Googling for "Math squiggle that looks like a cursive P" is not a very elegant or convenient way of learning new symbol names.
I wish every proof or equation came with a little table that gave the English pronunciation and some context for each symbol used.
It would make it a lot easier to look up tutorials & ask questions.
(I think I saw there was a newer one, but don't remember how)
You draw the symbol and get the TeX symbol name. I tried this one and it does give the right \wp (which in this case is confusing and you'd have to look up more about why it's named that)
But for classic ones, for instance the "upside down A" -> "forall" is very helpful and shakes newcomers to math syntax
"For the set of real numbers R, some positive integer n, and R^n, with both R and R^n with the usual topologies and sigma algebras, we have function f: R^n --> R, Lebesgue measurable and >= 0."
That is, in writing in math, a popular but implicit standard is, each symbol used, even if as common as R and n, is defined before being used.
Sooooo, right there in the math writing, the symbols are defined. Or, right, an author might assume that the reader knows what "the usual topology" or "Lebesgue measurable" are but does not assume the reader knows what the symbols mean. I.e., the issue is not something about helping readers with their knowledge of math but, instead, just being clear about the symbols. Or, can assume the reader DOES know about the real numbers but does NOT assume that R is the set of real numbers -- and correctly so because R might be the set of rational numbers, some group (from abstract algebra), nearly anything.
Again for physics, E = mc^2 and J = ns^2 are not the same, not within the standards, maybe even if say J is energy in Joules, n is mass, and s is the speed of light!!!
My unit tests are literally full of hieroglyphics. My favorite design doc to this day is one where I sprinkled Sumerian cuneiform throughout the text, e.g. 𒀭𒄑𒉋𒂵𒎌 and 𒂗𒆠𒄭 (Gilgamesh and Enkidu) instead of Alice and Bob.
That was, briefly, a real WTF moment.
[edit] oh my god, of course that one didn’t come from searching guitar topics, that makes no sense given the standard tuning. I’m pretty sure I was googling strings in the C language when I hit that one, lol. I did probably accidentally land on “g string” after searching without thinking about what would obviously come up, when looking up guitar topics, and must have combined the two incidents in my memory.
$ unicode ℘
U+2118 SCRIPT CAPITAL P
UTF-8: e2 84 98 UTF-16BE: 2118 Decimal: ℘ Octal: \020430
℘
Category: Sm (Symbol, Math); East Asian width: N (neutral)
Unicode block: 2100..214F; Letterlike Symbols
Bidi: ON (Other Neutrals)
Age: Assigned as of Unicode 1.1.0 (June, 1993)
That seems a ridiculous choice for a symbol — turning one of the most symmetrical letters upside down!
Background: https://philosophy.stackexchange.com/questions/51563/what-is...
If I write it out by hand, it's most likely just for my eyes anyway, and I'd type it out on a computer if I'd want others to have a look at it. But even if I gave someone else my handwritten note, I think from context it would be pretty clear what the "squiggly lines" are supposed to be.
Asking ChatGPT (or the like) is a good solution nowadays though: “The mathematical symbol that resembles a cursive "p" is likely the Weierstrass p, denoted as ℘. […]”
But then a lot of capital greek letters at least are identical to latin letters in those fonts, so I guess you have to choose carefully anyway... and pick the proper font/handwriting if you absolutely have to use nu. (Hopefully you don't.)
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.
ChatGPT 01-preview gave me:
User: what is the Math squiggle that looks like a cursive p?
Assistant: The mathematical symbol you’re referring to is likely the Weierstrass \wp function symbol, which resembles a cursive or script “p”:
All of those you're of course expected to properly distinguish in handwriting.
I'm sure most of them have some sort of canonical name, but I'm usually tempted to read them with different intonations.
(Oh and of course each of those needs a separate Unicode character to preserve the "semantics". Which I imagine is thrilling edgy teenagers in YouTube comments and hackers looking for the next homograph attack)
That page in 'Studii di logica matematica' appears to be https://archive.org/details/peano-studii-di-logica-matematic... .
It also uses an upside-down C and upside-down E.
>>> import unicodedata
>>> unicodedata.name('℘')
'SCRIPT CAPITAL P'
>>> ord('℘')
8472
Good enough for me.
Notably, this is distinct from ("MATHEMATICAL SCRIPT CAPITAL P").
> Books were printed in Fraktur, where the p looks quite normal, i.e., quite different from a handwritten Sütterlin p which could explain, why it hasn't been replaced in the publication of Amandus Schwarz.
Indeed. ("MATHEMATICAL FRAKTUR CAPITAL P") is also separate (but also, Unicode considers these mathematical symbols to exist separately from "text written in Fraktur script". So you get separate characters allocated for these symbols, but they're not intended to be suitable for printing in Fraktur - which is supposedly a presentation (i.e. typeface selection) issue.
Personally I'm not convinced that mathematical symbols derived from Latin or Greek (or other) scripts really have any claim to being separate "characters". Surely that's what variation selectors are for?
> In Unicode the letter ℘ is given the codepoint U+2118 in the block "letterlike symbols", named "script capital p". But in fact it's lowercase.
Unicode technical note https://www.unicode.org/notes/tn27/ clarifies:
> Should have been called calligraphic small p or Weierstrass elliptic function symbol, which is what it is used for. It is not a capital "P" at all. A formal name alias correcting this to WEIERSTRASS ELLIPTIC FUNCTION has been defined.
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):
> where a mathematician writes "Σ", a programmer simply writes "sum".
Communities develop shorthand and terms of art for things they write a lot. Mathematicians need to write lots of sums; programmers have their own shorthand and terminology.
You're reading something. "Oh this has something to do with Weierstrass...."
"Fake-Handwritten R" is an extra fancy calligraphic version which is not hard to distinguish. The Fraktur R is a pain to write, but you can write an upright "Re" as an alternative.
The basic issue is that using single symbols for variables is very convenient (both more concise and less ambiguous than writing out full or abbreviated words when writing complicated mathematical expressions), but there are infinitely many possible variables and only a small set of symbols.
⸻
1. I would put Donald Knuth in that category, given his choice to not include blackboard bold in his original inventory of characters for Computer Modern, but that might just as much have been a choice based more on limitations of the computing systems he was working with at the time (or his needs for typesetting The Art of Computer Programming which were the primary driver of TeX).
As for "where things are going" – this has been changing extremely gradually over the past 60 years. If the trend accelerates maybe you'll stop seeing both variants in wide use in about another century.
⸻
1. I have a vague notion that it might show up in figured bass once in a great while, but I could be wrong.
You never learned to use capital and lowercase letters differently? Why did you capitalize the 'i' in "I'll"?
And? So is 3.
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.
[ ], but [ ]; however [ ] and [ ], so [ ]....
I grind hundreds of flashcards every night to learn Japanese and I can assure you that one thing we are not short of is symbols. Chinese characters use ~218 basic symbols which can be stacked and combined to form tens of thousands of characters. There are 350 symbols just for counting different kinds of things.
R is unambiguous if it's in blackboard bold, but otherwise it can mean almost anything. n is likely interpreted as a non-negative integer if left undefined, but you usually need to establish explicitly if it can be 0.
One method I considered involved using those little self-wedging widgets that squeeze down tighter as the thing being suspended is pulled harder. (These widgets were once commonly used with overhead POTS telephone lines.)
So I asked around and the broad consensus in my area was that one of these widgets is called a "horse cock."
And while everyone who knew what I was talking could say it with a very straight face, I did not even bother with trying to Google "horse cock" before deciding to go in a different direction with that project.
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.
I think the difference is that you are a programmer and not a mathematician (I'm guessing) and are saying, effectively, that what you are subjectively familiar with is objectively more universally understood.
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).
I do still remember the day our math professor taught us both symbols. He did it very purposefully, like he knew it was all riding on him, and we'd all be lost if he didn't pass the arcane knowledge down.
[0] https://mathoverflow.net/questions/18593/what-are-the-worst-...
Combine that with Göttingen being the capital of the maths world at the time [2], and I wouldn't be surprised if that dispute had some (now mostly forgotten) influences on funny maths squiggles in general.
Tangentially, the original question feels somewhat asked in bad faith imo, calling many names "bad" with unearned authority, and implicitly seeking popular votes to support their position. Also sentences like:
> BTW Abramowitz & Stegun uses P. Wow. See p 629.
It's great if you're passionate about maths, but clutching pearls over the use of "P" instead of "℘" is a bit much (reminds me of the "π vs τ" debate and how upset that seems to make some mathematicians. Meanwhile Euler, who came up with using "π" as a circle constant, wasn't consistent about what value he gave it at all[3] - he'd just pick whatever circumference-to-radius ratio worked best for his proof at hand).
It's pretty clear that "℘" essentially originated as a Fraktur-based glyph that most Germans of the time would intuitively read as the equivalent of "P" in Antiqua. The letter "P" is pronounced "Pe" in German. No mathematician would have been confused by Abramowitz & Stegun's notation, just like writing "R" instead of "ℝ" won't confuse anyone either.
Also Milton Abramowitz was a Jewish man. He might have felt a certain way about using letters associated with German nationalism, but that's just me speculating.
[0] https://en.wikipedia.org/wiki/S%C3%BCtterlin
[1] https://en.wikipedia.org/wiki/Antiqua%E2%80%93Fraktur_disput...
[2] https://theconversation.com/how-one-german-city-developed-an...
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.
https://mathoverflow.net/questions/73492/how-misleading-is-i...
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).
A word is easy to search, but something like “~~>>=>” doesn’t really give anything and it’s not nearly as cute as the writers of the libraries seem to think it is.
I know about Hoogle but that’s not a solution, as that only searches documentation, not stuff like Stackoverflow.
https://www.google.com/search?q=*%3E&iflsig=AL9hbdgAAAAAZzeB...*
On the other hand "Wolfram" (tspfka "Mathematica") seems to not only use the uppercase blackboard bold for Reals, Integers etc but also use lowercase blackboard bold for i, e, c_x (arbitrary constants) etc. Which is just annoying.
What was particularly funny was his look of complete incomprehension at why he was getting this message.
In any case, there are lots of camera based apps for either OCR (So you could maybe search for the character) or image search or LLM search (I didn't try ChatGPT).
I did try zooming 300% and grabbing that character as well as the whole title as an image at 100% zoom with Google Lens. It still failed in both cases.
Are you saying special symbols aren't more common in mathematics than in programming? I simply disagree. Mathematicians hardly use strings at all, e.g. for function names or variables, while they are very common in programming. Mathematicians mostly use single letters in Roman or Greek alphabet, and sometimes with various strange styles like fraktur, double strokes etc.
No, I agree that programming uses more ASCII. I'm saying that using a smaller alphabet (e.g., hex), doesn't make it easier to understand. Programming is just as arcane and difficult to understand - even programmers have trouble understanding each other's code, and generally it's believed that the understanding requires documentation in English.
A horse cock can also be known as an overhead service entrance wedge clamp, which is a surprising mouthful of nomenclature given the parlancial context.
(I don't know what a Hubbell device is -- searching for that just brings up a million wiring devices (outlets, switches, and such) made by Hubbell.
But maybe that's the point?)
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-----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.)
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.
E.g. the two Rs we are talking about here both stand for the same word - Real. Except one is Real as in the Real numbers, and one Real as in the real part of a complex number.
If you go with a random symbol, you're putting a different kind of cognitive overhead because you have to map a random symbol you never saw before to a specific concept. Here you just have to distinguish font, and even that is often not necessary, because you often are dealing with a branch of maths that only uses one of the meanings.
Yes, that's why they're a good example of assigning semantic significance to the font that something is written in.
> Well because I can have upper and lowercase letters in the same font.
What do you think that means?
Try this one: I can have Arial and Calibri letters in the same font.
Where a 'font' is a data file used by word processors to render ASCII or Unicode, it's just as true.
If you think a 'font' means something other than that, what is it, and how does your definition preserve the idea that a capital A and a lowercase a are distinct in some dimension that isn't their 'font'?
The same applies to the scripts used by e.g. Chinese, Arabian, and Korean speakers.
So naturally I am not a "fluent" writer of ξ and ζ, and since I virtually always write those characters in isolation instead of as part of words, it's a different mode of practice even when I do use them.
It's the same on the keyboard, by the way. My keyboard does not have ξ or ζ keys, it's all special.