Date: Thu, 06 Jun 1996 13:49:52 -0400
To: Athena Discuss
Subject: Re: State of the subject (esp to SFT, #2 or is it #3?)
FISHERGM@jmu.edu wrote:
> Does this mean that when
> Archimedes jumped out of his bath over the law of floating
> bodies, and shouted Eureka, I've found it, he was actually
> in Egypt at the time, and reading a papyrus in the bath?
> Or more titillating, did he learn it from an Egyptian
> he was bathing with? One of the Cleopatras, perchance?
> (But of course some say they were Macedonians). This
> is all in fun, S F, a little comic relief (I hope).
The situation is rife with comic possibilities...
especially for the cynically-inclined. For the more
credulous, "say it a'int so, Joe" types, there is just
an overwhelming sadness about the whole thing. Still,
I can manage a chuckle now and then, and I thank you
for injecting some levity into Archimedes and his
inspirational bath-water! Not perhaps that he needed it,
he was so full of gas!
> Well, yes, I came to that conclusion too, but I didn't know
> til now it was your conclusion also, and I didn't want to risk
> starting an off-subject argument. I wondered whether it was
> Zadeh or Ziadeh, but lost the 50-50 chance.
You're right. Another topic, different list. Try comp.ai.fuzzy.
> Well, numerous people have called me a Renaissance Man, by which
> I think they usually mean I'm a dilettante. Actually, the
> specialty I'm more or less certified in is the foundations
> of the real number system, and its extensions involving
> various other fields (in the algebraic sense), including
> non-archimedean ones (egad --- non-archimedean!!! this refers
> to the postulate attributed to Archimedes to the effect that
> given any two positive numbers x and y in the system of numbers
> he was using, there's a natural number n such that nx > y -- is
> there any evidence he stole this, too? -- as you may know,
Not that I'm aware of, but his entire corpus is rendered
suspect, which is not to deny that plagiarists sometimes
have good ideas of their own. It's just that a plagiarist
is like a witness impeached, whose true statements become
confounded with his false ones; for the plagiarist, his own
honest contributions become suspect, impossible to distinguish
from the plagiarised parts.
Aristotle stands similarly impeached, more so by James
(Stolen Legacy) than by Diop. If I may be permitted to plagiarise
myself, I had occasion once to post to a different newsgroup
the following:
James shows striking parallels between
Egyptian writings that antedate Aristotle, and teachings later
credited to the latter. The parallels are evidently on too
massive a scale, encompassing mathematics, physics, theology,
ethics, economics, politics, poetry, art, rhetoric, logic and
metaphysics, to be passed off as coincidence. Evidently, not
even Aristotle himself claimed authorship of all these works,
for his own list differs from a second list of 400 books
attributed to him compiled many years after his death, in 200
BC, by Hermippus, at the Alexandrine Library. A third list of
1000 books, compiled by Ptolemus, appeared in the first or
second century A.D.
More important still than the correct crediting of works
historically attributed to Aritotle, is the true direction of
historical revisionism, for this is what many object to when
first confronting the likes of James and Ben-Jochanan.
Martin Bernal, who is not an Afroncentrist "revisionist" by
any means, has advanced as a major thesis in his "Black
Athena" (1987) the notion of the "Aryan model" -- revisionist
history of the 19th and 20th centuries, which sought,
consciously or otherwise, to deny black contributions at the
very origins of civilization -- in contrast to what he calls
the "Ancient model". According to Bernal (ibid., p. xv):
"I was staggered to discover that what I began to
call the 'Ancient Model' had not been overthrown
until the early 19th century, and that the version
of Greek history which I had been taught -- far
from being as old as the Greeks themselves --
had been developed only in the 1840s and 50s."
Bernal goes on to describe "Stolen Legacy" thus:
"Stolen Legacy ... relying heavily on ancient
sources, showed the extent to which the
Greeks admitted they had borrowed their learning
from the Egyptians..." --ibid., p. 435
Bernal remarks, with some bemusement (ibid., pp. 401,435)
that Stolen Legacy was "not considered as scholarship by
academics, and not even stocked by libraries." He continues,
"on the one hand, my training made me recoil at the lack of so
many of the outward trappings of scholarship; on the other, I
found that my intellectual position was far closer to the
black literature than it was to orthodox ancient history."
Let me close this post, which is already too long, with a
personal observation: when I first heard the term "afrocentric
history" my first reaction was "what a crock!" Surely, any
sort of "centrism" as applied to scholarship is wrong-headed,
in the same way that it would be wrong-headed to even conceive
of, say, "afrocentric nuclear physics". So, black though I
am, I recoiled. It is only several books later (Cheikh Anta
Diop is especially enlightening), that I see the point. The
notion of afrocentric history is only necessary because of the
*eurocentric* distortions and revisionism of the 19th and 20th
centuries to which we have all been subjected, mostly
unknowingly, and to the general derogation of black people.
In the end, it will be the truth that sets us all free, at
which point the only appellation necessary for history, as for
science, would be "truth-centric". Even if the afro-centrists
sometimes err on minute points of fact, I still somehow doubt
that the "Aryan model" will be left standing after even the
most rigorous scrutiny is applied to the afro-centrist
scholars.
> non-archimedean systems like those initiated in Abraham Robinson's
> non-standard analysis, admit infinitesimals and actual (non-Cantorian)
> infinitely large numbers, which are dear to the hears of many
> physicists, chemists and engineers). My most recent article
> appeared in a book called *Real Numbers, Generalizations of the
> Reals, and Theories of Continua*, edited by Philip Ehrlich, Synthese
> Library (Kluwer Academic) 1994, p 107-146. The article is called
> "Veronese's Non-Archimedean Linear Continuum*, and I like
> to try to impress people by pointing out that the article
> following it is by Henri Poincare' (and the article
> preceding it is by J H Conway, on "The Surreals and Reals").
Interesting. I like to think of the reals as a labelling scheme,
one that in principle allows an infinitesimal point in a continuum
to be uniquely labelled, distinguishing it from every other point.
But that this labelling scheme is more an accomplishment of the
imagination than an accomplishment that may be realized practically.
It cannot be realized practically, because to do so would require
an unending sequence of words (digits) to so characterize any
point in a continuum. In a finite life, we do not have the time.
Therefore, inevitably, we approximate reals--infinitesimal points--
by pairs of rational numbers, one constituting a lower bound,
the other an upper bound, and we may choose the level of precision
that we want. This is an important notion for the fuzzy set theory,
because, seen in its most abstract generality, fuzzy set theory
allows us to mediate between the point idealization of empirical
data as belonging to the reals, and the fuzzy reality that empirical
data are in general *clusters* of reals, moreover clusters for which
the boundaries are not as crisp as the bracketing implied by
use of rational lower and upper bounds. Thus, as applied to
measurement in general, and thence to issues of statistical and
other inference, fuzzy may be seen as bringing the reals back from
the level of mere idealization, important though that is, back to the
empirically realizable (no pun intended). But we both digress.
> Gordon Fisher fishergm@jmu.edu
Regards,
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