### Aztec Arithmetic

Pretty cool paper in this morning's "Science". Basically by surveying Aztec land plots, Geologists believe they have found evidence of an "indigenous arithmetic" in the Aztec DRAWINGS

From Science:

Aztec Arithmetic Revisited: Land-Area Algorithms and Acolhua Congruence Arithmetic
Barbara J. Williams1 and María del Carmen Jorge y Jorge2*

Acolhua-Aztec land records depicting areas and side dimensions of agricultural fields provide insight into Aztec arithmetic. Hypothesizing that recorded areas resulted from indigenous calculation, in a study of sample quadrilateral fields we found that 60% of the area values could be reproduced exactly by computation. In remaining cases, discrepancies between computed and recorded areas were consistently small, suggesting use of an unknown indigenous arithmetic. In revisiting the research, we discovered evidence for the use of congruence principles, based on proportions between the standard linear Acolhua measure and their units of shorter length. This procedure substitutes for computation with fractions and is labeled "Acolhua congruence arithmetic." The findings also clarify variance between Acolhua and Tenochca linear units, long an issue in understanding Aztec metrology.

1 Department of Geography and Geology, University of Wisconsin–Rock County, Janesville, WI 53546, USA.
2 Instituto de Investigaciones en Matemáticas Aplicadas y en Sistemas, FENOMEC, Universidad Nacional Autónoma de México, Ciudad Universitaria, 04510 México D.F., Mexico.

I don't know. To me congruence is a very visual thing: proportions are readily analyzed as patterns. "Homothetie" (sorry using the french mathematical word) is taught in 10th grade for good reason, it is easy to grasp and the mathematical tools, vector analysis, is trivial to apply. But to me it doesn't really mean they have ARITHMETIC, rather than GEOMETRY. GEOMETRY is visual, like you constraint the resizing of a picture in Photoshop by linking length and height as you resize. You don't need formal training in algebra to grasp these notions. Only when you abstract the trivial visual understanding of congruence and you try to lay it down in equations do you need the tools of arithmetic. In other words, there may be physical constraints, I don't know maybe division of labour, that may explain why the proportions of these fields. It also entirely possible that the Aztec architect was high all the time, I mean both on drugs and looking at those fields from a distance, literally, and thought those proportions looked good and they are actually VERY CLOSE to the "golden number" proportions, which looks good to the human brain and is very close to the C drawings.

That being said, I haven't bothered to actually read the "proof" included in the paper.

pcleddy said…
well, hegel talks a lot about implicit and explicit knowledge, and it seems to me to play a role here

i am the type that can't throw a football right, or ski down a hill until some excellent and fortunate teacher gives me the explicit physical notions that i can use to breakdown the phenomena, and tweak the variables to make things work. eg friction applied by weight upon a ski w/ a particular vector. hey, i'm turning!

and i envy the fucks who just pick up the ball, have dad toss a few w/ them, and, badda boom, they are throwing the runner out from center field.

hate = envy

nothing beats intuition. i guess we need a term for extuition for sorry ass types like myself

anyhow, this seems a case of intuition over explication. not that it doesnt do wonders. but i think the "western" turn, is the endless fascination w/ the explicit deconstruction

and, hence, the artist's guffaw at the nerd. the nerd that designed the factory that makes his bread

"the power or faculty of attaining to direct knowledge or cognition without evident rational thought and inference"
Marcf said…
right exactly, intuition in this case may just be a natural propention to enjoy proportions. The golden ratio applied to aerial field design may just be an expression of balance more than it is an explicit proof of math knowledge. Like I said instead of pulling a Roy (working vaguely from intuition ) I will read the paper article when I get it and give it a fair chance, if I can understand it. Science is a bitch.
pcleddy said…
wanted to run more shit by you:

http://www.evworld.com/article.cfm?storyid=1409

ya, i am in some paranoid circles :) we dont watch TV, so need a thrill somehow