At its core, Funes is not really about memory - I've always felt that is a convenient hook to hang a piece of metaphysics. I prefer to regard it as a parable about identity and what it means that a thing is a particular thing.
"To think is to ignore (or forget) differences, to generalize, to abstract. In the teeming world of Ireneo Funes there was nothing but particulars..."
Funes would never have invented the Turing machine, because for him, instead of an infinite tape with a finite repertoire of symbols, a single square with an infinite repertoire of symbols would have sufficed.
For him, even the single square would not exist, only its many many ways it could be. And each separately.
> "No sólo le costaba comprender que el símbolo genérico perro abarcara tantos individuos dispares de diversos tamaños y diversa forma; le molestaba que el perro de las tres y catorce (visto de perfil) tuviera el mismo nombre que el perro de las tres y cuarto (visto de frente)."
> "Not only he struggled to understand that the generic symbol for dog would encompass so many disparate individuals of many sizes and diverse shapes; he was upset that the dog at three and fourteen (from the side) had the same name that the dog at quarter past three (from the front)."
Maybe it helps to regard it as an elaborate variation on The Ship of Theseus: https://en.wikipedia.org/wiki/Ship_of_Theseus
Note that it's many years since I read it and I tended to read Borges to avoid having to read actual books on philosophy. ;)