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It's debatable whether Heisenberg did the former, causing the mistaken experiment results that led the Nazi atomic program to conclude that a bomb wasn't viable. See for scientific entertainment (there's a good BBC movie about this starring Daniel Craig as Werner Heisenberg)

I read it as Snape being happy that Voldemort offered Lily an out: his deal with Voldemort must have been "please let Lily live and I'll do anything". The memory confirms the story that Voldemort gave Lily an option out ("stand aside"). So he considers Voldemort to have held up his side of the bargain.

This interpretation does not bode well for the Dumbledore-Snape alliance (which already seemed to be in bad shape in MoR)

Harry should just threaten to destroy Azkaban, and say that Dumbledore can testify that he has the power to do it.

Chapter 61: 'There was another pause, and then Madam Bones's voice said, "I have information which I learned four hours into the future, Albus. Do you still want it?"'

This seems like a useless question. A bit of information was already conveyed representing the fact that Amelia Bones was 4 hours into the future & found some information that would be useful to Dumbledore. Is this not sufficient information transfer in and of itself to prevent Dumbledore traveling backwards?

Sorry if I'm confused, but reasoning about time is hard, and my diagrams are not as helpful as Snape's and Dumbledore's.

I think a fossilized hominid might have worse than average chance of having no living descendants too: To be fossilized they have to undergo a fossilization event, which is probably correlated with disaster: and given that ancient human did not stray far from their genetic siblings (and progeny) this probably indicates a high chance of that disaster affecting their progeny. I certainly wouldn't rely on it.

Nevertheless, given my cultural heuristic for what counts as most important, it would probably be father (in terms of how much various cultures put a value on either the father or the mother), or most recognized powerful ancestor (Salazar Slytherin in this case).

I think Voldemort would have been staggeringly stupid NOT to have kept a remnant of his father's body given how much blood magic requires these types of ingredients.

This is unrelated to the current plot, but rather a more general thought: We know Severus is the most accomplished occlumens in the world. Might he also be the most accomplished legilimens as well? It seems that Severus, being Voldemort's spy who spends inordinate amounts of time under Dumbledore's command, would natually come under the Dark Lord's suspicions, prompting plenty of sessions of eye-staring where Voldemort verifies his allegience. Severus, of course, passes all these checks, but could he not also be legilimensing Voldemort at the same time? If the only prerequisite of Legilimency is a staring match, could Severus be probing Voldemort's mind as well as receiving the reverse probe (and successfully defending it).

I feel as if Severus' role in the story could be even more important (especially post Voldemort's resurrection) in HPMOR than it was in canon, simply because he has so many opportunities for strategic play that were not fully explored in canon. (Admittedly, the Dumbledore killing double-play was staggeringly magnificent bastard worthy.)

While I agree that this might be the case, there is a logical defense for the case where Harry is non-Voldemort. Consider, if you were Voldemort hiding horcruxes. Where would you put them?

Now if you are not very smart, you would probably put up some protections, and you will expect the hero to try to break them. If you were smarter, there would be some feints and double feints and deceptions involved in the process. But if you were very smart, you would go for the hardest locations, as Harry named. These might represent a kind of "fixed point" of hiding places: You know the hero will find out, but its not like you could do any better. The perfectly-logical-Quirrell knows that Harry will figure it out, but nonetheless, he has no better option! Any other choices would only make the quest easier, not harder.

Now since Harry is brilliant, he figures this out independently. Because with the above fixed-point theorem that these 5 locations are the hardest possible even assuming common knowledge of the theorem and the 5 locations among your foes, then every sufficiently smart thinker will come to the exact same conclusions independently, which in this case are Voldemort and Harry.

(Personally I disagree with the locations as Harry says them: There is one better: Randomize everything that Harry said. Of the 5 hardest options, make a probability distribution over them [weighted by difficulty: I would expect the space version to be weighted higher as it seems harder to find things in space than say the earth version of digging a hole a kilometer under the ground of which there are a much smaller number of hiding spots.] Then, randomize each version so that the launch trajectory (in the space case) or the burial site (in the earth case) is selected randomly. Finally, build a machine that will do the randomized selection and auto-launch independently, so that you yourself are unaware of the selected locations. Even obliviation seems weak: perhaps there are ways to be unobliviated ex-post.

This way, a machine chooses 7 modes (space/air/water) randomly for your 7 horcruxes. I imagine there would be 4 space horcruxes, 2 air horcruxes, 0.5 water horcruxes, etc. (depending on the probability distribution chosen) Ideally you would obliviate yourself ex-post so that you don't remember the probability distribution you chose. Then once the modes have been selected for each horcrux the machine spits out for each of the horcruxes a random trajectory/location and launches. Then you destroy the machine (and sufficient surroundings so that remaining bits of information cannot be used to reconstruct even partially the entropy bits surrounding the machine to regenerate the random numbers). Then you obliviate yourself of every thing.

Even then, this isn't foolproof, because a smart enough person looking to find out where your horcruxes are would arrive at the same conclusions and realize what you've done. But it is the strongest possible that could be done. (That is, if I haven't made a mistake: which I don't claim to have. I'm not Quirrelmort/Harry smart, I'm dumber. Presumably if they came up with the solution it would be without any holes I might have overlooked)

Randomization is the only hope here. Your solution needs to be sufficiently hard that you yourself cannot ex-post figure out where they are, so that the hero cannot either. The more random, the larger the search space for any future searcher, and no additional information can be obtained. Harry does grasp this by suggesting obliviating yourself after randomly selecting a trajectory for the space case, but I would make that more rigorous and have a very strong random number generator of which you were a not part of.)