Calculus
Craven, Jim
jcraven at SPAMclark.edu
Mon Apr 23 11:13:24 MDT 2001
J Enyang wrote:
Jim,
I don't know anything about the history of Mayan mathematics and would be
interested to know more about the subject. However, I don't think anyone
seriously claims that zero was "discovered in Europe" as you put it. Might
I suggest a bit of research on Indo-Arabic numberals?
Re cultures and mathematics, my greatgrandparents in central Africa were
familiar with the first few hundred positive integers. But they did not
know zero, algebra or any higher mathematics. Nor did they posses a
written script of any sort -- the traditions were purely oral. But,
needless to say, I don't think of anyone as more or less human for it.
So, yes to hell with Eurocentrism. But I won't dignify Eurocentrism by
contesting its (thoroughly spurious and contemptible) claims on its terms.
Regards,
J.Enyang
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.
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).
Jim C
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