2606: Weird Unicode Math Symbols

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Weird Unicode Math Symbols
U+2A0B ⨋ Mathematicians need to calm down
Title text: U+2A0B ⨋ Mathematicians need to calm down


This comic proposes joke explanations for various unicode symbols with obscure or no known uses, see the table below.

It may have been inspired by this blog post U+237C ⍼ RIGHT ANGLE WITH DOWNWARDS ZIGZAG ARROW. It was posted four days prior to this comic's release. The blog post went viral (in a limited sense) the same day the comic was published, perhaps as a consequence of it mentioning one of the symbols of the comic, Larry Potter. This caused the blogger to update his post with a reference to both xkcd and explain xkcd:

"XKCD #2606 mentions ⍼ and its Explain XKCD entry cites this post"

The title text includes yet another special symbol ⨋, and this symbol prompts Randall to ask Mathematicians to calm down. See more details in the table below, where the title text symbol is mentioned in the last entry.

Table of symbols[edit]

Codepoint Symbol Unicode Name Actual use Randall's meaning Explanation
U+29CD Triangle with Serifs At Bottom No known mathematics use, but resembles the National Park Service cartographic symbol for a campsite.[1] Shark May look like a shark fin sticking out of the water.
U+23E7 Electrical Intersection Indicates where wires branch off Traffic circle Looks like a diagram of a roundabout as might be shown on a minimap beside a routing direction.
U+2A33 Smash product The quotient of the product of the underlying spaces of two pointed spaces, where points in the product space are identified if they contain either labeled point as an element. Hashtag Looks somewhat like the hash symbol (#) – commonly used for indicating tags called hashtags in social media – turned by 45 degrees.
U+2A7C Greater-Than with Question Mark Above Used in proofs to indicate a greater-than relation that should exist but hasn't been proven yet (non-rigorous) Confused alligator One metaphor used when teaching inequality signs in primary school is that the sign looks like an alligator mouth "eating" the larger number. Question marks are commonly used in cartoons to indicate confusion on the part of a character.
U+299E Angle with S Inside Plural for the angle symbol (∠) [2][3] rarely used Snack May look like a mouth eating an S, where the S symbolizes some snack food, or the word "snack".
U+2A04 N-ary Union Operator with Plus Disjoint union[4] (joining a family of sets that have no elements in common) Drink refill Looks like a cup with a plus to indicate adding drink to the cup.
U+2B48 Rightwards Arrow Above Reverse Almost Equal To Pairs with which could conceivably mean assignment of an approximation, but neither seem to be in use. Possibly intended to describe ill-defined projections. Snakes over there Looks like two squiggles to represent snakes and an arrow indicating the direction where they may be found.
U+225D Equal To By Definition Indicates an equation where the left side is to be defined as the right side[5] usually used in proofs to indicate a definition is being introduced Definitely, for sure "Def" is a contraction of "definitely" used in slang; the equal sign looks like a double underline, indicating heavy emphasis.
U+237C Right Angle with Downwards Zigzag Arrow No purpose is known.[6] Speculation includes a diode with a gate, proof by contradiction, a proofreaders' mark to split a word, and indication of polarization direction. Larry Potter Looks like the letter "L" and a lightning bolt. Harry Potter is known for having a lightning bolt-shaped scar on his forehead. The character Larry Potter figured in a fraudulent legal claim against J.K. Rowling.
U+2A50 Closed Union with Serifs and Smash Product Indicates that a collection of topological spaces is closed when taking arbitrary unions and smash products. That is, if you take the union of any collection of topological spaces in the collection (even uncountably many), or the smash product of them, the result will also be in that collection. This is apparently important because the sets can't be isomorphic (one cannot be rearranged to be exactly the other.) [7] Spider caught with a cup and index card Spiders or other bugs found within someone's house or workspace may be caught with a glass and something flat, often a card or a magazine, to be released outside. The projecting lines of the smash product symbol resemble the legs of a spider. Confusingly, some fonts display this symbol with different numbers of "legs": eight, as a 45°-rotated hash symbol, or six as an asterisk.
U+2A69 Triple Horizontal Bar with Triple Vertical Stroke Emblem of the Romanian Iron Guard fascist political movement; Loosely resembles part of the IACR logo, as depicted in 153: Cryptography; possibly a four-by-four tic-tac-toe board.[8] ℍ𝕒𝕤𝕙𝕥𝕒𝕘 Hash symbol with one extra vertical and horizontal line, or perhaps a hash symbol which has been accidentally double-struck or overprinted.
U+2368 APL Functional Symbol Tilde Diaeresis Used for a two-argument operation to commute (swap) its arguments or allow it to use a single provided argument in both argument slots, and to convert a value into a constant function :/ Looks like a confused or disappointed face. Randall's use is in fact common among APL programmers in the comments, as documented here and here.
U+2118 Script Capital [sic] P A stylized round hand 'p' used by Weierstrass for his "p-function," with features of both capital 𝒫  and small 𝓅. Sometimes also used as the power set operator. Snake This symbol coils around like a long snake, with a tapering-off tail on one end and a small "head" on the other.
U+2AC1 Subset with Multiplication Sign Below Indicates that one set is subset of another by means of a product
Looks like the letters "Ux" sideways; UX is a common abbreviation for user experience.
U+232D Cylindricity A symbol used in geometric dimensioning and tolerancing (GD&T) to represent a parameter called "cylindricity" which describes the statistical deviation of an ensemble of surfaces from a reference cylinder. example use Rolling dough between your hands to shape it into a ball Looks like two flat hands (perhaps like stick-figure arms) rolling a ball between them. Rolling dough between one's hands to make it into a ball is an important step in making many kinds of pastry and bread.
U+2A13 Line Integration with Semicircular Path Around Pole Very rare symbol for half of a closed contour or line integral which contains the origin in its interior. Contour integrals which circle the origin are very important in complex analysis. If such an integral were split into two parts, each could be represented by this symbol (which can be mistaken for , the integral not including the pole, with a wider and more complete arc around an offset dot.) [9] Integral that avoids a bee on the whiteboard Looks like an integral symbol with a bump that goes around a dot, as if a professor was drawing an integral on a whiteboard but did not want to disturb a bee that had landed right in the path of their marker.
U+2A0B (title text) Summation with Integral The sum of the sum of the discrete elements (∑) and the integrals (∫) over the connected pieces. This symbol requires context to be meaningful but could occur, for instance, when computing probabilities using mixed distributions.

see also

Mathematicians need to calm down Each of the two symbols is specifically used to represent a kind of summation that is calculated completely differently from the other. Combining them could produce frustration for people unfamiliar with the usage. The comment given may make fun of mathematicians' tendency to form increasingly complex expressions in their work. It may as well be a pun on the pronounciation of the letter Esh (Shhhh).


Weird Unicode Math Symbols

And their meanings

U+29CD Shark
U+23E7 Traffic circle
U+2A33 [The word "hashtag" with the letters slanted counterclockwise]
U+299E Snack
U+2A04 Drink refill
U+2B48 Snakes over there
U+225D Definitely, for sure
U+237C Larry Potter
U+2A50 Spider caught with a cup and index card
U+2A69 [The word "hashtag" but with extra horizontal and vertical lines]
U+2368  :/
U+2118 Snake
U+2AC1 [The words "user experience" rotated clockwise 90 degrees]
U+232D Rolling dough between your hands to shape it into a ball
U+2A13 Integral that avoids a bee on the whiteboard

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Apparently, nobody knows what U+237C ⍼ means (https://ionathan.ch/2022/04/09/angzarr.html)

For me it looks very like as designation of where electrical cable is burrowed. It should come with numbers near angle hands designating depth and offset from sign. But it just a guess, of course 05:30, 14 April 2022 (UTC)
There are at least four people on (https://news.ycombinator.com/item?id=31012865) who claim to have seen the symbol in the wild: German/Dutch proof by contradiction, diode with a gate, Finnish proofreaders mark indicating when and how to split a word, and indicating which way EM waves are polarized -- 11:42, 14 April 2022 (UTC)
I think that is "larry potter" as the lightning symbol, and the L comes from the L shape the lightning is over imo. 14:47, 14 April 2022 (UTC)Bumpf

Can someone add a column where we try to crowdsource a description for the "mathematical use of symbol" ?

I'm curious what those symbols actually mean, and the unicode titles don't give that much information.

I do not doubt that have enough math geeks on here to find the answer to most of then :-D

Thanks! Flekkie (talk) 01:20, 14 April 2022 (UTC)

i agree w Flekkie's comment Blue in real life (talk) 02:27, 14 April 2022 (UTC)

If you make edits, please don't immediately delete all of mine because you think yours are better. It shows you conflicting edits for a reason. Some explanations are nonsensical, like defining a smash product as the "result of dividing two product spaces." The smash product is specifically the quotient of the underlying spaces of two pointed spaces where points in the product spaces are identified if they contain either labeled point as an element. Other claims are simply mistaken. For instance, the ≝ symbol is used to introduce a definition, not to declare that the definition has been achieved in a proof. The claim that "A union on smash product appears to be one where the sets are nit isomorphic" is totally meaningless. The symbol ⩩ is not merely decorative but is intended as a supplemental math symbol like all the others. I couldn't track down its purpose. The APL symbol description somehow never bothers to mention APL. This is all very cursory, which is fine, but just please don't delete my work while doing it. 04:15, 14 April 2022 (UTC)

I'm done, page is yours. I'd been working on it for an hour and every time I tried to save, a new edit came in. I did my best to reconcile them but by the fifth I just saved a copy of what was there and pasted mine over. I immediately got to work on recovering what I had pasted over as indicated in the edit comment and like I said, I'm done. I've merged to the best of my ability and have no more interest in this page.
--FrankHightower (talk) 04:37, 14 April 2022 (UTC)
I'm very sorry if I was one of those who stepped on your edits. I was originally trying to fix brokenness in the table.
^^^^^^ is the symbol for preferring many small edits over not saving your work often in a batch-mode collaborative editing environment. 04:55, 14 April 2022 (UTC)
since adding a column means adding a cell to every row, I thought it would be easier/better to put something in each cell. I wasn't expecting this --FrankHightower (talk) 18:12, 15 April 2022 (UTC)
Don't worry about it, idk why I was so upset. It's that feeling you get when you click "save" and then suddenly it's gone. If anything's still missing, I'll just restore it. 05:41, 14 April 2022 (UTC)

I wish we had as much research on ⧍ and ⩩ as we have for ⍼. 05:16, 14 April 2022 (UTC)

No clue what those are for. The first is a triangle with serifs? The triangle symbol (not capital delta) is often used in geometry to represent a triangle, but why in the world would you give a geometric figure serifs? I think I may have seen the triple cross-hatch somewhere, but I couldn't say where. Maybe it's the chess commentary symbol for being mated so badly it's embarrassing. 05:41, 14 April 2022 (UTC)
I'm guessing what must have happened is the code page in question was filled in by a typographer with more graphic design than mathematical experience, who likely added made-up "missing" symbols as the design-logical extensions of the symbols they were given, presumably to be on the safe side in case they had what appeared to be a possibly incomplete set. There are some awesome ones in there, like "⩐" TEST-TUBE PARTHENOGENISIS, and "⨻" THE ILLUMINATI IS DEAD. 06:07, 14 April 2022 (UTC)
The ⧍ character has the same origin as ⍼, namely that they were both part of ISO/IEC TR 9573-13 with no explanation given. You can find it in some old charts online, like here: [10], under `trisb`/codepoint E27E. ionchy (talk) 07:03, 14 April 2022 (UTC)
I am sure that I have seen maps with such a symbol used for campsites, and without the bold strokes of the top sides as the National Park Service draws it. I haven't found any yet, but I have found one without the center base -- like _/\_ -- on a 1960s era map. 07:07, 14 April 2022 (UTC)
As for ⩩, the character just before it in the Unicode code chart [11], ⩨, has the text "identical and parallel to", so it's possible the horizontal lines in this one also means "identical to". I don't know what three vertical lines mean though, and in Unicode there's three (!) different characters with similar glyphs: U+2980 ⦀, U+2AF4 ⫴, and U+2AFC ⫼. ionchy (talk) 07:28, 14 April 2022 (UTC)
Identical both vertically and horizontally? 07:32, 14 April 2022 (UTC)
I found one suggestion that the dodecathorp should be used to refer to very big numbers... 08:33, 14 April 2022 (UTC)
Three vertical bars means "similar to", so that'd be identical to and similar... to. OK that doesn't work. 04:05, 19 April 2022 (UTC)

Apparently, Randall reads Hacker News like the rest of us... -- 09:38, 14 April 2022 (UTC)

Did you know that ⩩ was a logo of the Romanian fascist group Iron Guard?

Wow. "Saint Michael's Cross, the (Iron Guard) movement's symbol designed by Codreanu." I prefer the 4x4 tic-tac-toe board.... 12:29, 14 April 2022 (UTC)

Not that I have special knowledge (above aspiring-polymath level), but for "Rightwards Arrow Above Reverse Almost Equal To" and its leftwards sibling (the current suggestion being that it's an assignment of an approximation) I'd posit that it's a directional approximation specific to chaotic systems. For a precise a=b in a system where small changes to one side can effect large changes in the other, uncertainty or deliberate approximation of either of them may still map well enough to the value across the desired ≈ relationship, but that is only acceptably so unidirectionally. Hence (and I wouldn't know which would be the better convention) the arrow depicts the direction of either the dependence or the more dominant option, whichever it is that almost-ties the values tovether. (I also really ought to check what the reverse almost-equal-to sign is used for, it could be radically different from the 'forwards' version in some field, for which the directionality might even be trivially understood by context.) 11:25, 14 April 2022 (UTC)

Any sources? I found several papers on the topic you describe naively searching on those keywords, and while they are packed with notation, I couldn't find any arrows or approximate equality signs, let alone any sort of composition of the two. 12:47, 14 April 2022 (UTC)
No sources except in my (above-IP's, just to confirm) head. It's just something I might use it for, if let loose on a whiteboard for some reason, not something for which I've seen it used. It's a situation I've encountered often enough in my own amateur numerical analysis, but under self-taught/self-experimenting circumstances where I was probably just (inefficiently) re-inventing the wheel. And if I've been commenting code (itself strings of conventional syntactical symbols), as a usually futile attempt to remind future-me what I was doing, I would have been using longhand to describe what I was either basing my functions on or actually asking them to test... So no surprise that a paper-search didn't match much of my description. ;) 14:39, 14 April 2022 (UTC)

No idea how Randall got that wrong, but U+2A50 (⩐) is totally catching a snowflake with your tongue. 15:02, 14 April 2022 (UTC)

While cute, I think it'd probably be better to remove the Unicode letters in the chart for the second hashtag (⩩). Not only would it mess up screenreaders, but it doesn't actually look like the image in question. Perhaps it would be better to upload an image and give it some alt text to describe it. --Trlkly (talk) 00:12, 15 April 2022 (UTC)

Could the strange-looking characters be made to look like the image in question using Unicode combining diacritical marks? BunsenH (talk) 15:31, 15 April 2022 (UTC)
A screen reader should read it as "Double struck H, Double struck a, double struck s..." etc. which seems a pretty accurate readout to me --18:12, 15 April 2022 (UTC)

Calming down - Sigma long S[edit]

Calming down may refer to the pronounciation of the Letter Esh https://en.m.wikipedia.org /wiki/Esh_(letter)

"Other links: XKCD #2606 mentions ⍼ and its Explain XKCD entry cites this post" yooo people the blog post now mentions us! Someone put this in trivia or something Mushrooms (talk) 09:01, 15 April 2022 (UTC)

Ah, yes, so the article we reference that we think Randall references has now referenced both him and us and so now we ought to reference that? Seems perfectly Ok to me! :-p
(P.S. Hello to that author. You should just be glad that you're not Wikipedia... ;) ) 11:19, 15 April 2022 (UTC)
The blog author is User:Ionchy, who has contributed to the discussion above. 13:47, 15 April 2022 (UTC)

Any of these that are particularly obscure and someone doesn't find and post here what its actual existing use is will be impossible to research later, as people talking about this comic will end up dominating the results of any attempt to search for the symbol.-- 00:08, 19 April 2022 (UTC)

Regarding the angzarr symbol, ⍼ - I can't remember exactly where I got this idea from, but someone might be able to check it out. I think it might have been a symbol from WW2 to enable 3-D coordinates to be mapped onto 2-D paper. It might have been used in the study of 3-D trajectories. The right-angle in the image represents the X and Y axes. The zig-zag represents the z axis. The arrow pointing downwards or outwards towards the viewer represents the 3rd dimension. This symbol was placed in the z axis to indicate that this axis which continues in a straight line from the y axis below the x axis, is not the negative y axis, but the z axis. Regarding the triangle symbol, ⧍ - this is the delta math symbol, e.g. https://sciencing.com/delta-math-6678201.html - 19:08, 6 May 2022 (UTC)

GPT-3's ideas about ⍼[edit]

Responses from GPT-3's davinci-002 model with https://beta.openai.com/playground default settings in bold:

What does the symbol ⍼ mean?
The symbol ⍼, known as a "diaeresis" or "umlaut", is used in some languages to indicate that the two vowels it is placed over are to be pronounced separately, rather than as a single vowel sound.
No, it isn't either of those.
It means "integral" in APL.
Well, that's a better guess, but also wrong.
It's actually a symbol used in chemistry to indicate that two atoms are bonded together covalently.
No, that's a colon, :. Try again?
It's actually a symbol used in physics to indicate that two particles are interacting.
That seems very plausible! What is your source?
The symbol ⍼ is actually used in mathematics to indicate that a function is continuous.
In math, might it indicate an indefinitely-valued relation over a finite domain.
I.e. for the domain {1,2,3,4} the relation "is even" would be symbolized
⍼ 2 4 2 4 2 ...
The symbol ⍼ is not typically used to indicate an indefinitely-valued relation over a finite domain.
More like, the relation "nearest other evens" for the domain {1, 2, 3, 4} would map to, in order, {{0,2}, {0, 4}, {2, 4}, {2, 6}}. But that's not an indefinitely-valued relation or a finite domain, as each integer maps to exactly two other integers.
The symbol ⍼ is not typically used to indicate an indefinitely-valued relation over a finite domain.
Well it doesn't indicate that a function is continuous, either. So what does it actually mean?
The symbol ⍼ is actually used in set theory to indicate that a function is one-to-one.
No. I liked your physics idea, meaning two particles interacting.
But that's not it either.
The symbol ⍼ is actually used in logic to indicate that a formula is valid.
How? Give an example?
The symbol ⍼ can be used to indicate that a formula is valid if the following holds
⍼(p ∨ q) ↔ (⍼p ∨ ⍼q)
In other words, the formula is valid if the statement "p or q" is true if and only if the statement "p is valid or q is valid" is true.
What are p and q there?
P and Q can be any formulas. So, for example, if P is the formula "x+1=2" and Q is the formula "x=1", then the formula "P or Q" is true if and only if either "x+1=2" is valid or "x=1" is valid.
What does it mean for a formula to be valid?
A formula is valid if it is true in all possible circumstances. So, for example, the formula "x+1=2" is valid if and only if, no matter what value x takes, the statement "x+1=2" is always true.
Is the formula "x+1=2" valid?
No, the formula "x+1=2" is not valid, because there are some values of x for which the statement "x+1=2" is not true. For example, if x=0, then "x+1=2" is not true.
So is ⍼x>x-1 true?
No, the formula "x+1=2" is not valid, because there are some values of x for which the statement "x+1=2" is not true. For example, if x=0, then "x+1=2" is not true.
Is the formula "x>x-1" valid?
Yes, the formula "x>x-1" is valid, because no matter what value x takes, the statement "x>x-1" is always true.
What if x is infinity?
The formula "x>x-1" is still valid if x is infinity, because no matter what value x takes, the statement "x>x-1" is always true.
Is infinity minus one less than infinity?
No, infinity minus one is not less than infinity, because infinity minus one is still infinity.
So how can the formula "x>x-1" be valid?
The formula "x>x-1" is valid because it is true in all possible circumstances. So, for example, if x=0, then "x>x-1" is true because 0 is greater than 0-1. If x=1, then "x>x-1" is true because 1 is greater than 1-1. If x=infinity, then "x>x-1" is still true because infinity is greater than infinity minus one.
Is infinity greater than infinity minus one?
No, infinity is not greater than infinity minus one, because infinity minus one is still infinity.
You just contradicted yourself.
No, I didn't contradict myself. The formula "x>x-1" is valid because it is true in all possible circumstances. So, for example, if x=0, then "x>x-1" is true because 0 is greater than 0-1. If x=1, then "x>x-1" is true because 1 is greater than 1-1. If x=infinity, then "x>x-1" is still true because infinity is greater than infinity minus one.
That last sentence is a direct contradiction of your previous statement.
No, it's not a contradiction. The formula "x>x-1" is valid because it is true in all possible circumstances. So, for example, if x=0, then "x>x-1" is true because 0 is greater than 0-1. If x=1, then "x>x-1" is true because 1 is greater than 1-1. If x=infinity, then "x>x-1" is still true because infinity is greater than infinity minus one.

Oh, well. 00:38, 9 May 2022 (UTC)

Enter with Alt[edit]

how to type these with Alt+numpad? 16:19, 11 May 2022 (UTC)

On Windows, you mean? Use regedit.exe to create a registry key under HKEY_CURRENT_USER of type REG_SZ called EnableHexNumpad, and set its value to 1, and then reboot. Then you can enter Unicode symbols by holding down the Alt key and typing the plus sign on the numeric keypad followed by the hexadecimal character value. For some reason this doesn't work in Internet Explorer, but does in Chrome, Firefox, and most other applications. 04:43, 12 May 2022 (UTC)