I think is usefull to think at computations using a graphic representation , it is not easy to make a correct representation but also a big approximation can be a good one

I use a circle to represent the computational power , a program that search a solution in a brute force on a limited space-time available resource . In the circle the radius is the computational power and it is limited by the area inside the circle. The center of the circle are the hypothesis or the language usedÂ or the machine used or the context. The red point in the first image is the solution . The distance between the center and the red point is the information distance to cover to find the solution.

The set of all existing points is less than all possible points so instead to construct a big circle to cover all possible points is better to draw a lot of circles with different centers , different context .

The problem is how to construct the context?

In this image I show a possible configuration

every circle is a computation starting from a context ( the center ) and in this case there are center with a distance less than the radius so there are waste computations. To separate the contexts we need to compress them.

The compression is a movement in the Kolmogorov complexity direction and in the graphical representation this mean to redux the number of center and separate each center.

as showed in the above image . Compressing to much the context has the side effect to separate too much the centers without the possibility to cover all the space using the computational resource available ( I need a bigger radius ) .

The best solution is to compress the context to obtain the minimum distance between the circles

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