Saturday, December 15, 2012
Ones and ohs
The image above is a Penrose Tiling pattern borrowed from Wikipedia. Pretty neat. Selvam uses the Penrose pattern based on the Golden Ratio in nearly all her work. One of the problems with the types of chaotic systems she deals with is that every frigging thing is chaotic. Even computer calculations are chaotic to a degree because of rounding errors that build with each new calculation using a value with a rounding error. The computers are useful even though inaccurate because we know about rounding errors and correct in short problems. One third is 0.333333333... forever, 1/3 is simple, it is 1/3, one third, one part in three. WE simplify, computers don't.
The golden ratio (1+5^0.5)/2 = 1.6180339887 blah blah blah is never repeating. So if you are into the Golden Ratio, computers and complex problems, you are screwed. Ah, but... what if you use the Golden Ratio Base? The then computer ones and zeros would be (1+5^0.5)/2 or zero, with the placement of the zero indicating a power of the Golden Ratio.
When WE created base 2 for computers and the logic associated with base two compatible with a base 10 world, WE created problems. The damn French done it! Metric sucks because the world is not base 10! Hell, base 12 or base 60 would make more sense than base 10. But since WE have an average of 10 fingers and ten toes, WE think in base 10.
It is too late to fix that, evolution may eventually give us an extra dew claw per appendage,but for now we are stuck with ten. It may not be too late for computers though.
This may be my craziest post ever, but from a few trial calculations, climate really does like Phinary.
My quote of the day: When you use base 2 to produce a base 10 answer for a base phi problem you end up right where we are :)