You can think of it as Eigenvectors spanning a subspace. Sure, you can choose a different base, but that shouldn't make much of a difference. If it does, you are not spanning the same subspace?

There are different realizations of the same effective functions in the animal kingdom already. Consider octopuses, spiders, etc. Their brains realize similar functionality via quite different structural organization.

But do you subjectively experience the exact structure of your brain? Evidently, you can only discern some abstract meta-level. An effective function.