Ian Stewart Delivers... again

I’ve read 4 popular math books already this year and they’ve all been great… though all very different. What a quick start to the new year!

Ian Stewart volumes are consistently good, but with that said there’s also a certain “sameness” to his prolific work — popular topics treated with clarity and wisdom, but not necessarily terribly new, inspiring, or original; just clear basic elucidation. So I was hesitant to read his latest volume (out in 2019, but more readily available in the U.S. now) with a title, “Do Dice Play God?” (a play off an Einstein quote, and also off an earlier book he wrote), which I found a little too ‘cutesy.’ and not all that informative of the content. 

However, I not only thoroughly enjoyed this volume, but consider it one of his best, and most important yet… not because it’s any more original or otherwise outstanding than Stewart's other writing, but because he is covering some of the most currently important topics for the lay public: statistics, probability, uncertainty (and how they relate to critical thinking) — indeed this is likely the best volume I’ve seen for presenting these crucial subjects to a general audience, and Stewart isn’t even a statistician by profession (and professional statisticians may find technical flaws in his text). The range of topics and examples, even though well-worn, is great and lucidly presented. I think many will be surprised at just how good (and relevant) it is! Not sure, but I suspect this Stewart effort may have been partly overshadowed in 2019 by the release of David Spiegelhalter's also-excellent (and somewhat more technical) volume, "The Art of Statistics."

If you’re already ensconced in the nuances and debates involving statistics these days you won’t find much new or original in this volume, but for the mass public this is a fantastic introduction (and there are many good ones) to these important concerns — Stewart offers just enough detail without diving too deep into the weeds to leave readers behind (although admittedly, some numeracy is required). Moreover, at various points he also moves the discussion away from abstraction and theory, to stress how prediction, probability, and uncertainty are especially pertinent to our daily lives and current societal issues.

One interesting sidenote to me: toward the end of the book Stewart ambles off into a number of more complex theoretical physics topics, and this is a trend I’ve been seeing in a number of math books… focusing more-than-usual, at some point, on physics. Perhaps just my imagination, but it seems as if the linkages between math and physics (always strong of course) are becoming even more central to both fields as time goes on. Physics has always recognized the foundational basis of mathematics, but more and more the linkages between the two fields seem to be feeding back-and-forth off of one another in pursuit of new insights (just my impression).

Anyway, if you’ve been wanting a primer on what all the fuss is about in statistics these days (or you know someone who needs such), read this book (or buy it for a friend).
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...I'll soon be posting a review of Matt Cook's highly-entertaining "Sleight of Mind" (with an end-of-March publication date), but the next volume in my reading queue looks to be another fascinating 2019 read, a biography of James Simon, "The Man Who Solved the Market."

n-body problems

Sunday reflection:

"...a lot of effort was devoted to the three-body problem: the motion of a system consisting of three point masses (such as Sun, Earth, Moon) moving under Newtonian gravitation. It's easy enough to write down the appropriate equations of motion; but immensely harder to solve them... As an aside: it has been said that one can gauge the progress of science by the value of n for which the n-body problem cannot be solved. In Newtonian mechanics the 3-body problem appears to be insoluble. In Relativity, it is the 2-body problem that causes trouble. Quantum Theory gets hung up on the 1-body problem (a particle); and Relativistic Quantum Field Theory runs into trouble with the 0-body problem (the vacuum)!"
                                                                                -- Ian Stewart

Healthy Mathematics

This Sunday reflection from Ian Stewart in the 2nd edition (1992) of “The Problems of Mathematics”:

“Some observers have professed to detect, in the variety and freedom of today’s mathematics, symptoms of decadence and decline. They tell us that mathematics has fragmented into unrelated specialties, has lost its sense of unity, and has no idea where it is going. They speak of a ‘crisis’ in mathematics, as if the whole subject has collectively taken a wrong turning. There is no crisis. Today’s mathematics is healthy, vigorous, unified, and as relevant to the rest of human culture as it ever was… If there appears to be a crisis, it is because the subject has become too large for any single person to grasp… today’s mathematics is not some outlandish aberration: it is a natural continuation of the mathematical mainstream. It is abstract and general, and rigorously logical, not out of perversity, but because this appears to be the only way to get the job done properly. It contains numerous specialties, like most sciences nowadays, because it has flourished and grown. Today’s mathematics has succeeded in solving problems that baffled the greatest minds of past centuries. Its most abstract theories are currently finding new applications to fundamental questions in physics, chemistry, biology, computing, and engineering. Is this decadence and decline? I doubt it.”

Science Is Provisional... And Mathematics a Luxury

Sunday reflection:

“That’s how real science advances… Three steps forward, two steps back. Mathematicians have the luxury of living in a logical bubble, where once something is proved true, it remains true. Interpretations and proofs may change, but the theorems don’t get unproved by later discoveries. Though they may become obsolete or irrelevant to current concerns. Science is always provisional, only as good as the current evidence. In response to such evidence, scientists reserve the right to change their minds.”

— Ian Stewart in Epilogue to “Calculating the Cosmos”

Mathematicians Undaunted...

Sunday reflection:

"[Andrew] Wiles's landmark proof of Fermat's last theorem amounted to about one hundred pages of highly technical mathematics, prompting the science journalist John Horgan to write a provocative article titled "The Death of Proof." Horgan assembled a variety of reasons why proofs were becoming obsolete, including the rise of the computer, the disappearance of proofs from school math, and the existence of blockbusters like Wiles's. It was an interesting attempt to wrench defeat from the jaws of victory, to treat a historic achievement as bad news. Yes, we put a man on the moon, but look at all the valuable rocket fuel we had to use up.
"Wiles's proof may be a blockbuster, but it tells a ripping yarn. He had to use massive mathematical machinery for so simple a question, much as a physicist needs a particle accelerator many miles in circumference to study a quark. But far from being sloppy and unwieldy, his proof is rich and beautiful. Those hundred pages have a plot, a story line. An expert can skim through the details and follow the narrative, with its twists and turns of logic, and its strong element of suspense: will the hero overcome the last theorem in the final pages, or will the ghost of Fermat continue to taunt the mathematical profession? No one declared literature dead because War and Peace was rather long or because Finnegans Wake was not being read in schools. Professional mathematicians can handle a hundred pages of proof. Even ten thousand pages -- the total length of the classification theorem for finite simple groups, combining the work of dozens of people over a decade or more -- does not daunt them."

-- Ian Stewart, from "Letters to a Young Mathematician"


(p.s... sometime tomorrow I'll likely have a review of the new John Conway biography posted at MathTango)  ...Now HERE.

Parochial Math

Today's 'Sunday reflection' from Ian Stewart, in "Letters to a Young Mathematician":

"I think human math is more closely linked to our particular physiology, experiences, and psychological preferences than we imagine. It is parochial, not universal. Geometry's points and lines may seem the natural basis for a theory of shape, but they are also the features into which our visual system happens to dissect the world. An alien visual system might find light and shade primary, or motion and stasis, or frequency of vibration. An alien brain might find smell, or embarrassment, but not shape, to be fundamental to its perception of the world. And while discrete numbers like 1, 2, 3, seem universal to us, they trace back to our tendency to assemble similar things, such as sheep, and consider them property: has one of my sheep been stolen?...

"What is mathematics? It is the shared social construct created by people who are aware of certain opportunities, and we call those people mathematicians. The logic is still slightly circular, but mathematicians can always recognize a fellow spirit."


[p.s... also, another new interview up at MathTango this morning!]

God, Is She a Geometer?...

"Our minds may indeed be just swirls of electrons in nerve cells; but those cells are part of the universe, they evolved within it, and they have been molded by Nature's deep love affair with symmetry. The swirls of electrons in our heads are not random, not arbitrary, and not -- even in a godless universe, if that is what it is -- an accident. They are patterns that have survived millions of years of Darwinian selection for congruence with reality....
"Perhaps we have created a geometer God in our own image, but we have done it by exploiting the basic simplicities that nature supplied when our brains were evolving. Only a mathematical universe can develop brains that do mathematics. Only a geometer God can create a mind that has the capacity to delude itself that a geometer God exists.
"In that sense, God is a mathematician; and She's a lot better at it than we are. Every so often, She lets us peek over her shoulder."

-- Ian Stewart in "Letters To a Young Mathematician"


[…If you have a favorite math-related passage that might make a nice Sunday morning reflection here let me know (SheckyR@gmail.com). If I use one submitted by a reader, I'll cite the contributor.]   

A Sunday Reflection in One Sentence

Friday, at MathTango I posted the longest math potpourri I've ever done... To compensate, today's Sunday reflection is the shortest passage I've ever used ;-):

"As mathematicians the world over say, everything is either impossible or trivial."

-- from Ian Stewart's charming, "Letters to a Young Mathematician"

Bridging Art and Science... Mathematics

Long, wonderful, thought-provoking, almost rambling article from Ian Stewart last month in New Scientist on "the power and glory of mathematics":

http://www.newstatesman.com/sci-tech/2013/05/third-culture-power-and-glory-mathematics

Beginning with reference to a classic 1959 C.P. Snow lecture, Stewart argues that mathematics, unlike almost any other field of study, "spans the divide" between the arts and sciences, and makes many interesting points along the way.

Some excerpts to poke your interest…:

"...the mathematical subculture is gravely misunderstood by most members of the public, many prominent scientists, nearly all artists, the vast majority of politicians and almost every bureaucrat on the planet."

"For mathematics to be useful in today’s society, it has to be invisible. If anyone using a mobile phone had been required first to take a PhD in mathematics, the device would never have appealed to a large enough market to make it worth anyone’s while to manu­facture. However, without a significant number of engineers who know some very advanced and apparently esoteric mathematics, mobile phones wouldn’t work."

"If 10 per cent of the $9bn spent on Cern’s Large Hadron Collider had been allo­cated to research in the mathematical sciences instead, the benefits to society would have been far greater and would have occurred more rapidly. The development of the next generation of supercomputers, a project estimated to cost about $1bn, is struggling to find funding. The result would be a machine with applications throughout the sciences – for example, in climate change and in the design of new materials and alternative energy sources – and it would dominate future computer technology."

"However, the nature and importance of mathematics do not rest solely on its practical uses or its artistic merit. It has an intrinsic intellectual interest and an idiosyncratic beauty. What makes it so hard to grasp the subject’s nature is that it combines many disparate elements in one ever-growing, ever-changing body of knowledge. It is practical, arcane, precise, obscure, abstruse, rooted in nature, rooted in the human imagination; its history spans 4,000 years, and what was discovered long ago is often just as valid and important today. It is absolutely huge, increasing by a conservative one million pages a year, and it is all one thing.  Its internal connections link entirely different sub-disciplines in an intricate, dynamically changing web, so that yesterday’s dead end may suddenly become today’s essential technique."

 Set aside some time to read... and think about... the whole piece.

More Blogs Than You Can Shake a Protractor At

Probability enthusiasts may enjoy this blog, "Probability Puzzles," that I've only recently discovered (thanks to a @pickover tweet).

http://bayesianthink.blogspot.com/

Or, if your interest is specifically math education, David Wees has put up a list of well over 300 blogs dealing with the subject:

http://davidwees.com/content/mathematics-education-blogs

Great list... many wonderful blogs... finding the time to sort through them all; aye, there's the rub!

...Meanwhile, my review of Ian Stewart's latest book, "Visions of Infinity," is over at MathTango here. (Bottom line: Get it!)

Have a Little Math With Your Weekend

For some weekend entertainment….

Sol Lederman's latest installment of his "Inspired by Math" podcast series is with Ian Stewart, one of the most prolific and widely-known of all modern math popularizers. I've been pleasantly surprised by the degree to which 'math people,' including such prominent and busy ones as Stewart, Keith Devlin, Steven Strogatz and others, are willing to share themselves with the learning community, through such online outlets. It is really wonderful, and I think a reflection of the desire on the part of mathematicians to transform their subject from one that is too-often feared to one for eager engagement. So set aside an hour and listen to Dr. Stewart talk about what inspires him:

http://wildaboutmath.com/2013/01/11/ian-stewart-inspired-by-math-14/

There is also a new math blog in the blog corral of Scientific American: "The Roots of Unity" from Evelyn Lamb; subheading "Mathematics: Learning It, Doing It, Celebrating It" -- looks like it'll be good (and I've added it to the right-hand column links):

http://blogs.scientificamerican.com/roots-of-unity/

Ian Stewart on Black-Scholes

             (Black-Scholes Equation)

Good piece (as usual) from Ian Stewart on some of the mathematics underlying the financial crash:

http://www.guardian.co.uk/science/2012/feb/12/black-scholes-equation-credit-crunch

From the article:

"Anyone who has followed the crisis will understand that the real economy of businesses and commodities is being upstaged by complicated financial instruments known as derivatives. These are not money or goods. They are investments in investments, bets about bets. Derivatives created a booming global economy, but they also led to turbulent markets, the credit crunch, the near collapse of the banking system and the economic slump. And it was the Black-Scholes equation that opened up the world of derivatives."

Stewart Delivers... Again

"Instead of isolated clusters of scientists, obsessed with their own narrow specialty, today's scientific frontiers increasingly require teams of people with diverse, complementary interests. Science is changing from a collection of villages to a worldwide community. And if the story of mathematical biology shows anything, it is that interconnected communities can achieve things that are impossible for their individual members.
Welcome to the global ecosystem of tomorrow's science."

-- the end of Ian Stewart's latest book, "Mathematics of Life"


I received a review copy of Ian Stewart's latest book, "Mathematics of Life," causing me to ask just one simple question: does Dr. Stewart ever sleep!? Stewart is one of the most prolific popular math writers out there, and virtually always worth reading. I won't do a full review since I assume most readers likely already know and enjoy Ian Stewart's works... or, if you don't, than there's nothing I can do or say to cure your malady...

Certainly some of the material in this book has appeared elsewhere in previous Stewart books, but still this book is different (and unlike most popular math writing), in being so focused on the intersection of math and biology; a relationship that is rapidly expanding, but not often concentrated on.

From the title (and Stewart's past writing) one might assume the volume would be mostly math with biology sprinkled in, but actually I'd say the reverse is true: it is largely biological discussion with the math sprinkled in. The book is a great introduction to basic ideas for interested laypersons, or high schoolers and middle-schoolers interested in these fields, but also includes material for more advanced readers. The first 100 pages or so are largely historical and I thought a bit of a yawner, but following that are 200 very engaging and interesting pages surveying subjects from evolution, genetics and DNA, virus and protein structure, knots, symmetry, extraterrestrial life... a smorgasbord of topics. I especially liked Stewart's discussions of the biological concept of "species" and population dynamics, but there is much else of interest here, and the book progresses nicely as it moves along. Stewart consistently offers enough information for the reader to chew on and prod one's interest, but without being so technical or jargon-laden as to intimidate readers.
... so in short, don't be put off if the first 100 pages don't grab you; the next 200 pages are a great ride, that will have something appealing for every math-lover.

I recommend it for your shelf... right alongside a couple dozen other Stewart volumes... and, I also recommend Dr. Stewart go get some sleep now!