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"I think most of us, including my math-phobic Facebook friends, would find the second version easier to follow and understand." I guess I'm in the minority. I p

"I think most of us, including my math-phobic Facebook friends, would find the second version easier to follow and understand." I guess I'm in the minority. I preferred the words (though the translation was a bit ungainly).

Crito 12y ago
A combination of both, something like Knuth's idea for Literate Programming, would be the best I think. Of course that would be way more work for whoever has to type it all up, so I don't think it has much of a chance to catch on.
bsdetector 12y ago
I'd say the problem with math notation is that it simply has too many symbols. It has a different symbol for everything because it was designed as a handwritten system. For you mathematicians, think what you would do if you woke up tomorrow and all the math symbols had been replaced with emoji? I think most normal people would just learn the four operators and that's all... you know: megaphone, pizza slice, backpack, and recycle. Math is what it is, designed for a pre-computer world, but what really kills me is when programmers use untypeable symbols like α (alpha), which at least is an actual letter in one language, or worse yet random unicode like · ("middle dot") or ∕ (division sign, not /). There's just no excuse for that.
- xamuel 12y ago
  The reason for using different scripts (Greek etc.) is to sort symbols by broad categories. Done right, it actually makes things more readable (to the sophisticated reader, which is the mathematician's target audience anyway). It's almost like an implicit type system: (within a particular context) Greek letters mean ordinals, lowercase Roman letters mean predicate logic variables, uppercase German letters mean universes... It would be much less fun, and much harder, to follow an intense mathematical work if the variables were all in the same font.
  - bsdetector 12y ago
    Yes that's the pre-computer I was talking about. Sophisticated mathematicians should be concerned about if it is machine readable or not. If it's machine readable then you can use whatever font, color, or any other style you want that helps you to read it. The viewer can abbreviate descriptive names to single glyphs if you want. Programming is much less fun, and harder to follow, without syntax highlighting. But it doesn't follow that we should manually be color coding syntax and variables, or that integers should always be blue. That's essentially the case with the "readability" of mathematics.
    - SixSigma 12y ago
      > Programming is much less fun, and harder to follow, without syntax highlighting. That's your opinion.
      - spc476 12y ago
        Then there's Color Forth, where color is used as syntax (http://www.colorforth.com/cf.htm http://www.colorforth.com/cf.htm).
    - Q6T46nT668w6i3m 12y ago
      Why? I write mathematics to share with mathematicians, not machines. Would you ask a poet to make the same sacrifice for machine comprehension?
      - sukilot 12y ago
        A poem can mean whatever any reader wants it to. In math objective truth matters.
        Q6T46nT668w6i3m 12y ago
        > A poem can mean whatever any reader wants it to. In math objective truth matters. Maybe? Penelope Maddy, et al, have convinced me that this isn’t as clear as we’d like: http://www.socsci.uci.edu/~pjmaddy/bio/DualistVol15_Maddy.pdf http://www.socsci.uci.edu/~pjmaddy/bio/DualistVol15_Maddy.pd...
- lmm 12y ago
  In many languages it's normal for a single symbol to encode a whole concept. Alphabetic scripts are artefacts of cultures that didn't have access to decent paper, and had to use a small number of simple forms that could be scratched / carved / etc. and remain recognizable.
  - douche 12y ago
    > Alphabetic scripts are artefacts of cultures that didn't have access to decent paper, and had to use a small number of simple forms that could be scratched / carved / etc. and remain recognizable. This is largely incorrect. Outside of Han China and a few other areas in its historical cultural area of influence, alphabetic scripts won over ideographs, and won big time. The Egyptians developed paper-like papyrus thousands of years before the first uses of "paper" paper, and they largely abandoned their ideographic hieroglypics in favor of the Heiratic and Demotic scripts, which are syllabaries, for all but formal usages. Now if the Mongols or the Khitans or the Uygher steppe empires had been able to impose their scripts on the Chinese after conquering them, instead the assimilation going the other way, Unicode might be a considerably smaller clusterfuck today.
- ajuc 12y ago
  Math notation is OK, our ways to represent it digitaly are bad (because math notation isn't 1-dimensional string of symbols, it's actually 2-dimensional). The solution is to make a way to represent it properly, not to throw it away (because we don't have a better 1-dimensional alternative).
- Q6T46nT668w6i3m 12y ago
  It’d be fine. Notation doesn’t replace prose. The best feature of mathematical notation is its ambiguity. It needs to be parsed by a human, not a machine. Poetry is similar. There’s tradition, but few rules.
- j2kun 12y ago
  > what really kills me is when programmers use untypeable symbols Maybe the problem is that "untypeable" symbols should be easier to type. Mathematicians get by just fine with their typesetting system. Maybe the problem is that programmers are constrained by ASCII, and mathematicians have the upper hand because they have the freedom to define their own notation. Maybe the "problem" is a matter of perspective.

Crito 12y ago

A combination of both, something like Knuth's idea for Literate Programming, would be the best I think. Of course that would be way more work for whoever has to type it all up, so I don't think it has much of a chance to catch on.

bsdetector 12y ago

I'd say the problem with math notation is that it simply has too many symbols. It has a different symbol for everything because it was designed as a handwritten system. For you mathematicians, think what you would do if you woke up tomorrow and all the math symbols had been replaced with emoji? I think most normal people would just learn the four operators and that's all... you know: megaphone, pizza slice, backpack, and recycle. Math is what it is, designed for a pre-computer world, but what really kills me is when programmers use untypeable symbols like α (alpha), which at least is an actual letter in one language, or worse yet random unicode like · ("middle dot") or ∕ (division sign, not /). There's just no excuse for that.

xamuel 12y ago
The reason for using different scripts (Greek etc.) is to sort symbols by broad categories. Done right, it actually makes things more readable (to the sophisticated reader, which is the mathematician's target audience anyway). It's almost like an implicit type system: (within a particular context) Greek letters mean ordinals, lowercase Roman letters mean predicate logic variables, uppercase German letters mean universes... It would be much less fun, and much harder, to follow an intense mathematical work if the variables were all in the same font.
- bsdetector 12y ago
  Yes that's the pre-computer I was talking about. Sophisticated mathematicians should be concerned about if it is machine readable or not. If it's machine readable then you can use whatever font, color, or any other style you want that helps you to read it. The viewer can abbreviate descriptive names to single glyphs if you want. Programming is much less fun, and harder to follow, without syntax highlighting. But it doesn't follow that we should manually be color coding syntax and variables, or that integers should always be blue. That's essentially the case with the "readability" of mathematics.
  - SixSigma 12y ago
    > Programming is much less fun, and harder to follow, without syntax highlighting. That's your opinion.
    - spc476 12y ago
      Then there's Color Forth, where color is used as syntax (http://www.colorforth.com/cf.htm http://www.colorforth.com/cf.htm).
  - Q6T46nT668w6i3m 12y ago
    Why? I write mathematics to share with mathematicians, not machines. Would you ask a poet to make the same sacrifice for machine comprehension?
    - sukilot 12y ago
      A poem can mean whatever any reader wants it to. In math objective truth matters.
      - Q6T46nT668w6i3m 12y ago
        > A poem can mean whatever any reader wants it to. In math objective truth matters. Maybe? Penelope Maddy, et al, have convinced me that this isn’t as clear as we’d like: http://www.socsci.uci.edu/~pjmaddy/bio/DualistVol15_Maddy.pdf http://www.socsci.uci.edu/~pjmaddy/bio/DualistVol15_Maddy.pd...
lmm 12y ago
In many languages it's normal for a single symbol to encode a whole concept. Alphabetic scripts are artefacts of cultures that didn't have access to decent paper, and had to use a small number of simple forms that could be scratched / carved / etc. and remain recognizable.
- douche 12y ago
  > Alphabetic scripts are artefacts of cultures that didn't have access to decent paper, and had to use a small number of simple forms that could be scratched / carved / etc. and remain recognizable. This is largely incorrect. Outside of Han China and a few other areas in its historical cultural area of influence, alphabetic scripts won over ideographs, and won big time. The Egyptians developed paper-like papyrus thousands of years before the first uses of "paper" paper, and they largely abandoned their ideographic hieroglypics in favor of the Heiratic and Demotic scripts, which are syllabaries, for all but formal usages. Now if the Mongols or the Khitans or the Uygher steppe empires had been able to impose their scripts on the Chinese after conquering them, instead the assimilation going the other way, Unicode might be a considerably smaller clusterfuck today.
ajuc 12y ago
Math notation is OK, our ways to represent it digitaly are bad (because math notation isn't 1-dimensional string of symbols, it's actually 2-dimensional). The solution is to make a way to represent it properly, not to throw it away (because we don't have a better 1-dimensional alternative).
Q6T46nT668w6i3m 12y ago
It’d be fine. Notation doesn’t replace prose. The best feature of mathematical notation is its ambiguity. It needs to be parsed by a human, not a machine. Poetry is similar. There’s tradition, but few rules.
j2kun 12y ago
> what really kills me is when programmers use untypeable symbols Maybe the problem is that "untypeable" symbols should be easier to type. Mathematicians get by just fine with their typesetting system. Maybe the problem is that programmers are constrained by ASCII, and mathematicians have the upper hand because they have the freedom to define their own notation. Maybe the "problem" is a matter of perspective.