Oz and the Wizard:

The Test

By Oz and John Baez

Oz fell back into bed with a groan.

"Absolutely typical." thought Oz. "The deal was that I sweep the floors, and the Wiz answers the questions. Now I sweep the floors AND answer the questions."

Oz muttered dark thoughts under his breath and kicked angrily at his bunk, which promptly collapsed in a cloud of dust. Oz looked at it gloomily.

"Trouble is that all the Wiz's notes fade away after a week or two so he can reuse the paper. Hmmmm. OK, so I can go and look at my Hard Drawn Descriptions (or HDD's) that I carved on the rocks outside, but it's blowing a blizzard. In any case some have been taken by the trolls who used the rocks for Gremlin Pancake Fodder (or GPF's) so they aren't what you could call complete." muttered Oz despairingly to himself.

"Oh, well, I suppose I had better try" he thought, and walked over to the cavern's mouth. The snow was blowing a force 12 and the temperature was 250K. No way was Oz going out there! Oz returned glumly to his hole in the rock and started to think. This unexpected mental activity was not nice. In fact the pain was pretty bad, but he tried hard. Synapses that had been asleep for years complained bitterly about being woken up by a sharp electric shock, and out of condition neurons puffed around frantically trying to make sense of the unfamiliar impulses.

"OK, so why must a black hole always form when the energy density within a region of space becomes large enough. Hey, this is practical stuff. We haven't done any practical stuff! The bast**d! Now if we had seen some worked out expressions for the Schwarzchild metric, then it would have been much easier. It would also have been nice if someone had given some relationship between force and curvature, no matter, doubtless it will come up in due time."

At this moment, the wizard was in the back room reading a parchment that his slaves had fetched him... a recently written disquisition on n-categories, by a wizard far across the seas. He frowned. It seemed his competitor was catching up... he had been spending too much time on that apprentice of his, and neglecting his serious work. He decided to put in a good several hours trying to see just what the other fellow had done. Just as he was reaching for his quill, to take some notes, a large bell off in the corner began ringing. "Damn! What is it now?" the wizard cried. "Someone is making a conceptual error somewhere... Bell! Tell me, who is screwing up?"

"It's Oz, sir," said the bell, in a melodious high-pitched voice. "He's trying to solve a general relativity by treating gravity as a force!"

"Gravity as a FORCE??? What? Are you sure it's Oz? I told him millions of times that in GR, freely falling objects simply follow geodesics! The whole point of GR is that gravity is not described as a force! I'm sure he knows that. It can't possibly be Oz! Tell me it's not!"

"Yes, it's Oz sir, I can sense his aura very clearly. He's in his cave."

"FORCE? What the hell is he trying to do, anyway?"

"He's trying to solve that problem you gave him, on why sufficiently dense matter collapses to form a black hole."

"God's wounds, why doesn't he just use the course notes! I told him the exact formula for how the stress energy tensor curves spacetime and makes initially parallel geodesics converge! Doesn't he see what that implies?"

"Apparently not, sir."

"Why, I'll go out and hide that fellow, teach him a thing or two about force..." The wizard stormed towards the door, cape swirling behind him and static electricity building for an enormous discharge, when all of a sudden he halted... he had a thought. Why not get that other fellow, Ed Green, to help Oz out? Why do all the work himself? True, Ed never seemed to enter into the wizard fantasy realm, but if he could be reached in his own realm, he could probably be coaxed into helping Oz on these test problems. It would probably be good for Ed, too.

"Courier!" The wizard clapped his hands, and a phoenix appeared in a puff of smoke. "Tell Ed Green to help Oz with those test questions. You will have to leave this realm and take on a form suitable for the realm of Mundania. I think he lives in Manhattan. Perhaps you should be bicycle courier."

"Is he wired?"

"Yes, certainly. I've communicated with him that way before."

"Well then," said the Courier, "With your permission, I will simply take a little snippet of the spacetime continuum, say the last five minutes in Oz's cave and this room here. Don't worry, I won't actually cut it out; I'll just copy it, edit and compress it a bit, translate it into ASCII form, and email it to him. That's more efficient than sending me off to Manhattan, no?"

The wizard smiled. "You're so clever. I can never get used to these labor-saving conveniences. Go right ahead. Post it to sci.physics while you're at it. Ask him to help Oz solve this GR problem without referring to that archaic and misleading notion of the "force" of gravity."