On Sat, Jul 13, 2024 at 06:21:58PM -0400, John Clark wrote: > On Sat, Jul 13, 2024 at 4:29 PM Brent Meeker <[email protected]> wrote: > > > > All Turing machines have the same computational capability. > > > Well that certainly is not true! There is a Turing Machine for any computable > task, but any PARTICULAR Turing Machine has a finite number of internal > states > and can only do one thing. If you want something else done then you are going > to have to use a Turing Machine with a different set of internal states. >
Hi Brent - you're just being a bit sloppy with terminology. All universal Turing machines are equivalent computationally, but not all Turing machines are universal. It's a moot point about whether a human can be considered a universal Turing machine - a human's finite lifetime is a problem, so you'd really need to consider something like a society of humans whose organisation extends beyond the finite lifetime of an individual human. Even then, there may well be limits to the amount of computation physically possible in the universe, depending on the universe's geometry (which gets us into Tipler's Omega point theory, for example). Cheers -- ---------------------------------------------------------------------------- Dr Russell Standish Phone 0425 253119 (mobile) Principal, High Performance Coders [email protected] http://www.hpcoders.com.au ---------------------------------------------------------------------------- -- 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/20240720024930.GB15533%40zen.
