Harry Potter and the Methods of Rationality

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