The Complete Roderick

‘No but Father, I just thought you could—’

‘Nuts. Nuts! Look the poor crud wasn’t even Catholic, first of all. You don’t need a priest. Get a minister, maybe the guy over at that new motel church, yeah? The Little Olde Church O’ Th’ Interstate, yeah?’

‘But Father, I just thought, maybe he had like a baptism of desire or—’

‘Great, kid. Terrific thought there. You know it’s never too late with God, you can get sent into the game in the last minute of the last quarter and still score… Listen, I’ll try to fit him into my prayers, okay? I’m pencilling him in on the roster right now, okay? Now how about getting off the line, I’m expecting a top-priority call from Thailand.’

‘Yes, but couldn’t Father Warren maybe—?’

‘Father Warren is sick. Goodbye.’

The long hands, now bulged about with tape and gauze like a boxer’s weapons, rummaged through old xerox copies of Philosophy and Proceedings of the Aristotelian Society. At times he would stop, outwardly appearing to rest or perhaps to try to remember what he was looking for. But inwardly the wheels never stopped, never slowed.

Zeno would say it was impossible, motion. For before a wheel can make a full revolution, it must make a half-revolution, before that a fourth, before that an eighth, before that a sixteenth… faced with an infinity of infinitesimal movements before it can move at all, the wheel gives up.

Father Warren sighed. How easy now to smile at Zeno’s simple paradoxes! Now with the two-handed engine at the door, waiting to crack the very hinges of the universe!

Mrs Feeney opened the door a crack. ‘Won’t you eat anything, Father? Just, even a glass of milk?’

He waved a lump of bandage. ‘Too busy, too busy here.’ Milk! To build bones, no doubt. As if that were any kind of solution but a calcium solution, calcium being a metal sure, but can these metal bones live? Let her answer that, yes or no. He lifted the glass, praying inwardly:

‘Father if it be Thy will, let this cup pass away, but if it be not Thy will, then let me take this cup and throw the dice therein.’ He felt a sudden coldness within, and saw the glass was now empty. ‘For Thou playest not dice with the universe,’ and even Pascal said it was a safe bet. So give the wheel its turn, and roll the bones.

But what did Luke say? Not Luke, Lucas, Lucas… something about Godel’s paradox was it, where… The hands pawed wildly for a moment — or an hour — was he looking for Godel or J. R. Lucas, now, ‘On Not Worshipping Facts’ was it? But the article is a fact itself, is that a para… here, here now to get it down once for all time. Holding the pen awkwardly, he began:

Godel’s paradox shows that within any mathematical system it is possible to write formulae representing statements outside the system. Then if a certain formula is true, its corresponding meta-mathematical statement is true, and vice versa. Moreover

Moreover what? Godel equals GOD + EL, stop it, stop it!

Moreover one can write a formula Z corresponding to the meta-mathematical statement: ‘The formula Z is unprovable in the system.’ If the system proves Z, Z is true and therefore the statement is true, making Z unprovable: a contradiction. Therefore the system cannot prove Z, so the statement is true. But that means that Z is true, but unprovable in the system.

Thus for every mathematical system (without internal inconsistencies) there must be one formula which is true but unprovable.

Lucas goes on to show that all machines are mathematical systems of this kind, since all of their operations can be written into formulae. Thus for every—

‘Father, did you want anything else, a sandwi—?’

‘GO AWAY DAMN YOU DAMN YOU GO AWAY!’ Damned interfering old biddy sticking her nose in the door just when he was getting to the, where, where was it, yes:

Thus for every machine there must likewise be a formula Z representing the metamachine statement: ‘The formula Z cannot be proved in the machine.’ In other words, there is one thing the machine cannot do. This reduces the mind-machine debate to a simple contest: The mechanist first presents Lucas with a machine proposed as a model of the mind. Lucas then points out something the mind can do but the machine cannot (prove Z). The mechanist can now alter the machine so it can handle Z, but then it is a different machine. There is now a different unprovable formula Y to baffle it. And so on. The contest continues until the mechanist either produces a machine for which there is no unprovable formula at all — which he can never do — or admits defeat. The mind must win.

Father Warren paused a moment, then added: HA HA HA HA HA!

But—

But what if the machine could alter itself? What if every time Lucas pointed out a gap in the machine mind, the machine simply plugged it? What if the machine could learn and change? So that it begins by saying ‘Gee Father I don’t know…’ and before you know it, it’s inside your head yes inside your head, twisting the controls, stop it, stop it!

Lucas’s bright paradox began to look tarnished already, like Zeno’s whirligig, only an amusement, a game the game position — stop it! — only a trivial, a puppy chasing its tail, that was it, a puppy chasing its own, but if, but what if…?

He looked up, but there was no one at the door.

But what if the machine caught up with Lucas, what if it surpassed him and turned the tables? What if it began setting formulae Lucas could not prove, what then? Write, he commanded his hand. Anything, write. And after a moment the hand moved, writing A.M.D.G., A.M.D.G., faster and faster, trailing a glory of gauze:

A.M.D.G., They have pierced my hands and my feet they have numbered numbered all my bones I believe in God the Fact the

And he saw the whirling puppy snap up its tail, then its hind legs, front legs collar and head snapping up its tail and so on, damn him, and so on!

‘Now, you good sisters been doing a darn good job here,’ said Father O’Bride. He stood with one shoe up on the desk, scraping mud from his cleats. Points of light glancing from his 30-function sports watch danced in the corners of the office behind Sister Filomena, who stood with downcast eyes. ‘As I see it, you gave that Wood kid every chance. Every chance. Not your fault if he fumbles instead of running with the ball, is it? Nope. And boy does he fumble! Let’s just run over his track record, okay?’ He swaggered to the little portable blackboard and erased a football diagram. Then he stood, one fist on the hip of his SHAM OCKS uniform (from which the erroneous C had been removed), the other hand flicking and catching a piece of chalk as though it were a decision coin. Finally he wrote 1.

‘One,’ he said. ‘Discipline. The little creep fouled up Sister Olaf’s religion class, but good! Then I tried to have a man-to-man rap with him, where did I get? Zilchtown, that’s where. Kid’s not even in the same ballgame, can you dig that?’

‘Yes Father. We—’

‘So I says to myself fine, okay, I’ll bench him a while, give him a couple hard workouts with Father Warren, he’ll come around. Only what happens? Father Warren hits into the rough and stays there! And that’s what hurts. Sister, that’s what really hurts. I see him sitting there day after day, busting his… his brains over these dumb