Chapter 86: Multiple Hypothesis Testing

https://www.lesswrong.com/posts/Wx2CKWmKnNnXYpWz6/chapter-86-multiple-hypothesis-testing-1

(International news headlines of April 7th, 1992:) Toronto Magical Tribune: ENTIRE BRITISH WIZENGAMOTREPORTS SEEING ’BOY-WHO-LIVED’FRIGHTEN A DEMENTOR EXPERT ON MAGICAL CREATURES:"NOW YOU’RE JUST LYING" FRANCE, GERMANY ACCUSE BRITAINOF MAKING THE WHOLE THING UP New Zealand Spellcrafter’s Diurnal Notice: WHAT DROVE BRITISH LEGISLATURE INSANE?COULD OUR GOVERNMENT BE NEXT? EXPERTS LIST TOP 28 REASONSTO BELIEVE IT’S ALREADY HAPPENED American Mage: WEREWOLF CLAN TO BECOMEFIRST INHABITANTS OF WYOMING The Quibbler: MALFOY FLEES HOGWARTSAS VEELA POWERS AWAKEN Daily Prophet: LEGAL TRICKS FREE"MAD MUGGLEBORN"AS POTTER THREATENS MINISTRYWITH ATTACK ON AZKABAN Hypothesis: Voldemort*(April 8th, 1992, 7:22pm)* The four of them gathered once more around the ancient desk of the Headmaster of Hogwarts, with its drawers within drawers within drawers, wherein all the past paperwork of the Hogwarts School was stored; legend had it that Headmistress Shehla had once gotten lost in that desk, and was, in fact, still there, and wouldn’t be let out again until she got her files organized. Minerva didn’t particularly look forward to inheriting those drawers, when she inherited that desk someday—if any of them survived. Albus Dumbledore was seated behind his desk, looking grave and composed. Severus Snape was standing next to the dead Floo and its ashes, hovering ominously like the vampire that students sometimes accused him of pretending to be. Mad-Eye Moody had been meant to join them, but was yet to arrive. And Harry... A boy’s small, thin frame, perched on the arm of his chair, as though the energies running through him were too great to allow ordinary seating. Set face, sweaty hair, intent green eyes, and within it all, the jagged lightning-bolt of his never-healing scar. He seemed grimmer, now; even compared to a single week earlier. For a moment Minerva flashed back to her trip to Diagon Alley with Harry, what seemed like ages and ages ago. There’d been this somber boy inside that Harry, somehow, even then. This wasn’t entirely her own fault, or Albus’s fault. And yet there was something almost unbearably sad about the contrast between the young boy she’d first met, and what magical Britain had made of him. Harry had never had much of an ordinary childhood, she’d gathered; Harry’s adoptive parents had said to her that he’d spoken little and played less with Muggle children. It was painful to think that Harry might have had only a few months of playing beside the other children in Hogwarts, before the war’s demands had stripped it all away. Maybe there was another face that Harry showed to the children his own age, when he wasn’t staring down the Wizengamot. But she couldn’t stop herself from imagining Harry Potter’s childhood as a heap of firewood, and herself and Albus feeding the wooden branches, piece by piece, into the flames. "Prophecies are strange things," said Albus Dumbledore. The old wizard’s eyes were half-lidded, as though in weariness. "Vague, unclear, meaning escaping like water held between loose fingers. Prophecy is ever a burden, for there are no answers there, only questions." Harry Potter was sitting tensely. "Headmaster Dumbledore," said the boy with soft precision, "my friends are being targeted. Hermione Granger almost went to Azkaban. The war has begun, as you put it. Professor Trelawney’s prophecy is key information for weighing up the balance of my hypotheses about what’s going on. Not to mention how silly it is—and dangerous—that the Dark Lord knows the prophecy and I don’t." Albus looked a grim question at her, and she shook her head in reply; in whatever unimaginable way Harry had discovered that Trelawney had made the prophecy and that the Dark Lord knew of it, he hadn’t learned that much from her. "Voldemort, seeking to avert that very prophecy, went to his defeat at your hands," the old wizard said then. "His knowledge brought him only harm. Ponder that carefully, Harry Potter." "Yes, Headmaster, I do understand that. My home culture also has a literary tradition of self-fulfilling and misinterpreted prophecies. I’ll interpret with caution, rest assured. But I’ve already guessed quite a bit. Is it safer for me to work from partial guesses?" Time passed. "Minerva," said Albus. "If you would." "The one..." she began. The words came falteringly to her throat; she was no actress. She couldn’t imitate the deep, chilling tone of the original prophecy; and yet somehow that tone seemed to carry all the meaning. "The one with the power to vanquish the Dark Lord approaches… born to those who have thrice defied him, born as the seventh month dies..." "And the Dark Lord shall mark him as his equal," came Severus’s voice, making her jump within her chair. The Potions Master loomed tall by the fireplace. "But he shall have power the Dark Lord knows not… and either must destroy all but a remnant of the other, for those two different spirits cannot exist in the same world." That last line Severus spoke with so much foreboding that it chilled her bones; it was almost like listening to Sybill Trelawney. Harry was listening with a frown. "Can you repeat that?" said Harry. "The one with the power to vanquish the Dark Lord approaches, born to those who have thrice defied him, born as the seventh month—" "Actually, hold on, can you write that down? I need to analyze this carefully—" This was done, with both Albus and Severus watching the parchment hawklike, as though to make sure that no unseen hand reached in and snatched the precious information away. "Let’s see..." Harry said. "I’m male and born on July 31st, check. I did in fact vanquish the Dark Lord, check. Ambiguous pronoun in line two… but I wasn’t born yet so it’s hard to see how my parents could have thrice defied me. This scar is an obvious candidate for the mark..." Harry touched his forehead. "Then there’s the power the Dark Lord knows not, which probably refers to my scientific background—" "No," said Severus. Harry looked at the Potions Master in surprise. Severus’s eyes were closed, his face tightened in concentration. "The Dark Lord could obtain that power by studying the same books as you, Potter. But the prophecy did not say, power the Dark Lord has not. Nor even, power the Dark Lord cannot have. She spoke of power the Dark Lord knows not… it will be something stranger to him than Muggle artifacts. Something perhaps that he cannot comprehend at all, even having seen it..." "Science is not a bag of technological tricks," Harry said. "It’s not just the Muggle version of a wand. It’s not even knowledge like memorizing the periodic table. It’s a different way of thinking." "Perhaps..." the Potions Master murmured, but his voice was skeptical. "It is hazardous," Albus said, "to read too far into a prophecy, even if you have heard it yourself. They are things of exceeding frustration." "So I see," Harry said. His hand rose up, rubbed the scar on his forehead. "But… okay, if this is really all we know… look, I’ll just put it bluntly. How do you know that the Dark Lord actually survived?" "What?" she cried. Albus just sighed and leaned back in the vast Headmaster’s chair. "Well," Harry said, "imagine how this prophecy sounded back when it was made. You-Know-Who learns the prophecy, and it sounds like I’m destined to grow up and overthrow him. That the two of us are meant to have a final battle where either of us must destroy all but a remnant of the other. So You-Know-Who attacks Godric’s Hollow and immediately gets vanquished, leaving behind some remnant which may or may not be his disembodied soul. Maybe the Death Eaters are his remnant, or the Dark Mark. This prophecy could already be fulfilled, is what I’m saying. Don’t get me wrong—I do realize that my interpretation sounds stretched. Trelawney’s phrasing doesn’t seem natural for describing only the events that historically happened on October 31st, 1981. Attacking a baby and having the spell bounce off, isn’t something you’d normally call ‘the power to vanquish’. But if you think of the prophecy as being about several possible futures, only one of which was actually realized on Halloween, then the prophecy could already be complete." "But—" Minerva blurted. "But the raid on Azkaban—" "If the Dark Lord survived, then sure, he’s the most likely suspect for the Azkaban breakout," Harry said reasonably. "You could even say that the Azkaban breakout is Bayesian evidence for the Dark Lord surviving, because an Azkaban breakout is more likely to happen in worlds where he’s alive than worlds where he’s dead. But it’s not strong Bayesian evidence. It’s not something that* can’t possibly happen* unless the Dark Lord is alive. Professor Quirrell, who didn’t start from the assumption that You-Know-Who was still around, had no trouble thinking of his own explanation. To him, it was obvious that some powerful wizard might want Bellatrix Black because she knew a secret of the Dark Lord’s, like some of his magical knowledge that he’d told to only her. The priors against anyone surviving their body’s death are very low, even if it’s magically possible. Most times it doesn’t happen. So if it’s just the Azkaban breakout… I’d have to say formally that it isn’t enough Bayesian evidence. The improbability of the evidence assuming that the hypothesis is false, is not commensurate with the prior improbability of the hypothesis." "No," Severus said flatly. "The prophecy is not yet fulfilled. I would know if it were." "Are you sure of that?" "Yes, Potter. If the prophecy had already come true, I would understand it! I heard Trelawney’s words, I remember Trelawney’s voice, and if I knew the events that matched the prophecy, I would recognize them. What has already happened… does not fit." The Potions Master spoke with certainty. "I’m not really sure what to do with that statement," Harry said. His hand rose up, absently rubbed at his forehead. "Maybe it’s just what you* think* happened that doesn’t fit, and the true history is different..." "Voldemort is alive," Albus said. "There are other indications." "Such as?" Harry’s reply was instant. Albus paused. "There are terrible rituals by which wizards have returned from death," Albus said slowly. "That much, anyone can discern within history and legend. And yet those books are missing, I could not find them; it was Voldemort who removed them, I am sure—" "So you can’t find any books on immortality, and that proves that You-Know-Who has them?" "Indeed," said Albus. "There is a certain book—I will not name it aloud—missing from the Restricted Section of the Hogwarts library. An ancient scroll which should have been at Borgin and Burkes, with only an empty place on a shelf to show where it was—" The old wizard stopped. "But I suppose," the old wizard said, as though to himself, "you will say that even if Voldemort tried to make himself immortal, it does not prove that he succeeded..." Harry sighed. "Proof, Headmaster? There are only ever probabilities. If there are known, particular books on immortality rituals which are missing, that increases the probability that someone attempted one. Which, in turn, raises the prior probability of the Dark Lord surviving his death. This I concede, and thank you for contributing the fact. The question is whether the prior probability goes up enough." "Surely," Albus said quietly, "if you concede even a chance that Voldemort survived, that is worth guarding against?" Harry inclined his head. "As you say, Headmaster. Though once a probability drops low enough, it’s also an error to go on obsessing about it… Given that books on immortality are missing, and that this prophecy would sound somewhat more natural if it refers to the Dark Lord and I having a future battle, I agree that the Dark Lord being alive is a probability, not just possibility. But other probabilities must also be taken into account—and in the probable worlds where You-Know-Who is not alive, someone else framed Hermione." "Foolishness," Severus said softly. "Utter foolishness. The Dark Mark has not faded, nor has its master." "See, that’s what I mean by formally insufficient Bayesian evidence. Sure, it sounds all grim and foreboding and stuff, but is it that unlikely for a magical mark to stay around after the maker dies? Suppose the mark is certain to continue while the Dark Lord’s sentience lives on, but a priori we’d only have guessed a twenty percent chance of the Dark Mark continuing to exist after the Dark Lord dies. Then the observation, ‘The Dark Mark has not faded’ is five times as likely to occur in worlds where the Dark Lord is alive as in worlds where the Dark Lord is dead. Is that really commensurate with the prior improbability of immortality? Let’s say the prior odds were a hundred-to-one against the Dark Lord surviving. If a hypothesis is a hundred times as likely to be false versus true, and then you see evidence five times more likely if the hypothesis is true versus false, you should update to believing the hypothesis is twenty times as likely to be false as true. Odds of a hundred to one, times a likelihood ratio of one to five, equals odds of twenty to one that the Dark Lord is dead—" "Where are you getting all these numbers, Potter?" "That is the admitted weakness of the method," Harry said readily. "But what I’m qualitatively getting at is why the observation, ‘The Dark Mark has not faded’, is not adequate support for the hypothesis, ‘The Dark Lord is immortal.’ The evidence isn’t as extraordinary as the claim." Harry paused. "Not to mention that even if the Dark Lord is alive, he doesn’t have to be the one who framed Hermione. As a cunning man once said, there could be more than one plotter and more than one plan." "Such as the Defense Professor," Severus said with a thin smile. "I suppose I must agree that he is a suspect. It was the Defense Professor last year, after all; and the year before that, and the year before that." Harry’s eyes dropped back to the parchment in his lap. "Let’s move on. Are we certain that this Prophecy is accurate? Nobody messed with Professor McGonagall’s memory, maybe edited or subtracted a line?" Albus paused, then spoke slowly. "There is a great spell laid over Britain, recording every prophecy said within our borders. Far beneath the Most Ancient Hall of the Wizengamot, in the Department of Mysteries, they are recorded." "The Hall of Prophecy," Minerva whispered. She’d read about that place, said to be a great room of shelves filled with glowing orbs, one after another appearing over the years. Merlin himself had wrought it, it was said; the greatest wizard’s final slap to the face of Fate. Not all prophecies conduced to the good; and Merlin had wished for at least those spoken of in prophecy, to know what had been spoken of them. That was the respect Merlin had given to their free will, that Destiny might not control them from the outside, unwitting. Those mentioned within a prophecy would have an glowing orb float to their hand, and then hear the prophet’s true voice speaking. Others who tried to touch an orb, it was said, would be driven mad—or possibly just have their heads explode, the legends were unclear on this point. Whatever Merlin’s original intention, the Unspeakables hadn’t let anyone enter in centuries, so far as she’d heard. Works of the Ancient Wizards had stated that later Unspeakables had discovered that tipping off the subjects of prophecies could interfere with seers releasing whatever temporal pressures they released; and so the heirs of Merlin had sealed his Hall. It did occur to Minerva to wonder (now that she’d spent a few months around Mr. Potter) how anyone could possibly know that; but she also knew better than to ask Albus, in case Albus tried to tell her. Minerva firmly believed that you only ought to worry about Time if you were a clock. "The Hall of Prophecy," Albus confirmed lowly. "Those who are spoken of in a prophecy, may listen to that prophecy there. Do you see the implication, Harry?" Harry frowned. "Well, I could listen to it, or the Dark Lord… oh, my parents. Those who had thrice defied him. They were also mentioned in the prophecy, so they could hear the recording?" "If James and Lily heard anything different from what Minerva reported," Albus said evenly, "they did not say so to me." "You took James and Lily there?" Minerva said. "Fawkes can go to many places," Albus said. "Do not mention the fact." Harry was staring directly at Albus. "Can I go to this Department of Mysteries place and hear the recorded prophecy? The original tone of voice might be helpful, from what I’ve heard." Light glinted from the reflection of Albus’s half-moon glasses as the old wizard slowly shook his head. "I think that would be unwise," Albus said. "For reasons beyond the obvious. It is dangerous, that place which Merlin made; more dangerous to some people than others." "I see," Harry said tonelessly, and looked back down at the parchment. "I’ll take the prophecy as assumed accurate for now. The next part says that the Dark Lord has marked me as his equal. Any ideas on what that means exactly?" "Surely not," said Albus, "that you must imitate his ways, in any wise." "I’m not dumb, Headmaster. Muggles have worked out a thing or two about temporal paradoxes, even if it’s all theoretical to them. I won’t throw away my ethics just because a signal from the future claims it’s going to happen, because then that becomes the only reason why it happened in the first place. Still, what does it mean?" "I do not know," said Severus. "Nor I," she said. Harry took out his wand, turned it over in his hands, gazing meditatively at the wood. "Eleven inches, holly, with a core of phoenix feather," Harry said. "And the phoenix whose tail feather is in this wand, only ever gave one other, which Mr… what was his name, Olive-something… made into the core of the Dark Lord’s wand. And I’m a Parselmouth. It seemed like a lot of coincidence even then. And now I find out there’s a prophecy stating that I’ll be the Dark Lord’s equal." Severus’s eyes were thoughtful; the Headmaster’s gaze, unreadable. "Could it be," Minerva said falteringly, "that You-Know-Who—that Voldemort—transferred some of his own powers to Mr. Potter, the night he gave him that scar? Not something he intended to do, surely. Still… I don’t see how Mr. Potter could be his equal, if he had any less magic than the Dark Lord himself..." "Meh," said Harry, still looking meditatively at his wand. "I’d fight the Dark Lord without any magic at all, if I had to. Homo sapiens didn’t become the dominant species on this planet by having the sharpest claws or hardest armor—though I suppose some of that point may be lost on wizards. Still, it’s beneath my dignity as a human being to be scared of anything that isn’t smarter than I am; and from what I’ve heard, on that particular dimension the Dark Lord wasn’t very scary." The Potions Master spoke, his voice taking on some of his customary contemptuous drawl. "You imagine yourself more intelligent than the Dark Lord, Potter?" "Yes, in fact," said Harry, pulling back the left sleeve of his robes, and rolling up the shirtsleeve beneath to expose the bare elbow. "Oh, that reminds me! Let’s make sure nobody here has the clearly visible tattoo in the standard, easily checkable location which would mark them as a secret enemy spy." Albus made a quieting gesture that halted the Potions Master before he could say anything scathing. "Tell me, Harry," Albus said, "how would you have crafted the Dark Mark?" "Nonstandard locations," Harry said promptly, "not easily found without embarrassment and fuss, though of course any security-conscious person would check anyway. Make it smaller, if possible. Overlay another non-magical tattoo to obscure the exact shape—better yet, cover it with a layer of fake skin—" "Cunning indeed," Albus said. "But tell me, suppose you could craft any conditions you wished into the Mark, fading it or raising it as you wished. What would you do then?" "Make it completely invisible at all times," Harry said in tones of stating the obvious. "You don’t want there to be any detectable difference between a spy and a non-spy." "Suppose you are more cunning still," Albus said. "You are a master of trickery, a master of deception, and you employ your abilities to the fullest." "Well—" The boy stopped, frowning. "It seems unnecessarily complicated, more like a tactic a villain would use in a role-playing game than something you’d try in a real-life war. But I suppose you could put fake Dark Marks on people who aren’t really Death Eaters, and keep the Dark Marks on the real Death Eaters invisible. But then there’s the question of why people would start believing in the first place that the Dark Mark identified a Death Eater… I’d have to think about it for at least five minutes, if I were going to take the problem seriously." "I ask you this," Albus said, still in that mild tone, "because I did indeed, in the early days of the war, perform such tests as you suggested. The Order survived my folly only because Alastor did not trust in the bare arms we saw. I had thought, afterward, that the bearers of the Mark might hide it or show it at their will. And yet when we hied Igor Karkaroff before the Wizengamot, that Mark showed clear on his arm, for all that Karkaroff wished to protest his innocence. What true rule may govern the Dark Mark, I do not know. Even Severus is still bound by his Mark not to reveal its secrets to any who do not know them." "Oh, well that makes it obvious," Harry said promptly. "Wait, hold on—you were a Death Eater?" Harry transferred his stare to Severus. Severus returned a thin smile. "I still am, so far as they know." "Harry," said Albus, eyes only for the boy. "What do you mean, that makes it obvious?" "Information theory 101," the boy said in a lecturing tone. "Observing variable X conveys information about variable Y, if and only if the possible values of X have different probabilities given different states of Y. The instant you hear about anything whatsoever that varies between a spy and a nonspy, you should immediately think of exploiting it to distinguish spies from nonspies. Similarly, to distinguish reality from lies, you need a process which behaves differently in the presence of truth and falsehood—that’s why ‘faith’ doesn’t work as a discriminant, while ‘make experimental predictions and test them’ does. You say someone with the Dark Mark can’t reveal its secrets to anyone who doesn’t already know them. So to find out how the Dark Mark operates, write down every way you can imagine the Dark Mark might work, then watch Professor Snape try to tell each of those things to a confederate—maybe one who doesn’t know what the experiment is about—I’ll explain binary search later so that you can play Twenty Questions to narrow things down—and whatever he can’t say out loud is true. His silence would be something that behaves differently in the presence of true statements about the Mark, versus false statements, you see." Minerva’s mouth was hanging open, she realized; and she closed it abruptly. Even Albus looked surprised. "And after that, like I said, any behavioral difference between spies and nonspies can be used to identify spies. Once you’ve identified at least one magically censored secret of the Dark Mark, you can test someone for the Dark Mark by seeing if they can reveal that secret to somebody who doesn’t already know it—" "Thank you, Mr. Potter." Everyone looked at Severus. The Potions Master was straightening, his teeth bared in a grimace of angry triumph. "Headmaster, I can now speak freely of the Mark. If we know we are caught for a Death Eater, before others who have not yet seen our bare arms, our Mark reveals itself whether we will it or no. But if they have already seen our arms bare, it does not reveal itself; nor if we are only being tested from suspicion. Thus the Dark Mark seems to identify Death Eaters—but only those already found, you perceive." "Ah..." Albus said. "Thank you, Severus." He closed his eyes briefly. "That would indeed explain why Black escaped even Peter’s notice… ah, well. And Harry’s proposed test?" The Potions Master shook his head. "The Dark Lord was no fool, despite Potter’s delusions. The moment such a test is suspected, the Mark ceases to bind our tongues. Yet I could not hint at the possibility, but only wait for another to deduce it." Another thin smile. "I would award you a good many House points, Mr. Potter, if it would not compromise my cover. But as you can see, the Dark Lord was quite cunning." His gaze grew more distant. "Oh," Severus breathed, "he was very cunning indeed..." Harry Potter sat still for a long moment. Then - "No," Harry said. The boy shook his head. "No, that can’t actually be true. First of all, we’re talking about the kind of logic puzzle that would appear in chapter one of a Raymond Smullyan book, nowhere near the level of what Muggle scientists do for a living. And second, for all I know, it took the Dark Lord five months of thinking to invent the puzzle I just solved in five seconds—" "Is it that inconceivable to you, Potter, that anyone could be so intelligent as yourself?" The Potions Master’s voice held more curiosity than scorn. "It’s called a base rate, Professor Snape. The evidence is equally compatible with the Dark Lord inventing that puzzle over the course of five months or over the course of five seconds, but in any given population there’ll be many more people who can do it in five months than in five seconds..." Harry pasted a hand against his forehead. "Darn it, how can I explain this? I suppose, from your perspective, the Dark Lord came up with a clever puzzle and I cleverly solved it and that makes us look equal." "I remember your first day of Potions class," the Potions Master said dryly. "I think you have a ways still to go." "Peace, Severus," Albus said. "Harry has already accomplished more than you know. Yet tell me, Harry—why do you believe the Dark Lord is less than you? Surely he is a damaged soul in many ways. But cunning for cunning—you are not yet ready to face him, I would judge; and I know the full tally of your deeds." The frustrating thing about this conversation was that Harry *couldn’t say his actual reasons for disagreeing, *which violated several basic principles of cooperative discourse. He couldn’t explain how Bellatrix had really been removed from Azkaban—not by You-Know-Who in any guise, but by the combined wits of Harry and Professor Quirrell. Harry didn’t want to say in front of Professor McGonagall that the existence of brain damage implied that there were no such things as souls. Which made a successful immortality ritual… well, not impossible, Harry certainly intended to forge a road to magical immortality someday, but it would be a lot harder and require much more ingenuity than just binding an already-existent soul to a lich’s phylactery. Which no intelligent wizard would bother doing in the first place, if they knew their souls were immortal. And the true and honest reason Harry knew the Dark Lord couldn’t have been that smart… well… there wasn’t any tactful way to say it, but... Harry had been to a convocation of the Wizengamot. He’d seen the laughable ‘security precautions’, if you could call them that, guarding the deepest levels of the Ministry of Magic. They didn’t even have the Thief’s Downfall which goblins used to wash away Polyjuice and Imperius Curses on people entering Gringotts. The obvious takeover route would be to Imperius the Minister of Magic and a few department heads, and owl a hand grenade to anyone too powerful to Imperius. Or owl them knockout gas, if you needed them alive and in a state of Living Death to take hairs for Polyjuice potions. Legilimency, False Memories, the Confundus Charm—it was ridiculous, the magical world was supersaturated with ways to cheat. Harry might not do any of those things himself, during his own takeover of Britain, since he was constrained by Ethics… well, Harry might do some of the lesser ones, since Polyjuice or a temporary Confundus or read-only Legilimency all sounded better than an extra day of Azkaban… but... If Harry hadn’t been constrained by Ethics, it was possible he could’ve wiped out the eviller sections of the Wizengamot that day; all by himself, using only a first-year’s magical power, on account of being clever enough to figure out Dementors. Though Harry might not have been in such a great political position after that, the surviving Wizengamot members might’ve found it easy and cheap to disavow his actions for P.R. purposes and condemn him, even if the smarter ones realized it was for the greater good… but still. If you were completely unrestrained by ethics, armed with the ancient secrets of Salazar Slytherin, had dozens of powerful followers including Lucius Malfoy, and it took you more than ten years to fail to overthrow the government of magical Britain, it meant you were stupid. "How can I put this..." Harry said. "Look, Headmaster, you’ve got ethics, there’s a lot of battle tactics you don’t use because you’re not evil. And you fought the Dark Lord, a tremendously powerful wizard who wasn’t so restrained, and you held him off anyway. If You-Know-Who had been super-smart on top of that, you’d be dead. All of you. You’d have died instantly—" "Harry," Professor McGonagall said. Her voice was faltering. "Harry, we almost did all die. More than half the Order of the Phoenix died. If not for Albus—Albus Dumbledore, the greatest wizard in two centuries, Harry—we surely would have perished." Harry passed a hand across his forehead. "I’m sorry," Harry said. "I’m not trying to minimize what you went through. I know that You-Know-Who was a completely evil, incredibly powerful Dark Wizard with dozens of powerful followers, and that’s… bad, yes, definitely bad. It’s just..." *All that isn’t on remotely the same threat scale as the enemy being smart, in which case they Transfigure botulinum toxin and sneak a millionth of a gram into your teacup. *Was there any safe way to convey that concept without citing specifics? Harry couldn’t think of one. "Please, Harry," said Professor McGonagall. "Please, Harry, I beg you—take the Dark Lord seriously! He is more dangerous than—" The senior witch seemed to be having trouble finding words. "He is far more dangerous than Transfiguration." Harry’s eyebrows went up before he could stop himself. A dark chuckle came from Severus Snape’s direction. Um, said the voice of Ravenclaw within him. Um, honestly Professor McGonagall is right, we’re not taking this as seriously as we’d take a scientific problem. The difficult thing is to react at all to new information, instead of just flushing it out the window. Right now it looks like we didn’t shift belief at all after encountering an unexpected, important argument. Our dismissal of Lord Voldemort as a serious threat was originally based on the Dark Mark being blatantly stupid. It would require a focused effort to de-update and suspect the whole garden-path of reasoning we went down based on that false assumption, and we’re not putting in that effort right now. "All right," Harry said, just as Professor McGonagall seemed to be about to speak again. "All right, to take this seriously, I need to stop and think for five minutes." "Please do," said Albus Dumbledore. Harry closed his eyes. His Ravenclaw side divided into three. Probability estimate, said Ravenclaw One, who was acting as moderator. That the Dark Lord is alive, and as smart as we are, and hence a genuine threat. Why aren’t all his enemies already dead? said Ravenclaw Two, who was prosecuting. Note, said Ravenclaw One, we had already thought of that argument so we can’t use it to shift belief again each time we rehearse it. *But what’s the actual flaw in the logic? *said Ravenclaw Two. In worlds with a smart Lord Voldemort, everyone in the Order of the Phoenix died in the first five minutes of the war. The world doesn’t look like that, so we don’t live in that world. QED. Is that really certain? asked Ravenclaw Three, who’d been appointed as the defender. *Maybe there was some reason Lord Voldemort *wasn’t fighting all-out back then - Like what? demanded Ravenclaw Two. Furthermore, whatever your excuse, I demand that the probability of your hypothesis be penalized in accordance with its added complexity - Let Three talk, said Ravenclaw One. Okay… look, said Ravenclaw Three. First of all, we don’t know that anyone can take over the Ministry just with mind control. Maybe magical Britain is really an oligarchy and you need enough military power to intimidate the family heads into submission - *Imperius them too, *interjected Ravenclaw Two. - and the oligarchs have Thief’s Downfall in the entrances to their homes - Complexity penalty! cried Ravenclaw Two. More epicycles!

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https://www.lesswrong.com/posts/Wx2CKWmKnNnXYpWz6/chapter-86-multiple-hypothesis-testing-1?commentId=DW5aJKRK4Ydnto6kP

Harry didn’t want to say in front of Professor McGonagall that the existence of brain damage implied that there were no such things as souls.Harry is wrong here. Yes, the existence of brain damage implies that there are no such things as souls, but that is true only in worlds where we don’t observe people behaving like their normal selves in the absence of their (uninjured) brains. In this magical universe, we do see people behaving like their normal selves in the absence of their brains, just take a look at Animagi for example. And while just saying "souls" does not explain how this happens, we can at least perceive that brains are not the only possible forms for people’s consciences. Harry has not yet evicted his cached thoughts about souls, he has not yet given the matter sufficient attention in the presence of new evidence. I think what’s blocking his progress on figuring out souls is that he still believes that a "soul" has to be immortal, which is incompatible with the effects of brain damage. An alternative interpretation is that "souls" are not immortal in the sense of being independent from people’s brains, but rather that their "instantiations" track the form of the brain as a person goes on thinking with it, but put it on pause during those moments where the brain is absent from the material world (or something equivalent).

Comment

https://www.lesswrong.com/posts/Wx2CKWmKnNnXYpWz6/chapter-86-multiple-hypothesis-testing-1?commentId=BRKBZZ45QcXhsFEb2

Also, from what Harry knows about how magic works, if a dark wizard expected himself to have a soul and created a dark ritual to anchor it to an object and avoid death, magic could plausibly just make him a "soul" for the occasion. Brooms working by Aristotelian physics and aguamenti are also a giveaway that magic doesn’t care how the universe would ordinarily work.

https://www.lesswrong.com/posts/Wx2CKWmKnNnXYpWz6/chapter-86-multiple-hypothesis-testing-1?commentId=rKHjH6otkTBccxFyx

If the Killing Curse has an indefinite lifespan and ends only upon severing a soul, there may be accidental casualties of humans on the other side of the earth or perhaps alien life. Perhaps a hive mind would die instantly to a Killing Curse.

Comment

https://www.lesswrong.com/posts/Wx2CKWmKnNnXYpWz6/chapter-86-multiple-hypothesis-testing-1?commentId=9iFgEHnJaAmnNPA8j

I wouldn’t expect many accidental deaths. Think about how often people shoot off guns in crowded urban areas and no one is hit. The Killing Curse is cast very rarely; there are no recreational curse ranges you go out to. The other side of the earth is millions upon millions of square kilometers; humans take up much less than a meter each. So… For aliens, it would be astronomically more so: probably not a single Killing Curse would ever come anywhere near an inhabited solar system, much less hit someone there on a planet. (That would happen only if driven by plot necessity, which famously sneers at mere probability.)

Comment

This is entirely true and my original comment only stated there would be "many" deaths because of poor word choice from my sleep deprived self.

https://www.lesswrong.com/posts/Wx2CKWmKnNnXYpWz6/chapter-86-multiple-hypothesis-testing-1?commentId=umCJG6cAd69a3K6H2

I honestly don’t think I’ve ever seen such a smart stupid person. It really almost hurts, and I hope as this Harry grows and matures he figures it out. I’ve been rooting for him all along, but he really is a conceited little prick isn’t he? Or is empathy, having no immediate tangible benefits, of no use to him. rolls eyes