Every Turing machine definition I’ve ever seen says that the tape has to be truly unbounded. How that’s formalized varies, but it always carries the sense that the program doesn’t ever have to worry about running out of tape. And every definition of Turing equivalence I’ve ever seen boils down to “can do any computation a Turing machine can do, with at most a bounded speedup or slowdown”. Which means that programs on Turing equivalent computer must not have to worry about running out of storage.
You can’t in fact build a computer that can run any arbitrary program and never run out of storage.
One of the explicitly stated conditions of the definition is not met. How is that not relevant to the definition?
Yes, this is correct, with the important caveat that the memory is unbounded by the systems descriptor/programming language, not the physical laws or anything else which is the key thing you missed.
Essentially speaking, it’s asking if modern computers can cope with arbitrary extensions to their memory and time and reliability without requiring us to write new programming languages/coding, not if a specific computer at a specified memory and time limit is Turing complete.
Looking at your comment more, I think this disagreement is basically a definitional dispute, in a way, because I allow machines that are limited by the laws of physics but are not limited by their systems descriptor/programming language to be Turing complete, while you do not, and I noticed we had different definitions that led to different results.
I suspect this was due to focusing on different things, where I was focused on the extensibility of the computer concept as well as the more theoretical aspects, whereas you were much more focused on the low level situation.
A crux might be that I definitely believe that given an unlimited energy generator, it is very easy to to create a universal computer out of it, and I think energy is much, much closer to a universal currency than you do.
Yes, this is correct, with the important caveat that the memory is unbounded by the systems descriptor/programming language, not the physical laws or anything else which is the key thing you missed.
Essentially speaking, it’s asking if modern computers can cope with arbitrary extensions to their memory and time and reliability without requiring us to write new programming languages/coding, not if a specific computer at a specified memory and time limit is Turing complete.
Looking at your comment more, I think this disagreement is basically a definitional dispute, in a way, because I allow machines that are limited by the laws of physics but are not limited by their systems descriptor/programming language to be Turing complete, while you do not, and I noticed we had different definitions that led to different results.
I suspect this was due to focusing on different things, where I was focused on the extensibility of the computer concept as well as the more theoretical aspects, whereas you were much more focused on the low level situation.
A crux might be that I definitely believe that given an unlimited energy generator, it is very easy to to create a universal computer out of it, and I think energy is much, much closer to a universal currency than you do.