Oz and the Wizard:

The Test

By Oz and John Baez

One day Oz was sweeping up the spent debris from one of G. Wiz's more extravagant attempts at quantising time. The floor was littered with shrivelled up discarded electrons, photons and failed universes. Bundles of fibrous ectoplasm still writhed through multiple internal dimensions as they died a ghastly and grisly death. Microscopic black holes popped randomly amongst the detrius as they gave up the last of their energy in a whimper of unbeingness.

"What a bl**dy mess." Thought Oz, "All that power and he just scatters everything around. You'd think he would at least organise it to collect itself into a heap at the end".

G. Wiz staggered through the curtain of his inner sanctum. (You know, THAT curtain.) He looked grey and worn. His usually unlined and jovial face was covered with more wrinkles than a 'father of the college' and he was haggard and grim.

"I'm out of magic herbs," said G. Wiz "I shall have to go off to the high mountainside and collect some more, or I'll be a goner. Tidy this up and have the rest of the day off. And DON'T do anything stupid whilst I am away."

"Right-oh, your magicness sir." said Oz, pretty pi**sed off. "No sooner said than done y'r wizardness."

"OK, see you at sunset." said G. Wiz as he tottered out of the door.

"Hours of work here," thought Oz "No sooner said than done, indeed! Humph, he's never even held a broom!"

Oz swept up, put the debris into the black hole recycler and cleaned the larger scorch marks from the white quartzite floor. Then he ate the dry and stale bread as supplied by the wizard. "Good for the brain" the wiz always said, although Oz had never actually seen the Wiz ever eat any himself.

The G. Wiz wasn't due back for hours.

"I wonder HOW he works out the Riemann curvature of spacetime?" thought Oz. "Maybe that'll be powerful and general enough magic to put a spell on that wench in the village pub? I bet it's really simple. Perhaps if I just had a peek inside the sanctum I could spot a tome, read it, and who knows what I'll be able to do then?"

Oz cautiously walked over to the curtain and lifted a corner. A cold and hostile wind blew out and the hair on the back of Oz's neck stood on end. A blue corona flickered round the edges of the curtain but Oz still looked in.

Books and papers were scattered all over. Some flickered in and out of existence and others were supported by massive steel frames although they looked quite small and light.

"Ahah," though Oz "some of these are weighty tomes indeed."

Oz walked cautiously in. Unbeknownst to him the sky outside the cavern went black, and small thunderbolts played space invaders with little black clouds in the erie and supernatural gloom.

At the back he saw a book.

"Riemann curvature of transdimensional spacial entities in 26 dimensional quarternion metaspace", was embossed in gold on its aged and worn dragonskin spine. It seemed to have a lot more pages inside than you could get between the covers.

"Ahah," thought Oz, "just the thing for me."

He opened the book and froze. There was a heavy and hostile breathing right behind his left ear. "OhmygodthewizisbackandIamforthehighjump" thought Oz. Last time he had been turned into a frog for a week. He hadn't minded the flies (they were crunchy), or even the moths (juicy but a bit dusty) but the dry air had played hell with his skin.

Oz slowly, very slowly, turned his head to the left and found himself eye to eye, and nose to nose, with a very fit, healthy and young looking G. Wiz. He didn't look pleased at all. Restrained thunderbolts could be seen limbering up through his glowing red pupils. Oz decided to say nothing, and hoped it wouldn't hurt too much. His hair slowly and deliberately lifted off his head in an effort to get as far away from Oz as possible.

"Well, well, well," growled the G. Wiz in technicolour surround sound with accentuated near lethal subsonics. "What have we here?" Oz was silent. Very silent. Mostly because he didn't dare to breath.

Then the Wiz said, "A budding mathematical physicist, eh? Reading up on STRING THEORY, eh?" As he spoke, he lifted his staff, and myriads of small glowing loops, vibrating and glowing, appeared near its tip. Oz took a step back without thinking, mesmerized yet frightened by the sight.

"In a rush to leave?" asked the wizard, his voice dripping sarcasm. "I thought you would ENJOY seeing some strings, being such an expert on them." The strings grew and shone ever more blindingly, expanding and rippling, humming and singing at incredibly high frequencies. As Oz stared at them he was shocked to see that they did not live in ordinary 3-dimensional space: they vibrated in directions that he had never seen or conceived of before. He tried to see clearly what was going on but the more they expanded, the more dimensions they seemed to inhabit.

"Beautiful, no? So... you did not heed my warnings about going into the back room. You want to compute Riemann curvature, no doubt. But do you have what it takes? That's the question." The shimmering vibrations now filled the room, which shook with their energy. The very fabric of space seemed to start dissolving as they encircled Oz... the very laws of classical logic seemed to dissolve (or was it just that Oz was scared witless) leaving behind some deeper, more powerful substratum of reality following its own profound logic, crystal clear yet unspeakable. "If you just wanted to grind away at calculations there would be no problem, but I'm afraid you want INSIGHT. You do want INSIGHT into physics, don't you?" Speechless, Oz was barely able to nod, barely able to hear the wizard or follow what he said.

The wizard laughed. "Yes, you want INSIGHT. But are you prepared to pay the price? You want to understand the laws of the universe --- but would you know yourself any longer if you did?" The wizard exploded into light, Oz staggered over, and everything went black.

Oz awoke to find himself in his cave, lying on the straw-filled bunk. He didn't remember going there... he had a splitting headache... the last thing he remembered was opening a book on something or other in 26 dimensions, and the wizard catching him. Ugh! He propped himself up, and it felt as if his head was about to burst. He looked around and saw a piece of paper lying on the ground near his bed, with glowing writing on it, which faded and dissolved as he read:

"Dear Oz --

If you wish to learn more general relativity I am afraid you will need to pass a test of your valor. So: answer me the following questions:

1. Explain why, when the energy density within a region of space is sufficiently large, a black hole must form, no matter how much the pressure of whatever substance lying within that region attempts to resist the collapse.

2. Explain how, in the standard big bang model, where the universe is homogeneous and isotropic --- let us assume it is filled with some fluid (e.g. a gas) --- the curvature of spacetime at any point may be determined at each point.

3. In the big bang model, what happens to the Ricci tensor as you go back in past all the way to the moment of creation?

I have taught you enough to answer these questions on your own. Slip the answers under my door --- I'm busy.

Best wishes, G. Wiz

(Hint: read the course outline, you fool.)"

Oz fell back into bed with a groan.