Huh. This whole exchange makes me more certain than I am missing something crucial, but reading and dissecting it repeatedly does not seem to help. And apparently it’s not the issue of not knowing enough math. I guess the mental block I can’t get over is “why TL4?”. Or maybe “what other mental constructs could one use in place of TL4 to make a similar argument?”
Maybe paper-machine or someone else on #lesswrong will be able to clarify this.
Not sure why you are asking, but yes, I pointed some out 5 levels up. They clearly have a complexity penalty, but I am not sure how much vs TL4. At least I know that the “sloppy programmer” construct is finite (though possibly circular). I am not sure how to even begin to estimate the Kolmogorov complexity of “everything mathematically possible exists physically”. What Turing machine would output all possible mathematical structures?
What Turing machine would output all possible mathematical structures?
“Loop infinitely, incrementing count from 1: [Let steps be count. Iterate all legal programs until steps = 0 into prog: [Load submachine state from “cache tape”. Execute one step of prog, writing output to “output tape”. Save machine state onto “cache tape”. Decrement steps.] ]”
The output of every program is found on the output tape (albeit at intervals). I’m sure one could design the Turing machine so that it reordered the output tape with every piece of data written so that they’re in order too, if you want that. Or make it copypaste the entire output so far to the end of the tape, so that every number of evaluation steps for every Turing machine has its own tape location. Seemed a little wasteful though.
(Yep. More a than b, it still feels pretty unnatural to me.)
Huh. This whole exchange makes me more certain than I am missing something crucial, but reading and dissecting it repeatedly does not seem to help. And apparently it’s not the issue of not knowing enough math. I guess the mental block I can’t get over is “why TL4?”. Or maybe “what other mental constructs could one use in place of TL4 to make a similar argument?”
Maybe paper-machine or someone else on #lesswrong will be able to clarify this.
Have you got one?
Not sure why you are asking, but yes, I pointed some out 5 levels up. They clearly have a complexity penalty, but I am not sure how much vs TL4. At least I know that the “sloppy programmer” construct is finite (though possibly circular). I am not sure how to even begin to estimate the Kolmogorov complexity of “everything mathematically possible exists physically”. What Turing machine would output all possible mathematical structures?
“Loop infinitely, incrementing
countfrom 1: [Letstepsbecount. Iterate all legal programs untilsteps= 0 intoprog: [Load submachine state from “cache tape”. Execute one step ofprog, writing output to “output tape”. Save machine state onto “cache tape”. Decrementsteps.] ]”The output of every program is found on the output tape (albeit at intervals). I’m sure one could design the Turing machine so that it reordered the output tape with every piece of data written so that they’re in order too, if you want that. Or make it copypaste the entire output so far to the end of the tape, so that every number of evaluation steps for every Turing machine has its own tape location. Seemed a little wasteful though.
edit: THANK YOU GWERN . This is indeed what I was thinking of :D
Hey, don’t look at me. I’m with you on “Existence of T4 is untestable therefore boring.”