On Wed, Jul 31, 2024 at 10:49 AM PGC <[email protected]> wrote:
*> I checked the paper again and instead of a response through my phone, > I'll try to be a bit clearer and leave out the psychology: * > > *The misconception is that humans cannot be Turing machines because they > lack infinite tape. In "On Computable Numbers, With An Application To The > Entscheidungsproblem," Turing describes Universal Turing Machines (UTMs) > using finite tables of instructions, with no inherent need for infinite > resources. Each UTM operates based on a finite set of rules and > transitions, handling finite inputs and outputs. The notion of an infinite > tape is often misinterpreted; Turing's idea was that the tape could be > extended as needed for any computation, ensuring sufficient resources for > finite tasks rather than literally requiring an infinite resource. Turing's > formalism re UTM does not involve actual infinities; UTMs are finite > machines with finite instructions. * > > *Turing addresses the ambiguity of functions that may not halt, consistent > with practical computing where some algorithms may run indefinitely. > Therefore, the argument that humans cannot be Turing machines due to a lack > of infinite tape is based on a misinterpretation of Turing's work. Turing's > detailed description of UTMs involves finite tables, instructions, and > inputs, making it clear that UTMs are finite in every way. This aligns with > the practical realities of computation and human cognition, reinforcing the > idea that human cognitive processes can be viewed as computational within > Turing's theoretical framework.* > *I mean, if you approach a UTM with a set of instructions that require the > full expression of some transcendental number committed to memory in > decimals, then hopefully the UTM is rich enough in reasoning abilities to > ask you for your medical history/habits, instead of letting you start > expressing the full description of your instructions. 😅 Looking at the > paper, this seems too absurd to even mention there.* > Another way to say that is that whenever you observe a Turing Machine that has stopped (a.k.a. has finished its calculation) you will find it has only used a finite amount of tape, and whenever you observe a Turing Machine that is still running you will also observe that it has only used a finite amount of tape. John K Clark See what's on my new list at Extropolis <https://groups.google.com/g/extropolis> mt0 -- 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 [email protected]. To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/CAJPayv0WD8LcHDhxkKwpnp6fXKTU%2BN0vEzz9WtG3bS9FFf_Gdw%40mail.gmail.com.
