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DanArmak comments on Harry Potter and the Methods of Rationality discussion thread, part 11 - Less Wrong Discussion
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This comment gave me the obvious-in-retrospect idea of cloning things with a Time-Turner. Consider:
This is all starting to remind me of the Seventh Voyage of Ijon Tichy... It looks like I'll have to draw diagrams.
Can someone teach me how?
I don't think you can have more than 6 versions of yourself present at any given time, since any more than that and information is traveling more than 6 hours back. (at least from the perspectives of the earliest and latest self-clone)
But still, 6 x Dumbledore+Fawkes is quite the army.
Edit: Also,
You don't actually need to go through animagus+pouch to transport more than one person on an unrestricted Time-Turner. (Canon also agrees on this if I recall correctly)
Yes, Hermione took Harry with her in the awesome part of Book 3.
How important is maintaining continuity for the time turners? If it IS important, then you can only end up with 6 you's (It's noon, go back to 11, pick up that you, go back to 10, pick up that you, etc...)
BUT! If your mission takes more than an hour, you will end up with a discontinuity, since then 6:00!you will not be back in time to be 7:00!you so that you's can pick him up.
If continuity is NOT important: Go back an hour. Now there are two of you's. Both you's wait around two hours, then both of you go back and pick up the past you's. Now there are four of you's. All four of you's wait around two hours, etc.... You'd end up with 64 you's (assuming you can animagus into a something really small to fit in the pouch that is)
Aaaaagh! Time travel makes my head hurt
Reality computes in one swoop. It simply wouldn't happen.
Consistency is important. We see this in full force in the Azkaban arc.
To get 6 of yourself, starting at noon, you wouldn't go back to 11, then "together" go back to 10. You have already created a paradox because the original 11 o'clock you was supposed to wait until noon and then go back in time. Instead, at 11, you would walk into a room with 5 other copies of you waiting, and then at noon, you and 4 of those copies would go back in time to 11.
I believe the only restriction is on not traveling back more than six hours by wall-clock time. It's never stated that you can't travel back into the same hour more than six time using more than one Time-Turner.
The universe makes it rather obvious that you can't. How do we know that? Because the economics of Time-Turners is such that they are only valuable if you have exactly one and any additional time-turners are irrelevant. If time-turners worked that way then...
... You would want as many as you could get. And Hogwarts wouldn't be able to loan them out. If each person can only use 1 time-turner (as I say), then the economic demand is at most the population who's aware of time-turners. If you can use infinitely many time turners, then demand is without limit. The price for them would increase, and Hogwarts wouldn't be free to hand them out like they relatively were inexpensive.
They would have a very high price, and powerful or rich wizards would use them as much as they want. People as rich as Lucius Malfoy would be wearing twenty five time-turners like they were the rapper flava-flav. Upon hearing about Azkaban being attacked, you'd immediately go back six hours instead of one because there would be no reason to not do it. Harry, upon exiting the Azkaban wards, would have run into a patrol of a thousand disillusioned Dumbledores patrolling the sky. Hermione would have gotten arrested, and McGonagall would temporarily recall all the time-turners so that Harry or Dumbledore could have a week of turned time to come up with a defense.
No, the universe does not appear as it would if time turners could be stacked. Indeed if they could, things would look drastically different.
I don't think there's a strong economic argument against multiple Time-Turners -- I can think of a number of reasons why the demand for additional loops might run into diminishing returns pretty quickly. Starting with self-consistency problems -- if the simplest solution to a factoring problem that leverages Time-Turning is "DO NOT MESS WITH TIME", then it wouldn't surprise me too much if the simplest self-consistent solution to more complicated and dangerous tasks that involve self-reference is a mysterious death or incapacity on the first iteration. This would be noticed, and Time-Turner abuse would be avoided. Then there's jet lag, synchronization issues, and any number of other things. More than one Time-Turner would definitely be useful (and desired), but the twenty-fifth wouldn't be anywhere close to as useful as the first.
That being said, I think you present pretty solid behavioral reasons why we can probably assume it's impossible.
For some reason I found this image irresistibly hilarious. The sky is filled with two thousand twinkling stars!
Very true. Only defense is that people are generally dumb and unimaginative. But that's a pretty good defense in a fictional universe, even if it is a fully general response to some things.
Didn't Harry ask Dumbledore if it's possible to get more than 30 hours in a day using multiple time-turners and getting a negative answer?
I'm not sure he got a plainly stated negative answer. Can someone look that up?
Dumbledore doesn't give a straight answer when Harry asks if more than one time turner can be used to get more than 30 hours.
On the other hand, we may infer that thirty hours is the limit from e.g. Amelia Bones' behavior in the Azkaban arc:
That's just the usual limit on information not traveling more than six wall-clock hours back in time, total. It doesn't say or imply that you can't loop yourself more than six times within a small stretch of wall-time.
Actually, if you can loop yourself more than six times at any small stretch of wall-time then you can get more than 30 subjective hours in one 24 wall-time day.
But it's implied you can't actually do that, which is why I think no more than 6 copies at any given time. Plus, if it were possible you could basically use any one day as a stopping point groundhog-day style in which you can (for example) brute-force read the entire Hogwarts library.
At any rate, the general limiting principle is that information cannot travel more than 6 hours backwards, Which I think means that when you draw a graph of a person using time-turners where you represent her using an arrow (going right for positive time, and left in 1h jumps for time-turner use), Then you can't have more than 6 hours of left-arrow in any given 24h wall-time section.
That would get rather crowded.
The Ministry has access to Time-Turners too. Really, once both sides are using them they'd just have the effect of making battles much, much more awesome.
And you think that's keeping either side from escalating first, similar to not using Muggle weapons?
The Wizarding War is depicted as a limited conflict in canon, IIRC, and certainly in MoR. So you have a good theory. Voldemort was known for his tactical genius, presumably he found ways to escalate that couldn't be so easily duplicated by the enemy.
The problem with this is that they're not clones, they're future versions. So a potion can only be used once, a Time Turner duplicated still only has six "charges," and so on.
Oops. Very stupid and basic error on my part. You're right, it's not exponential duplication, if you have N turners you get 6*N duplicates. Will fix.
Still useful for clone-armies and for duplicating artifacts of power.
They wouldn't disappear. They would, after a period, go back in time in order to become one of the other people in the battle.
Using a time turner to make clones in battle is a very, very dangerous idea. Harry has been warned, strenuously, by Professor McGonnagal that he should not directly interact with himself, and we have an anecdote about an auror/criminal pair that went insane because they abused time turners. I imagine that one of the more stable time loops would involve the original Dumbledore/Harry getting disabled before going back in time for the first time.
But yeah, the cloning objects thing is a reasonable use of a Time Turner.
Edit to add: If by collaborating on tricky problems, you are referring to e.g. academic problems, rather than problems of strength, this amounts to a rather absurd charade. If you use a Time Turner to put 6 copies of yourself in a room, and in an hour they succeed in answering the problem, that means that at the beginning of the hour, 5 of them already knew the answer.
I realize that. For other observers' practical purposes, they would disappear.
Meh, she worries about that kind of thing too much.
There are ways to compute problems such that you do not know the information you are computing. Homomorphic Encryption for example.
Good point, though I don't think this would ever be useful. In the unlikely scenario that Time-Traveling Tom has a problem amenable to a straightforward, parallelized algorithm which requires six Tom-hours while Tom needs the solution within two hours, he may as well just go back six hours, "thread" his thoughts, not bother with any communication.
Well... there are other such scenarios. Spend 6 hours brainstorming on an idea. Only mention FAILED ideas aloud amongst your fellow Turn-clones. Do so in a manner that requires "keying" to what specifically you're thinking about at the time. (Such as minutes-into-the-hour). After 6 iterations, acquire profit.
This has the added advantage that it follows the "DO NOT MESS WITH TIME" restriction of following by rote.
I'm not sure I understand what you mean by "keying." Could you elaborate, and explain how you end up with a scenario that is more stable from "Time's perspective" than, say, clone #5 just summarizing all the ideas at the beginning of the hour? The scenarios I can come up with seem to involve information magically appearing (which the universe doesn't seem to like, as in Harry's integer factorization algorithm), or fail to provide a benefit over just thinking on one's own for six hours.
clone #5 summarizing means clones 1-4 never actually have the ideas, but cannot contribute any further to the solution-space beyond claiming they had those ideas. This doesn't create an additive effort to deriving a desired answer from the available solutions-space of your problem.
By "keying" I mean something that informs other iterations of the idea you're currently having and its invalidity without telling them the idea. "The thought I had at 5:14 -- it won't work. Move on."
This allows all six iterations to contribute towards deriving a viable answer without running into loops which require recursion to reach a stable state, which seems to be the kinds of loops that the Turners don't allow. (Helping a previous version's okay as long as they don't know where the help is coming from; but factoring integers instantly is not.)
I see. So I guess there is some benefit gained from this, but it is very minor. It seems to me that the simplest rule that explains why Harry's integer factorization is not okay, but, for example, the "silver on the tree" password from the end of TSPE is okay, is the following: if you would gain information at time T, and send information from time T to any time S < T, then it must be the case that you would have gained that same information even if you hadn't learned it at time S.
Now consider your "keying" scenario. We have clones 0-5, and at time 1 clone x goes back to time 0 and becomes clone x+1. When clones give a "time key," it will be a number between 0 and 6, identifying a clone/wall-clock pair. Now suppose at wall-clock time T clone 1 says: "the thought I had at time P doesn't work." Assume for simplicity that time P refers to clone 0 at a wall-clock time S > T (though it would work out the same anyway). Now at time S, when clone 0 has the thought, he has two choices. On the one hand, he can continue working out why it doesn't work, but in this case he gains only the minor benefit of knowing in advance that it will not work out. On the other hand, he can move on and not consider the thought, but at time T as clone 1 just repeat (without knowing why), the fact that it doesn't work. In that case, he gained information that he would not have learned had he not told himself. Or, in your terminology, recursion was required in order to reach a stable state.
that doesn't follow. Where would Harry have gotten the pies if not from Harry+1?
The recursion is non-iterative beyond the number of loops actually manifested, however. Each individual only adjusts the one previous, and only in immediately non-iterative manners. "Nope. Nope. Nope. Maybe. Nope. Nope. Maybe."
That lets you prune out failed items but doesn't recurse back to an instantaneous success.
He got them from the breakfast table. Where did he get the idea to get them? Well, he would have seen the pies later on anyway. Just like he would have learned about time turners later on in the day anyway, but a more stable scenario was obtained by learning about them earlier.
I'm not quite sure how to parse this. If you would think about an idea at time T, but don't because future you tells you it won't work out, that means your whole thought process going forward has completely changed. But maybe the thing you start thinking about instead doesn't work out, so someone warns you about the idea at time T+epsilon. And so on. So if you are proposing that Time works by iterating through a number of scenarios until you get to something stable, the situation you've pointed to "requires recursion." (It's worth pointing out that Harry, when he gets his Time Turner, doesn't think this is a likely answer to how Time works.) But perhaps I am not understanding you correctly?
My main objection to the scenario you are proposing, though, is that you are gaining information as a result of some work, but that work is never performed. Try taking your scenario to its logical extreme. You sit in a room with one copy of future-you, and a large composite number N on a sheet of paper. On scrap work hidden from future-you, you write down an integer K. If you are not told that K does not divide N, you check. If it does, you keep track of the factor of N you have found. In any case, you then systematically select a new integer K' to check for divisibility. Once you have a complete factorization, you sit quietly, and at the end of the hour you go back in time. Then, you let past-you know the "keys" for all of the integers that weren't factors. Thus, you must have ended up only trying actual factors. So, you have a slightly more complicated version of Harry's factorization algorithm.
Edit to add: I guess this situation actually still is still an exponential time algorithm, since you still have to consider every possibly integer. But you could do, for example, graph isomorphism testing in polynomial time with a similar method: try constructing a map by first finding what vertex 1 should map to. Future you says "nope, nope, maybe," and on "maybe" you try to figure out where to put vertex 2, given that vertex 1 maps to whatever. If the graphs are not isomorphic, future you will say "no" to every choice for vertex 1, so you have your answer in polynomial time. Otherwise, you will construct the isomorphism in polynomial time.
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I forget if we're discussing MoR or canon, but either way I object. In canon, my objection is pedantic: it's Hermione who was warned, and she only later passed on that warning to Harry. In MoR, Harry has interacted with himself, a few times, and while they didn't all go well, there were no disasters.
Not that strenuously:
You're right, I misremembered. Still, I think there is a lot to suggest that interacting directly with one's time-clones (as opposed to waiting with one's eyes closed while a clone drops off a message, for example), particularly in battle, is a bad idea. You would never observe a future-you doing something ineffective in combat---failing to dodge or block, or casting an ineffective spell, for example---since, after observing that mistake, you would be prepared for it in the future. So the only consistent possibilities involve losing or running away before you can go back in time, or winning right away.
But, since you know these are the only consistent possibilities, if you showed up to a battle intending to use a Time Turner and didn't see your time clones appear at the very beginning, you would deduce that you would not win, and therefore (if you could) you would run away. So, I expect that from Time's perspective, the most stable solution for people who intend to use Time Turners in battle is for them to not do battle at all.
He has never interacted directly with himself in a way that involves seeing a copy of himself, or coordinating actions in real-time, as would be the case in a battle. Harry has so far always heeded Professor McGonnagal's advice, and looked the other way when his time clones are around. Though, as pedanterrific points out, I have overstated the severity of McGonnagal's warning.
Just Say No to time travel in stories. There's no end to this kind of stuff. Use it to throw pies. Fine. But please don't make it a magic bullet to resolve some plot line.
When time travel is well-defined, it's not a problem. For example, I don't think anyone has ever accused Primer of using time travel as a magic bullet.
And Homestuck just doesn't have any plot point which isn't time travel in some way.
Except Primer-style time travel, where you can actually change the future of the universe by going back in time, is not very well-defined. Leaving aside the difficulty of reconciling such time travel with relativity, it is unclear to me what the rules are that govern returning to a particular time slice. What aspects of the past state are allowed to change, and what must remain the same? Are there any constraints at all?
The sort of time travel we see in the Harry Potter books (SPOILER jura uneel naq tnat geniry onpx va gvzr gb fnir Fvevhf Oynpx) is a much better example of well-defined time travel. There's no "changing the future" involved. Every causal loop is subject to strong consistency constraints.
Well, every story that has people traveling or communicating faster than light basically has not-well-defined time travel in it. Which includes most scifi ever written, I'd guess.
That's not really what I meant. There are well-defined frameworks of physical law that permit faster-than-light travel. Newtonian physics is an example. So even though FTL travel requires some suspension of disbelief, you're not usually at sea about what the rules are that govern the phenomenon. It's not like magic.
The problem with the way time travel is often depicted is that it is like magic. There's no clear set of rules constraining which properties of the time slice can change when the traveler returns to it, and which must remain the same. Surely there must be some constraints. After all, if every single property is allowed to change, it wouldn't really count as traveling back to the same time slice. But where do these constraints come from and what are they?
It's a difference, but not a qualitative one, I feel. After all, reality is entangled and there's no well-defined framework of physical law that allows FTL travel and also reduces to something like relativity as long as you don't turn on your magical engine. Everyone who doesn't have a magical FTL engine would still see your FTL travel as being time travel, and the same questions would have to be answered as you raise below: what changes are allowed, etc.
OTOH, if you go by which suspension of disbelief is easiest and most natural, and if you let go of your belief in scientific physical laws. then the most natural thing to believe in is magic. It's what all humans believed in up to historically recent eras. The kind of magic that doesn't usually have builtin rules in the sense of laws of the universe or of magic itself. It just has limitations corresponding to the knowledge/power/wisdom of the magician. The more common constraining rules in such stories are actually moralistic (good winning, etc.)
This is a popular but incorrect idea. If you interpret special relativity via (neo-)Lorenz Ether Theory, you can have perfectly mundane kind of FTL without any problematic time travel, you'd just have a preferred reference frame. It'd be possible to send messages to the past according to some reference frames (in spacelike fashion), but not others, and you'd never get to communicate information in time loops. There is no serious problem with reconciling FTL and special relativity, FTL goes the way of ether for Occam's razor reasons, not because it doesn't make sense conceptually.
There are perfectly consistent models of a relativistic universe with well-defined rules that allow tachyons (particles that travel faster than light). Frank Arntzenius has a great paper on this. These models don't allow "future-changing" time travel, though.
Incidentally, does anyone know of a work of fantasy that has clearly articulating "law-like" constraints governing the use of magic? The awesome webcomic Unsounded seems to be attempting something like this, but the details are still fuzzy.
Most works of fantasy do this to some extent. For example, the One Power in Wheel of Time has very well-specified mechanics, though of course a lot of the complexity is left as an exercise for the reader. The metal-based magic in the Mistborn books is simpler, and likewise well-defined. You can also have works like Cardcaptor Sakura, which is basically an anime about a collectible card game; here, the cards operate according to some very specific rules, and each card has a narrow function, but the card list is very large and fairly arbitrary.
Interesting. That paper is behind a paywall, unfortunately.
But my knowledge of physics is very limited and I probably wouldn't understand the full paper anyway. (What tachyon interactions with non-tachyons does he allow?) I doubt, though, that any model of tachyons allows you to accelerate your normal-matter spaceship to FTL speeds the way most soft scifi takes for granted.
More as a magic LSD substitute.