down. “The Quantum Universe” is not a dry undergraduate text book, but nor is it a particularly easy read.
The subject matter is hard. Quantum mechanics, which describes in subatomic detail a shadowy world in which cats can be simultaneously alive and dead, is notoriously difficult to grasp. Its experiments yield bizarre results that can be explained only by embracing the maths that describe them, and its theories make outrageous predictions (such as the existence of antimatter) that have nevertheless later been verified. Messrs Cox and Forshaw say they have included the maths “mainly because it allows us to really explain why things are the way they are. Without it, we should have to resort to the physicist-guru mentality whereby we pluck profundities out of thin air, and neither author would be comfortable with guru status.”
That stance might comfort the authors, but to many readers they will nonetheless seem to pluck equations out of thin air. Yet their decision to include some of the hard stuff leaves open the possibility that some readers might actually engage in the slog that leads to higher pleasures. For non-sloggers alternative routes are offered: Messrs Cox and Forshaw use clockfaces to illustrate how particles interact with one another, a drawing of how guitar strings twang and a photograph of a vibrating drum. A diagram, rather than an equation, is used to explain one promising theory of how matter acquires mass, a question that experiments on the Large Hadron Collider at CERN, the European particle-physics laboratory near Geneva, will hopefully soon answer.
The authors have wisely chosen to leaven their tome with amusing tales of dysfunctional characters among scholars who developed quantum mechanics in the 1920s and beyond, as well as with accounts of the philosophical struggles with which they grappled and the occasional earthy aside. Where the subject matter is a trifle dull, Messrs Cox and Forshaw acknowledge it: of Heinrich Kayser, who a century ago completed a six-volume reference book documenting the spectral lines generated by every known element, they observe, “He must have been great fun at dinner parties.” And they make some sweeping generalisations about their colleagues who pore over equations, “Physicists are very lazy, and they would not go to all this trouble unless it saved time in the long run.”
Whether or not readers of “The Quantum Universe” will follow all the maths, the authors’ love for their subject shines through the book. “There is no better demonstration of the power of the scientific method than quantum theory,” they write. That may be so, but physicists all over the world, Messrs Cox and Forshaw included, are longing for the next breakthrough that will supersede the claim. Hopes are pinned on experiments currently under way at CERN that may force physicists to rethink their understanding of the universe, and inspire Messrs Cox and Forshaw to write their next book—equations and all.
This must certainly be the quote of the week from English author Alan Bennett’s play Forty Years On:
Foster: I’m still a bit hazy about the Trinity, sir. Schoolmaster: Three in one, one in three, perfectly straightforward. Any doubts about that see your maths master.
Living systems are distinguished in nature by their ability to maintain stable, ordered states far from equilibrium. This is despite constant buffeting by thermodynamic forces that, if unopposed, will inevitably increase disorder. Cells maintain a steep transmembrane entropy gradient by continuous application of information that permits cellular components to carry out highly specific tasks that import energy and export entropy. Thus, the study of information storage, flow and utilization is critical for understanding first principles that govern the dynamics of life. Initial biological applications of information theory (IT) used Shannon's methods to measure the information content in strings of monomers such as genes, RNA, and proteins. Recent work has used bioinformatic and dynamical systems to provide remarkable insights into the topology and dynamics of intracellular information networks. Novel applications of Fisher-, Shannon-, and Kullback-Leibler informations are promoting increased understanding of the mechanisms by which genetic information is converted to work and order. Insights into evolution may be gained by analysis of the the fitness contributions from specific segments of genetic information as well as the optimization process in which the fitness are constrained by the substrate cost for its storage and utilization. Recent IT applications have recognized the possible role of nontraditional information storage structures including lipids and ion gradients as well as information transmission by molecular flux across cell membranes. Many fascinating challenges remain, including defining the intercellular information dynamics of multicellular organisms and the role of disordered information storage and flow in disease.
…[the reader] should not be discouraged, if on first reading of section 0, he finds that he does not have the prerequisites for reading the prerequisites.
Paul Halmos (1916 – 2006, Hungarian-born American mathematician
in Measure Theory (1950)
This is essentially the mathematician’s equivalent of the adage “Fake it ’til you make it.”
One must be truly enamored of the internet that it allows one to find and read a copy of Bernhard Riemann’s doctoral thesis Habilitation Lecture (in English translation) at the University of Göttingen from 1854!
His brief paper has created a tsunami of mathematical work and research in the ensuing 156 years. It has ultimately become one of the seminal works in the development of the algebra and calculus of n-dimensional manifolds.
In the 1930s, a French mathematician began writing journal articles and books. His name was Nicolas Bourbaki. He didn’t exist.
Bourbaki was and is actually a group of brilliant and influential mathematicians, mostly French but not all, whose membership changes but whose collective purpose remains the same: to write about mathematical topics they deem important. Between 1939 and 1967 “he” wrote a series of influential books about these selected topics, collectively called Elements of Mathematics.
A mysterious, mostly anonymous group of writers publishing momentous things under a single name is just really cool. But don’t try to read any of his stuff unless you are an expert mathematician.
Instead, read a wonderful story by novelist and award-winning chemist Carl Djerassi, called The Bourbaki Gambit. What do you think happens when a group of scientists, being discriminated against for various reasons, team up and use the “Bourbaki” approach to try to get their latest discovery taken seriously?
There’s an old mathematicians’ joke that goes like this:
Q: When did Nicholas Bourbaki quit writing books about mathematics?
A: When (t)he(y) realized that Serge Lang was only one person!
Holy cow! I discovered on Friday that Terence Tao, a Fields Medal winner, will be teaching a graduate level Real Analysis class this fall at UCLA.
Surprisingly, to me, it ony has 4 students currently enrolled!! Having won a Fields Medal in August 2006, this is a true shock, for who wouldn’t want to learn analysis from such a distinguished professor? Are there so few graduate students at UCLA who need a course in advanced analysis? I would imagine that there would be graduate students in engineering and even physics who might take such a course, but perhaps I’m wrong?
Most of his ratings on RateMyProfessors are actually fairly glowing; the one generally negative review was given for a topology class and generally seems to be an outlier.
On his own website in a section about the class and related announcements we seem to find the answer to the mystery about enrollment. There he says:
I intend this to be a serious course, focused on teaching the material in the course description. As such, students who are taking or auditing the course out of idle curiosity or mathematical “sightseeing”, rather than to learn the basics of measure theory and integration theory, may be disappointed. I would therefore prefer that frivolous enrollments in the class be kept to a minimum.
This is generally sound advice, but would even the most serious mathematical tourists really bother to make an attempt at such an advanced course? Why bother if you’re not going to do the work?!
R. A. Gatenby, B. R. Frieden