Received: from webgate.proteosys.de (mail.proteosys-ag.com [62.225.9.49]) by lucy.proteosys (8.11.0/8.9.3/SuSE Linux 8.9.3-0.1) with ESMTP id f4MFSgf32003 for ; Tue, 22 May 2001 17:28:42 +0200 Received: by webgate.proteosys.de (8.11.0/8.11.0) with ESMTP id f4MFSf701532 . for ; Tue, 22 May 2001 17:28:41 +0200 Received: from mail.Uni-Mainz.DE (mailserver1.zdv.Uni-Mainz.DE [134.93.8.30]) by mailgate2.zdv.Uni-Mainz.DE (8.11.0/8.10.2) with ESMTP id f4MFSf020053 for ; Tue, 22 May 2001 17:28:41 +0200 (MET DST) MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----_=_NextPart_001_01C0E2D3.E1C2F100" Received: from mailgate2.zdv.Uni-Mainz.DE (mailgate2.zdv.Uni-Mainz.DE [134.93.8.57]) by mail.Uni-Mainz.DE (8.9.3/8.9.3) with ESMTP id RAA10488 for ; Tue, 22 May 2001 17:28:40 +0200 (MEST) Received: from mail.listserv.gmd.de (mail.listserv.gmd.de [192.88.97.5]) by mailgate2.zdv.Uni-Mainz.DE (8.11.0/8.10.2) with ESMTP id f4MFSe020049 for ; Tue, 22 May 2001 17:28:40 +0200 (MET DST) X-MimeOLE: Produced By Microsoft Exchange V6.5 Received: from mail.listserv.gmd.de (192.88.97.5) by mail.listserv.gmd.de (LSMTP for OpenVMS v1.1a) with SMTP id <8.D8AF7CCC@mail.listserv.gmd.de>; Tue, 22 May 2001 17:26:49 +0200 Received: from RELAY.URZ.UNI-HEIDELBERG.DE by RELAY.URZ.UNI-HEIDELBERG.DE (LISTSERV-TCP/IP release 1.8b) with spool id 496793 for LATEX-L@RELAY.URZ.UNI-HEIDELBERG.DE; Tue, 22 May 2001 17:28:35 +0200 Received: from ix.urz.uni-heidelberg.de (mail.urz.uni-heidelberg.de [129.206.119.234]) by relay.urz.uni-heidelberg.de (8.8.8/8.8.8) with ESMTP id RAA25235 for ; Tue, 22 May 2001 17:28:34 +0200 (MET DST) Received: from relay.uni-heidelberg.de (relay.uni-heidelberg.de [129.206.100.212]) by ix.urz.uni-heidelberg.de (8.8.8/8.8.8) with ESMTP id RAA14534 for ; Tue, 22 May 2001 17:28:35 +0200 Received: from knatte.tninet.se (knatte.tninet.se [195.100.94.10]) by relay.uni-heidelberg.de (8.10.2+Sun/8.10.2) with SMTP id f4MFSY126888 for ; Tue, 22 May 2001 17:28:34 +0200 (MET DST) Received: (qmail 11243 invoked from network); 22 May 2001 17:28:29 +0200 Received: from delenn.tninet.se (HELO algonet.se) (195.100.94.104) by knatte.tninet.se with SMTP; 22 May 2001 17:28:29 +0200 Received: from [195.100.226.134] (du134-226.ppp.su-anst.tninet.se [195.100.226.134]) by delenn.tninet.se (BLUETAIL Mail Robustifier 2.2.2) with ESMTP id 911678.545307.990delenn-s1 for ; Tue, 22 May 2001 17:28:27 +0200 In-Reply-To: References: <15112.62969.545010.438829@gargle.gargle.HOWL> <15111.36254.279748.954703@hoelderlin.localdomain> <200105161742.MAA02503@riemann.math.twsu.edu> Return-Path: X-Sender: haberg@pop.matematik.su.se x-mime-autoconverted: from quoted-printable to 8bit by relay.urz.uni-heidelberg.de id RAA25236 Content-class: urn:content-classes:message Subject: Re: Multilingual Encodings Summary 2.2 Date: Tue, 22 May 2001 16:27:35 +0100 Message-ID: X-MS-Has-Attach: X-MS-TNEF-Correlator: From: "Hans Aberg" Sender: "Mailing list for the LaTeX3 project" To: "Multiple recipients of list LATEX-L" Reply-To: "Mailing list for the LaTeX3 project" Status: R X-Status: X-Keywords: X-UID: 4102 This is a multi-part message in MIME format. ------_=_NextPart_001_01C0E2D3.E1C2F100 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable At 13:34 +0200 2001/05/22, Lars Hellstr=F6m 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 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 >$$ > [[\phi,\emptyset],\varnothing] + [[\emptyset,\varnothing],\phi] + > [[\varnothing,\phi],\emptyset] =3D 0 >$$ >where $[a,b]:=3Dab-ba$ 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 ------_=_NextPart_001_01C0E2D3.E1C2F100 Content-Type: text/html; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable Re: Multilingual Encodings Summary 2.2

At 13:34 +0200 2001/05/22, Lars Hellstr=F6m = 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
<greg@matching.math.ucdavis.edu> 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
>$$
>  [[\phi,\emptyset],\varnothing] + = [[\emptyset,\varnothing],\phi] +
>  [[\varnothing,\phi],\emptyset] =3D = 0
>$$
>where $[a,b]:=3Dab-ba$ 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

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