It is one of those warm days at the end of winter when the sun is shining strongly, the air is calm, and it has got nice and warm in front of the cavemouth. Water tinkles gently down the icicles hanging from the wizards keep above and the sunshine glints warmly off the slowly melting snow.
Erg is finishing his alembic. He has liberated some of the wizard's sulphur and is well on the way to preparing some concentrated sulphuric acid. Trolls round here are mostly made of limestone and erg figures that a glass phial full of acid and thrown by his 'new improved catapult', or as he prefers to call it 'an Ergopelt' will cause them serious grief. Erg has a thing about Trolls, particularly when they dent his now shining armour. Erg has lost his city pallor and now looks lean and sunburned and he is much fitter from climbing up and down the steps in the wizards keep.
Oz is sitting on a stone, his mind a total blank. His mind is very good at being totally blank and feels safe like this. Whenever it thinks it's mouth opens and says something. This is dangerous around the wizard. One stray thought and one stray word and zzzZAP!
In their cave under the hillside the Troll family is asleep. They are full of Oz's tablets. Daddy troll is snoring, Reeee - mannnn, Reeee - mann, and baby troll is Weyl-ing quietly. Oz reflects that these trolls are behaving oddly. For example baby troll was christened (or rather stoned) Blockhead, which is a very troll sort of name. However both his parents seem to have nicknamed him Ricky. Odd.
Suddenly Wiz is seen floating down the steps of the keep. He looks happy and relaxed. Erg quickly hides his purloined sulphur under a stone.
"What a nice day," says Wiz. Oz and erg look at each other in amazement.
"Oh, and you can have that sulphur, by the way erg, I gave up using it long ago," commented Wiz quietly. Oz and erg looked stunned.
"What is that pile of stone tablets doing there?" asked Wiz waving vaguely at the pile of stone tablets partly covered by snow.
"Oh, thats my Hard Drawn Desciptions you told me to do." said Oz proudly. "It's taken me a lot of work to do them and there they are!"
"What!" exclaimed Wiz, "When I said put them on a HDD, I didn't mean a Hard Drawn Description, that's not what HDD stands for, I meant put them on a Hard Disk, you stupid blithering imbecile."
Well, Oz could see that Wiz was in a good mood. There were no incipient coronas forming round his head, and the thunderbolts inside his eyes all had their feet up and were watching Baywatch. Oz really couldn't see what difference it made carving them on stone disks except that the Trolls would have a bundle of fun rolling them down the hill. Ah, well, Wiz was probably right, even if Oz couldn't see it.
Wiz came over and sat down. "So, how's it all going my noble men?" he asked, to erg and Oz's astonishment. "I feel like some idle chatter, my work is going well, and that Wizard over the water hasn't got it quite right yet."
"Wellll," said Oz, "it would be quite nice just to talk over the subject a bit. You know, philosophise a bit about life, the universe and general relativity."
Erg dived for cover. He had experience of the wizard, mostly electrifying.
"Calm down there, erg!" laughed the wizard. "I'm really not as bad as you guys think. True, I do resort to some seemingly severe measures at times to further your education, but think: both of you are still alive and well, safe and sound, and growing more knowledgeable every day... and by the way, you have most delightful cave here! What more could you ask?"
"Well," said Oz (ignoring erg, who was peeking around a boulder, putting his finger to his lips in a desperate attempt to keep Oz from saying something that would send the wizard into a rage), "a little heat now and then on winter nights would be nice!"
"Heat?" chuckled the wizard. "What do you need heat for? It's just disorganized energy... only keeps one from thinking clearly. There's really nothing like a nice chilly winter night to focus ones attention on important matters, like theoretical physics! Why, when I was a lad, we never had any heat in our caves, it would have been unthinkable. People are getting soft these days. Never fear, you'll have all the heat you want, come summer."
"True," said erg, cautiously emerging from behind the boulder. G. Wiz seemed indeed to be in a good mood. Perhaps if he humored him everything would be okay.
"So, you wanted to talk things over, eh?" the wizard asked Oz. "You've been making good progress on the last two questions... I really hadn't expected you to go into nearly so much detail... of course you still need to figure out that black hole question... but on the whole I'm quite pleased. You're beginning to absorb the basic principles: that gravity in general relativity is not a force, that all you need to know is how energy-momentum affects the geometry of spacetime, and then to see what a particle does in free fall, you just calculate the geodesic it follows..."
"Umm, which we still haven't learned to do," added Oz. Erg looked distressed, this being a touchy subject.
"NOT UNTIL YOU PASS THE TEST!" thundered the wizard. Erg jumped off the log he was sitting on and fell over onto his back, panting with terror, and the wizard exploded in laughter. "Yes, indeed, the main thing you are missing is how to compute parallel transport, or the so-called "connection", given the metric. Once I tell you this --- assuming you pass the test --- you will know how to work out geodesics given the metric, since a geodesic is just a curve whose velocity is parallel transported along itself. And you will be able to compute the Riemann tensor, starting from its definition in terms of parallel translation around a wee parallelogram. And so you won't need to go skulking around and peeking at my books!" He winked and nudged Oz.
"But even before you know how to calculate all these things, I hope the principles are becoming clear. They're very beautiful, are they not?" asked the wizard, staring abstractedly at the dripping icicles. "It's all very simple, in the end: the geometry of spacetime was always known to affect the motion of matter... without spacetime geometry, how would matter know which way to go? But here we are seeing a wonderful instance of the principle that "if A affects B, B must affect A." The motion of matter in turn affects the geometry of spacetime! And it's all wound up into one equation..." He scratched it on the dirt of the cave floor,
G_{ab} = T_{ab}.
"Spacetime geometry on the left, the energy and momentum of matter on the right... they turn out to be exactly the same, or two different ways of talking about the same thing. Well, I'm getting a bit carried away here," he added. "But you should remind me to explain sometime how local conservation of energy and momentum follows from this equation! After you've passed that test and learned a bit more math."