The JavaScript argument doesn't really get at the point I was trying to make (poorly, probably). The parent was arguing that since almost all functions are uncomputable, "some aspects of reality might only be accurately described by uncomputable functions."

This seems unlikely to me. Functions are a mathematical abstraction. Almost all of those functions are uncomputable, but what does the universe care? In what manner could the universe be organized in such a way as to depend on an uncomputable function?

Perhaps a better question for my above post would have been:

Can we imagine any empirical experiment to distinguish between a universe that depends on uncomputable functions and one that does not?

Edit: And if not, in what sense can the universe actually depend on an uncomputable function if we can't distinguish?