## Thursday, July 13, 2017

### Spheres

I have an idea how to limit the size of the hidden variable values we search through. Imagine we have n following hidden variables:

hidden variable v1:{false,true,none};
hidden variable v2:{false,true,none};
...
hidden variable vn:{false,true,none};

Then for any visible state we specify an initial point:

v1=>none,
v2=>none,
...
vn=>none

Instead of all the space we only search a "sphere" with the grade defined as an amount of hidden variables that differ from the initial point (center). For grade 0 we only have a center. For grade 1 we have:

v1=>none
v2=>none
..
v(i-1)=>none
vi=>false or true
v(i+1)=>none

...
vn=>none

Thus we only have one variable - vi - that differs from the center. For grade = 2 we will have two such variables. For grade = n all the hidden variables will differ from the center:

v1=>false or true,
v2=>false or true,
...
vn=>false or true

My idea is to search through a sphere of k-th grade for a given center point. It may happen that the center points differ depending on the visible state.

I will implement the bobr code generator so that it only searches through such spheres.

My inspiration was programming. When we write a program we do not search through the whole space of the programs since it is huge. Instead we move in the space of programs step-by-step.