Books and revealed preferences

Revealed preferences are the preferences we demonstrate by our actions. These may be different from our stated preferences. Even if we’re being candid, we may not be self-aware.

One of the secrets to the success of Google’s PageRank algorithm is that it ranks based on revealed preferences: If someone links to a site, they’re implicitly endorsing it.

I got to thinking about revealed preferences when it comes to reference books the other day when I used some packing tape to keep the cover of my copy of Abramowitz and Stegun from falling off [1].

Instead of asking “What are some of your favorite books,” it might be more informative to ask “Which of your books show the most wear?” [2] This confounds frequent use and poor binding, but that’s life: there are always confounding effects.

My most worn math books are A&S, Bak and Newman, and Dunford and Schwartz .Bak and Newman was my undergraduate complex analysis book; I think it may have had a poor binding. Dunford and Schwartz got a lot of wear in college when I was into functional analysis.

I used A&S a lot in when I was developing a numerical library for Bayesian statistics. I still open it up occasionally, though not as often as I used to.

My volumes of TAOCP are in good shape, but I think that’s because they are well bound. I’ve cracked open Volume 2 quite a bit, though I hardly ever look at the other volumes.

What are some of your most worn books?

Related posts

[1] Yes, I know it’s available online, but I prefer the dead tree edition. And yes, I know there are more extensive references, but in my experience anything I need that isn’t in A&S is unlikely to be in any other reference book.

[2] Benford’s law was discovered via revealed preferences. Simon Newcomb noticed that the early pages of a book of logarithms were much dirtier than the later pages. (Yes, Newcomb discovered Benford’s law, consistent with Stigler’s law of eponymy.)

Banned math book

Courant & Hilbert is a classic applied math textbook, still in print nearly a century after the first edition came out. The actual title of the book is Methods of Mathematical Physics, but everyone calls it Courant & Hilbert after the authors, Richard Courant and David Hilbert. I was surprised to find out recently that this was once a banned book. How could there be anything controversial about a math book? It doesn’t get into any controversial applications of math; it applies math to physics problems, but doesn’t apply the physics to anything in particular.

The book was first published in Germany in 1924 under the title Methoden der mathematischen Physik. Courant says in the preface

… I had been forced to leave Germany and was fortunate and grateful to be given the opportunities open in the United States. During the Second World War the German book became unavailable and was even suppressed by the National Socialist rulers of Germany. The survival of the book was secured when the United States Government seized the copyright and licensed a reprint issued by Interscience Publishers.

Courant’s language is remarkably restrained under the circumstances.

I wondered why the book was banned. Was Courant Jewish? I’d never considered this before, because I couldn’t care less about the ethnicity of authors. Jew or Greek, bond or free, male or female, I just care about their content. The Nazis, however, did care. According to his Wikipedia biography, Courant fled Germany not because of his Jewish ancestry but because of his affiliation with the wrong political party.

***

I never had Courant & Hilbert as a textbook, but I was familiar with it as a student. I vaguely remember that the library copy was in high demand and that I considered buying a copy, though it was too expensive for my means at the time. I recently bought a copy now that the book is cheaper and my means have improved.

I covered most of the material in Courant & Hilbert in graduate school, albeit in a more abstract form. As I mentioned the other day, my education was somewhat top-down; I learned about things first in an abstract setting and got down to particulars later, moving from soft analysis to hard analysis.

One quick anecdote along these lines. I read somewhere that David Hilbert was at a conference where someone referred to a Hilbert space and he asked the speaker what such a thing was. Hilbert’s work had motivated the definition of a Hilbert space, but Mr. Hilbert thought in more concrete terms.

Books you’d like to have read

I asked on Twitter today for books that people would like to have read, but don’t want to put in the time and effort to read.

Here are the responses I got, organized by category.

Literature:

Math, Science, and Software:

History and economics

Religion and philosophy

Misc:

Review of Matrix Mathematics

Bernstein’s Matrix Mathematics is impressive. It’s over 1500 pages and weighs 5.3 pounds (2.4 kg). It’s a reference book, not the kind of book you just sit down to read. (Actually, I have sat down to read parts of it.) I’d used a library copy of the first edition, and so when Princeton University Press offered me a review copy of the second edition, I jumped on it.

Matrix Mathematics has a lot of information on linear algebra. As you’d expect from the title, it’s mostly about linear algebra. And despite it enormous size, it’s also dense. Mostly definitions and theorem statements. Some examples and proofs, but mostly statements of facts.

But there are a lot of other topics covered too. For example, I was surprised to see a section on Bell polynomials, a topic I ran across in my work and blogged about not long ago.

Why even have reference books these days when you can easily find so much online? For one thing, there’s still a lot you can’t easily find online. When you go beyond commonly known material, as this book does, it gets hard to search for what you need.

For another, an author goes to tremendous effort to arrange the information coherently. When you read a book you find things you didn’t know to search for. Maybe you start by looking up what you think you need to know in the index, but then you find out from context what you really needed to know.

I’m glad to add this to the books I keep close at hand. I can find what I need quickly, and that’s more important than it may seem. If I save a couple minutes, the benefit is not just that I get a couple more minutes work done. The main benefit is that I increase my chances of acting on an inspiration before it evaporates.

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 website 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.

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.