Harry Potter and the Methods of Rationality

"Now," Harry Potter said, "suppose that, just like with tallness, there's lots of little places in the recipe where you can have a piece of paper that says 'magic' or 'not magic'. If you have enough pieces of paper saying 'magic' you're a wizard, if you have a lot of pieces of paper you're a powerful wizard, if you have too few you're a Muggle, and in between you're a Squib. Then, when two Squibs marry, most of the time the children should also be Squibs, but once in a while a child will get lucky and get most of the father's magic papers and most of the mother's magic papers, and be strong enough to be a wizard. But probably not a very powerful one. If you started out with a lot of powerful wizards and they married only each other, they would stay powerful. But if they started marrying Muggleborns who were just barely magical, or Squibs... you see? The blood wouldn't mix perfectly, it would be a glass of pebbles, not a glass of water, because that's just the way blood works. There would still be powerful wizards now and then, when they got a lot of magic papers by luck. But they wouldn't be as powerful as the most powerful wizards from earlier."

Draco nodded slowly. He'd never heard it explained that way before. There was a surprising beauty to how exactly it fit.

"But," Harry said. "That's only one hypothesis. Suppose that instead there's only a single place in the recipe that makes you a wizard. Only one place where a piece of paper can say 'magic' or 'not magic'. And there are two copies of everything, always. So then there are only three possibilities. Both copies can say 'magic'. One copy can say 'magic' and one copy can say 'not magic'. Or both copies can say 'not magic'. Wizards, Squibs, and Muggles. Muggleborns wouldn't really be born to Muggles, they would be born to two Squibs, two parents each with one magic copy who'd grown up in the Muggle world. Now imagine a witch marries a Squib. Each child will get one paper saying 'magic' from the mother, always, it doesn't matter which piece gets picked at random, both say 'magic'. But like flipping a coin, half the time the child will get a paper saying 'magic' from the father, and half the time the child will get the father's paper saying 'not magic'. When a witch marries a Squib, the result won't be a lot of weak wizarding children. Half the children will be wizards and witches just as powerful as their mother, and half the children will be Squibs. Because if there's just one place in the recipe that makes you a wizard, then magic isn't like a glass of pebbles that can mix. It's like a single magical pebble, a sorcerer's stone."

Harry arranged three pairs of papers side by side. On one pair he wrote 'magic' and 'magic'. On another pair he wrote 'magic' on the top paper only. And the third pair he left blank.

"In which case," Harry said, "either you have two stones or you don't. Either you're a wizard or not. Powerful wizards would get that way by studying harder and practicing more. And if wizards get inherently less powerful, not because of spells being lost but because people can't cast them... then maybe they're eating the wrong foods or something. But if it's gotten steadily worse over eight hundred years, then that could mean magic itself is fading out of the world."

Harry arranged another two pairs of papers side by side, and took out a quill. Soon each pair had one piece of paper saying 'magic' and the other paper blank.

"And that brings me to the prediction," said Harry. "What happens when two Squibs marry. Flip a coin twice. It can come up heads and heads, heads and tails, tails and heads, or tails and tails. So one quarter of the time you'll get two heads, one quarter of the time you'll get two tails, and half the time you'll get one heads and one tail. Same thing if two Squibs marry. One quarter of the children would come up magic and magic, and be wizards. One quarter would come up not-magic and not-magic, and be Muggles. The other half would be Squibs. It's a very old and very classic pattern. It was discovered by Gregor Mendel who is not forgotten, and it was the first hint ever uncovered for how the recipe worked. Anyone who knows anything about blood science would recognize that pattern in an instant. It wouldn't be exact, any more than if you flip a coin twice forty times you'll always get exactly ten pairs of two heads. But if it's seven or thirteen wizards out of forty children that'll be a strong indicator. That's the test I had you do. Now let's see your data."

And before Draco could even think, Harry Potter had taken the parchment out of Draco's hand.

Draco's throat was very dry.

Twenty-eight children.

He wasn't sure of the exact number but he was pretty sure around a fourth had been wizards.