Harry Potter and the Methods of Rationality discussion thread, part 8

Unnamed

Update: Discussion has moved on to a new thread.

The hiatus is over with today's publication of chapter 73, and the previous thread is approaching the 500-comment threshold, so let's start a new Harry Potter and the Methods of Rationality discussion thread. This is the place to discuss Eliezer Yudkowsky's Harry Potter fanfic and anything related to it.

The first 5 discussion threads are on the main page under the harry_potter tag. Threads 6 and on (including this one) are in the discussion section using its separate tag system. Also: one, two, three, four, five, six, seven. The fanfiction.net author page is the central location for information about updates and links to HPMOR-related goodies, and AdeleneDawner has kept an archive of Author's Notes.

As a reminder, it's often useful to start your comment by indicating which chapter you are commenting on.

Spoiler Warning: this thread is full of spoilers. With few exceptions, spoilers for MOR and canon are fair game to post, without warning or rot13. More specifically:

You do not need to rot13 anything about HP:MoR or the original Harry Potter series unless you are posting insider information from Eliezer Yudkowsky which is not supposed to be publicly available (which includes public statements by Eliezer that have been retracted).

If there is evidence for X in MOR and/or canon then it's fine to post about X without rot13, even if you also have heard privately from Eliezer that X is true. But you should not post that "Eliezer said X is true" unless you use rot13.

Update: Discussion has moved on to a new thread.

You do not need to rot13 anything about HP:MoR or the original Harry Potter series unless you are posting insider information from Eliezer Yudkowsky which is not supposed to be publicly available (which includes public statements by Eliezer that have been retracted).

If there is evidence for X in MOR and/or canon then it's fine to post about X without rot13, even if you also have heard privately from Eliezer that X is true. But you should not post that "Eliezer said X is true" unless you use rot13.

I always wondered when/if Harry would figure out that the way magic works is evidence for the simulation argument. I just started rereading the old chapters, and found this in chapter 14:

You know right up until this moment I had this awful suppressed thought somewhere in the back of my mind that the only remaining answer was that my whole universe was a computer simulation like in the book Simulacron 3 but now even that is ruled out because this little toy [the time turner] ISN'T TURING COMPUTABLE!

I think his assumption that this rules out the simulation argument is misguided. Assume you have a universe that can compute things that a Turing machine cannot. Shouldn't people in this universe be able to build computers that can also compute things that a Turing machine cannot, since it would be built using their universe's physics?

Consider: The Time-Travel Turing machine (TTTM). This is just like a normal Turing machine, except it has two additional commands that can appended to state definitions: The 'accept' command simply marks that, at this point, all the bits to the right of the TTTM's position on the tape may be changed by an agent other than the current TTTM. The 'send' command copies all bits to the right of the TTTM on the tape, sends them back in time to the last 'accept' command, and puts them to the right of where the TTTM was then. TTTMs constructed such that no stable time loop is possible will just stop after encountering the first 'accept' command. All others go into stable time loops.

A TTTM could be used to simulate a world with time-travel that works that way, and you should be able to make one in a world with time-travel that works that way. Essentially, this means that if Harry is in a simulation, then the real world isn't Turing computable either. He could still be in a simulation, though.

Note (not related to my main point): A TTTM has the disadvantage of not being able to have time loops inside time loops, since it can't send anything back in time to before the last time it encountered the 'accept' command. One way of remedying this is by requiring that signals be sent longer ago than the previous step; if an 'accept' command is immediately followed by a 'send' command, the signal will go the second-last 'accept' instead. That way, the first bit to the right of the TTTM can be used to determine whether or not to chain the rest of the signal farther back. This formulation may have its own problems, though. I suddenly find the problems of how best to formulate a TTTM and what all it could do to be very interesting.

There's actually, unless I've made a stupid mistake, an even better algorithm that is Truing computable, if very slow:

every time the value of a bit may depend on future events, split the universe and calculate both possibilities. If a branch ever implies a paradox prune that branch and pretend it never happened.

Actually, while this indeed would require a ludicrous amount of branching for an universe where arbitrary chunks of matter can be transported back to any given plank time, all those branches would need to be computed anyway for MWI quantum mechanics. So all you're really doing is tweaking the MEASURE of each branch.

9TobyBartels15y

It's also an invalid conclusion for other reasons. Harry hasn't actually done anything uncomputable with a time turner, and the one occasion that he came close (trying something computable but slow), all that he got for his pains was ‘DO NOT MESS WITH TIME’. It's very easy to compute this. Even if Harry does something that seems uncomputable, that proves nothing [ETA: although of course it is evidence and Harry's estimate of simulation should go down in accordance with Bayes's Rule], since he only observes finitely many experiments, and any finite result is (trivially) computable. It's always possible that the system could break down when you push it further. (Presumably it has an error catcher that outputs ‘DO NOT MESS WITH TIME’ when this happens.) As far as we know, the real world is computable, and it's computed this story. Therefore nothing in it is definitely uncomputable.