I’ll try to mention that the fact that computability is not equivalent to simulatability is the reason I wouldn’t edit my post like that. I will always make clear when I’m switching to a non-standard frame.
I loved it! 😉 However I’d love more meat on what problems are better seen through the lens of simulability. Could you elaborate or provide a specific example?
For a good example from a Turing Machine, obviously, the halting function would be the obvious example of simulability but not computability. Basically any function that is turing reducible to the halting problem would be a good example of simulability but not computability for Universal Turing Machines.
Yes, I get that « periodically switching between non computable tasks » is your paradigmatic case for simulability. The question is: what do you think could get accomplished through this definition? In other words, I could take a pen and write « This is a non standard number. », but that would still be just one piece of paper. In what sense is the notion of simulability better than that?
Essentially, I’m using the definition of the first paragraph of this wikipedia article, where you imitate a real world system. although in this case, the model of the real world and the real world are the same object, so the simulation connotations usually used in lower-scale regimes break down, and thus I will be treating simulation and the real world as the same object.
Ok then that’s standard language and there’s no need to redefine it, you’re right.
Let’s try another example if you indulge my curiosity. If I use some cryptographic method you won’t be able to crack it without hypercomputing, but you could simulate cracking it if you could guess the secret. Is that the kind of thing you have in mind?
I’ll try to mention that the fact that computability is not equivalent to simulatability is the reason I wouldn’t edit my post like that. I will always make clear when I’m switching to a non-standard frame.
For a good example from a Turing Machine, obviously, the halting function would be the obvious example of simulability but not computability. Basically any function that is turing reducible to the halting problem would be a good example of simulability but not computability for Universal Turing Machines.
Yes, I get that « periodically switching between non computable tasks » is your paradigmatic case for simulability. The question is: what do you think could get accomplished through this definition? In other words, I could take a pen and write « This is a non standard number. », but that would still be just one piece of paper. In what sense is the notion of simulability better than that?
Essentially, I’m using the definition of the first paragraph of this wikipedia article, where you imitate a real world system. although in this case, the model of the real world and the real world are the same object, so the simulation connotations usually used in lower-scale regimes break down, and thus I will be treating simulation and the real world as the same object.
Link is below:
https://​​en.wikipedia.org/​​wiki/​​Simulation
Ok then that’s standard language and there’s no need to redefine it, you’re right.
Let’s try another example if you indulge my curiosity. If I use some cryptographic method you won’t be able to crack it without hypercomputing, but you could simulate cracking it if you could guess the secret. Is that the kind of thing you have in mind?