A Mathematical Near Death Experience

As I’ve alluded to from time to time, I’m trying to learn relativity — not the popularizations, of which there are many, but the full Monty as it were, with all the math required. I’ve been at it a while as the following New Year’s Resolution of a few years ago will show.

“Why relativity? It’s something I’ve always wanted to understand at a deeper level than the popularizations of it (reading the sacred texts in the original so to speak). I may have enough background in math, to understand how to study it. Topology is something I started looking at years ago as a chief neurology resident, to get my mind off the ghastly cases I was seeing.

I’d forgotten about it, but a fellow ancient alum, mentioned our college president’s speech to us on opening day some 55 years ago. All the high school guys were nervously looking at our neighbors and wondering if we really belonged there. The prez told us that if they accepted us that they were sure we could do the work, and that although there were a few geniuses in the entering class, there were many more people in the class who thought they were.

Which brings me to our class relativist. I knew a lot of the physics majors as an undergrad, but not this guy. The index of the new book on Hawking by Ferguson has multiple entries about his work with Hawking (which is ongoing). Another physicist (now a semi-famous historian) felt validated when the guy asked him for help with a problem. He never tooted his own horn, and seemed quite modest at the 50th reunion. As far as I know, one physics self-proclaimed genius (and class valedictorian) has done little work of any significance. Maybe at the end of the year I’ll be able to read the relativist’s textbook on the subject. Who knows? It’s certainly a personal reason for studying relativity. Maybe at the end of the year I’ll be able to ask him a sensible question.”

Well that year has come and gone, but I’m making progress, going through a book with a mathematical approach to the subject written by a local retired math prof (who shall remain nameless). The only way to learn any math or physics is to do the problems, and he was kind enough to send me the answer sheet to all the problems in his book (which he worked out himself).

I am able to do most of the problems, and usually get the right answer, but his answers are far more elegant than mine. It is fascinating to see the way a professional mathematician thinks about these things.

The process of trying to learn something which everyone says is hard, is actually quite existential for someone now 76. Do I have the mental horsepower to get the stuff? Did I ever? etc. etc.

So when I got to one problem and the profs answer I was really quite upset. My answer appeared fairly straightforward and simple, yet his answer required a long derivation. Even though we both came out with the same thing, I was certain that I’d missed something really basic which required all the work he put in.

One of the joys of reading math these days (at least math books written by someone who is still alive) is that you can correspond with them. Mathematicians are so used to being dumped on by presumably intellectual people, that they’re happy to see some love. Response time is usually under a day. So I wrote him the following

“Along those lines, you do a lot of heavy lifting in your answer to 3a in section 4.3. Why not just say the point you are trying to find in R’s world is the image under M of the point (h.h) in G’s world and apply M to get t and z.”

Now usually any mathematician I EMail about their books gets back quickly — my sardonic wife says that it’s because they don’t have much to do.

Fo days, I heard nothing. I figured that he was trying to figure out a nice way to tell me to take up watching sports or golf, and that relativity was a mountain my intellect couldn’t climb. True existential gloom set in. Then I go the following back.

“You are absolutely right about the question; what you propose is elegant and incisive. I can’t figure out why I didn’t make the simple direct connection in the text itself, because I went to some pains to structure everything around the map M. But all that was fifteen or more years ago, and I have no notes about my thinking as I was writing.”

A true mathematical (and existential) near death experience.

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