From: Roly Sookias (rolysookias@talk21.com)
Date: Mon Jan 07 2002 - 10:18:14 MST
In response to Hermitaņo's post:
[hermit]
1) Anything designed by a committee is likely to be a disaster. The camel is
said to be a mouse designed by a committee. In my experience this is true.
ADA is a perfect example.
[roly]
ok, so maybe the fundamentals SHOULD in fact be created by a single person,
but I think that if the system (of whatever kind) were to become globally
accepted, it would be advisable if it was at least scrutinised by a
committee or assembly after it's creation, so that any problems could be
straightened out through a logical discourse between experts in the field
and a variety of ways, some better than others, could be suggested for
getting around any problems.
Also, some difficulties may not be apparent to the original constructor,
but would be highlighted by wider scrutiny. I think it would be very
important to bind the committee together and encourage them not to form
splinter groups (as with Ido for Esperanto, although this was due to the
not-so-wise old doctor freezing esperanto riddled with hundreds of problems)
on condition that the tongue would remain changeable and that other
committee members would listen to and consider their views. As I stated,
Esperanto was pretty much a one-man-job and here's a site that explains why
this kind of job should not be done again:
<http://www.xibalba.demon.co.uk/jbr/ranto.html>.
As for the camel and mouse thing, clearly the camel fills a completely
different ecological niche to the mouse a is not better, or worse designed!
Heh.
[hermit]
2) A "math language" already exists - but it is symbolic rather than verbal
for the simple reason that mathematics is not a verbal activity (another
reason why this is an exercise in futility).
[roly] Although later drawn upon silently from the mind, is not the learning
of the "times tables" a verbal process? How can we possibly know if maths is
or could be a potentially verbal activity if our culture has no easy form
(such as the mathstongue -and I now use tongue to distinguish it as a SPOKEN
language) of communicating it, or remembering it verbally? It could be that
we are used to just symbols, so we stick with just symbols, although I do
see your argument.
[hermit]
The language, APL was designed
by Ken Iverson (one person!) in the 1950s as a rationalization of
mathematical notation. The notation was implemented as a computer language
in the early 1960s and has been used to specify most systems produced by IBM
since that date.
[roly]
For a mathstongue, we aren't just talking one company here; the tongue would
want to be universally acceptable and therefore wouldn't just have to be
mathematically sound, but would have to be linguistically so, and that is no
easy task!
[hermit]
The symbol set is specified at
http://www.math.uwaterloo.ca/~ljdickey/apl-rep/tables/ The language is best
learnt from the Gilman and Rose introductory work. Various implementations
are available in the public domain although IMO the commercial
implementations have some advantages (but tend to be expensive). A principle
reason that the language is useful is that an equation expressed in APL is
succinct and can be executed directly.
[roly]
thanks for getting that info.
[hermit]
3) As an aside, as any mathematically literate person can tell you, the
symbol PI embodies the entire transcendental value of PI to whatever degree
of precision is required - and since 1995, we have been able to calculate
the value of any digit without requiring the preceding digits. In the real
world, precision beyond the fourth digit is seldom used.
[roly]
How have they been able to do that? I'm just plain interested!
[hermit]
4) Circus trick feats of memory or arithmetic do not form any part of
serious mathematics (although the ability to recognize integrals is useful).
The ability to think rationally, symbolically and visually (graphically) is
important - and verbal conceptualisation has been shown to be
counterproductive as it hinders the visualization process.
[roly]
Interesting point there. Is there any information you have about the
suppression of visualisation by language? - again, I'm just plain
interested. I can see that visualisation can be very useful and important,
but surely language could be used as effectively, and perhaps more quickly
and precisely than visuals? I know I have no evidence for this, and I am
simply putting this as a question, not sating that it is what I believe to
be true.
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