Harry Potter and the Methods of Rationality

"It's going to be really hard to distinguish between 2 and 6," Harry said, "it's in the blood either way, you'd have to try and track the decline of wizardry and compare that to how many kids different wizards were having and measure the abilities of Muggleborns compared to purebloods..." Harry's fingers were tapping nervously on the desk. "Let's just lump 6 in with 2 and call them the blood hypothesis for now. 4 is unlikely because then everyone would notice a sudden drop when the wizards switched to new foods, it's hard to see what would've changed steadily over 800 years. 5 is unlikely for the same reason, no sudden drop, Muggles weren't doing anything 800 years back. 4 looks like 2 and 5 looks like 1 anyway. So mainly we should be trying to distinguish between 1, 2, and 3." Harry turned the parchment to himself, drew an ellipse around those three numbers, turned it back. "Magic is fading, blood is weakening, knowledge is disappearing. What test comes out differently depending on which of those is true? What could we see that would mean any one of these was false?"

"I don't know!" blurted Draco. "Why are you asking me? You're the scientist!"

"Draco," Harry said, a note of pleading desperation in his voice, "I only know what Muggle scientists know! You grew up in the wizarding world, I didn't! You know more magic than I do and you know more about magic than I do and you thought of this whole idea in the first place, so start thinking like a scientist and solve this!"

Draco swallowed hard and stared at the paper.

Magic is fading... wizards are interbreeding with Muggles... knowledge is being lost...

"What does the world look like if magic is fading?" said Harry Potter. "You know more about magic, you should be the one guessing not me! Imagine you're telling a story about it, what happens in the story?"

Draco imagined it. "Charms that used to work stop working." Wizards wake up and find that their wands are sticks of wood...

"What does the world look like if the wizarding blood gets weaker?"

"People can't do things their ancestors could do."

"What does the world look like if knowledge is being lost?"

"People don't know how to cast the Charms in the first place..." said Draco. He stopped, surprised at himself. "That's a test, isn't it?"

Harry nodded decisively. "That's one." He wrote it down on the parchment under Tests:

A. Are there spells we know but can't cast (1 or 2) or are the lost spells no longer known (3)?

"So that distinguishes between 1 and 2 on the one hand, and 3 on the other hand," said Harry. "Now we need some way to distinguish between 1 and 2. Magic fading, blood weakening, how could we tell the difference?"

"What kind of Charms did students used to cast in their first year at Hogwarts?" said Draco. "If they used to be able to cast much more powerful Charms, the blood was stronger -"

Harry Potter shook his head. "Or magic itself was stronger. We have to figure out some way of telling the difference." Harry stood up from his chair, began pacing nervously through the classroom. "No, wait, that might still work. Suppose different spells use up different amounts of magical energy. Then if the ambient magic weakened, the powerful spells would die first, but the spells everyone learns in their first year would stay the same..." Harry's nervous pacing sped up. "It's not a very good test, it's more about powerful wizardry being lost versus all wizardry being lost, someone's blood could be too weak for powerful wizardry but strong enough for easy spells... Draco, do you know if more powerful wizards within a single era, like powerful wizards from just this century, are more powerful as children? If the Dark Lord had cast the Cooling Charm when he was eleven, could he have frozen the whole room?"

Draco's face screwed up as he tried to recollect. "I can't remember hearing anything about the Dark Lord but I think Dumbledore's supposed to have done something amazing on his Transfiguration O.W.L.s in fifth year... I think other powerful wizards were good in Hogwarts too..."

Harry scowled, still pacing. "They could just be studying hard. Still, if first-year students learned the same spells and seemed about as powerful then as now, we could call that weak evidence favoring 1 over 2... wait, hold on." Harry stopped where he stood. "I have another test that might distinguish between 1 and 2. It would take a while to explain, it uses some things that scientists know about blood and inheritance, but it's an easy question to ask. And if we combine my test and your test and they both come out the same way, that's a strong hint at the answer." Harry almost ran back to the desk, took the parchment and wrote: