I wish to applaud Ron, and then Ka-Ping, for marking up an example fully. I think it helps a great deal to have concrete ones to consider. The most striking thing to me about the markup done is the extent to which it resembles the TeX solution that is both widely proposed and opposed. That said, I think that it also suggests the point that either you do just enough markup for presentation purposes, or you have to do a lot more. A partial enhancement is fraught with opportunities for confusion. One simple example of what worries me is provided by the case where Ron carefully put in a "&FunctionApplication;" because he noted that \div was an operator, and specially marked <mo>(ν\cdot\nabla)</mo>, but did not make special arrangements in the use of -∇p. The ∇ is as much an operator as \div or \curl (∇ is notation for the gradient, \grad, and \div = \grad \cdot and \curl = \grad \cross --- in an informal manner of speaking). It seems there are lots of possibilities for only partial markup and hanging ambiguities inherent in trying to distinguish, in ways that authors and editors are unfamiliar with, parts of the semantics of math notations. When it comes to the naming of classical objects that I mentioned, I was only starting to point out that it seemed natural. Indeed you'll find that authors frequently adopt macros for them, in part because their presentation is often done specially (bold, blackboard or roman, say). I don't actually see it as a bad idea to have a certain fairly large list of classical objects with agreed and documented definitions as part of a standard. If you think of Asian languages then you can see that dealing with a reasobaly large name space for ideographs, which all have widely agreed meanings, is not an unsolvable problem. A collection of classical items for math would not be all that large. Actually I'm not proposing that here, but a small basic collection, say, including naturals integers rationals reals complexes quaternions octonions Classical Groups: GL, SL, U, SU, O, SO, SP, Osp, Special functions: Hermite, Legendre, Bessel (I, J, K, ...), ... Hahn, Charlier, Krawtchouk, ... Racah, Clebsch-Gordan Probability distributions: Gauss or normal, student, .... ... wouldn't be that bad to assemble. In any case we do need to provide, I would suggest, a capability that _allows_ authors to use such constructions as these easily and, if at all possible, unambiguously. Computer algebra systems already have large collections of common-place objects identified, as do handbooks and tables. However, it could well be that all this is rather at the level of the planned "macro capability" rather than being of importance at this stage in the deliberations. I do not at all disagree now with the goals that Ron reiterated: (a) render to various sensory media in such a way that a "knowlegeable" human can interpret the notation properly (b) allow for paths by which authors or others may upgrade the notation to one with fuller semantical attributes It has to be true that we are intending that math notation be read by people who know something of math: advanced documents are to be read by specialised readers. It is just when it is to be read by machinery that we are more careful. As the example quoted by Fateman to the DLI list showed, even what we think is very well-specified may well be wrong or meaningless. The more complicated notation or markup is the easier it is to convince oneself that it is probably right because a machine says so. That is a problem in teaching and it's going to be a problem with HTML/Math too. Patrick > >It's unclear to me whether we have a strong(ish?) disagreement here. >I'm certainly not in favor of *requiring* that authors name the >well-known objects of their papers. This would be too much to expect, >in my opinion (no one expects the analogue in standard text, I imagine >a vast menuing system (probably equivalent to ZF) to classify "all" >objects, and do we expect to name the various non-standard models? -- >where do we stop?) > >I do want to define an HTML-Math wherein authors are able to specify >such things if they wish. My view of the project to date has been >that we are trying to define a language which will (a) render to the >various sensory media in such a way that a "knowlegeable" human can >interpret the notation properly, and (b) allow for paths by which >authors or other third parties may upgrade the notation to one >with fuller semantical attributes. If this group has widely >diverging opinions on the degree to which semantics must be carried, >we'll probably have difficulty settling on a standard. > >But do we differ in this? Maybe not. Ping's statement > >> It makes the most sense for the conceptual entity "the complex numbers" >> to be represented by a separate named entity. It is certainly *not* a >> variable named "C" in any sense -- and you would need it to be distinguished >> for it to be properly rendered to speech. > >is much stronger than I would have said myself. There actually is a >good sense (a formalist or nominalist sense) in which "the complex >numbers" are adequately represented by "C", and I'm fairly certain >that Raman reliably distinguishes this "C", as do those who read the >"C", by context. > > >-RonReceived on Monday, 8 July 1996 08:57:37 UTC
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