3 ms·

Wouldn't that be backwards? The purpose of notation is to aid human thought and communication. Technology should adapt to whatever notation would be most useful

by svat 9y ago

Wouldn't that be backwards? The purpose of notation is to aid human thought and communication. Technology should adapt to whatever notation would be most useful to mathematicians, rather than mathematicians adapting their notation for the sake of technology (like “more easily typesettable”). The blackboard-bold fonts are an interesting example of this, with computer typefaces being created for what mathematicians use in the real world. (Though Knuth and Serre and some other mathematicians don't approve of them in typesetting.) Besides, typesetting is a small part of the usage of notation; most of it is written in private by mathematicians for themselves or collaborators, in the classroom for students, in talks for each other, etc. (Typeset papers are a low-bandwidth communication medium, though good for broadcast and archival.) While it may make sense to optimize the ease of creation of typeset mathematics (and that is what Knuth etc. have done to some extent), changing the notation (for this reason) is not a sensible place to do that. (Some related links: https://micromath.wordpress.com/2010/09/24/psychophysiology-of-blackboard-teaching-2/ https://micromath.wordpress.com/2010/09/24/psychophysiology-... http://sites.math.rutgers.edu/~zeilberg/Opinion60.html http://sites.math.rutgers.edu/~zeilberg/Opinion60.html http://okasaki.blogspot.com/2008/01/why-i-dont-use-powerpoint-for-teaching.html http://okasaki.blogspot.com/2008/01/why-i-dont-use-powerpoin... http://sites.math.rutgers.edu/~zeilberg/Opinion78.html http://sites.math.rutgers.edu/~zeilberg/Opinion78.html Section 3 of https://arxiv.org/abs/math/9404236 https://arxiv.org/abs/math/9404236)

canjobear 9y ago
The cryptic nature of math notation is a major hindrance for people learning and using it: for detailed arguments along these lines see [1]. Maybe if math notation were forced to be easily typesettable, it would be simpler or more programming-language-like. [1] https://mitpress.mit.edu/sites/default/files/titles/content/sicm/book-Z-H-5.html https://mitpress.mit.edu/sites/default/files/titles/content/...
- safisher 9y ago
  https://xkcd.com/927/ https://xkcd.com/927/
- svat 9y ago
  My point was that the notation should be optimized for the people using it, not for the technology used to typeset it. If the notation is suboptimal for the people then it can definitely be changed, but that's a different reason. Note that some of these notational improvements may actually make it harder to typeset. For example, the second part of Knuth's paper "Two Notes on Notation" (https://arxiv.org/abs/math/9205211 https://arxiv.org/abs/math/9205211) introduced improved notation for the Stirling numbers "of the first kind" and "second kind", replacing easier-to-typeset but less informative notation like S(n,k). This notation has gained a good degree of acceptance, the paper won a writing award (https://www.maa.org/programs/maa-awards/writing-awards/paul-halmos-lester-ford-awards https://www.maa.org/programs/maa-awards/writing-awards/paul-...), and another paper citing it calls this “The best thing that has happened to the Stirling numbers during their 400 years of chequered history” (https://www.jstor.org/stable/2974533?seq=1 https://www.jstor.org/stable/2974533?seq=1). (See also a talk of his on Notation https://www.youtube.com/watch?v=KjbuyB4dQa0&list=PLoROMvodv4rNMsVRnSJ44WuwbminUqXX2&index=14 https://www.youtube.com/watch?v=KjbuyB4dQa0&list=PLoROMvodv4... for which someone has taken notes: https://crypto.stanford.edu/pbc/notes/misc/notation.html https://crypto.stanford.edu/pbc/notes/misc/notation.html) I think there are valid questions to be raised on which people to optimize for: whether the students encountering the notation for the first time, or the people who use it every day for years. In either case (to make my point again) it's a question about people, and not about the technology — a programming-like notation isn't better unless that's how the people who use it think (or want to think).

by svat 9y ago

canjobear 9y ago

The cryptic nature of math notation is a major hindrance for people learning and using it: for detailed arguments along these lines see [1]. Maybe if math notation were forced to be easily typesettable, it would be simpler or more programming-language-like. [1] https://mitpress.mit.edu/sites/default/files/titles/content/sicm/book-Z-H-5.html https://mitpress.mit.edu/sites/default/files/titles/content/...

safisher 9y ago
https://xkcd.com/927/ https://xkcd.com/927/
svat 9y ago
My point was that the notation should be optimized for the people using it, not for the technology used to typeset it. If the notation is suboptimal for the people then it can definitely be changed, but that's a different reason. Note that some of these notational improvements may actually make it harder to typeset. For example, the second part of Knuth's paper "Two Notes on Notation" (https://arxiv.org/abs/math/9205211 https://arxiv.org/abs/math/9205211) introduced improved notation for the Stirling numbers "of the first kind" and "second kind", replacing easier-to-typeset but less informative notation like S(n,k). This notation has gained a good degree of acceptance, the paper won a writing award (https://www.maa.org/programs/maa-awards/writing-awards/paul-halmos-lester-ford-awards https://www.maa.org/programs/maa-awards/writing-awards/paul-...), and another paper citing it calls this “The best thing that has happened to the Stirling numbers during their 400 years of chequered history” (https://www.jstor.org/stable/2974533?seq=1 https://www.jstor.org/stable/2974533?seq=1). (See also a talk of his on Notation https://www.youtube.com/watch?v=KjbuyB4dQa0&list=PLoROMvodv4rNMsVRnSJ44WuwbminUqXX2&index=14 https://www.youtube.com/watch?v=KjbuyB4dQa0&list=PLoROMvodv4... for which someone has taken notes: https://crypto.stanford.edu/pbc/notes/misc/notation.html https://crypto.stanford.edu/pbc/notes/misc/notation.html) I think there are valid questions to be raised on which people to optimize for: whether the students encountering the notation for the first time, or the people who use it every day for years. In either case (to make my point again) it's a question about people, and not about the technology — a programming-like notation isn't better unless that's how the people who use it think (or want to think).