[hyperpallium]

tl;dr having multiple genotypes for the same phenotype is inevitable if the genotype space is smaller than the phenotype space; the mapping is not injective (it's not one-to-one); a projection.

Making this local, where adjacent points map to the same phenotype can be trivial, e.g. ignoring one dimension of a 10 column row in a database. But an interesting local mapping seems much rarer: where you can change one dimension in one step (and still get the same phenotype), then change a different dimension in the next step, etc, so that the path through space is not just one dimension varying, but a jagged winding path.

This is important for the "path" (or connected genotypes with the same phenotype) to have a large surface area, which increases the chance of contact with the path of another phenotype (and that phenotype has some usefulness).

That's the main problem: that there be adjacency "transfer points" between useful phenotypes. It seems to me that in the huge exponentially large spaces we're talking about, they would be very rare, unless the mapping had some special qualities (which would make sense if the mapping itself had been selected by evolution - so the "selfish gene" is only secondarily in charge; the mapping is the primary one - and possibly, mutation strategies, like sex, and other as-yet undiscovered ones, that might be analogous to factoring or expanding, so the genotype can change dramatically in one step, but remain equivalent).