Comment author: Desrtopa 28 March 2012 06:23:09PM *  33 points [-]

I think that taking advantage of muggles in lots of ways is against the law, so imperiusing or memory charming a billionaire would be forbidden. I wouldn't be at all surprised if people have thought of and maybe tried using time turners to cheat the muggle lottery, so I'd give fair odds that's illegal too. When it comes to arbitrage though, remember that while wizards in general may not be tremendously stupid, they tend to be incredibly clueless about the muggle world; remember that Arthur Weasley can pass as a premier expert on muggle artifacts. The fact that the values of gold and silver in the muggle world are totally divorced from their value in the wizarding world is likely to be very little known, and the concept of arbitrage may be completely foreign to them as well (look how primitive their whole financial system appears to be.)

The fact that Mr. Bester, Harry's occlumency instructor, said he wished he could remember "That trick with the gold and silver" implies that a) the idea is not obvious to most wizards, and b) he thinks he would at least stand a chance of getting away with it.

Comment author: Eponymuse 29 March 2012 12:23:24AM 10 points [-]

I completely agree. Recall also Draco's speech about muggles scratching in the dirt, and his reaction to Harry's estimate of the lunar program budget. It's not just wizards not paying attention to relative values of gold and silver in the muggle world---for the most part, the possibility that there could be a substantial amount of either in the muggle world doesn't occur to them. Now you might expect muggleborns to know better, even after making allowances for the fact that they enter the wizarding world at age 11. On the other hand, if a muggleborn is clever enough to see the potential for profit, they might also be clever enough to see what Harry apparently does not---that calling attention to the fact that the muggles are ripe for exploitation is a Bad Idea.

Comment author: Logos01 28 March 2012 04:23:03PM 0 points [-]

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.)

Comment author: Eponymuse 28 March 2012 07:21:50PM 0 points [-]

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.

Comment author: Logos01 28 March 2012 04:52:22AM 0 points [-]

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.

Comment author: Eponymuse 28 March 2012 02:05:27PM 0 points [-]

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.

Comment author: Logos01 28 March 2012 02:50:52AM 2 points [-]

There are ways to compute problems such that you do not know the information you are computing. Homomorphic Encryption for example.

Comment author: Eponymuse 28 March 2012 04:08:16AM 0 points [-]

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.

Comment author: DanArmak 25 March 2012 03:13:15AM 0 points [-]

I'm not sure he got a plainly stated negative answer. Can someone look that up?

Comment author: Eponymuse 25 March 2012 03:28:27AM 0 points [-]

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.

There was another slight pause, during which Harry went on smiling. He was a little apprehensive, actually a lot apprehensive, but once it had become clear that Dumbledore was deliberately messing with him, something within him absolutely refused to sit and take it like a defenseless lump.

"I'm afraid Time doesn't like being stretched out too much," said Dumbledore after the slight pause, "and yet we ourselves seem to be a little too large for it, and so it's a constant struggle to fit our lives into Time."

On the other hand, we may infer that thirty hours is the limit from e.g. Amelia Bones' behavior in the Azkaban arc:

"I'll check if we have anything from six hours forward," said the voice of Madam Bones, "if so they wouldn't have told me, but I'll have them tell you. Do you have anything you want to tell me, Albus? Which of those two possibilities is it looking like?"

Comment author: [deleted] 25 March 2012 02:48:48AM *  0 points [-]

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

Comment author: Eponymuse 25 March 2012 03:05:20AM 3 points [-]

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.

Comment author: DanArmak 25 March 2012 12:26:55AM *  9 points [-]

This comment gave me the obvious-in-retrospect idea of cloning things with a Time-Turner. Consider:

  • You can make up to six copies of yourself, plus all the items you can carry in magical pouches, which will coexist for slightly less than an hour. Or fewer copies that will coexist for longer.
  • If you have n Time-Turners, you can end up with 6n copies of yourself + items.
  • We have seen that a single Time-Turner can take along an Animagus in a pouch. I speculate that many Animagi (perhaps in separate pouches) can be taken. You can thus use a single Time Turner to duplicate people besides the one actually using it. It's even possible that non-Animagi can be duplicated, if there's some suitable charm for temporarily turning people into animals, maybe.
  • You could probably also duplicate Fawkes.
  • If Dumbledore ever really goes to fight a serious battle, he'll go as an army of multiple-of-six Dumbledores. Some of them will magically disappear every hour until only one remains, but imagine the firepower!
  • Why did Voldemort ever need the Death Eaters? He should have just stolen a few Time-Turners from the ministry. No-one could have resisted an attack by an army of Voldemort clones, super-coordinated by virtue of half the clones remembering being the other half a few hours ago.
  • How are new Time-Turners made? Assuming it's not a lost art, and can be done in under 5 hours, then someone could start cloning himself, make new Turners while back in time, use those to keep cloning himself, and eventually reach literally unlimited populations of himself inside the same time period of a few hours. Those populations could then cooperate on some... trickier problems.

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?

Comment author: Eponymuse 25 March 2012 02:43:18AM *  2 points [-]

Some of them will magically disappear every hour until only one remains, but imagine the firepower!

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.

Comment author: Eponymuse 23 March 2012 10:34:18PM *  0 points [-]

The only mechanisms I know of by which Omega can accurately predict me without introducing paradoxes is by running something like a simulation, as others have suggested. But I really, truly, only care about the universe I happen to know about, and for the life of me, I can't figure out why I should care about any other. So even if the universe I perceive really is just simulated so that Omega can figure out what I would do in this situation, I don't understand why I should care about "my" utility in some other universe. So, two box, keep my $100.

Edit: I should add that my not caring about other universes is conditional on my having no reason to believe they exist.

Comment author: Eponymuse 23 March 2012 11:10:02PM 1 point [-]

Ah. But under mild assumptions about how Omega's simulation works, I can expect that with some probability p bounded away from zero, I am in a simulation. So with probability at least p, there is another universe I care about, and I can increase utility there.

So, I guess I do pay $100, but only because my utility function values the utility of others. I remain unconvinced that paying is winning for someone with a different utility function.

Comment author: Eponymuse 23 March 2012 10:34:18PM *  0 points [-]

The only mechanisms I know of by which Omega can accurately predict me without introducing paradoxes is by running something like a simulation, as others have suggested. But I really, truly, only care about the universe I happen to know about, and for the life of me, I can't figure out why I should care about any other. So even if the universe I perceive really is just simulated so that Omega can figure out what I would do in this situation, I don't understand why I should care about "my" utility in some other universe. So, two box, keep my $100.

Edit: I should add that my not caring about other universes is conditional on my having no reason to believe they exist.

Comment author: buybuydandavis 23 March 2012 09:31:29AM 1 point [-]

Why rescue Bellatrix? So that there is an uncontestable witness that Harry Potter is Voldemort. Malfoy is afraid of Harry. Bella is likely out and about telling death eaters that Harry is Voldemort. Lucius found out. He wants to extract Draco and take away Harry's allies.

I theorized earlier that this was Malfoy's plot to gain leverage over Harry and Albus. Now I think it's Malfoy trying to fight Voldemort.

Comment author: Eponymuse 23 March 2012 08:47:34PM 3 points [-]

I find it very unlikely that Bella is in contact with anyone except the healer. Why would Quirrell want her running around and discussing the escape with people? It's also unlikely that she remembers any part of the escape from Azkaban at all, including Harry's role. Remember that she was Obliviated.

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