U+237C ⍼ RIGHT ANGLE WITH DOWNWARDS ZIGZAG ARROW

Known as right angle with downwards zigzag arrow, angle with down zig-zag arrow, \rangledownzigzagarrow, and ⍼, no one knows what ⍼ is meant to represent or where it originated from. Section 22.7 Technical Symbols from the Unicode Standard on the Miscellaneous Technical block doesn’t say anything about it.

The original proposal that included this character is Proposal for Encoding Additional Mathematical Symbols in the BMP (N2191) from 14 March 2000, with origins from the STIX project. That project page links to a number of relevant files dating all the way back to 1997, and most importantly to the very first collation of character tables by Barbara Beeton last updated on 24 June 1997. Here we find that, in table &ac-&cirmid under codes with TR 9573 names, an entry for the character.

AFII ISO TR9573 entity ISO TR9573 description D97C ⍼ angle with down zig-zag arrow

(This table is later merged into a larger table.) A table from 18 July 1997 clarifies that these are characters from the technical report TR 9573-13. A later table from 7 Feburary 1998 with accompanying glyphs confirms that this is indeed the character we’re looking for.

Unicode Glyph SGML Name Description E248 angzarr ISOAMSA angle with down zig-zag arrow

The Unicode code point E248 is, of course, not its current actual code point. That one is located in a Private Use Area (PUA) in the Basic Multilingual Plane (BMP), and so was likely a temporary encoding within STIX before acceptance into Unicode proper. The AFII code point D97C will be explained later, as will what AFII stands for and what it is.

Related is the Mathematical Markup Language (MathML) Specification: Section 6.2.5.1 ISO Symbol Entity Sets provides the same tables as STIX, and our character can again be found in group ISO AMS-A.

ISO/IEC TR 9573-13:1991 and pals

The technical report, whose long name is ISO/IEC TR 9573-13:1991 Techniques for using SGML — Part 13: Public entity sets for mathematics and science, was published in July 1991. Although their site claims there was never a newer version, there is a document with the same name last updated on 8 December 2003. It indeed lists U+237C in Section 7.1 isoamsa, but evidently this came after it was added to the Unicode Standard.

The actual tech report itself doesn’t provide much more information than the newer document, shown in the capture above: all it contains is its short name, the glyph, its old code point D97C, and a description. (If you’re a UBC student or faculty, you can get access to the tech report via Techstreet or here.) The only other reference is found in Section 6.2.5 Arrow Relations, which gives the same entity listings as ISOasma.ent in the Debian package sgml-data. The Foreword, though, mentions that this tech report replaces an earlier annex.

h) Part 13 replaces ISO 8879:1986 annex D (in part)

Taking a look at ISO/IEC TR 9573:1988 Techniques for using SGML as well, which people at UBC can also access via CSA onDemand as CAN/CSA-Z243.210.1-89 (R2018), it also indicates that the symbols it uses comes from ISO 8879.

However, this Annex D of ISO 8879:1986 Standard Generalized Markup Language (SGML) (which UBC people can again access as CAN/CSA-Z243.210-89 (R2014) via CSA onDemand) doesn’t contain our character, neither under ISO ASM-A as expected, nor anywhere else.

Back in TR 9573-13, Section 5 mentions that the symbols tables contain

a glyph identifier, registered in accordance with ISO/IEC 10036. The glyph identifier is shown in decimal and hexadecimal representation;

this refers to the code point D97C/55676. While ISO/IEC 10036:1993 Procedure for registration of glyph and glyph collection identifiers only describes glyph registration, the actual 10036 registry exists online. Our character can be found among code points 556xx. In 2020, the glyph table was standardized as ISO/IEC TR 10036:2020 Registered glyph identifiers, containing the same glyphs.

55676

The registry indicates that this glyph is among thousands inherited from the Association for Font Information Interchange (AFII). They had their own registry as well, cited by ISO/IEC 10036:1996, Annex D Bibliography.

Association for Font Information Interchange (AFII) International Glyph Register, Volume 1: Alphabetic Scripts and Symbols. 1993.

The AFII is long dissolved in favour of Unicode over their glyph registry; an email from Asmus Freytag, their former president, describes its history just before dissolution. Notably, it appears that anyone could register a glyph with the AFII for a fee of 5$ to 50$ (about 8.60$ to 86$, accounting for inflation). Even if the International Glyph Register can be found, it likely merely contains another table with the glyph, the indentifier, and the short description. To know its origins would require the original registration request that added the character, but it’s unlikely that such old documents from a now-defunct non-profit organization in the 90s would have been kept or digitized.

UPDATE: After asking on the TeX Stack Exchange about the origin and meaning of the character, Barbara Beeton herself gave a response.

I had no idea what it meant or was used for, thus assigned it a “descriptive name” when collating the symbols for the STIX project. (I still have no idea, nor can supply an example of the symbol in use.) […] it is the case that ISO 9573-13 existed long before either AFII or the STIX project were formed. […] I once asked Charles Goldfarb what the source of these entities was, but remember that he didn’t have a definitive answer.

So its appearance in AFII’s registry comes after TR 9573-13, which explains the fact that the registry was published in 1993 while the tech report in 1991, although the tech report does reference ISO/IEC 10036, whose earliest version was apparently published in 1993. It’s possible both were worked on simultaneously but one was officially released before the other.

UPDATE UPDATE: In a follow-up comment, Beeton says:

Although I did ask, no one was able to tell me whether there was a single source or the entities were just picked up from a number of sources. And the inclusion of “AMS” in the names of the entity collections likewise remained mysterious.

If she was unable to find a source while actively working with AFII and STIX back in the 90s, I doubt I would be able to uncover anything new now, three decades later. Here, then, I close the book on my investigation. The meaning of ⍼ will be whatever meaning is assigned by whoever uses it next… if anyone uses it at all.

Addendum: the Glyph

What is the glyph supposed to look like? Obviously without a definitive source, we can’t answer this question, but we can look at what various interpretations of a downwards zig-zag arrow overtop a right angle exist, starting with a vector reproduction of the glyph in the 10036 registry, originally a 96 px × 96 px GIF and supposedly copied from AFII’s registry.

The zig-zag in question has a horizontal middle bar, with the lower bar crossing the corner of the angle. Then we have the glyph from TR 9573-13, which is luckily available as a proper PDF with vector glyphs rather than a scanned document.

The zig-zag in question also contains a horizontal middle bar, but the lower bar doesn’t cross the angle corner. The arrowhead has a rather unusual shape, but is in line with the arrowheads of the other glyphs. Strangely, the vertical bar of the right angle doesn’t have a consistent width. Next is a vector reproduction of the glyph from both STIX and MathML, which were originally 32 px × 32 px GIFs.

For some reason, the middle bar of the zig-zag is now diagonal rather than horizontal. There’s also an extra pixel at the bottom bend, and the arrow now crosses the corner of the right angle. Fun fact: the horizontal bar of the right angle is a single pixel shorter than the vertical bar. Then we have the glyph as designed in the Unicode proposal document.

This one just looks like a vectorized version of the previous pixellated version. I don’t think the pixellated glyph is a downsampled version of this glyph, since the arrowhead in this glyph is larger and extends beyond the angle corner.

These last four are examples of the character in four different fonts that provide it: GNU Unifont, STIX Two, Julia Mono, and Noto Sans Math/Noto Sans Symbols. Unifont’s glyph looks like an improved version of the pixellated version: the extra pixel is gone, both bends are the same size around the vertical bar, and the arrowhead is slightly larger and more distinguishable. STIX Two’s resembles the proposal version but with a fancier arrowhead. Julia Mono’s is a little weird: the bottommost bar of the zig-zag isn’t straight, and the vertical bar of the angle again has inconsistent widths. Finally, Noto Sans’ glyph doesn’t even have a zig-zag; They’ve chosen to interpret the character as a wavy arrow rather than a zig-zag arrow. All of these have an arrow crossing the right angle corner, which seems to be a distinguishing characteristic of the character.

---

Other links:

• What is ⍼ used for? on Math Stack Exchange
• Twitter thread about this post
• Ellis (sigil), a chaos magic symbol that looks suspiciously similar to ⍼
• The Assault on Reality, the origin of Ellis (referred to as the Linking Sigil)