Well, it’s been a while since I posted this, but maybe I should have made myself clearer. I only posted to say that the assumption of an AI giving us magic doesn’t need the additional assumption of time travel. The six hour time limit is for predicting the position, movement and interactions of everyone (both people and animals) ‘close’ to a potential time traveler. Prophecies are vague enough to not need this detail of prediction and can therefore be made for further into the future.
As to the question whether this AI assumption is actually the correct one I can only refer you to this quote from chapter 25:
So the words and wand movements were just triggers, levers pulled on some hidden and more complex machine. Buttons, not blueprints.
And just like a computer program wouldn’t compile if you made a single spelling error, the Source of Magic wouldn’t respond to you unless you cast your spells in exactly the right way.
Which could be a hint in this direction. I assume Eliezer’s quote on an AI not being a part of the story is just that, the story will be about Harry’s struggle with Voldemort, not about tracking down any sources of Magic.
I agree that obeying Novikov consistency seems to be a good description of the universe in HPMoR, but it is only a partial description since something prevented Harry from using this consistency to factor natural numbers in polynomial time, which should be possible in a universe that is ‘only’ Novikov consistent (meaning you need additional assumptions to prevent this).
something prevented Harry from using this consistency to factor natural numbers in polynomial time, which should be possible in a universe that is ‘only’ Novikov consistent (meaning you need additional assumptions to prevent this).
This had not occurred to me.
I thought this was simply a flaw in Harry’s methodology—he’s too self-aware for it to work. You need something that will reliably act according to the script, and only as described on the script—in short, a machine, not a person. Harry had failed to consider the possibility of messages that do not consist of factors.
I don’t think Eliezer makes a distinction here. Had Harry done this with a computer program it would probably output (and send back) the exact error message it would generate from getting said message as input, or something like that.
I was thinking of this myself, but only humans can be sent back in time using a time-turner. And since said humans probably also has to be magical I would guess another requirement is that they have to be scared off by the ‘Do not mess with time’ message (i.e. anyone getting that message and still trying to send a ‘0’ back in time would not be able to use the time-turner in the first place). So no ‘creating’ a human with this factoring algorithm instead of (or in addition to) a personality programmed into their brain-structure.
Harry can even do that experiment easily with our current technology, he just needs a printer and a scanner. He can even go somewhere else when he goes back in time to stop magic from messing with the computer.
The only way I can see this fail is if the time-turner either refuses to work when he tries to do this (per whatever requirements it puts on its users) or just kills him outright (given the threatening nature of ‘Do not mess with time’). So he should probably enlist someone else to take the message for him.
Either way, it would be nice to see Harry thinking of this experiment in HPMOR.
Of course, Harry doesn’t know why his experiment failed. In fact, the Do Not Mess With Time probably scared him out of trying to exploit the time travel mechanics.
That’s kinda impressive, actually—Eliezer found a way to avoid exploits that could break the system that follows naturally within the system. I doubt he’ll ruin all his hard work by having Harry figure it out, but you never know.
Well, it’s been a while since I posted this, but maybe I should have made myself clearer. I only posted to say that the assumption of an AI giving us magic doesn’t need the additional assumption of time travel. The six hour time limit is for predicting the position, movement and interactions of everyone (both people and animals) ‘close’ to a potential time traveler. Prophecies are vague enough to not need this detail of prediction and can therefore be made for further into the future.
As to the question whether this AI assumption is actually the correct one I can only refer you to this quote from chapter 25:
Which could be a hint in this direction. I assume Eliezer’s quote on an AI not being a part of the story is just that, the story will be about Harry’s struggle with Voldemort, not about tracking down any sources of Magic.
I agree that obeying Novikov consistency seems to be a good description of the universe in HPMoR, but it is only a partial description since something prevented Harry from using this consistency to factor natural numbers in polynomial time, which should be possible in a universe that is ‘only’ Novikov consistent (meaning you need additional assumptions to prevent this).
This had not occurred to me.
I thought this was simply a flaw in Harry’s methodology—he’s too self-aware for it to work. You need something that will reliably act according to the script, and only as described on the script—in short, a machine, not a person. Harry had failed to consider the possibility of messages that do not consist of factors.
… I thought. Hmm. I need to think about this.
I don’t think Eliezer makes a distinction here. Had Harry done this with a computer program it would probably output (and send back) the exact error message it would generate from getting said message as input, or something like that.
Besides had this trick been possible in any way the story would pretty much be over, as solving every problem in PSPACE in polynomial time would all but guarantee Harry’s ascension to godhood.
Magic breaks computers, remember?
If there is ANY input other than the correct answer that will not generate a paradox, you’re doing it wrong.
Ah yes, I had totally forgotten about that. It is a much better explanation than what I thought of.
It should still be possible to build a completely mechanical way of doing this. I don’t think Harry’s realized that, though.
I was thinking of this myself, but only humans can be sent back in time using a time-turner. And since said humans probably also has to be magical I would guess another requirement is that they have to be scared off by the ‘Do not mess with time’ message (i.e. anyone getting that message and still trying to send a ‘0’ back in time would not be able to use the time-turner in the first place). So no ‘creating’ a human with this factoring algorithm instead of (or in addition to) a personality programmed into their brain-structure.
I was thinking of a human taking back the message without reading it.
That is a very nice solution indeed.
Harry can even do that experiment easily with our current technology, he just needs a printer and a scanner. He can even go somewhere else when he goes back in time to stop magic from messing with the computer.
The only way I can see this fail is if the time-turner either refuses to work when he tries to do this (per whatever requirements it puts on its users) or just kills him outright (given the threatening nature of ‘Do not mess with time’). So he should probably enlist someone else to take the message for him.
Either way, it would be nice to see Harry thinking of this experiment in HPMOR.
Of course, Harry doesn’t know why his experiment failed. In fact, the Do Not Mess With Time probably scared him out of trying to exploit the time travel mechanics.
That’s kinda impressive, actually—Eliezer found a way to avoid exploits that could break the system that follows naturally within the system. I doubt he’ll ruin all his hard work by having Harry figure it out, but you never know.