ATON is a hopefully evolving classification theory. It aspires to unify knowledge around numbers and prefers naive methods. Some of the older posts are wrong but I'll keep them for the sake of continuity.

Monday, June 21, 2010

Eight aspects of economy

Economy is determined by the methods of production and consumption. It determines the other aspects of societies, as much as it is determined by them. The simplest form of economy is gathering and hunting, and it seems to form a duality;

(Gathering,Hunting)

since hunter gathers the gatherer. Grazers, which are essentially gatherers, are usually accompanied by hunters. Although hunters can not exist without grazers, grazers are in turn shaped by hunters.

A similar duality exists for the next stage of economy;

(Farming,Industrial)

Farming is a tool intensive occupation, more than that of gathering and hunting. Industrial production is a step ahead of farming in that, it is a machine intensive occupation. Machines are tools of tools; they bring together many tools and operate them according to flowcharts. This is also reflected in their utilization in production lines.

The next natural stage of economy is also a duality;

(Information,Intelligence)

We have recently entered the information economy. As it matures, it paves the way for its partner; artificial intelligence. AI systems are already here and evolving with the intensive use of the systems of information.

What is the next stage, if there will be such a thing? Intelligence is strongly linked to psychology, which is the foundation of our spirituality. By implication, there seems to be another duality as the last stage of the evolution of economy;

(Spiritual,Artistic)

In fact all four dualities already exist in many forms, but only one is dominant at any time. Currently we are transiting from the industrial to the information economy. One can only wonder what kind goodies will evolve after the AI economy matures and paves the way to the next stage.

Thursday, January 14, 2010

Self similarity of z/log(z)

I made the following pics by temporally iterating 3 spatial iterations;

z/log(z)
(z/log(z)) / log(z/log(z))
[(z/log(z)) / log(z/log(z))] / log[(z/log(z)) / log(z/log(z))]

The temporal iteration number is 170. Bailout is 40. The 4th pic is a close-up of the 3rd. They came about after a Google group discussion.

The 3 pictures similarity is amazing I thought. Just like the temporal iteration increasing resolution, the spatial iteration seems to do the same. I think there is a strong link here to the prime numbers, whose distribution is known to be self similar. Apart from the known fact that the primes are semi uniformly distributed in x/log(x), they seem to obey the H-fractal in their further patterns.

Another very interesting point here is that the both temporal and spatial iterations limit to 'e' at the outer region of the shape;

...(z/log(z)) / log(z/log(z))... -> e

demonstrating the binary structure of 'e'.









































































The tip of the last amplified to the limit of my pc. Note the slight angle. Numbers seem to prefer a side, as far as this function is concerned. This may be due to the accumulation of errors. If not, then this is also very interesting.



















The semi-stable points. What is the link to the zeros of the Riemann's Zeta function?

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