Tom Lehrer and Math humor

[old_prof]

This bluesky thread just came to my attention https://bsky.app/profile/opalescentopal.bsky.social/post/3luxxx27nos23

I'm pulling out the pieces of it here, to save people the effort:

With Tom Lehrer's passing, I suppose this is a moment to share the story of the prank he played on the National Security Agency, and how it went undiscovered for nearly 60 years.

I worked as a mathematician at the NSA during the second Obama administration and the first half of the first Trump administration. I had long enjoyed Tom Lehrer's music, and I knew he had worked for the NSA during the Korean War era.

The NSA's research directorate has an electronic library, so I eventually figured, what the heck, let's see if we can find anything he published internally!

And I found a few articles I can't comment on. But there was one unclassified article-- "Gambler's Ruin With Soft-Hearted Adversary".

The paper was co-written by Lehrer and R. E. Fagen, published in January, 1957.

The mathematical content is pretty interesting, but that's not what stuck out to me when I read it.

See, the paper cites FIVE sources throughout its body. But the bibliography lists SIX sources.

What's the leftover?

Well, you can look through the entirety of the body of the paper. It'll take you a while, but you can pretty quickly pick up that sources 1, 2, 4, 5, and 6 are all cited.

But if you know anything about Lehrer's musical career, you can probably figure it out by looking at the bibliography.

See, entry 3 in the bibliography is "Analytic and Algebraic Topology of Locally Euclidean Metrizations of Infinitely Differentiable Riemannian Manifolds" by one N. Lobachevsky.A

nd if you've ever heard Leher's song "Lobachevsky", you may have just finished that title with "Bozhe moi!"

Now, it's important to note: this paper was published internally in 1957. Tom Lehrer had recorded and released "Songs by Tom Lehrer" in 1953, with "Lobachevsky" included. The song had already achieved some success....

but nobody at the NSA noticed when he and Fagan dropped it in as a reference.

It struck me as a very Lehrer-ish sort of prank. It's harmless, it's light-hearted, and it thumbs its nose a bit at stuffy respectability through its unfailing pretense of seriousness.

How had other people reacted to the joke, I wondered?

So I sent an email to the NSA historians. And I asked them: hey, when was this first noticed, and how much of a gas did people think it was? Did he get in trouble for it? That sort of stuff.

The answer came back: "We've never heard of this before. It's news to us."

In November of 2016, nearly 60 years after the paper was published internally, I had discovered the joke.

A few years later, I filed to have the paper declassified, and the NSA eventually agreed, and even put it up on their webpage: media.defense.gov/2021/Jul/14/...

Once that had happened, I wrote to Mr. Lehrer with a copy of the paper and a letter asking if he had ever gotten in trouble for it.

He kindly wrote back, including a copy of the paper that had been published in Journal of SIAM in 1958, under a slightly different title. Nobody, he said, caught him.

 

[LetsMisBehave]

My parents were both Tom Lehrer fans, and all BDSM aficionados should enjoy the Masochism Tango

 

[TheLobster]

The fact that apparently no one, not even the most meticulous and secretive American security agency at the height of the Cold War, takes care to properly review and vet the papers they publish is not what I'd call humorous. Intensely troubling, more like.

 

[MrPixel]

I dunno. Even the most stuffed of stuffed shirts have lapses, especially when the humor is subtle.

My favorite example is from back in the late '60s with an IBM programming manual. The language manual - COBOL, I believe - was documenting the COMMON shared variable declaration. Something like "COMMON(X,Y,Z)". Except the example was "COMMON(MAN,COLD,GHIA)". We were chuckling about that one for years.

 

[Britva415]

COMMON(CHAMELEON)

 

[Kumquatqueen]

GHIA?

When you read a paper, you generally go through the text and when there's a reference, you might check what it goes to, if you're interested in whether the argument stacks up. A spurious reference in the list at the end wouldn't be noticed - and if you're reading from a NSA perspective, then you wouldn't care about the references at all, only the new writing.

 

[BeechLeaf]

*boink* On second reading I just got the Karmann Ghia reference.

I heard about that NSA paper somewhere else recently - where? I have a feeling Lehrer mentioned it in an interview that I watched a video of, but that might not be the case.

 

[TarnishedPenny]

My parents used to play his LPs up at their cottage when I was young. I laughed then, but am only now starting to get his depth.

I hadn't heard he had died. Rats.

 

[nice90sguy]

The one I remember was the paper written by the famous comsologists and physicists Ralph Alpher and Hans Bethe , who added George Gamow as an author, even though he had nothing to do with it.

When I was a kid, my cousin inroduced me to Tom Lehrer's music, and also to George Gamow's amazing book "One Two Three Infinity", which started me on my love of maths. In that book, written in the 1950's, Gamow talks about big numbers, and coins the word "Googol" (actually his son made it up), for 1 with a hundres zeros after it, and "Googolplex", 1 with a googol zeros. The spelling of the words are as he wrote it.

 

[Bramblethorn]

The paper is available here, BTW: https://www.nsa.gov/portals/75/documents/news-features/declassified-documents/gamblers-ruin.pdf

When you read a paper, you generally go through the text and when there's a reference, you might check what it goes to, if you're interested in whether the argument stacks up. A spurious reference in the list at the end wouldn't be noticed - and if you're reading from a NSA perspective, then you wouldn't care about the references at all, only the new writing.

Pretty much, though there are a couple of things that could have aroused suspicion even for a reader who didn't know the "Lobachevsky" song.

One is that the title of the purported Lobachevsky paper appears quite unrelated to the topic of Lehrer's paper. Lehrer's paper is about a random-walk gambling type problem in probability theory: at each stage in the game you have probability p of winning a dollar or (1-p) of losing a dollar, but you can't go below zero (the "soft-hearted adversary" part: how long on average does it take for you to win N dollars?

But the Lobachevsky title suggests a paper concerned with geometry, of the kind one might consider when dealing with curved space and relativistic physics. It's not impossible that it could be relevant; mathematics produces some weird connections between apparently unrelated topics. But it stands out enough that if I were reading a paper on one-dimensional random walks and noticed that title in the references, I would be pretty curious about how this could be relevant.

The other is that the Lobachevsky paper is cited as "unpublished". I expect you already know but for those who don't, citing unpublished work in scientific writing is considered a questionable practice. It's essentially saying "you're just going to have to take my word for it" in an arena where the expectation is that researchers should as far as possible avoid standing on one another's trust. The main point of giving references is so that readers can go check them out and confirm the things the author's asserting, which obviously can't be done with an unpublished source.

Sometimes it's unavoidable. I've cited one or two "unpublished"/"personal communication" sources myself when there was no alternative. But especially in combination with the first point, a reader might wonder what's so important about this Lobachevsky paper that the authors were willing to cite unpublished work, and perhaps also how these American authors happened to have access to unpublished work by a Russian mathematician who'd been dead for a hundred years. From a security perspective, the NSA would probably want to know if its staff had contacts in Russia...

But if either of those points did raise suspicion in somebody unfamiliar with the song, evidently they kept that to themselves.

 

[Bramblethorn]

Speaking of easter eggs in academic writing, there's this footnote from Lara Pudwell's "Digit Reversal Without Apology":

 

[BeechLeaf]

The Collins Dictionary of Mathematics is a compact work, with very short entries for a large number of topics, so the 15 lines devoted to the topic plagiarism make it one of the longest entries in the book. It discusses Lehrer, Newton, Lobachevsky, and so on. It begins:

plagiarism, n. a labour-saving but lawyer-enriching form of research, relatively rare in mathematics, but ascribed, solely on grounds of scansion, by then Harvard mathematician Tom Lehrer in his 1953 song to the 19th-century Russian geometer Nikolai Ivanovich Lobachevsky.

 

[Kumquatqueen]

Speaking of easter eggs in academic writing, there's this footnote from Lara Pudwell's "Digit Reversal Without Apology":

View attachment 2595319

I had a lecturer explain how there were two competing theories for how molecules get into the nucleus - essentially either the nuclear membrane recognises the molecule or the molecules are attracted to the gaps in the nucleus. He outlined the evidence for each theory and explained why he therefore thought one was right.

"Also, the chap proposing the other theory has just been sentences to 12 years for attempted murder. He's better known as the Edinburgh Safeway Tonic Spiker. But in science we're not supposed to hold that sort of thing against him, so I assure you I only dismiss his theory because it's wrong."

 

[Zootonius]

I've enjoyed Lehrer's stuff a long time. Him more famous song must be Poisoning Pigeons in the Park. But he did edgy stuff for his time, like I Got It from Agnes, which is about VD. And the boy scout song Be Prepared, which has the line,

Don't solicit for your sister, that's not nice,
Unless you get a good percentage of her price
And ends with,

And if you come across a Girl Scout
Who is similarly inclined,
Don't be nervous, don't be flustered, don't be scared.
Be prepared!