Fourier transforms and Morpho menelaus (plus Jokes with Racial Slurs)

This morning I was in a public place reading Ian Stewart's Why Beauty Is Truth: A History of Symmetry. I was reading this passage on p. 111:

We should not give Galois all the credit for this transformation. He was riding a wave that had been set in motion by Lagrange, Caughy, Ruffini, and Abel.

As I read this reference to "transformation" and "a wave," in a history of mathematics, a man walked in and sat down a few tables away, facing me. He was wearing this shirt, except that his was blue rather than black:

I continued reading, and in the very next paragraph found this:

Liouville spoke to the French Academy -- the body that had mislaid or rejected Galois's three memoirs -- in the summer of 1843.

Wanting to refresh my memory of what had happened with Galois's three memoirs, I flipped back a few pages (to p. 103) and reread this:

As I mentioned, in February 1830 Galois submitted a memoir on the theory of equations to the Academy for the Grand Prize. The secretary, Joseph Fourier, took it home to give it the once-over. The ill-fortune that constantly dogged Galois's career struck again: Fourier promptly died, leaving the memoir unread.

That's Joseph Fourier, for whom the Fourier transform is named. This is a paper book and thus not searchable, but according to the index, this is the only mention of Fourier in the book.

The word transform made me think of the butterfly on the cover of Stewart's book, since this insect is famous for the transformation, or metamorphosis, it undergoes in the course of its life cycle. On a hunch, I googled fourier transform butterfly just to see what would come up. My mathematical education has been quite rudimentary, and I didn't know the first thing about Fourier transforms, but my hunch turned out to be a good one. It led me to the Wikipedia article "Butterfly diagram," which begins thus:

In the context of fast Fourier transform algorithms, a butterfly is a portion of the computation that combines the results of smaller discrete Fourier transforms (DFTs) into a larger DFT, or vice versa (breaking a larger DFT up into subtransforms).

What really caught my eye was the accompanying illustration:

I would have thought that the graph's resemblance to a butterfly was pretty self-explanatory, but whoever put the article together thought it necessary to include a picture of an actual butterfly -- and not just a simple drawing of a generic butterfly, but an entomologically accurate picture of a particular species: Morpho menelaus. The caption even mentions the seemingly irrelevant fact that the butterfly pictured is a morpho.

As a reminder, what attracted me to Stewart's book in the first place was the synchronicity of finding a Morpho menelaus butterfly on the cover:

I haven't finished Stewart's book, but if the index is anything to go by, it has nothing about butterfly diagrams, and the only reference to Fourier is the one quoted above, about how he died before he could read Galois's memoir. Whatever the logic behind putting a butterfly on the cover, it presumably had nothing to do with Fourier transforms.

What prompted the Google search that led me to the butterfly diagram was the connection between butterflies and the idea of transformation. This led me to a blue morpho butterfly like that on Stewart's cover but rotated 90 degrees. A few pages later, Stewart introduces this definition of symmetry: "A symmetry of some mathematical object is a transformation that preserves the object's structure" (p. 118). Then, using an equilaterals  triangle as an example, he explains why 90-degree rotation does not preserve structure and is thus not a symmetry of that object:

Nor is it a symmetry of Morpho menelaus.

Speaking of triangles, last night I somehow ended up discovering the existence of this book on Amazon:

This a case in which you shouldn't judge a book by its cover. The free sample Amazon offers contains neither jokes with racial slurs nor instructions on how to avoid such jokes. Instead, it has jokes like this one -- which I don't think contains a racial slur, though I suppose it may, much like the punchline, have been lost in translation:

A vicar changed into speaking to one in all his parishioners. He stated "When you get to my age you spend lots extra time considering the hereafter." "What do you assert that", enquires the parishioner. The vicar replies "Well, I frequently discover myself going right into a room and wondering what did I are available pay attention after."

Kind of reminds me of this one: