[dragonwriter]

> My computer is for all practical purposes Turing complete

“For all practical purposes” is a long way of saying “not”; a large-but-finite tape is not infinite, and the key properties of Turing completeness (both universal computation and the consequent equivalence with all other Turing complete systems) do not hold with “finite but large tapes”, no matter if large is 640 kilobytes or 640 quettabytes. Particularly, differently structured “Turing complete but for finite size” systems of similar actual capacity in bytes are not guaranteed to be able to compute the same subset of all computable results. (Actually Turing machines with the same size tape would be, but “Turing complete but for size” does not imply a consistent ratio between problems of material storage space to equivalent Turing machine tape size.)

[kaba0]

Can you give me any way that can differentiate between my practical machine with memory sized n, and a real infinite Turing machine in a finite amount of time t?

If not, than for all purposes the two are the exact same, which is my point. This is not the case with LLMs.