From: L' Ermit (lhermit@hotmail.com)
Date: Mon Jan 07 2002 - 11:34:36 MST
<snip>
[hermit 1] 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 1] 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 2] Learning the "times table" is arithmetic, not mathematics.
Mathematicians differentiate between these. Only accountants (and some
Virians it seems) conjoin the two, not realizing that there is more to
mathematics than memory and arithmetic.
[hermit 1] 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 1] 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 2] Actually Ken was a professor of mathematics at Princeton at the
time, and while his notational research was sponsored by IBM it certainly
was not "for" IBM. The use is also not restricted to IBM - I was simply
attempting to illustrate the application of it (in systems design and
specification). Most actuaries and statisticians use it, as do many
astronomers and project managers. Both Harvard and Princeton used (use?) it
to teach mathematics - amazing that Harvard uses <em>anything</em> developed
at Princeton - which speaks to its utility <grin>.
<snip>
[hermit 1] 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 1] How have they been able to do that? I'm just plain interested!
[Hermit 2] Bailey, Borwein and Plouffe published a method to determine this
for base 16 encoding in 1996, and Simon Plouffe generalized this in 1997
["The quest for Pi", D H Bailey, J M Borwein, P B Borwein, and S Plouffe,
The Mathematical Intelligencer 19 (1997), 50-57.] Plouffe's home page is at
http://www.lacim.uqam.ca/plouffe/ and he has an article explaining the
method at
http://www.lacim.uqam.ca/plouffe/articles/BaileyBorweinPlouffe.pdf.
[hermit 1] 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 conceptualization has been shown to
be counterproductive as it hinders the visualization process.
[roly 1] 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.
[Hermit 2] I'm not sure where to source this. I learnt about this from a
cognitive psychologist, who was working on this (using PET analysis) in the
late 1990s, but don't have any formal references and can't recall her name
just now. I'll try to find a copy of the proceedings of the conference where
I met her.
[Hermit 2] As I recall it, the effect is apparently similar to those optical
illusions which can look like one of two things to you, but not at once,
i.e. while you can see the one image you cannot see the other - you have to
choose which image will be seen at any time. In the same way, when your
brain is processing a signal in one domain (aural), it cannot simultaneously
process it in the other (visual), but has to switch between them, and as
this is handled by completely separate areas of the brain, the information
has to be handed-off between them which is apparently slow and error prone.
Mathematicians (she was researching on grad students and gifted children)
apparently handle mathematical concepts almost exclusively in the visual
centers (rather than the speech centers) even when mathematical material is
presented to them aurally - while non-mathematicians involve the speech
centers and thalamus to a much greater degree even when such material is
presented to them visually. She was examining the hypothesis that there is a
genetic component as well as a sexual component to this (females use more
areas of the brain than males to handle most things - males use fewer areas
more intensely) in order to determine whether some people are more
genetically predisposed to mathematics or whether it is more a matter of
conditioning.
PS here is an easy to recall mnemonic: "How I want a drink, alcoholic of
course, after the heavy lectures involving quantum mechanics. All of thy
geometry, Herr Planck, is fairly hard."
(Hint: Count the letters in each word. Takes you to 24 digits. There are
extensions which go further.]
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