The letter ℘: name and origin? (2017)

As somebody who spends a fair amount of time studying math heavy material that uses math that I never studied formally, this stuff is the bane of my existence. It's one thing to see a random Greek letter, where at least I very likely know what the character "is" (eg, "rho" or "psi" or whatever) and can at least pronounce it to myself and make a mental note "go back and see what rho stands for in this equation". But exactly like you say "squiggle that looks like a cursive P" doesn't easily admit a mental placeholder, AND it's hard to look up later to find out exactly what it is. I've really wanted to tear my last hair out over this a few times. And I am pretty sure one recent such occasion involved this exact character, so this really hits home!

And never mind that cognitive load that comes from managing the use of symbols that are the "same symbol" modulo something the typeface. Trying to read something like

"Little b equals Fraktur Bold Capital B divided by (q times Cursive Capital B) all over Gothic Italic B", blah, blah... then throw in the "weird little squiggle that looks kinda like a 'p' but not quite". It's insane.

The Unicode charts for the mathematical symbol ranges can serve as a visual index: [0]

They open as PDFs and have grids of all the symbols, along with useful metadata such as related and similar symbols, common substitutes, alternate names, etc. You won't find everything in those ranges - some things are elsewhere in Unicode, in their native language or already located elsewhere in an earlier version - but it's a great resource. Even for symbols that are merely letters in some language's alphabet, Unicode sometimes provides a unique codepoint (character) for their use in mathematics.

[0] https://www.unicode.org/charts/

That provides each table as a separate PDF downlod: mathematics covers ~20 PDFs, each named for its contents. It may be faster to download the entire Unicode standard as one PDF (~140 MB):

https://www.unicode.org/Public/16.0.0/charts/

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.

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.

I also find it frustrating, but I’ve come to appreciate that it’s a way to at least partially sidestep the hard problem of naming things. There are still idioms and choices to make, but using abstract symbols makes it easier to play with the abstract concepts being presented.

My most-used programming language is Go, but I’ve been writing mainly Swift for the past year or so. While there’s a lot I like about Swift, its verbosity leads me to waste an inordinate amount of time pondering what the correct verbiage ought to be, and I often miss Go’s more terse, often single-character naming convention.

> My most-used programming language is Go, but I’ve been writing mainly Swift for the past year or so. While there’s a lot I like about Swift, its verbosity leads me to waste an inordinate amount of time pondering what the correct verbiage ought to be, and I often miss Go’s more terse, often single-character naming convention.

Huh. I was expecting that comparison to go the other way given Go's notorious verbosity in terms of error handling, generics etc.. Maybe people compensate for verbosity in one area by being more concise in others (though that doesn't explain e.g. APL).

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

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)

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

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

I distinctly remember the first time a lecturer used the "dx/dt" "symbol" in normal algebraic operations (that is, multiply both equation sides by dt and so on). I was so shocked it's actually not a elaborate differentation symbol, but something with actual division. Next time it was similar with integration, where the dx was substituted by some other function of du.

I swear I treated those as some grammar token, which doesn't hold any real meaning. I've been using those as such for years before.

Technically, dx/dt is not a fraction, but, but, ...

https://mathoverflow.net/questions/73492/how-misleading-is-i...

I would say that Go is extremely explicit, but I wouldn’t say it’s verbose.

Or, I suppose you could say that Go is semantically verbose (explicit error handling, no/low use of generics, no operator overloading), but syntactically concise (short variable names). Swift is the opposite, being semantically concise (extremely heavy use of generics, default arguments) but syntactically verbose (labeled arguments, English-like clauses, result builders).

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.

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

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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.)

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.