CharlesB at SPAMCNCL.ci.detroit.mi.us
Mon Apr 23 12:08:50 MDT 2001
>>> jcraven at clark.edu 04/23/01 01:24PM >>>
Response: Note that the term discovered was written "discovered" as in a
sarcastic use of the term discovered. Sort of like Columbus--or the Vikings
or the whatever non-Indigenous "discovered" America. How do you "discover" a
place with people already there? Same with the concept of Zero. As to who
first discovered--and used--the concept of Zero, I have no idea.
CB: Anyway, whoever discovered zero, discovered nothing,as you say below.
In Indigenous mathematics, the logic was dialectical and simple and yet not
so simple: If you have SOMEthing, you cannot have such a concept without the
concept of NOthing (like the concept of good without the concept of evil and
vice versa). Each SOMEthing, can be viewed as a quantity and a quality and
has a positive and negative aspect.
If you add or subtract NOthing to a SOMEthing, or a quantity of SOMEthings,
(0 +/-6 = 6) you can only have the original amount of SOMEthings. If you
multiply NOthing by whatever number, NOthing is NOthing and therefore
however many NOthings you still have ( 0 x 6 = 0) NOthing. Since they
understood that +1 or +2 SOMEthings implied a given distance from a
reference point, and that -1, -2 SOMEthings also implied equal (and
opposite) distances from a given reference point, there must be some central
and defining reference point for counting +/1 SOMEthings; that must be
NOthing or Zero.
On the division problem, the Mayans, Aztecs and Incas, who produced
incredibly complex temples, on the shere-faces of some mountains in
locations and with such precision as could not be duplicated with "modern"
tools and engineering methods and machinery, had a concept of "infinte
divisibility" (as embodied in Zeno's paradox: If I set out to demonstrate
against U.S. imperialism in Washington, D.C. and each day I go half the
remaining distance, I will never get there); some of the 5-ton blocs laid
next to/on-top of each other are so closely spaced and alligned that not
even a piece of paper can be slipped between them; they had to divide and
sub-divide with incredible precision and very fine sub-division. Since they
knew that as the divisor of each whole was halved, it doubled the dividend (
1/1 = 1; 1 / 1/2 = 2; 1 / 1/4 = 4 etc, therefore 1/0 must be indeterminate
or close to infinity...) Further, as the Mayan Calendar (approx 1750 BCE) is
still know as the most accurate among the world's calendar's (
astronomically speaking and in terms of predictive validity), Mayans
obviously had very precise concepts of time and movements of /changes in
things over time (differentiation and integration).
CB: So calculus has a big part of its origin in division by zero and related concepts
? and the Mayans had a form of calculus ?
In arithmetic they must mean that you can't divide by zero, because we are not ready
to deal with that yet. But I think kids could understand exploration of the concept of
dividing by zero.
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