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.
Magic did not appear to work like this, to put it mildly. Magic's attitude toward laws like Conservation of Energy was somewhere between a giant extended middle finger, and a shrug of total indifference. Aguamenti created water out of nothingness, so far as anyone knew; there was no known lake whose water level went down each time. That was a simple fifth-year spell, not considered impressive by wizards, because creating a mere glass of water didn't seem amazing to them. They didn't have the wacky notion that mass ought to be conserved, or that creating a gram of mass was somehow equivalent to creating 90,000,000,000,000 joules of energy. There was an upper-year spell Harry had run across whose literal incantation was 'Arresto Momentum!' and when Harry had asked if the momentum went anywhere else he'd just gotten a puzzled look. Harry had kept an increasingly desperate eye out for some kind of conservation principle in magic, anywhere whatsoever...
...and the whole time it had been right in front of him in every Potions class. Potions-Making didn't create magic, it preserved magic, that was why every potion needed at least one magical ingredient. And by following instructions like 'stir four times counterclockwise and once clockwise' - Harry had hypothesized - you were doing something like casting a small spell that reshaped the magic in the ingredients. (And unbound the physical form so that ingredients like porcupine quills dissolved smoothly into a drinkable liquid; Harry strongly suspected that a Muggle following exactly the same recipe would end up with nothing but a spiny mess.) That was what Potions-Making really was, the art of transforming existing magical essences. So you were a little tired after Potions class, but not much, because you weren't empowering the potions yourself, you were just reshaping magic that was already there. And that was why a second-year witch could brew Polyjuice, or at least get close.
Harry had kept scanning through Moste Potente Potions, looking for something that might disprove his shiny new theory. After five minutes he'd flipped the older boy another Sickle (over his protests) and kept going.
The potion of giant strength required a Re'em to trample the mashed Dugbogs you stirred into the potion. It was odd, Harry had realized after a moment, because crushed Dugbogs weren't strong themselves, they were just... very, very crushed after the Re'em got through with them.
Another recipe said to 'touch with forged bronze', i.e., grasp a Knut in pliers so you could skim the potion's surface; and if you dropped the Knut all the way in, the book warned, the potion would instantly superheat and boil over the cauldron.
Harry had stared at the recipes and their warnings, forming a second and stranger hypothesis. Of course it wouldn't be as simple as Potions-Making using magical potentials imbued in the ingredients, like Muggle cars fueled by the combustion potential of gasoline. Magic would never be as sensible as that...
And then Harry had gone to Professor Flitwick - since he didn't want to approach Professor Snape outside of class - and Harry had told Professor Flitwick that he wanted to invent a new potion, and he knew what the ingredients ought to be and what the potion should do, but he didn't know how to deduce the required stirring pattern -
After Professor Flitwick had stopped screaming in horror and running in little circles, and Professor McGonagall had been called into the ensuing fierce interrogation to promise Harry that in this case it was both acceptable and important for him to reveal his underlying theory, it had developed that Harry had not made an original magical discovery, but rediscovered a law so ancient that nobody knew who had first formulated it:
A potion spends that which is invested in the creation of its ingredients.
The heat of goblin forges that had cast the bronze Knut, the Re'em's strength that had crushed the Dugbogs, the magical fire that had spawned the Ashwinder: all these potencies could be recalled, unlocked, and restructured by the spell-like process of stirring the ingredients in exact patterns.
(From a Muggle standpoint it was just odd, a deranged version of thermodynamics invented by someone who thought life ought to be fair. From a Muggle standpoint, the heat expended in forging the Knut hadn't gone into the bronze, the heat had left and dissipated into the environment, becoming permanently less available. Energy was conserved, could be neither created nor destroyed; entropy always increased. But wizards didn't think that way: from their perspective, if you'd put some amount of work into making a Knut, it stood to reason that you could get exactly the same work back out. Harry had tried to explain why this sounded a bit odd if you'd been raised by Muggles, and Professor McGonagall had asked bemusedly why the Muggle perspective was any better than the wizarding one.)
The fundamental principle of Potions-Making had no name and no standard phrasing, since then you might be tempted to write it down.
And someone who wasn't wise enough to figure out the principle themselves might read it.
And they would start having all sorts of bright ideas for inventing new Potions.
And then they would be turned into catgirls.
It had been made very clear to Harry that he wasn't going to be sharing this particular discovery with Neville, or Hermione either after the next armies' battle. Harry had tried to say someth
ing about Hermione seeming really off lately and this being just the sort of thing that might cheer her up. Professor McGonagall had said flatly that he wasn't even to think it, and Professor Flitwick had raised his little hands and made a gesture as of snapping a wand in half.
Although the two Professors had been kind enough to suggest that if Mr. Potter thought he knew what the potion's ingredients should be, he might be able to find an already-existing recipe that did the same thing; and Professor Flitwick had mentioned several volumes in the Hogwarts library that might be useful...
The vast parchment-like screen now showed only an aerial view of the forest, from which you could barely make out the camouflaged forms of three armies, split up into two groups each, converging to fight their three-way battle.
The benches of the Quidditch stadium were now rapidly filling up with the more easily bored sort of spectator who only wanted to be there for the final battle and skip out on all the boring points along the way. (If there was anything wrong with Professor Quirrell's battles, it was widely agreed, it was that his spectacles didn't last nearly as long as Quidditch matches, once they actually started. To this Professor Quirrell had replied only, Such is realism, and that had been that.)
Within the huge window - it was all one window now, observing from a great height - the vague collections of tiny camouflaged forms grew closer.
Closer.
Almost touching -
The vast white parchment window showed the first touch of battle between Sunshine and Chaos, a screaming mass of running children with smiley-faces upon their breasts, charging forward with Contego shields held high and others shouting "Somnium!" -
Until one of their number shrieked "Prismatis!" in a terrified voice and the entire charge came to a sudden halt before the sparkling wall of force that had appeared in front of them.
Tracey Davis had walked out from behind the trees.
"That's right," said Tracey, her voice low and grim as she leveled her wand on the barrier. "You should fear me. For I am Tracey Davis, the Darke Lady! That's Darke Lady spelled D-A-R-K-E, with an E!"
(Amelia Bones, Director of the Department of Magical Law Enforcement, was sending an inquiring look at Mr. and Mrs. Davis, both of whom looked like they would have dearly preferred to die on the spot.)
Behind the Prismatic Barrier, there was some kind of hushed argument taking place among the Sunshine Soldiers, one of whom in particular seemed to be getting scolded by several of the others.
Then, a moment later, Tracey flinched.
Susan Bones had come to the front of the Sunshine contingent.
("Goodness," said Augusta Longbottom. "What do you suppose your grand-niece has been learning at Hogwarts?")
("I don't know," Amelia Bones said calmly, "but I shall owl her a Chocolate Frog and instructions to learn more of it.")
The Prismatic Barrier vanished.
The Sunshine Soldiers resumed their charge forward.
Tracey yelled, her voice high with strain, "Inflammare!" and the Sunshine charge came to another sudden halt as a line of fire blazed up between them in the half-dry grass, extending to follow the path of Tracey's wand as she pointed it; an instant later Susan Bones cried "Finite Incantatem!" and the flames dimmed, brightened, dimmed in the contest of their wills, other soldiers raising their wards to aim at Tracey; and that was when Neville Longbottom plunged shrieking out of the sky.
One of the Dragon Warriors, Raymond Arnold, made a hand-sign, pointing forward and oblique left; and there was a sudden hushed hiss of whispers among the Dragon Army contingent as they all quietly reoriented themselves in the direction of the enemy. The Sunnies knew they were there, of course both armies knew; but somehow, in this moment, they had all become instinctively quiet.
The Dragons crept forward further, and then further, the dull camouflaged forms of the Sunnies beginning to appear among the distant trees, and still nobody spoke, nobody bellowed the call to charge.
Draco was now at the forefront of his soldiers, Vincent behind him and Padma only a shade further back; if the three of them could take the shock of Sunshine's best, the rest of Dragon Army might stand a chance.
Then Draco saw one Sunnie staring at him from the distance, in the vanguard of her own army; staring at him with a look of fury -
Across the forest battleground, their eyes met.
Draco had only a fraction of a second to wonder, in the back of his mind, what Hermione Granger was so angry about, before the shout went up from both their armies; and they were all running forward to the charge.
The other Chaotics had appeared now from among the trees, some had dropped out of trees, and the battle was in full force now, everyone firing in every direction at anything that looked like an enemy. Plus a number of Sunnies crying "Luminos!" at Neville Longbottom as the Chaos Hufflepuff twisted and rocketed up through the air on courses that could only be described as, indeed, "chaotic" -
And it happened, the way it happened only one time out of twenty in mock aerial combat, that Neville Longbottom's broomstick glowed bright red beneath his clenched hands.
It should've meant that Longbottom was out of the game.
Then, in the Hogwarts stands, among the watching crowds of students, a scream went up -
Combat realism. It was Professor Quirrell's one master rule. You could get away with anything if it was realistic, and in real life, a soldier didn't just vanish when their broomstick got hit by a curse.
Neville was falling toward the ground and screaming "Chaotic landing!" and the Chaotics were wrenching their attention away from fights to cast the Hover Charm (and run at the same time so they wouldn't be sitting ducks), almost everyone else stopping to gape -
And Neville Longbottom slammed into the leaf-laden forest ground, landing on one knee, one foot, and both hands, as though he were kneeling down to be knighted.
Everything stopped. Even Tracey and Susan paused in their duel.
In the stadium, all crowd noises vanished.
There was a universal silence composed of astonishment, concern, and sheer dumbstruck gaping awe, as everyone waited to see what would happen next.
And then Neville Longbottom slowly rose to his feet, and leveled his wand at the Sunshine Soldiers.
Though nobody on the battlefield heard it, a large segment of the stadium audience had begun chanting, in steadily rising notes each time the word was uttered, "DOOM DOOM DOOM DOOM DOOM", because you just couldn't see that and not think it required musical accompaniment.
"The crowd is cheering your grandson," said Amelia Bones. The old witch was favoring the screen with a measuring look.
"So they are," said Augusta Longbottom. "Some, if I hear correctly, are cheering, Our blood for Neville! Our souls for Neville!"
"Quite," said Amelia, taking a sip from a teacup which had not been there moments earlier. "It shows the lad has leadership potential."
"These cheers," continued Augusta, her voice taking on an even more stunned quality, "seem to be coming from the Hufflepuff benches."
"It is the House of the loyal, my dear," said Amelia.
"Albus Percival Wulfric Brian Dumbledore! What in Merlin's name has been happening in this school?"
Lucius Malfoy was watching the screens with an ironic smile, his fingers tapping at his armrest in no discernible pattern. "I do not know what is more frightening, the thought that he has some hidden plan behind all this, or the thought that he does not."
"Look!" cried the Lord of Greengrass. The dapper young man had risen half out of his chair, pointing his finger at the screen. "There she goes!"
"We'll both take him at once," Daphne whispered. She knew that a few fear-filled minutes of real combat experience, a handful of times each week, might not be enough to match Neville's regular dueling practice with Harry and Cedric Diggory over the same period. "He's too much for one of us, but both of us together - I'll use my Charm, you just try to stun him -"
Hannah, beside her, nodded, and then they both screame
d at the top of their lungs and charged forward, the Hover Charms of two supporting Sunshine Soldiers moving them faster and making them light on their feet, Daphne already crying "Tonare!" even as Hannah kept a huge Contego shield moving in front of them, and with a brief extra lift they leapt over the heads of the front screen of soldiers and landed in front of Neville with their hair billowing high around them -
(Photographs were strictly prohibited at all Hogwarts games, but somehow this moment still ended up on the front page of the next day's Quibbler.)
- and in the same instant, because fighting older bullies had burned away the slightest traces of hesitation, Hannah fired her first Sleep Hex at Neville (she'd started the incantation while she was still in the air) even as Daphne, concentrating more on speed than on force, slashed down with her Ancient Blade at where she thought Neville's thighs would be after he dodged -
But Neville leapt up, not sideways, leapt up higher than he should've been able to go, so that her glowing sword cut only the air beneath his feet. Somehow Daphne realized what it meant, that Neville still had other Chaotics Hovering him, in time for her to raise her Blade up over her head, but Neville fell too fast and when his Blade smashed into hers it was like being hit by a Bludger. It knocked Daphne off her feet and sent her sprawling backward onto the grass, hitting the ground hard on her back. It might have been all over for her, then, if Neville hadn't landed too hard himself and gone to his knees with a pained gasp. And then before Neville could bring his glowing Blade down, Hannah shouted "Somnium!" and Neville lurched frantically backward - though of course no spell had actually come from Hannah's wand, the Hufflepuff girl couldn't really have fired again that fast - which gave Daphne a second to scramble to her feet and get both hands around her wand again -
"Dear Merlin," said Lady Greengrass. Her voice seemed unsteady, the aristocratic poise well-punctured. "My daughter is fighting with the Charm of the Most Ancient Blade. In her first year. I never knew she possessed - such extraordinary talent -"
Harry Potter and the Methods of Rationality Page 130