I actually agree that if we assume that there’s a finite maximum of atoms, we could in principle reformulate the universal computer as a finite state automaton, and if we were willing to accept the non-scalability of a finite state automaton, this could actually work.
The fundamental problem is that now we would have software that only works up to a specified memory limit, because we essentially burned the software into the hardware of the finite automaton and if you are ever uncertain of how much memory or time a problem requires, or more worryingly if we were ever uncertain about how much resources we could actually use, then our “software” for the finite automaton is no longer usable and we’d have to throw it away and recreate a new computer for every input length.
Turing Machine models automatically handle arbitrarily large inputs without having to throw away expensive work on developing the software.
So in essence, if you want to handle the most general case, or believe unbounded atoms are possible, like me, then you really want the universal computer architecture of modern computers.
The key property of real computers that makes them Turing Complete in theory is that they can scale with more memory and time arbitrarily without changing the system descriptior/code.
More below:
(If we assume that we can only ever get access to a finite number of atoms. If you dispute this I won’t argue with that, neither of us has a Theory of Everything to say for certain.)
I think I understand the question now.
I actually agree that if we assume that there’s a finite maximum of atoms, we could in principle reformulate the universal computer as a finite state automaton, and if we were willing to accept the non-scalability of a finite state automaton, this could actually work.
The fundamental problem is that now we would have software that only works up to a specified memory limit, because we essentially burned the software into the hardware of the finite automaton and if you are ever uncertain of how much memory or time a problem requires, or more worryingly if we were ever uncertain about how much resources we could actually use, then our “software” for the finite automaton is no longer usable and we’d have to throw it away and recreate a new computer for every input length.
Turing Machine models automatically handle arbitrarily large inputs without having to throw away expensive work on developing the software.
So in essence, if you want to handle the most general case, or believe unbounded atoms are possible, like me, then you really want the universal computer architecture of modern computers.
The key property of real computers that makes them Turing Complete in theory is that they can scale with more memory and time arbitrarily without changing the system descriptior/code.
More below:
https://www.dwarkesh.com/p/adam-brown