In mathematics a solution to a problem has to be less complex than the problem itself, otherwise the problem has no solution. This is not pie-in-sky theory there are mathematical problems where the solution is more complex than the problem therefore they are theoretically unsolvable.

Analysing the complexity of some chess positions may sometimes lend itself to the theory of unsolvable problems. As GM Natalia said in a different blog, the complexity of a position may not lie in the depth of combinations, but the evaluation of the position after the transactions. Evaluation being HOW does this position benefit me or my opponent. The transactions involved may be simple but the position arrived at may be difficult to evaluate, hence many GM draws where both parties decide that a seemingly simple looking position is frought with too much uncertainty and no one wants to risk the journey

as far as I know the more complex a position is:

1- the more is sharp

2- more possible solutions are available

3- the deeper the combinations have to be calculated

In theory if such measure exists it could be possible to identify the most complex chess games ever played