Harry Potter and the Methods of Rationality

change the whole, and that meant removing the whole Form and replacing it with a different one. What would it even mean to Transfigure only half of a metal ball? That the metal ball as a whole had the same Form as before, but half that ball now had a different Form?

'Mr. Potter,' said Professor McGonagall, 'what you want to do isn't just impossible, it's illogical. If you change half of something, you did change the whole.'

'Indeed,' said Dumbledore. 'But Harry is the hero, so he may be able to do things that are logically impossible.'

Minerva would have rolled her eyes, if she hadn't gone numb a long time ago.

'Supposing it was possible,' said Dumbledore, 'can you think of any reason why the results would differ in any way from ordinary Transfiguration?'

Minerva frowned. The fact that the concept was literally unimaginable was presenting her with some difficulty, but she tried to take it at face value. A Transfiguration imposed on only half of a metal ball...

'Strange things happening at the interface?' said Minerva. 'But that should be no different than Transfiguring the object as a whole, into a Form with two different parts...'

Dumbledore nodded. 'That is my own thought as well. And Harry, if your theory is correct, it implies that what you want to do is exactly like any other Transfiguration, only applied to a part of the subject rather than the whole? No changes at all?'

'Yes,' Harry said firmly. 'That's the whole point.'

Dumbledore looked at her again. 'Minerva, can you think of any reason whatsoever why that would be dangerous?'

'No,' said Minerva, after she had finished searching through her memory.

'Likewise myself,' said the Headmaster. 'All right, then, since this ought to be exactly analogous to ordinary Transfiguration in all respects, and since we cannot think of any reason whatsoever why it would be dangerous, I think that the second degree of caution will suffice.'

Minerva was surprised, but she didn't object. Dumbledore was by far her senior in Transfiguration, and he had tried literally thousands of new Transfigurations without ever choosing a degree of caution that was too low. He had used Transfiguration in combat and he was still alive. If the Headmaster thought the second degree was enough, it was enough.

That Harry was certainly going to fail was, of course, completely irrelevant.

The two of them started setting up the wards and detection webs. The most important web was the one that checked to make sure no Transfigured material had entered the air. Harry would be enclosed in a separate shell of force with its own air supply just to be certain, only his wand allowed to leave the shield, and the interface tight. They were inside Hogwarts so they couldn't automatically Apparate out any material that showed signs of spontaneous combustion, but they could launch it out a skylight almost as fast, the windows all folded outward for exactly that reason. Harry himself would go out a different skylight at the first sign of trouble.

Harry watched them working, his face looking a little frightened.

'Don't worry,' said Professor McGonagall in the middle of her running description, 'this almost certainly won't be necessary, Mr. Potter. If we expected anything to go wrong you would not be allowed to try. It's just ordinary precautions for any Transfiguration no one has ever tried before.'

Harry swallowed and nodded.

And a few minutes later, Harry was strapped into the safety chair and resting his wand against a metal ball - one that, based on his current test scores, should have been too large for him to Transfigure in less than thirty minutes.

And a few minutes after that, Minerva was leaning against the wall, feeling faint.

There was a small patch of glass on the ball where Harry's wand had rested.

Harry didn't say I told you so, but the smug look on his sweating face said it for him.

Dumbledore was casting analytic Charms on the ball, looking more and more intrigued by the moment. Thirty years had melted off his face.

'Fascinating,' said Dumbledore. 'It's exactly as he claimed. He simply Transfigured a part of the subject without Transfiguring the whole. You say it's really just a conceptual limitation, Harry?'

'Yes,' Harry said, 'but a deep one, just knowing it had to be a conceptual limitation wasn't enough. I had to suppress the part of my mind that was making the error and think instead about the underlying reality that scientists figured out.'

'Truly fascinating,' Dumbledore said. 'I take it that for any other wizard to do the same would require months of study if they could do it at all? And may I ask you to partially Transfigure some other subjects?'

'Probably yes and of course,' Harry said.

Half an hour later, Minerva was feeling equally bewildered, but considerably reassured about the safety issues.

It was the same, aside from being logically impossible.

'I believe that's enough, Headmaster,' Minerva said finally. 'I suspect partial Transfiguration is more tiring than the ordinary sort.'

'Getting less so with practice,' said the exhausted and pale boy, voice unsteady, 'but yeah, you've got that right.'

The process of extracting Harry from the wards took another minute, and then Minerva escorted him to a much