[wbl]

Once there was a lecture at Yale, and Serge Lang, a frequent loud critic of bad notation was in the audience. There was a function Xi, and soon it was joined by its complex conjugation. Then they were divided. Serge Lang walked out.

[gjm11]

That's delightful, but I fear many in the audience here may not quite see why. So, at the risk of explaining too much:

The Greek letter xi is one of those where the capital and lowercase versions are very different. Lowercase is a bit like a curly E. Uppercase is (at least if you're writing it in a hurry) basically three horizontal lines on top of each other.

The operation called complex conjugation can be notated in two ways, but the more common one among mathematicians is to put a horizontal bar above the thing being conjugated.

So the conjugate of Xi is ... four parallel horizontal lines.

And now we divide Xi (three horizontal lines) by Xi-bar (four horizontal lines), getting: eight horizontal lines.

[neochief]

You were explaining this for someone like me. Thanks for that!

[hanche]

In fact, here is the dreaded letter: Ξ And its lowercase version: ξ

[thaumasiotes]

The letter in actual use seems more likely to be printed as a two-tiered Z.

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[exmadscientist]

For Ξ or ξ?

Back in my grad school days ξ was almost always handwritten as just some sort of squiggle you'd struggle to associate with the character "ξ" unless you already knew what it was supposed to be. My classmates were very surprised that I could (can!) somehow write it as something that actually is recognizable as ξ, quickly and consistently.

(But they missed what my hand muscles do to ζ, so it all balances out.)

[thaumasiotes]

The form I gave you is the capital. It's noted in the wikipedia article, but not discussed: https://en.wikipedia.org/wiki/Xi_(letter)

I spent a while browsing a Flickr group of "Greek signs", which unfortunately tended toward formality. I noticed zero examples of the joined form. There were a handful of standard Ξ, and two oddities - three examples of the letter being printed 王, and one example in which Ξ was used as the lowercase form. ( https://www.flickr.com/photos/robwallace/11888342614/in/pool... ) I guess it's easier to write than ξ is?

The letter doesn't appear to be all that common in general, unless you live in an Alexandropolis.

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Having done some more looking, I still haven't found a joined Ξ, but I have found some examples of the standard form in graffiti and handwriting (e.g. https://www.flickr.com/photos/telemax/4257624412/in/pool-gre... ). The 王 form also appears in graffiti. It's probably displacing the double-Z form.

[sumanthvepa]

Thank you. That actually was helpful. In print it might have been legible, but on a blackboard that would been difficult to read.

[jacobolus]

It was a joke. The lecturer (Barry Mazur, at Harvard) had made a T-shirt with Lang's catchphrase "This notation sucks" and was trying to get Lang to say it with the most over-the-top example of bad notation he could come up with so he could bring the shirt out, but Lang didn't say anything so the whole thing was a bust.

[bradrn]

A lovely story, but sadly this recollection from Paul Vojta disagrees on his reaction: https://www.ams.org/notices/200605/fea-lang.pdf (see p547)