Is a game situation in chess topologically invariant?

[moriheru]

The thought just struck my mind, while I was reading "The art and craft of problem solving", whether a game of chess can be topologically defended and is topologically invariant. For example a game play where only the pawn has been moved to E3 is some sort of topological figure and the initial game situation is another topological figure. Will the two be topologically invariant? By game situation I mean some arrangement of pieces on a board . Any thoughts...

 

[fresh_42]

By game situation I mean some arrangement of pieces on a board .

You need not explain the only understandable part of your question, although it is commonly called a position.

Any thoughts...

Yes, what is "topological" here? Can you define a topology, that reflects the game somehow? Only then it makes even sense to talk about invariants and the term "topological".

 

[WWGD]

You need not explain the only understandable part of your question, although it is commonly called a position.

Yes, what is "topological" here? Can you define a topology, that reflects the game somehow? Only then it makes even sense to talk about invariants and the term "topological".

I assume certain moves may somehow disconnect a figure , and some moves may create or remove loops?

 

[fresh_42]

I assume certain moves may somehow disconnect a figure , and some moves may create or remove loops?

This sounds as it's a the first step towards a position evaluation algorithm, which are meanwhile pretty good. Nevertheless, I doubt that the main tool to do this is of topological nature, rather heuristic methods from game theory. Topologies are in my opinion at best induced by some measures or evaluation functions. I doubt that the other way around is worthwhile.

 

[WWGD]

This sounds as it's a the first step towards a position evaluation algorithm, which are meanwhile pretty good. Nevertheless, I doubt that the main tool to do this is of topological nature, rather heuristic methods from game theory. Topologies are in my opinion at best induced by some measures or evaluation functions. I doubt that the other way around is worthwhile.

Yes, I agree, I did not give it too much thought, just trying to understand what s/he may have meant. EDIT: I guess since Topology is now being used to analyze data for noise ( e.g., Persistent Homology) , who knows where else it may apply?