On Sunday, July 14, 2024 at 3:51:27 AM UTC+2 John Clark wrote:
Yes it's possible to have a universal Turing machine in the sense that you can run any program by just changing the tape, however ONLY if that tape has instructions for changing the set of states that the machine can be in. It still boggles my mind that matter is Turing-complete. And this despite parts of physics being not Turing emulable. We can implement Turing Machines with matter, and even with constraints in the physical world, it appears to be the basic principle of brains, cells, and computers. Just for clarity’s sake, we should distinguish the idea of Turing/universal machine with some demonstrative physical implementation, like some computer, tape machine, or LLM running on my table/in the cloud: By Turing machine, I mean a T machine u such that phi_u(x, y) = phi_x(y). We call “u” the computer, x is named the program, and y is the data. Of course, (x, y) is supposed to be a number (coding the two numbers x and y). And yeah, you can specify it with infinite tape, print, read, write heads, and many other formalisms that have proven equivalent etc. but the class of functions is the same. The set of partially computable functions from N to N with the standard definitions and axioms. There are a lot of posts distinguishing this computer here, that LLM there, that brain in my head etc. ostensively, as if we knew what we were talking about. If we believe we are Turing emulable at some level of description, then we are not able to distinguish between ourselves and our experiences when emulated in say Python, which is emulated by Rust, which is emulated by Swift, which is emulated by Kotlin, which is emulated by Go, which is emulated by Elixir, which is emulated by Julia, which is emulated by TypeScript, which is emulated by R, which is emulated by a physical universe, itself emulated by arithmetic (e.g. assuming arithmetical realism like Russell and Bruno), from “our self” emulated in Rust, emulated by Python, emulated by Go, emulated by Swift, emulated by Julia, emulated by Elixir, emulated by Kotlin, emulated by R, emulated by TypeScript, emulated by arithmetic, emulated by a physical universe… That’s the difficulty of defining what a physical instantiation of a computation is (See Maudlin and MGA). For if we could distinguish those computations, we’d have something funky in consciousness, which would not be Turing emulable, falsifying the arithmetical realism type approaches. And if you have that, I’d like to know everything about you, your diet, reading habits, pets, family, beverages, medicines etc. and whether something like gravity is Turing emulable, even if I guess it isn’t. Send me that message in private though and don’t publish anything. -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/602ae080-85fe-4a99-ab85-194dec7aae0fn%40googlegroups.com.
