[HN Gopher] Math Symbol Frequencies
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Math Symbol Frequencies
Author : tosh
Score : 46 points
Date : 2025-06-07 20:33 UTC (1 days ago)
(HTM) web link (leancrew.com)
(TXT) w3m dump (leancrew.com)
| VonTum wrote:
| I had a bit of a chuckle that apparently 5 out of 50000 opening
| "(" parentheses weren't closed, but then I saw that 2 out of
| 12000 "]" brackets weren't opened! What criminal is using these
| standalone?
| rphln wrote:
| Mixing them should be relatively common when denoting
| intervals, as in "(a, b]" or "[a, b)", so that'd be one cause
| for being unbalanced. But even so, the math on their usage
| still doesn't add up.
| gfaure wrote:
| There is the normal notation for half-open ranges, which would
| lead to unbalanced brackets.
| smcin wrote:
| Ah. Good point.
| orlp wrote:
| You won't like bra-ket notation then :)
| xelxebar wrote:
| Probably not this, but J uses lonely brackets and braces as
| standalone operators: https://code.jsoftware.com/wiki/NuVoc.
| devrandoom wrote:
| I hope you irony of your comment isn't lost.
| jxjnskkzxxhx wrote:
| I mean.... You just used those standalone.
| layer8 wrote:
| It seems weird that [?] would be the sixth-most frequent symbol,
| while [?] doesn't figure at all.
| mkl wrote:
| Agreed. Even stranger to me is @ as the fourth most common
| operator, supposedly more common than +. The whole thing seems
| dubious.
| layer8 wrote:
| I would suspect that the @ comes from author email addresses.
| It's not entirely wrong to call that an operator. ;)
| mmooss wrote:
| Do papers tend to have more email addresses or more plus
| signs? I'd expect the latter, by a lot.
| mkl wrote:
| No, the data (as described in So's thesis) was mathematical
| expressions extracted from TeX source code, so the
| surrounding text and email addresses etc. were ignored.
| Skimming through by eye I can't see @ in any of So's
| tables, and searching for the hex Unicode value the tables
| list for every other character yields no hits: @ is not in
| the tables.
|
| [?] is there anomalously frequently, and @ is missing, so
| something seems to have gone wrong, probably at multiple
| stages in the pipeline.
| dleeftink wrote:
| The table byline says: "The @ symbol is used to encode
| mathematical formulas for the computer. It is not visible to
| the user."
| yorwba wrote:
| Its number of occurrences is 103,090. In the master's thesis
| identified as the original source https://cs.uwaterloo.ca/~sm
| watt/home/students/theses/CSo2005... the Unicode value of the
| operator occurring 103,090 times is given as 2061, and the
| thesis helpfully explains that
|
| _Unicode 2061, 2062 and 2063 are invisible operators. TeX
| does not have any of these invisible operators. These
| invisible operators result from the TEX to MathML
| conversion._
|
| _- 2061 - Function application_
|
| _- 2062 - Invisible times_
|
| _- 2063 - Invisible separator_
|
| And Wikipedia says that function application may be
| represented as
|
| _U+2061 FUNCTION APPLICATION ( ⁡, ⁡) -- a
| contiguity operator indicating application of a function;
| that is an invisible zero width character intended to
| distinguish concatenation meaning function application from
| concatenation meaning multiplication._ https://en.wikipedia.o
| rg/wiki/Function_application#Represent...
|
| I'm not sure though how an automated conversion process would
| be able to distinguish between these.
| seanhunter wrote:
| There definitely is some sort of methodological problem. It
| thinks \otimes is more than 4 times more frequent than the
| plain good old fashioned integral sign. There's absolutely no
| way that is the case.
| dleeftink wrote:
| A related report from way back, that counts expressions instead
| of symbols[0]. The counting procedure used in OP's referenced
| table might benefit from first extracting expressions, and then
| counting individual symbol frequencies.
|
| [0]: Watt, S. M. A Preliminary Report on the Set of Symbols
| Occurring in Engineering Mathematics Texts. In _Proceedings of
| MICA 2008: Milestones in Computer Algebra 2008_.
| omoikane wrote:
| I wonder if these tables are telling us that it's more
| conventional to write "a < b" as opposed to "b > a". Is there a
| style guide for writing equations?
| jostylr wrote:
| Could be. We tend to think of a number line going in that
| order, that is, the lower numbers are to the left. What is
| interesting is that being > 0 is often a condition, such as
| epsilon > 0. Though that is often paired with something like 0
| < |x-a| < epsilon. I have often wondered about an alternate
| mathematics in which the inequality sign was always pointed in
| the same direction and whether that would ease the difficulty
| students have with inequalities.
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