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 Sender: Mailing list for the LaTeX3 project <[log in to unmask]> From: Hans Aberg <[log in to unmask]> Date: Tue, 22 May 2001 17:27:35 +0200 In-Reply-To: Reply-To: Mailing list for the LaTeX3 project <[log in to unmask]> Parts/Attachments: text/plain (80 lines) At 13:34 +0200 2001/05/22, Lars Hellström wrote: >The conceivable limitations this would impose (and you still haven't >produced a single example of a published paper in which there would have >been any limitation at all!) If you want examples, I think it is best to inquiry in say the newsgroups sci.math, sci.math.research. Greg Kuperberg <[log in to unmask]> maintains a math archive which is a front to the xxx.lanl.gov archive -- perhaps you can check with him. > are negligible The past experience with LaTeX is that mathematicians that did not like whatever limitations there were did not use LaTeX at all. A lot of work has been done so that mathematicians should be able to feel comfortable with LaTeX. > in comparison to the >limitations posed by the blackboard as the primary medium for new >mathematical notation and the fine motor skills of the average >mathematician. If you don't believe this, you can try the following >experiment: > >1. On a blackboard, using a piece of chalk, write down the calculations >showing Jacobi's identity >$$> [[\phi,\emptyset],\varnothing] + [[\emptyset,\varnothing],\phi] + > [[\varnothing,\phi],\emptyset] = 0 >$$ >where $[a,b]:=ab-ba$ is the commutator, the underlying ring is associative >but not commutative, and using precisely those glyphs from Computer Modern >to denote your variables (you've claimed yourself that they can be used to >denote different quantities). > >2. Convince another mathematician that it is possible to see which symbol >is which without relying on the structure of the calculations. I have no idea what you are trying to prove here: The handwritten math and the typeset math are entirely different media, and they are not exchangeable. Also, some mathematicians would today use only TeX and overhead pictures, and would rarely use the blackboard at all. Further, in the days of typewriters, one would use some kind of markup, like different colors, or various forms of underlining, in order for the typesetter to be able to select the right typeset glyph. All that is needed is some kind of translation table. So use whatever is legible in handwriting, or on the blackboard, and then use a suitable translation table for the typeset output. If you give talk in math using a blackboard, it is common that the notation is invented as the talk is going on: One checks that the audience can follow what one is speaking about. It is not even the case that what may work in handwriting will work on a blackboard or vice versa. Otherwise, if you want examples from differential geometry, I use a different notation for the Levi-Civita connection on a Lorentz manifold (as in general relativity) and the "del" used in physics as applied to three-space: The latter has some fattening like an inverted uppercase delta that the former does not have. But neither are boldface. I recall that I designed the former as a special glyph. I made this choice in order to conform to the traditions in the different fields differential geometry and physics. If you want to use \emptyset and \varnothing side by side, I have no problem in conjuring up a possible example: Say a paper in denotational semantics which uses math to denote \varnothing to denote the empty set. Then \emptyset could be used to denote a polymorphic variable pointing to an empty object. Or suppose one is studying grammars, where \epsilon is used as to denote the empty transition; then it would be natural to use \varepsilon if one say is using analysis to study complexity, or for some other use. Whatever: When one starts to combine mathematical fields, then it suddenly becomes difficult to find good symbols.   Hans Aberg