The Halting Problem of Evil

Because this is just what you always wanted to read as meditation for the First Week of Advent!

Of course you have heard of Gödel's theorems; they are:

1. Any sequential programming language that can implement interpreters for arbitrary sequential programming languages also implements programs that, for some input, do not converge.
   
2. In particular, for any sequential programming language $L$ (such as LISP) that can implement interpreters for arbitrary sequential programming languages, there is no convergent program in any sequential language that separates convergent $L$ programs from non-convergent $L$-programs.
   

What's that, you say? The LISP programming language is significantly younger than Gödel's theorems? Uncertain of the serializability of LISP itself? Not to worry! This is what happens when mutually-interpetable (or bisimulant) things get mixed up in a mathematician's brain. As it happens, what Gödel did, to prove his theorem, was to show that you could implement LISP (or some other sequential programming languge) in The Arithmetic of the Natural Numbers. I don't know precisely why he did that, though it might have something to do with everyone who cared at that point having a firm belief that they understood what the natural numbers were, and no-one anywhere had ever yet heard of a machine programming language (though they certainly DID have programmable machines, such as farmland and the Gutenberg press and the Jacquard Loom and the Player-Piano; what all these things lacked was recursion, but never mind).

Another way to read the theorem (as applied to programs) is that by far the best way to find out what a program does is to run the program, as naturally as possible. This is very much like (as Dr. Thursday reminds us) the way (as Uncle Gilbert remarked) the point of playing a game is to find out who wins! Now, with programs as with other games, there is definitely a risk involved, due to the halting problem and its corollaries, in running a program. You never know, for instance, that the thing will not chew up your whole machine (or try) before it stops unless you carefully run it within a tiny virtual machine; but on the other hand, unless you have an arbitrary quantity of free space to build a virtual machine in (or a working copy of your working machine), you may never know if some insidious program is going to behave in surprisingly different ways, given the space to do so in.

Of course, God Himself knows what every deterministic pattern of any size looks like at the edges, in exquisite detail; but this should be thought quite something else from creating a living thing that plays within the pattern for His delight. And how much more fraught than running a program, a deterministic thing in a deterministic piece of the universe (bar radioactive decay — and we know Who has ordered radioactive decay) is it to give life to a free and willful thing? But how else could anyone, ever, anywhere, in any way, be good? It is, of course, impossible, to be good without first being, and furthermore being free and willful; the dumb or speaking dead machines are useful or nuissance at times, but not (in themselves) good or evil. And never mind that he cannot be saved who will not be saved, still more can none be saved who is not at all.

Of course, this is all just an infinitessimal slice of the way the “problem of evil” isn't so much a theological problem as it is a natural hazard (and an intrinsic one) within any creation sufficient for containing moral life. [Although C. S. Lewis may have expressed it more eloquently, he certainly never invoked the mathematical certainty of Gödel's theorems, which nonetheless seem suprisingly a-propos; I think we may guess he also never had to program a computer, and it's neither a surprising nor deficient omission.] I also have to admit that this sort of analytical precision has a very cold feel to it, out of proportion with the fact of suffering; the recurrently strange H.H. F. Pp. I recently remarked on the especially poignant case of suffering children — Stilwell excerpts here.

It would seem that those things God has allowed are permitted for some end; and it further seems that suffering, especially suffering in children, does induce its witnesses to charity, and that is indeed a very good thing. Suffering makes the sufferer more lovable. In some cases this is through a change in the sufferer, but as often as not it is by a change in the rest of the world. And this effect, that suffering ordinarily leads to charity, is not a mathematical necessity (I'm sure), but rather a sign of God's goodness, the stamp of part of His character in the world.

A Cautionary Tale

I was going to put up a mathy-philosophical post, with the grand-frivolous title "The Halting Problem of Evil"; it's already quite long, though I've no clue how to finish it, and something rather jarring has occurred since I started that, so this is what we have instead.

Thanks be to God for his most graciously and gratuitously preserving me (and everyone else) from some of the more adverse possible effects of my own stupidity; because, for silly reasons, I was not standing in front of the stove when the glass pie plate exploded (I thought I was steaming the broccoli …), covering the room with thousands of beautiful glittering pointy slivery shards; and for reasons unknown I was already wearing slippers, and standing next to the broom, and the door to the next room was closed. Alas, the pie was inextricably burned onto its own broken shards at that point (and starting to smoke, on the erroneous burner), and the stew was littered with them, too. But no serious injuries were there, just a brief alarm and some hours of scrupulous sweeping.

Analogically

In addition to their practises of exposure and sewering and Molochian sacrifice of “useless” babies, the hedonistic pagans of long ago (and of not so long ago) who had really more wealth than they could practically use, would also artificially extend the sense delight of savour and eating and all that, by means of the vomitorium, which is exactly what it sounds like (when not discussing theatre-in-the-round or volcanoes).

And the reason I bring it up with that lead-in, is to point out one gleamingly hopeful point in which we are, today, still a bit better than those pagans of the bronze-age: this kind of behaviour is still obviously abhorent. It is also still practised, but (in the West) most often finds its expression in an extreme form of plerophobia more commonly known as bulimia. I say this is a hopeful fact, because we actually do remember that a particular act which can be a great pleasure also has a purpose, a telos; we still know that applied engineering to subvert the purpose, to isolate or exaggerate the pleasure of it is actually a diseased and dangerous and literally disgusting game. The world that used to be Christendom is suffering reproductive bulimia, and can't get away from its hunger. Is it any wonder?

A dead comment.

Dear Paul,

(btw, I don't at all mind not being one of your notable theologians! It would be quite a relief, had I ever thought so much as to worry about it, actually... )

Of course, I'm not about to invite you to partake of detraction; in fact I'm happy to remain ignorant of which proponents you mean.

I have, on the other hand, met a number of gnostics among the detractors of either form. To that extent, I hadn't thought about it, and my only conjecture now is that gnosticism is much too easy to fall into, and can end up looking like pretty much anything: it doesn't surprise me anywhere.

To Mr. Kerr I might reply, first: the issue of the Calendars is smoked pickerel; devotees of the E.F. as such are no more intrinsically schismatic nor judaizing than our brothers the Copts, or the Greeks, or the Armenians (or Anglican Use Catholics, for that matter). For the question of understanding, I should say that the internal consistency of a ritual and its language is more important unto understanding than is initial fluency in its idiom. I might put this another way: before I met the Extraordinary Form my Latin was entirely gathered from the musical tutelage of a number of protesants choral conductors (that and the Pange Lingua Gl. we sang every Holy Thursday). The transition from a purely sensual encounter with these ancient prayers and their classical settings (for which I should be aeviternally grateful to my sundered teachers) to an almost-continual living prayer in their ancient form has been something like the old sense of ekstasis — a standing outside what was so familiar as to seem oneself before — but without any of the really-gnostic so-called charismatic nonsense of a dull "esctasy".

To be sure, the Priest must, morally, know what each part of the Mass is when he is celebrating it (and not pray it "like a parrot", to allude to recent remarks), but asking one to understand what it means, from fluency in the words on up, is like asking Augustine to comprehend the Trinity. Mass is supposed to form us, and we to learn from it; that couldn't happen if we had some firm belief that we knew it already.

From the perspective of internal consistency, the current Ordinary Form is... well, I should say, it is much too rough and raw, and will need some centuries of mellowing before we can give it a fair comparison with the Extraordinary. I find the order of it disorienting in places, jumpy and disjointed, now; but as for having it in English, I would only complain that the translation is just too easy. And any translation of the Extraordinary (to follow along with, e.g.) will suffer the same difficulty.

Without being gnostics, let's rejoice in the Mysterious, anyway!

sincerely

The future King

Whatever you think of the fellow, Malcolm Gladwell certainly has an ear for an interesting story and fine delivery, not to mention a keen intuition for dissonance.

And so it was that he, somehow, began to open up the story of Goliath of Geth, and his death not quite at the hand of King Saul's servant the court musician, David son of Jesse of Bethlehem, a young shepherd. The battle of the Elah in the war of the Philistines and the Israelites was never joined, for neither force could find acceptable terrain from which to strike; and so to break this stalemate, the Philistines proposed a trial by single combat and sent forth the giant; none of Israel's army dared singly approach this monster, save David; and when David had toppled him, all the host of the Philistines fled.

I don't propose to tell you Gladwell's telling of the tale; rather, I found that it raises the interesting questions (which he doesn't address) of Why did they flee? and Why is this story recorded and remembered among David's accomplishments?

One of the key differences between King Saul and King David is the David's personal humility in the Kingship. Saul angers the Lord by turning the Kingship into a means for his own personal glory: trying to keep the king of the Amalechites as a pet, for instance; counting the Israelites so as to boast of how great his kingdom is; presuming on his royal authority to insinuate himself among the cohenim. David, in contrast, is humble. When David offers sacrifice, it is as King of Jerusalem, "in the line of Melchizedek"; in the household of King Saul he does not put himself forward, but awaits his assigned tasks, in which tasks Saul sees that the Lord is with David; even the way David does later fall into abusing his kingship — it is heinous, and yet it is done as privately as can be, doing nothing to advance David in glory; and in the Elah, facing Goliath, again it becomes clear (in my case, with Gladwell's help) that David, unlike Goliath, is not in this fight for any glory.

Goliath for the Philistines proposed a duel, a wrestling match, "pistols at dawn". His compatriots look up to him (not just that he's tall), and he is clearly eager to triumph over whatever champion Israel might send to him. He has no idea what he is getting into. He is the fruit of a culture that prizes a warrior skilled in his art, a culture that reads divine approbation in divinely appointed outcomes, and reads every battle as a battle of the little gods because it has no God. David, the shepherd, cares nothing for this nonsense, and gives no honour to battle for its own sake nor to warriors for war's sake; the Philistines (like the Klingons) would say he has no honour; in a twist of modern usage, today's bloodsport aesthetes would call David a philistine of the arena. David is not in the fight to triumph over Goliath, but merely to win for God's chosen people. He doesn't put God to the test, he doesn't seek his own glory or protect his warriors' honour, but only makes durn sure that he wins.

The Philistines flee because they see that these people fight dirty. These people have no fear of the gods who come and go for warriors' valour or to avenge poor sporting. They will keep on fighting however they can whatever befall, just to stay where they are. And clearly the little gods have no power over them, for here they still are in spite of all the bad luck and dishonour they're plainly heaping on themselves. What else can be done with them?

What we have here is an equivocation

Specifically, "Catholic" can (it really can!) mean two, quite opposite things. Of course, what Catholic is supposed to mean is also supposed to get skeptics really annoyed when we point it out.

Catholic can and is supposed to mean "Universal": the Catholic faith is good for everybody, and God whom we worship is God of all, though that's not what he has usually called himself.

But, on the other hand, Catholic can mean "Christian" — you know, those funny folk who talk about turning the other cheek and heaping coals behind your back and have that Nicene Creed thing... or even more weirdly, those Papist Romanizing so-called "Christians", with their surfeit of holidays and authoritarian reading of scripture and... you know, a tiny sect, and anything but universal.

In the latter sense, and in so far as the latter sense remains that understood by everyone who says it, no, God is not "catholic". God does not belong to sects, in either sense of "belong to". That "sect" belongs to Him, but that's another matter.

God is good for everyone; lots of people don't know Him yet, and a few actually hate Him. One Church knows of Him what He Himself has revealed.

Callooh, Callay!

Today the 'blogger internal tracker tells me that on 16061 occasions has something asked it for a page from this blog. I happen to know a few of those are me, and a lot are referal spam, but some of them might well have been you!

But, more than this, 16061 seems to be a prime palindrome, so I'm glad just to have caught the counter when it was at such a number. Whee!

a man of simple pleasures