[HN Gopher] Space Math
___________________________________________________________________
Space Math
Author : auggierose
Score : 93 points
Date : 2022-04-18 08:59 UTC (14 hours ago)
(HTM) web link (aimath.org)
(TXT) w3m dump (aimath.org)
| math-dev wrote:
| My view is that math is highly expressive and constraining that
| expressivity through rules like don't type |x| is not a great
| idea
| 7373737373 wrote:
| There is probably some value in the
| generality/ambiguity/multiplicity of notation, but in my
| experience it hindered the learning process - eyes glazing over
| more often than they should
| ThatGeoGuy wrote:
| HN (and myself honestly) might be a bit biased in favour of
| Lisps, but if one wanted an unambiguous notation for mathematics,
| Polish notation / s-expr style writing would be the way to go.
|
| As for screen-readers -> parsing s-expressions and converting
| them into a more meaningful reading of the equation is within our
| power as well.
|
| That's not to say that everything should be a lisp, but in terms
| of unambiguously applying mathematical formulae, I think (* f (+
| x 1)) is very distinct from (f (+ x 1)).
|
| -\\_(tsu)_/- mileage may vary I suppose. As someone who uses
| LaTeX a lot myself, I'm not sure I'd be fully happy writing
| Scheme / Lisp instead either. But I'm not sure the article really
| gives us less ambiguity purely thanks to an extra whitespace.
| auggierose wrote:
| Agreed. I don't think Space Math represents a viable solution,
| I was just looking at it to survey the design space of math
| notation on a computer.
| sritchie wrote:
| If you want to try this out, give the sicmutils Computer
| Algebra System a go (I'm the maintainer). Repo lives here:
| https://github.com/sicmutils/sicmutils
|
| The library works in the browser as well, so interactive TeX
| rendering from Clojure symbolic expressions and functions is
| available at the quickstart page here:
| https://nextjournal.com/try/samritchie/sicmutils
| bjd2385 wrote:
| This reads like a code style guide, but for math. E.g., like
| https://google.github.io/styleguide/pyguide.html
| john-titor wrote:
| But let's be honest: If the notation is ambiguous, then the the
| authors did not do a good job explaining it in the first place.
| That's why scientific articles are not only equations but also
| text.
| Aardwolf wrote:
| Personally for unambiguous notation I'm more in favor for what
| programming languages do. Use an operator symbol like * for
| multiply. Spaces can get lost when hand-writing it...
| nickvec wrote:
| Looks neat, will have to give it a try. Just a heads up, the
| third paragraph misspells "mostly."
| auggierose wrote:
| It seems it doesn't exist, so will be difficult to give it a
| try :-)
| fennecs wrote:
| Not very hard to achieve similar results with LaTeX, just
| make liberal use of mathrm, custom commands and spacing, eg
|
| \mathrm{det}(A) shorten to \det{A}
| albinahlback wrote:
| I think many of the ideas originates from the problem that many
| users of Latex does not know how to combine proper Latex
| formatting with stylistic code. The output should be nicely
| formatted, and given the code it should be very easy to see what
| it will produce.
|
| As such, I do not like the second example with the code format
| int_5^20 4 x dx. The absence of backslash \ makes me think that
| "int" is a variable, "_5^20" is too tight for me, and dx also
| looks like a variable. Personally, I prefer typing \int_{5}^{20}
| 4 x \dd{x}, where \dd is your favorite differential typesetting
| (for me it is \mathop{}\\!\mathrm{d}).
|
| But I suppose it is only meant to be a substitute for MathJax and
| similar markup programs, and not actually Latex.
| auggierose wrote:
| By the way, this is the post that put Space Math on my radar:
|
| https://github.com/asciidoctor/asciimath/issues/32
| SiempreViernes wrote:
| Looks like a project to invent notation that put all the context
| inline with the equation, with the main motivation being: > A
| person using a screen reader (software that reads text out loud,
| typically to someone who cannot see the words) may hear the
| formulas pronounced incorrectly, giving the symbols a different
| meaning than intended. Space Math provides an easy way to resolve
| the ambiguity.
| sdenton4 wrote:
| This does seem like an instance where accessibility helps
| everyone. Imagine being able to click on a formula to have it
| read aloud, resolving any ambiguity in the rendered notation.
| SiempreViernes wrote:
| To me notational ambiguity is very rarely a problem, it's
| about as common seeing ambiguity resolved by the Oxford
| comma.
|
| There are some fields where it is frequent problem, but I
| doubt this proposals is what will get the statisticians over
| this death cult where they use "p" for everything ...
| sdenton4 wrote:
| It's not a problem when you're immersed in a particular
| field: It's mostly a problem for cross-silo communication
| and new blood. I'm sure the statisticians feel that the
| many uses of 'p' are perfectly unambiguous. :)
|
| Lowering barriers to understanding is inherently a good
| thing, and might even help some useful knowledge leak out
| of deeply isolated corners of academia.
| ThinBold wrote:
| The sagemath[1] suggests
|
| > Whitespace before and after assignment and binary operator of
| the lowest priority in the expression:
|
| The AMS style guide[2, p. 117] suggests
|
| > Align multiline equations on operators: verbs are aligned with
| each other and conjunctions are aligned with each other
|
| I find these improves readability of my TeX files.
|
| [1]:
| https://doc.sagemath.org/html/en/developer/coding_basics.htm...
| [2]: https://www.ams.org/publications/authors/AMS-StyleGuide-
| onli...
| vngzs wrote:
| I'd also like to recommend Knuth's lecture notes on
| mathematical writing [0].
|
| [0]: https://jmlr.csail.mit.edu/reviewing-
| papers/knuth_mathematic...
| auggierose wrote:
| Very interesting, I have to admit, I wasn't aware of the AMS
| Style Guide! The guide says it is partially based on an older
| AMS publication "Mathematics into Type", which is also freely
| available: https://www.ams.org/arc/styleguide/mit-2.pdf
| Strilanc wrote:
| I'm skeptical of this project. Existing unambiguous notations for
| mathematics do not start from the chaos of human conventions and
| then try to impose order. They start from rigorous unambiguous
| syntactical and semantic foundations; from programming languages
| basically.
|
| For example, when writing y = |x|^2 - 1, the fact that |x| is a
| function application of "abs" is the least of your worries. Even
| given that fact, you can disambiguate into a rather large variety
| of mathematica expressions. Perhaps you're defining a parametric
| curve, perhaps you're computing a boolean value for the
| comparison, etc, etc, etc.
| ouid wrote:
| The notations of these things are essentially unambiguous in
| the first place, since overloaded operators rarely have
| compatible type signatures, and when they do, the shadowing is
| just shy of explicit. Human mathematical notation is definitely
| very bad, but not because it's wildly ambiguous, it's because
| it's inconsistent.
| uKVZe85V wrote:
| TL;DR: A replacement for LaTeX mathematical notation, simpler to
| use, better suited, and not yet ready.
|
| > Mathematical notation can be ambiguous. [...] bad for students,
| because understanding how to talk about the notation is part of
| learning. And it is bad for anyone listening with a screen
| reader, because the words they hear could be different than the
| intended meaning.
|
| > Space Math is not a programming language: it is a convenient
| way to type math formulas while capturing the author's intent.
|
| > Space Math looks a lot like LaTeX math with all the backslashes
| and spacing adjustments deleted. But you can leave in the
| backslashes if you wish.
|
| > To take advantage of the new features of Space Math, insert
| spaces to indicate implied multiplication instead of a 2-letter
| variable, or function application instead of implied
| multiplication: c(t + 1) is the function c evaluated at t + 1,
| while c (t + 1) is the quantity c times the quantity t + 1. A
| little space makes all the difference. In TeX, those expressions
| are typeset identically and a screen reader has to guess how to
| pronounce them. In Space Math output, there will be a tiny gap to
| indicate the implied multiplication and a screen reader will
| pronounce both expressions correctly.
|
| > Is the point of Space Math to capture the semantics of the math
| expressions?
|
| > Space Math allows the writer to create the intended formula,
| and generally focuses on preserving the information needed to
| pronounce the expression correctly. When an expression can have
| multiple meanings, but the pronunciation is the same in all
| cases, typically Space Math does not attempt to make a
| distinction.
|
| Great but apparently not coded yet?
|
| > How can I use Space Math?
|
| > Space Math is currently under development, with the
| specification of the language as the first goal.
|
| > The second step is to write a parser, followed by output
| routines to convert Space Math to TeX or LaTeXML or MathML. This
| will enable Space Math to be used in PreTeXt. If Space Math is
| adopted by MathJax, then it can become widely available.
| davidgrenier wrote:
| I wonder how I would add \phantom- before x and 0 in the
| definition of abs(x).
|
| It looks like op's making decision for mathematical document
| author and since I already see multiple nitpickings like this,
| it looks like a bad idea waiting to happen.
___________________________________________________________________
(page generated 2022-04-18 23:02 UTC)