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November 13, 2007

The Dangers of Complex Analysis

Posted by John Baez

Todd Trimble passed on an anecdote that I can’t resist passing on to you. It’s about a dangerous habit we mathematicians have: the habit of taking everyday words and twisting their meanings to make them into technical terms.

It’s from a review by Gerald B. Folland in the American Mathematical Monthly (volume 780, Oct. 1998, page 780):

… But we mathematicians are unique in our propensity to commandeer everyday words (e.g., imaginary, compact, group, series, …) for our own purposes. Our patron saint is Lewis Carroll’s Humpty Dumpty: “When I use a word, it means just what I choose it to mean, neither more nor less.”

We are so used to this practice that we tend to forget what a stumbling block it can present to a nonmathematical audience. Reuben Hersh has written an excellent short article on this subject, so I will just add one anecdote. On April 9, 1975, Congressman Robert Michel brandished a list of new NSF grants on the floor of the House of Representatives and selected a few that he thought might represent a waste of the taxpayers’ money. One of them (on which I happened to be one of the investigators) was called “Studies in Complex Analysis.” Michel’s comment was, ” ‘Simple Analysis’ would, hopefully, be cheaper.” I shudder to think of what might happen if certain members of the current Congress discover that the NSF is supporting research on perverse sheaves.”

This reminds me of when I was an undergrad, toting a copy of Serge Lang’s Complex Analysis. Someone in my dorm said “Oh, you’re studying Freudian psychology!”

Do you have other examples of such misunderstandings?

Posted at November 13, 2007 12:42 AM UTC

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Re: The Dangers of Complex Analysis

A little more than ten years ago, a Canadian member of parliament gave a speech denouncing wasteful government spending, singling out in particular a grant entitled “Lie theory and its combinatorics”.

Posted by: David Savitt on November 13, 2007 7:01 AM | Permalink | Reply to this

Re: The Dangers of Complex Analysis

I’m drafting a paper at the moment provisionally entitled:

Fusion in Nuclear Spaces

Actually, I’m not. However, the real reason why I do my best to avoid algebraic geometry is because if I combine some aspects of my work with those of said subject I could get into serious trouble with papers such as

Blow-ups in Nuclear Spaces

Okay, so the above is “papers I could write if I wanted to get in trouble”. The following is a true story.

Back in the days of my PhD, I owned an old car (older than me) which was always in for repairs. One morning, I was waiting for it to be fixed whilst catching up on a little light reading (something on Feynman integrals and Wiener measures if I remember aright). So imagine my confusion when, from the other side of the garage, the mechanic yelled out:

You’ve got a crack in your manifold, mate!

I have tracked down a quote attributed to Kasner and Newman (whoever they might be) commenting on the different meanings of the word “function”, though my source does not give a date. A more amusing quote is the following from none other than Maxwell himself (commenting on another’s speech):

Mr Spencer in the course of his remarks regretted that so many members of the Section were in the habit of employing the word Force in a sense too limited and definite to be of any use in a complete theory of evolution. He had himself always been careful to preserve that largeness of meaning which was too often lost sight of in elementary works. This was best done by using the word sometimes in one sense and sometimes in another and in this way he trusted that he had made the word occupy a sufficiently large field of thought.

Posted by: Andrew Stacey on November 13, 2007 8:51 AM | Permalink | Reply to this

Re: The Dangers of Complex Analysis

Colin Adams tells the story in his Knot Book that he’s sitting doing some work in his office, when an undergraduate walks in and, attempting to make conversation, the student asks him what his favourite part of maths is. “Knot theory,” he says. “Yeah, me neither,” replies the student.

Posted by: Simon Willerton on November 13, 2007 9:09 AM | Permalink | Reply to this

Re: The Dangers of Complex Analysis

This point of confusion happens to me quite regularly, since knot theory is typically the part of my research that I explain to random people (at least they can visualize it).

Posted by: Ben Webster on November 13, 2007 10:30 AM | Permalink | Reply to this

Re: The Dangers of Complex Analysis

Ken Ribet (a well-known number theorist) greatly relishes telling people that he studies “arithmetic.”

Serge Lang’s “A Course in Arithmetic” is similarly confusing to people.

I have an old friend from college who’s an anthropologist. She also studies “representation theory.”

Posted by: Ben Webster on November 13, 2007 10:33 AM | Permalink | Reply to this

Re: The Dangers of Complex Analysis

Speaking of confusion, it’s easy to confuse him with another diminutive Frenchman whose name begins with Ser…

Posted by: James on November 13, 2007 1:02 PM | Permalink | Reply to this

Re: The Dangers of Complex Analysis

A physicist colleague of mine was carrying a book on “Group Theory”. Someone (I believe from the personnel department) saw him with the book and asked him, a little surprised: “Oh, so you are also interested in the welfare of employees?”

Posted by: Christine Dantas on November 13, 2007 10:41 AM | Permalink | Reply to this

Re: The Dangers of Complex Analysis

Once the 15 year old son of a friend came over and saw sitting on the coffee table a copy of Serre’s ‘Complex semi-simple Lie algebras’. He remarked ‘Complex… yet semi-simple…?’

Posted by: Chris Brav on November 13, 2007 1:17 PM | Permalink | Reply to this

Re: The Dangers of Complex Analysis

Jim Dolan told me an apocryphal story about the countrified mathematician who wanted to learn about Lie algebras, and saw an announcement for a lecture on real simple Lie algebras; he thought it would be something “real simple” that even he could understand. He was crestfallen when the speaker said he would be assuming that everyone was already familiar with complex Lie algebras…

Posted by: Todd Trimble on November 13, 2007 3:23 PM | Permalink | Reply to this

Re: The Dangers of Complex Analysis

It’s funny how these stories get distorted in the retelling. Jim heard that story from me, and I know what really happened.

At MIT, in the break between semesters, they reserve some weeks in January for random short courses, fun projects, and so on — a really great idea. It’s called the Independent Actitivies Period, or IAP for short. In the IAP, anyone can offer to give a course on anything.

When I was a grad student there, one of my classmates, Monty McGovern, was a student of Vogan working on Lie algebras. He gave an IAP course entitled “Real Simple Lie Algebras”. On the first day of the course there was a large crowd, hoping no doubt to get a really elementary introduction to those mysterious things called Lie algebras.

Imagine their disappointment when Monty’s first sentence was “I’ll assume you already understand the theory of complex simple Lie algebras, which is easier…”

The next class, far fewer people showed up.

Posted by: John Baez on November 13, 2007 4:43 PM | Permalink | Reply to this

Re: The Dangers of Complex Analysis

My copy of Sternberg has a bookshop price label attached that reads “Group Therapy and Physics”.

Posted by: Greg Egan on November 13, 2007 9:56 PM | Permalink | Reply to this

Re: The Dangers of Complex Analysis

There at least once existed an edition of Sakurai’s “Modern Quantum Mechanics” which knew about “communicator brackets”.

Posted by: Urs Schreiber on November 13, 2007 10:21 PM | Permalink | Reply to this

Re: The Dangers of Complex Analysis

A famous example is Deligne’s paper La conjecture de Weil : II, in which the running head actually reads: “La conjoncture de Weil”.

Posted by: none on May 31, 2008 10:39 AM | Permalink | Reply to this

Re: The Dangers of Complex Analysis

The secretaries of Caltech’s Math Department found this hilarious, although I heard it so long ago that I don’t recall the source.

It seems that a distinguished visiting scholar phones the Math Department to give them the title of the talk he’s scheduled to deliver. The secretary types up a notice of what she thinks she heard. It is copied, and put on bulletin boards all over campus.

When the distinguished visiting scholar arrives, he is astonished to see the auditorium overflowing with audience members.

His talk was supposed to be on “Convex Sets.” The posted announcements read: “Convicts and Sex.”

Posted by: Jonathan Vos Post on November 13, 2007 10:24 PM | Permalink | Reply to this

Re: The Dangers of Complex Analysis

First a 1939 quote from Herman Weyl:

‘The name “complex group” formerly advocated by me…has become more and more embarrassing through collision with the word “complex” in the connotation of complex number. I therefore propose to replace it by the corresponding Greek adjective “symplectic.”’

And then I have to mention the “maths debate” we once had at school (I’m not making it up!), much to the delight of us teenagers.

Posted by: Dan Piponi on November 15, 2007 2:16 AM | Permalink | Reply to this

Re: The Dangers of Complex Analysis

Similarily to Greg’s: The University of Victoria library has a book in their algebra section that some confused librarian has labelled “Combinatorial Group Therapy.” Sometimes I feel like I could use some of that.

Posted by: Nicholas on November 16, 2007 6:54 AM | Permalink | Reply to this

Re: The Dangers of Complex Analysis

There’s a book by Serge Lang called “Complex Multiplication” (which turns out to be a topic in elliptic curve theory). I knew about complex numbers from high school algebra, but couldn’t see how someone could write a whole book about how to multiply them…

Posted by: none on December 27, 2007 10:22 AM | Permalink | Reply to this

Re: The Dangers of Complex Analysis

I remember a story I’ve read somewhere about a government official overseeing construction of battleships, more than a hundred years ago. He complained that engineers decided to make ships’ engines with turret drilling machines. It was hard to persuade him that the term “turret drilling machines” doesn’t mean “drilling machines for making turrets”.

Posted by: MigMit on January 28, 2013 9:09 AM | Permalink | Reply to this

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