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gjm comments on Harry Potter and the Methods of Rationality discussion thread, part 20, chapter 90 - Less Wrong Discussion
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Here's how I would have saved Hermione if I were Harry.
In an accessible but seldom visited hallway of Hogwarts, a rail-way sign reads 6PM to 5PM Express.
At 5:00, a boy materializes under the sign. He is wearing a rail-way conductor's hat. He is holding a trunk. His name is Harry Potter.
Conductor Harry puts down the trunk. He opens the lid. Inside his Trunk of Holding are wooden seats numbered 1 through 1000. All seats appear to be empty.
Conductor Harry yells "Arriving at 5PM! Please add one tally to your forearm now".
Silently, hundreds of people draw a tally mark on their arms.
Conductor Harry steps away from the trunk and the hundreds invisible passengers of the 6PM to 5PM Express disembark.
At 5:10, Conductor Harry closes the trunk lid. He stashes the trunk [EDIT] and Time-Turner in the Great Hall.
At 5:12, Conductor Harry burns his conductor hat. He draws one tally mark on his previously blank arm, and puts on his invisibility cloak. He sighs. He has a long day ahead of him.
...
At 5:30 in the Astronomy Tower, a smelly and disheveled Harry Potter pulls off his invisibility cloak. He is covered with hundreds of tally marks, and looks like he hasn't slept in days. He yells "Screw this, I'm done!", collapses on the floor, and falls asleep.
...
At 5:40, the original Harry goes to his room. He has done no time traveling today, and has no tally marks on his arm.
Original Harry locates his trunk and his conductor's hat.
At 5:45, Original Harry brings his trunk and hat to the hallway with a 6PM to 5PM Express sign.
At 5:50, Original Harry puts on his conductor's hat. Harry -- now Conductor Harry -- opens the trunk, steps aside, and yells "All aboard the 6PM to 5PM Express!. Please go to your assigned seat."
Hundreds of invisible Harrys silently climb into the trunk. Each Harry counts the tallies on his arm and sits in the corresponding seat.
At 5:59, conductor Harry yells "Last Call for the 6PM to 5PM Express!"
At 6:00, conductor Harry closes his trunk. He picks up his trunk, and flips his time-turner.
Using this method, Harry can get as much time as he wants to study obliviation, transfigure large objects, or anything else, all with a single twist of his time turner. That's more than enough time to learn to obliviate yourself (and maybe the Weasley) and fake Hermione's death.
Somewhat-credible conjecture: It is not possible for one Time-Turner to transport another through time. So when conductor Harry, carrying his trunk supposedly full of passenger Harries (Harrys?), flips his Time-Turner ... something bad happens. Maybe the others get left behind somehow, or the Time-Turner just doesn't work, or the universe ends, or something. Consequence: at least in any consistent branch of the universe, Harry fails to get his army of copies.
Can't this be solved by having conductor Harry pass his Time-Turner to smelly Harry around 5:30 PM? Then none of the in-between Potters actually have Time-Turners.
I don't think so; he needs to use it himself at 6pm to transport everyone back, and smelly Harry mustn't go back himself. [EDITED to add: oops, I'm a twit; it looks like this works. So if this hack isn't viable in the MoRverse, it must be for some other reason, perhaps one of the ones below.]
My brain's fuzzy enough that I'm not confident there isn't some patch along those lines, though; if it turns out that there is, an alternative (which I can't rule out being already refuted by something in canon or HPMOR that I've forgotten) would be that a Time-Turner can transport at most one living person.
[EDITED to add: Actually there's an obviously better one, which is pretty clearly canonical and MoRonical (er, maybe that's not the best term): the 6-hour restriction is not per Time-Turner but per person. If that's "no more than 6 hours of time travel in any subjective 24 hours" rather than, or in addition to, "no further back than 6 hours", then as soon as Harry has a sixth-generation copy in his trunk, something bad happens, hence there is no consistent universe in which he gets a time-travelling army of size bigger than that.]
Of course another possibility is that (in the MoRverse and/or the Rowlingverse) this sort of hack is very much possible, but it seems like the sort of thing that would have been exploited to hell and back by ingenious folks like Voldemort and Dumbledore, so you probably get a more coherent fictional universe if there's some simple principle that prevents it.
The loop works because the conductor Harry that uses the Time-Turner at 6 PM is a younger version of the conductor Harry at 5 PM. Conductor Harry at 5:30 PM is going to go sit in the trunk at 6 PM, so he has no further need of the Time-Turner.
I think the most elegant formulation of a restriction that would prevent this (as well as all the things explicitly prevented in HPMoR) is that no path along which information or matter travels can stretch more than 30 hours per 24 hours.
So, you could put a 6-hour stretched pebble in someone's pocket, and they wouldn't be able to use a Time-Turner?
I'd say yes (until the 24 hours run out and the pebble stops being time-stretched).
Similarly, if you go back 6 hours in time and, say, cast a spell that creates fireworks visible from a large distance, you've just prevented everyone within that radius from using a Time-Turner.
Finally, I'm mostly sure that the incredibly-small-scale changes caused by simply going back in time 6 hours propagate quickly enough that only one person on Earth can use a Time-Turner on any given day.
So yeah, there's a bit of a problem here. Presumably this is one of those "it works how Merlin would have expected it to work" things.
Edited for objection: Harry stashes the Time-turner in the Great Hall (for expository reasons).