So, what I think is that for some continuous output and any epsilon you care to name, one can construct a totally normal computer with resources 1/delta that can approximate the continuous output to within epsilon.
Proceeding from there, the more interesting question (and the most observable question) is more like the computational complexity question—does delta shrink faster or slower than epsilon? If it shrinks sufficiently faster for some class of continuous outputs, this means we can build a real-number based computer that goes faster than a classical computer with the same resources.
In this sense, quantum computers are already hypercomputers for being able to factor numbers efficiently, but they’re not quite what I mean. So let me amend that to a slightly stronger sense where the machine actually can output something that would take infinite time to compute classically, we just only care to within precision epsilon :P
So, what I think is that for some continuous output and any epsilon you care to name, one can construct a totally normal computer with resources 1/delta that can approximate the continuous output to within epsilon.
Proceeding from there, the more interesting question (and the most observable question) is more like the computational complexity question—does delta shrink faster or slower than epsilon? If it shrinks sufficiently faster for some class of continuous outputs, this means we can build a real-number based computer that goes faster than a classical computer with the same resources.
In this sense, quantum computers are already hypercomputers for being able to factor numbers efficiently, but they’re not quite what I mean. So let me amend that to a slightly stronger sense where the machine actually can output something that would take infinite time to compute classically, we just only care to within precision epsilon :P