Re: “a serial machine can emulate a parallel one, thus this distinction isn’t relevant.”
Kolmogorov complexity/Solomonoff induction are language-specific. Not all languages are equivalent, and descriptions in different languages may be totally different lengths. It is true that any universal machine can simulate any other—but it takes a description of that simulator to do so, and that takes up space, which is a big deal, if the simulation is not tiny.
Re: They only depend to within a constant factor. That’s not the problem [...]
That /is/ a problem, when the “constant factor” is of the same order of magnitude as the things you are measuring. How complex it PI? “Print PI;” is not very complex, but its complexity grows if you have to implement a whole interpreter first.
The issue of what language to use /is/ a real issue. IMO, the case for using Turing machines is poor, because they are crappy one-dimensional serial computers, which were never intended for actual use.
My position is that we ought to use real small machines to measure complexity if we are doing practical things, such as judging scientific laws. But this is a moving target—and it means that we don’t know how to measure complexity properly yet, because we cannot yet construct molecular computers.
...but even in our current state of ignorance, we can do better than use a Turing machine. Almost anything is better than using a Turing machine.
Re: “I don’t believe most scientists would make such huge mistakes”—the CI really is pretty stupid, retrospectively, IMHO.
Re: “a serial machine can emulate a parallel one, thus this distinction isn’t relevant.”
Kolmogorov complexity/Solomonoff induction are language-specific. Not all languages are equivalent, and descriptions in different languages may be totally different lengths. It is true that any universal machine can simulate any other—but it takes a description of that simulator to do so, and that takes up space, which is a big deal, if the simulation is not tiny.
Re: They only depend to within a constant factor. That’s not the problem [...]
That /is/ a problem, when the “constant factor” is of the same order of magnitude as the things you are measuring. How complex it PI? “Print PI;” is not very complex, but its complexity grows if you have to implement a whole interpreter first.
The issue of what language to use /is/ a real issue. IMO, the case for using Turing machines is poor, because they are crappy one-dimensional serial computers, which were never intended for actual use.
My position is that we ought to use real small machines to measure complexity if we are doing practical things, such as judging scientific laws. But this is a moving target—and it means that we don’t know how to measure complexity properly yet, because we cannot yet construct molecular computers.
...but even in our current state of ignorance, we can do better than use a Turing machine. Almost anything is better than using a Turing machine.
Re: “I don’t believe most scientists would make such huge mistakes”—the CI really is pretty stupid, retrospectively, IMHO.