Exactly.  And even though we're conflating the model of evolution with the real 
thing, I find it difficult to believe the "space" operated on by evolution is 
entirely convex or even connected.  So, (point) mutation alone may *never* 
reach some regions, regardless of infinite individuals, infinite generations, 
or infinite space and time.

On 08/12/2017 09:07 AM, Marcus Daniels wrote:
> "Can we truly say that the crossover had nothing to do with the "innovation" 
> ... that it only preserved the innovation and the mutation caused it?  A 
> neutral mutation can't be considered an "innovation", right?"
> A function related by rotation might be a candidate for crossover.
> f(x,y,z,...) -> good
> f(y,z,x,...) -> good
> f(z,x,y,...) -> good
> f(x,z,y,...) -> bad
> Going through the combinations just by using mutation takes forever.  But 
> splicing at different points would help.   One could imagine for motor 
> functions these symmetry or shift detectors could be important.   (Here it is 
> just 1 dimensional.)


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