Harry Potter and the Methods of Rationality

So Harry had retrieved his copy of Magical Drafts and Potions, and begun looking for a safe but useful potion he could brew in the minutes before the battle started - a potion which would win the battle too fast for counterspells, or produce spell effects too strong for first-years to Finite.

Sometimes, even though you were looking straight at something, you didn't realize what you were looking at until you happened to ask exactly the right question...

What potion can I brew using only components gathered from an ordinary forest?

Every recipe in Magical Drafts and Potions used at least one ingredient from a magical plant or animal. Which was unfortunate, because all the magical plants and animals were in the Forbidden Forest, not the safer and lesser woods where battles were held.

Someone else might have given up at that point.

Harry had turned the pages from one recipe to another, skimming faster and faster in dawning realization, confirming what he had already read and was now seeing for the first time.

Every single Potions recipe seemed to demand at least one magical ingredient, but why should that be true?

Charms required no material components at all; you just said the words and waved your wand. Harry had been thinking about Potions-Making as essentially analogous: Instead of your spoken syllables triggering a spell effect for no comprehensible reason, you collected a batch of disgusting ingredients and stirred four times clockwise, and that arbitrarily triggered a spell effect.

In which case, given that most potions used ordinary components like porcupine quills or stewed slugs, you'd expect to see some potions using only ordinary components.

But instead every single recipe in Magical Drafts and Potions demanded at least one component from a magical plant or animal - an ingredient like silk from an Acromantula or petals from a Venus Fire Trap.

Sometimes, even though you were looking straight at something, you didn't realize what you were looking at until you happened to ask exactly the right question...

If making a potion is like casting a Charm, why don't I fall over from exhaustion after brewing a draught as powerful as boil-curing?

The Friday before last, Harry's double Potions class had brewed potion of boil-curing... although even the most trivial healing Charms, if you tried to cast them with wand and incantation, were at least fourth-year spells. And afterward, they'd all felt the way they usually felt after Potions class, namely, not magically exhausted to any discernible degree.

Harry had shut his copy of Magical Drafts and Potions with a snap, and rushed down to the Ravenclaw common room. Harry had found a seventh-year Ravenclaw doing his N.E.W.T. potions homework and paid the older boy a Sickle to borrow Moste Potente Potions for five minutes; because Harry hadn't wanted to run all the way to the library to find confirmation.

After skimming through five recipes in the seventh-year book, Harry had read the sixth recipe, for a potion of fire breathing, which required Ashwinder eggs... and the book warned that the resulting fire could be no hotter than the magical fire which had spawned the Ashwinder which had laid the eggs.

Harry had shouted "Eureka!" right in the middle of the Ravenclaw common room, and been severely rebuked by a nearby prefect, who'd thought Mr. Potter was trying to cast a spell. Nobody in the wizarding world knew or cared about some ancient Muggle named Archimedes, nor the ur-physicist's realization that the water displaced from a bathtub would equal the volume of the object entering the bathtub...

Conservation laws. They'd been the critical insight in more Muggle discoveries than Harry could easily count. In Muggle technology you couldn't raise a feather one meter off the ground without the power coming from somewhere. If you looked at molten lava spilling from a volcano and asked where the heat came from, a physicist would tell you about radioactive heavy metals in the center of the Earth's molten core. If you asked where the energy to power the radioactivity came from, the physicist would point to an era before the Earth had formed, and a primordial supernova in the early days of the galaxy which had baked atomic nuclei heavier than the natural limit, the supernova compressing protons and neutrons into a tight unstable package that yielded back some of the supernova's energy when it split. A light bulb was fueled by electricity, fueled by a nuclear power plant, fueled by a supernova... You could play the game all the way back to the Big Bang.