|(quoted from Lovesong of the Electric Bear)|
Und'grad1. What's he like? I heard he eats grass when he goes for a run.
Und'grad2. True, but he doesn't swallow it. He just spits it out down his front.
Und'grad2 And he keeps his teddy bear in his rooms too. Weird! (Prods bear)
Porgy Careful how you poke!
Und'grad1 Makes your average nutty mathematics professor look positively normal.
Porgy Oy! Leave my ears alone. And don't try to push your chubby finger up me I'll have you rusticated and then tarred and feathered! One word to Master is all it takes. Settle down!
Und'grad1 What's the bear reading?
Und'grad2. (looks) Principia Mathematica, by Bertrand Russell.
Porgy Yes indeed. My dear students, this noble tome attempts to establish the logical truth of mathematics. It was written before the Great War and we now know it is impossible to establish the logical truth of mathematics. So you could say I am reading it in some disappointment. Bertie Russell got it wrong, simple as that.
(Enter Turing with a grass-and slobber stained singlet and running shorts, panting.)
Porgy Indeed, reading between the lines of the equations, you might say the book is actually a surrender note to mathematics, from a hopelessly randy professor, whose thoughts were elsewhere.
(Turing takes over smoothly)
Turing Thank you, bear. (To Undergrads) It's become clear to the next generation of mathematicians, that mathematics is no longer classical or logical. The stuff used to build bombs and bridges with turns out to be unpredictable or ambiguous. Sometimes it stops, and won't go on. Maths is incomplete.
Porgy You're surely not planning to give this tutorial looking as if a camel has been sick down your front?
Turing (Turing removes singlet.) I was lucky enough to come across a clump of the herb called fat hen while I was running, which has got huge amounts of vitamin C in it; But when you're in movement, you see, there's not point in taking on board too much cellulose.
Porgy I've got an idea. Take off all your clothes and deliver your talk standing on the weighing machine. They'll never forget it.
Turing Would you like to take over the tutorial, bear?
Porgy I will, but can they hear me? Being inanimate myself, I have arrived at rather different conclusions to my master on higher maths. For instance, the Universal Machine is a useless theory.
Turing What is theoretically possible, can become possible. Drake worked out it was possible to sail round the world, in theory. Then he went ahead and did it.
Porgy A flat world is impossible, a round world is possible. The Universal machine is impossible. Because if you had something that is bigger than the universe you started with, then as soon as you have that, you'd have to start your calculations of size all over again to
include the Universal Machine, and so on ad infinitum. Do put some clothes on. None of them are impressed with your flat-earth theories.
Und'grad1Sir, We've got another tutorial we have to go to now.
Turing Gosh, is that the time? Very quickly, then. I shall summarise. Given that there is a mathematical equivalent for any action, the universal machine is a notional calculator which breaks down all actions into binary code. It is a computer.
Und'grad1I thought a computer was a person who worked out mathematical problems.
Turing A person, or a thing. It's all the same.
Und'grad2What does the Universal Machine make of the Entschheidungsproblem?
Turing Are you all familiar with the Entschheidungsproblem ? The philosophical problem of mathematical endings, unforeseen by Russell and Whitehead!
Porgy You can't hope to explain that in minus five minutes. They're already looking at you like a bunch of electrocuted sheep.
Turing What happens when a powerful computer comes to something incomputable? Certain mathematical formula are incomputable. The Universal Machine, having infinite resources, is able to shadow all the tasks that mathematics supports the real world with. So it is a model of reality, albeit a larger one.