Thursday's Dr. Thursday Post: Infinity

It may be a stretch of the imagination to connect last Sunday's gospel (the woman at the well) with our discussion of last Thursday - or perhaps not. The woman's "madness" was shattered - as if a spell was broken - by the Voice of Authority who told her "Go get your husband". So deep was her restoration that she was able to bring others to that same fountain... Ah. But for today I shall resist plunging into the deep waters this imagery brings up.

In thinking of insanity, and Lent, I must bring to your attention one of the most unusual and perhaps most insightful views of a gospel event I have ever read. The event is the "Good Thief" hanging in crucifixion next to Jesus - an apologist defending Christ even on Calvary! "We are but suffering as we deserve - but This One has done nothing wrong... Lord, remember me when You come into Your Kingdom."

The insightful view is not mine. It is contained in the rich notes and the amazing play-sequence, "The Man Born To Be King" of Dorothy L. Sayers (DLS), a series of radio plays she wrote on the life of Christ. I don't have the text here to transcribe, so I shall merely give you a hint of her argument. She claims that the Good Thief perhaps took Jesus to be a harmless nut-case - a crazy man - YET - the thief still treats Him kindly, and "plays along" - only to receive a most unexpected reply. The scene DLS only hints at is the one I love to ponder: for behold, later that day, the Lord would tell the thief, "Nope, I wasn't nuts, but it was kind of you to think so. The charity you showed to the harmless lunatic You showed unto Me!" A strange, yet somehow most dramatic view. Read it for yourself.

I had previously thought I would write up a "proof" about GKC's interesting mathematical bit about the circles, but there will be more of this philosophical geometry before you know it, and I don't feel like making such a long detour today. So let us proceed. We have finished GKC's comments on lunacy and madness - which he expresses using the mystery of the circles: infinite in one sense (for it has no end) yet still not so very large (for it is no bigger than it is drawn). We have seen an omnibus labelled "Hanwell" and thought about those unfortunates who believe themselves to be chickens, or glass, or Kings of England, or Jesus. We have heard of the limits of literature, the risks of reason - and been challenged to cut off our own head if it offends us. What is all this? Why are we seriously contemplating insanity? GKC has a reason, and not merely a poetic one.

Click here to continue the adventure.

GKC tells us himself what he is up to:

I have described at length my vision of the maniac for this reason: that just as I am affected by the maniac, so I am affected by most modern thinkers. That unmistakable mood or note that I hear from Hanwell, I hear also from half the chairs of science and seats of learning to-day; and most of the mad doctors are mad doctors in more senses than one. They all have exactly that combination we have noted: the combination of an expansive and exhaustive reason with a contracted common sense. They are universal only in the sense that they take one thin explanation and carry it very far. [CW1:225]

We might take this as the bridge-passage, the musical riff that brings us from Heretics to Orthodoxy. Recall that in Heretics we saw a long line of men - writers, thinkers, philosophers - men whom GKC respects, even admires - some of whom he would readily claim as friends - and yet men with whom he is in bitter and utter disagreement: "a Heretic - that is to say, a man whose philosophy is quite solid, quite coherent, and quite wrong." [Heretics CW1:46]

Those men are the men LIKE the lunatics. Note he does NOT say they ARE lunatics! He is not pulling an ad hominem argument. He is talking about a general idea, dealing with the IDEAS of those men. What does he tell us about them? He says those are the men with the SMALL PATTERNS, even though they are "infinite":

But a pattern can stretch for ever and still be a small pattern. They see a chess-board white on black, and if the universe is paved with it, it is still white on black. Like the lunatic, they cannot alter their standpoint; they cannot make a mental effort and suddenly see it black on white.[CW1:225]

He proceeds to give an example (about materialism) but almost immediately points out that he is NOT making an argument about the detail, but about the generality. He links the flaw in the materialist view of the kosmos back to the flaw in the man in the asylum. It may be true enough. But it is so much smaller a truth than can be found elsewhere.

I hope you are reading along with me - and so you will readily note that it is futile for me to try to skip the example. GKC himself tried to do that. In one of his amazing leaps, he goes from that example to a stark generality of epistemology (the study of knowledge itself): "In one sense, of course, all intelligent ideas are narrow. They cannot be broader than themselves." [CW1:226] It is the paradox of words, the strangeness of a homework assignment like "Define 'infinity' and use it in a sentence." It hints at another mysterious line of GKC's which he put in another mystery: "Alone on earth, the Church affirms that God himself is bound by reason." ["The Blue Cross" in The Innocence of Father Brown]

Whew, let's stop for a bit. Do you feel stuck in a swamp of ideas? You are wrong. It's the brisk fresh air. You are at a peak of a mountain, and seeing a vista. It's at these points where you feel most congested, you are actually most free, and actually presented with a greater wideness of vision than elsewhere. So let us pick this matter apart so we can grasp where we were and better handle where we're going next. I can't do all the epistemology, I didn't bring that in my knapsack today. Let's see if we can deal with it directly. Let's read it again:

"In one sense, of course, all intelligent ideas are narrow. They cannot be broader than themselves."

The point of the paradox is we can handle things far bigger than our hands - because we have words which can reduce infinity to eight letters. (Count them: I, N, F, I, N, I, T, Y.) The strict philosophers will now throw eggs at me, saying I have committed the "Fallacy of Equivocation", confusing the word "infinite" and the idea "infinite". But I catch the eggs, and scramble them to make our lunch. They are not reading along. (Recall "poetry floats on the infinite sea"...) It would be just as adequate for me to cite the Summa of Aquinas (I Q10 A1) to help them out, since they like that kind of citation, it shows I do read those kinds of things. Ahem! But for us, this "paradox" is as simple as this mountain-peak. We're stopped here - and need to choose a path. But we can choose ANY direction - as long as it's down. (We are walking, you know; remember we said last week, "let it be solved by walking".)

The "fallacy of equivocation" is a kind of error in logic, in the use of words. How about an example? Here's one: saying "God is limited because he is only three letters long". But GKC is telling us there is the same kind of error in saying "we cannot hold the idea of 'infinity' since it is INFINITELY BIG". It is a paradox in reason itself, not merely written by GKC, to state without further quibble, that Infinity is narrow, and God is limited. This is not because of the things-in-themselves, but because of our equipment. (We are on a journey, we are NOT going EVERYWHERE AT ONCE. We are walking, and so are SOMEWHERE.)

I will try once more. (This one is great, and will shock any computer scientists in the audience.) Watch carefully, and I will use YOUR computer to represent BIG integers, including for example, the number of electrons required to fill the sphere bounded by the diameter of the most distant galaxies. Or, even bigger: the factorial of that number. Or even bigger: that number raised to its own power... that many times. Big numbers. BIG big numbers. HUGE numbers. (Even more than GKC weighed.) I can even use the computer to deal with transfinite numbers, the mysterious "aleph-one", which is the cardinality of the real system of numbers. And there are even others... Wow, look: before your very eyes, all those things are being communicated by what I have just written! HAVE I NOT COMMUNICATED THEM TO YOU? Of course I have. They are formally represented - as ideas. No, not directly as tick-marks on a sheet of paper or tokens in a box. (Please. Don't be silly. When was the last time you saw 1000 of ANYTHING? We gave that up about 5000 years ago, when the Egyptians began to write Ç to stand for "ten".) You cannot represent such gigantic numbers by that means. It is like asking how much God weighs. It does not have meaning. But you can communicate the idea of such numbers - which means you have communicated the number. The idea of such vast quantities has a meaning, and so we can accomplish the communication of that idea. And if we failed to say it in symbols of mathematics, we would resort to the symbols of poetry: I think of "Tonight" in "West Side Story":

Today the minutes seem like hours,
The hours go so slowly...
And still the sky is light...

That is what GKC is saying. In order to talk about anything, and reason about anything, we use something narrow. We do not have the infinite time or an infinite box of tokens to play around with the real thing, so we use what we can.

OK. Maybe it was futile - I ought to stick to my own toys - so let's resume with GKC, and I will let the high-tech philosophy for others to play with. Perhaps this next sentence will tell you the same thing, which is just GKC's own version of the very important Principle of Contradiction: "Nothing can be, and not be, at the same time."

A Christian is only restricted in the same sense that an atheist is restricted. He cannot think Christianity false and continue to be a Christian; and the atheist cannot think atheism false and continue to be an atheist.
[CW1:226]

Again, please read this carefully. You need to think about the simple sentences, not about some deep quippy insult or brag. You can put in any partisan or sectarian words you like, and it has JUST the SAME meaning and power. YOU ARE ON A PEAK of FREEDOM, my friend, not stuck in a swamp! Try it again. Then we'll proceed.

Now that you have a NEW tool, then, we shall actually approach this example of materialism - and its opponent, spiritualism. (We are using the terms rather generically here; materialism means there is nothing but material: nothing spiritual at all. Whereas spiritualism means there also exists an unseen realm.)

I shall quote at length again, because you are surely tired of reading MY words, and also because the "verbal fireworks" here are SO good:

...there is a very special sense in which materialism has more restrictions than spiritualism. Mr. McCabe thinks me a slave because I am not allowed to believe in determinism. I think Mr. McCabe a slave because he is not allowed to believe in fairies. But if we examine the two vetoes we shall see that his is really much more of a pure veto than mine. The Christian is quite free to believe that there is a considerable amount of settled order and inevitable development in the universe. But the materialist is not allowed to admit into his spotless machine the slightest speck of spiritualism or miracle. Poor Mr. McCabe is not allowed to retain even the tiniest imp, though it might be hiding in a pimpernel. The Christian admits that the universe is manifold and even miscellaneous, just as a sane man knows that he is complex. The sane man knows that he has a touch of the beast, a touch of the devil, a touch of the saint, a touch of the citizen. Nay, the really sane man knows that he has a touch of the madman. But the materialist's world is quite simple and solid, just as the madman is quite sure he is sane. The materialist is sure that history has been simply and solely a chain of causation, just as the interesting person before mentioned is quite sure that he is simply and solely a chicken. Materialists and madmen never have doubts.
[CW1:226-7]

(An aside: if you are wondering who "McCabe" is, you can read his chapter in Heretics CW1:157 et seq. Joseph McCabe (1867-1955) was a Roman Catholic priest turned rationalist.)

And while I greatly doubt that you can possibly be satisfied with my writing, here I must leave you for today. Please try to think a little about these things. Not about the math, or about the epistemology, the knowledge OF meanings of words and ideas - but ABOUT the meanings, and the ideas.

Still lost? When we think about our mother (let us say) we do not think about her picture, but about HER. But when we talk about her, we may show the picture, or use that six-letter word - but everyone knows who it is we are talking about, even if they have never met her or seen her. IN THE SAME WAY: when we think about infinity, we do not think about that splendid and funny little proof of the math dudes about "increasing without bound" or about a bottomless box of tokens - nor simply about that eight-letter word - but we use that word to talk to others about, as I have just done with you.

And this limited limitlessness applies even to the matter of God, which we do not narrow to a mere word of three letters, and Who has even more meaning and even more intimacy to us than our very mothers...

Onward to the next the peak, dudes!

--Dr. Thursday