From: David Buchanan (DBuchanan@ClassicalRadio.org)
Date: Sat Nov 08 2003 - 19:28:55 GMT
Paul, Ian and all intellectuals:
Pirsig wrote:
"Another subtler confusion exists between the word, "intellect," that
can mean thought about anything and the word, "intellectual," where
abstract thought itself is of primary importance. Thus, though it may be
assumed that the Egyptians who preceded the Greeks had intellect, it can
be doubted that theirs was an intellectual culture."
Paul said:
...Because of my assumptions of what "thinking" meant regardless of time and
place in history, I had decided that the intellectual level began with "the
first thought". If this is the case, I assumed ancient Egyptians
participated in the intellectual level. However, since I received this
reply, I've spent more time looking at historical evidence from this period
and in doing so I have let go of a lot of preconceptions about what it was
to be a human prior to the 3rd millennia BC. I am really glad I did this.
dmb says:
One of the many books that I don't really have time to read may shed some
light on this idea. Mario Livio's "THE GOLDEN RATIO: The Story of Phi, the
World's Most Astonishing Number" is not specifically aimed at supporting
Pirsig's assertion of course, but it seems to do so anyway. (And I'm
thinking that Ian would be interested in this for an additional reason. The
golden ratio is intimately related to fractals.) In any case, the author
begins with a discussion of the origins of numbers in human history. The
following quotes are from chapter two of THE GOLDEN RATIO.
LIVIO WRITES:
Cardinal numbers simply determine the pluratity of a collection of items,
such as the number of children in a group. Ordinal numbers, on the other
hand, specify the order and succession of specific elements in a group, such
as a given date in a month or a seat in a concert hall. Originally it was
assumed that counting developed specifically to address simple day-to-day
needs, which clearly argued for cardinal numbers appearing first. However,
some anthropologists have suggested that numbers may have first appeared on
the historical scene in relation to some rituals that required the
successive appearance of individuals during ceremonies. If true, this idea
suggests that the ordinal number concept may have preceded the cardinal one.
Clarely, an even bigger mental leap was required to move from the simple
counting of objects to an actual understanding of numbers as abstract
quantities. Thus, while the first notions of numbers might have been related
primarily to CONTRASTS, asociated perhaps with survival - Is it ONE wolf or
a PACK of wolves? - the actual understanding that two hands and two nights
are both manifestations of the number 2 probably took centuries to grasp.
dmb adds:
It seems that the suggestion of some anthropologists fits quite nicely with
the things Pirsig says about ritual, how it preceeded intellect. Livio seems
to be painting a picture of the pre-historic use of numbers as serveing a
survival function and a social function. And finally, we can see that the
"mental leap" required to understand numbers as an abstract concept could
have been part of the transition from the social to the intellectual level.
LIVIO WRITES:
Pythagoras was born around 570 B.C. ... Pythagoras probably lived for some
time (As long as 22 years, according to some accounts) in Egypt, where he
would have learned mathematics, philosophy, and religious themes from the
Egyptian priests. After Egypt was overwhelmed by Persian armies, Pythagoras
may have been taken to Babylon, together with members of the Egyptian
priesthood. There he would have encountered the Mesopotamian mathematical
lore. Nevertheless, the Egyptian and Babylonian mathematics would prove
insuficient for Pythagoras' inquisitive mind, To both of these peoples,
mathematic provided practical tools in the form of "recipies" designed for
specific calculations. Pythagorags, on the other hand, was one of the first
to grasp numbers as abstract entities that exist in their own right.
dmb adds:
Here I think we can see what Pirsig means when he says the Egyptians had
intellect despite the fact that their culture can't rightly be called
intellectual. Their mathematical "lore" served a priestly/religious
function.
LIVIO WRITES:
Even though it is almost impossible to attribute with certainty any specific
mathematical achievements either to Pythagoras himself or to his followers,
there is no question that they have been responsible for a mingling of
mathematic, philsophy of life, and religion unparalleled in history. In this
respect it is perhaps interesting to note the historical coincidence that
Pythagoras was a contemporary of Buddha and Confucius. Pythagoras is in fact
credited with having coined the words "philosophy" and "mathematics". ...
Pythagoras and the Pythagoreans are best known for their presumed role in
the development and for the application of mathematics to the concept of
order, whether it is musical order, the order of the cosmos, or even ethical
order.
dmb says:
Pretty cool, huh? Something big seems to have been happening in the 5th
century before our common era, just as Plato was about to arrive on the
scene. And as I've tried to show in the "Systematic about the Sophists"
thread, Plato was a Pythagorean. It seems that intellect was born trying to
express the oldest idea known to man; that there is an order and rightness
in the universe, one that can be detected in music, cosmology, morals and
everything else.
Thanks,
dmb
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