Eloquent mathematical writing

Sir Michael Atiyah recommends Hermann Weyl’s book The Classical Groups for its clarity and beautiful prose. From my interview with Atiyah:

Hermann Weyl is my great model. He used to write beautiful literature. Reading it was a joy because he put a lot of thought into it. Hermann Weyl wrote a book called The Classical Groups, very famous book, and at the same time a book appeared by Chevalley called Lie Groups. Chevalley’s book was compact, all the theorems are there, very precise, Bourbaki-style definitions. If you want to learn about it, it’s all there. Hermann Weyl’s book was the other way around. It is discursive, expansive, it’s a bigger book, it tells you much more than need to know. It’s the kind of book you read ten times. Chevalley’s book you read once. …

In the introduction he explains that he’s German, he’s writing in a foreign language, he apologizes saying he is writing in a language that was “not sung by the gods at my cradle.” You can’t get any more poetic than that. I’m a great admirer of his style, of his exposition and his mathematics. They go together.

Here’s the portion of the preface that Atiyah is quoting, where Weyl apologies eloquently for his lack of eloquence in writing English.

The gods have imposed upon my writing the yoke of a foreign tongue that was not sung at my cradle.

“Was dies heissen will, weiss jeder,
Der im Traum pferdlos geritten,”

I am tempted to say with Gottfried Keller. Nobody is more aware than myself of the attendant loss of vigor, ease and lucidity of expression.

John Cook interviewing Michael Atiyah at HLF 2013

Photographer Bernhard Kreutzer came by while I was interviewing Atiyah at the first Heidelberg Laureate Forum in 2013.

Easter eggs and yellow pigs

An Easter egg is a hidden feature, a kind of joke. The term was first used in video games but the idea is broader and older than that. For example, Alfred Hitchcock made a brief appearance in all his movies. And I recently heard that there’s a pineapple or reference to a pineapple in every episode of the television show Psych.

Michael Spivak put references to “yellow pig” in some of his books. I’ve heard that he put allusions to yellow pigs in all his books, but I don’t have all his books, and I haven’t been able to find yellow pigs in two of his books that I do own.

Spivak’s calculus text is dedicated to the memory of Y. P.

Dedicated to the Memory of Y. P.

If you look up yellow pig in the index of the book, it will take you to a page that makes a passing reference to “whole hog.”

Spivak’s publishing company, Publish or Perish Press, originally used a pig as part of its logo.

Publish or Perish old logo

The web site now has no logo. His most recent book, Physics for Mathematicians: Mechanics I, uses a different logo.

The cover of Spivak’s Differential Geometry, Volume 1, second edition, has two yellow drawings of a pig.

Cover of Spivak's Differential Geometry, Volume 1, second edition

If you look up yellow pig in the index, it takes you to a page that doesn’t mention pigs, but does include a drawing that looks something like a ham.

Ham-like illustration from Spivak's Differential Geometry, volume 1

I do not see a reference to yellow pig in Spivak’s first book, Calculus on Manifolds. It was published by Benjamin Cummings. Maybe they would not allow Easter eggs, or maybe the idea of including Easter eggs didn’t occur to Spivak until he had his own publishing company. I also do not see a reference to yellow pigs in his recent Physics for Mathematicians book.

Summary of books mentioned above:

Product review policies

I’ve often reviewed books on this site and may review other products some day. I wanted to let readers and potential vendors know what my policies are regarding product reviews.

I don’t get paid for reviews. I review things that I find interesting and think that readers would find interesting.

I don’t do reviews with strings attached. Most publishers don’t try to attach strings. They simply ask me if I’d like a copy of their book, and that’s that. A couple publishers have tried to exert more control, and I don’t review their books.

I don’t write negative reviews because they’re not interesting. There are millions of products you won’t buy this year. Who cares about another thing not to buy? A negative review could be interesting if it were for a well-known product that many people were thinking about buying, but I haven’t been asked to review anything like that. If I find something disappointing, I don’t write a review.

Books need to be on paper. Electronic files are fine for reference and for short-form reading, but I prefer paper for long-form reading.

I’m open to reviewing hardware if it’s something I would use and something that I think my readers would be interested in. I haven’t reviewed hardware to date, but someone offered me a device that expect to review when it gets here.

Free technical books, mostly chemical engineering

Retiring professor Leonard Fabiano contacted me looking to give away a set of technical books, mostly chemical engineering books. If you’re interested please email him at lenfab@live.com.

Here are the books:

Chemical engineering books

Click on the image to see a larger version.

Two titles are not possible to read in the photo. These are

  • Conduction of heat in solids by Carslaw and Jaeger
  • Molecular Thermodynamics of Fluid Phase Equilibria by Prausnitz

Assignment complete, twenty years later

In one section of his book The Great Good Thing, novelist Andrew Klavan describes how he bluffed his way through high school and college, not reading anything he was assigned. He doesn’t say what he majored in, but apparently he got an English degree without reading a book. He only tells of one occasion where a professor called his bluff.

Even though he saw no value in the books he was assigned, he bought and saved every one of them. Then sometime near the end of college he began to read and enjoy the books he hadn’t touched.

I wanted to read their works now, all of them, and so I began. After I graduated, after Ellen and I moved together to New York, I piled the books I had bought in college in a little forest of stacks around my tattered wing chair. And I read them. Slowly, because I read slowly, but every day, for hours, in great chunks. I pledged to myself I would never again pretend to have read a book I hadn’t or fake my way through a literary conversation or make learned reference on the page to something I didn’t really know. I made reading part of my daily discipline, part of my workday, no matter what. Sometimes, when I had to put in long hours to make a living, it was a real slog. …

It took me twenty years. In twenty years, I cleared those stacks of books away. I read every book I had bought in college, cover to cover. I read many of the other books by the authors of those books and many of the books those authors read and many of the books by the authors of those books too.

There came a day when I was in my early forties … when it occurred to me that I had done what I set out to do. …

Against all odds, I had managed to get an education.


A different kind of network book

Yesterday I got a review copy of The Power of Networks. There’s some math inside, but not much, and what’s there is elementary.

I’d say it’s not a book about networks per se but a collection of topics associated with networks: cell phone protocols, search engines, auctions, recommendation engines, etc. It would be a good introduction for non-technical people who are curious about how these things work. More technically inclined folks probably already know much of what’s here.

Technical memento mori

The Latin phrase memento mori means “remember that you must die.” It has been adopted into English to refer to an object that serves as a reminder of death, especially a skull. This is a common theme in art, such as Albrecht Dürer’s engraving St. Jerome in His Study.

Saint Jerome in His Study (Dürer)

I keep a copy of the book Inside OLE as a sort of technological memento mori.

Inside OLE by Kraig Brockschmidt

At some point in the 1990’s I thought OLE was the way of the future. My professional development as a programmer would be complete once I mastered OLE, and this book was the way to get there.

Most of you probably have no idea what OLE is, which is kinda my point. It stands for Object Linking and Embedding, a framework that began at Microsoft in 1990. It was a brilliant solution to the problems it was designed to address, given the limitations of its time. Today it seems quaint. Now I’m doubly removed from OLE: hardly any Windows software developers think about OLE, and I hardly think about Windows development. The thing I was anxious to understand deeply was irrelevant to me a few years later.

Despite my one-time infatuation with OLE, throughout my career I have mostly focused on things that will last. In particular, I’ve focused more on mathematics than technology because the former has a longer shelf life. As I quipped on Twitter one time, technology has the shelf life of bread, but mathematics has the shelf life of honey. Still, man does not live by honey alone. We need bread too, even if it only lasts a day.

Related post: Remembering COM

Rigor and Vigor in Mathematics

I just started reading Frequency Analysis, Modulation and Noise by Stanford Goldman. The writing is strikingly elegant and clear. Here is a paragraph from the introduction.

Rigorous mathematics has a rightful place of honor in human thought. However, it has wisely been said that vigor is more important than rigor in the use of mathematics by the average man. In the particular case of this volume, the amount of rigor will be used that is necessary for a thorough understanding of the subject at hand by a radio engineer; but when it appears that rigor will confuse rather than clarify the subject for an engineer, we shall trust in the correctness of the results established by rigorous methods by the pure mathematicians and use them without the background of a rigorous proof.

The back of the book says  “Professor Goldman’s exposition is both mathematically and physically enlightening and it is unusually well written.” So far I agree.

(I found the 1967 Dover paperback reprint of the original 1948 hardback at a used book store. I looked at Dover’s site while writing this and it doesn’t seem to be in print.)

Non-technical books I’ve written about this year

Here are some of the non-technical books I’ve mentioned in blog posts this year. I posted the technical list a couple days ago.

Maybe I should say “less technical” rather than “non-technical.” For example, Surely You’re Joking, Mr. Feynman is a book about a physicist, but it’s at least as much a human interest book as a science book.



Technical books I’ve written about this year

Here are some of the books I’ve mentioned in blog posts this year. One of these books may be just the present for a geek in your life.

This post looks at technical books: math, science, engineering, programming. I’ll have a follow-up post with non-technical books I’ve written about. (Update: here’s the non-technical list.)


Science and engineering



Deserted island books

You’ve probably heard someone ask someone else what books they would take to a deserted island. It’s usually implied that you’re bringing books for pleasure, not books that would help you survive on the island or leave it.

People often answer the question with a list of their favorite books, perhaps skewed in favor of long books. But I don’t think you should take books that have been your favorites in the past. You should take what you think would be your favorite books on a deserted island. I expect my tastes there would be very different than they are in my current suburban life.

I think of books that I could only read on a desert island, books that I’ve enjoyed in small portions but ordinarily would not have the patience to read cover-to-cover. For example, I’ve found portions of Donald Knuth’s series The Art of Computer Programming enjoyable and useful, but I can’t say I’ve read it all. Perhaps on a deserted island with little to do and few distractions I’d enjoy going through it carefully line by line, attempting all the exercises. I might even learn MMIX, something I can’t imagine doing under ordinary circumstances.

Along those lines, I might want to take some works by Thomas Aquinas such as his Summa Theologica or his commentaries on Aristotle. The little I’ve read of Aquinas has been profound, and more approachable than I expected. Still, I find it hard to read much of him. Alone on an island I might take the time to read him carefully.

For math, I might want to take Spivak’s differential geometry series, depending on how long I expect to be on this island. If I’m going to be there too long and I’m limited on books, I might want to take something else that’s more dense and less familiar.

For science, I’d take Gravitation by Misner, Thorne, and Wheeler. I’ve intended to read that book for many years and have started a couple times. In college I couldn’t afford this price; now I can’t afford the time.

For fiction, I’d take Patrick O’Brian’s Aubrey/Maturin series because I haven’t read it, I’ve heard it is very well written, and it’s long.

The name we give to bright ideas

From The Book of Strange New Things:

… I said that if science could come up with something like the Jump it could surely solve a problem like that. Severin seized hold of that word, “science.” Science, he said, is not some mysterious larger-than-life force, it’s just the name we give to bright ideas that individual guys have when they’re lying in bed at night, and that if the fuel thing bothered me so much, there was nothing stopping me from having a bright idea to solve it …

Ursula K. Le Guin has it backward

Ursula K. Le Guin is asking people to not buy books from Amazon because they market bestsellers, the literary equivalent of junk food. She said last week

I believe that reading only packaged microwavable fiction ruins the taste, destabilizes the moral blood pressure, and makes the mind obese.

I agree with that. That’s why I shop at Amazon.

If I liked to read best-selling junk food, I could find it at any bookstore. But I like to read less popular books, books I can only find from online retailers like Amazon. If fact, most of Amazon’s revenue comes from obscure books, not bestsellers.

Suppose I want to read something by, I don’t know, say, Ursula K. Le Guin. I doubt I could find a copy of any of her books, certainly not her less popular books, within 20 miles of my house, and I live in the 4th largest city in the US. There’s nothing by her in the closest Barnes and Noble. But I could easy find anything she’s ever written on Amazon.

If you’d like to support Amazon so they can continue to bring us fine authors like Ursula K. Le Guin, authors you can’t find in stores that mostly sell packaged microwavable fiction, you can buy one of the books mentioned on this blog from Amazon.

Quaternions in Paradise Lost

Last night I checked a few books out from a library. One was Milton’s Paradise Lost and another was Kuipers’ Quaternions and Rotation Sequences. I didn’t expect any connection between these two books, but there is one.

photo of books mentioned here

The following lines from Book V of Paradise Lost, starting at line 180, are quoted in Kuipers’ book:

Air and ye elements, the eldest birth
Of nature’s womb, that in quaternion run
Perpetual circle, multiform, and mix
And nourish all things, let your ceaseless change
Vary to our great maker still new praise.

When I see quaternion I naturally think of Hamilton’s extension of the complex numbers, discovered in 1843. Paradise Lost, however, was published in 1667.

Milton uses quaternion to refer to the four elements of antiquity: air, earth, water, and fire. The last three are “the eldest birth of nature’s womb” because they are mentioned in Genesis before air is mentioned.