Thursday, May 19, 2011

GKC, the mathematician's delight

I have mentioned previously - at least I think I have - that I intensely dislike the idea of my computer running around loose. I do not want it spending its time as it chooses: I am its absolute master, and I wish it to be working at doing MY bidding, not at what the designers of its operating system have chosen to assign it for its idle time.

Of course, as a Chestertonian and a fortiori a Catholic Christian, there is NO SUCH THING as "idle time" - all times and events are sacred, and we can be holy and busy with the praise of God as we stroll vaguely down the street (in the public's view). But I am not speaking about the Chestertonian view of having "nothing to do" - a line from his Autobiography which was so striking it even got stuck into a "Calvin and Hobbes" comic:
For my own part, I never can get enough Nothing to do.
[GKC Autobiography CW16:202]
Sorry, I cannot find the citation for the C&H comic; I will hunt that later.

Now (ahem!) I was saying something about my computer. I want it to keep busy, and at useful work. So I have recently chosen to have it work on finding the prime palindromes which have 17 digits... yes, a lovely little task for a healthy young machine with nothing better to do. Recently it found that
is prime... what a good little machine. I would give it a treat, but my cookies won't fit in that little slot. Besides, I think it has enough cookies, even if Goggle sometimes says they are disabled. Hee hee.

I took a quick glance to see if Chesterton ever talked about primes. He mentions the Prime Minister a lot, but I know very little about England, and didn't know they have public servants to treat of number-theoretic matters. How advanced. I've seen GKC mention binomials and triangles and several other tech math things, but... well. I guess not.

However I found the word "prime" in an interesting context, which is quite relevant to the matter:
There are some things of which the world does not like to be reminded, for they are the dead loves of the world. One of these is that great enthusiasm for the Arcadian life which, however much it may now lie open to the sneers of realism, did, beyond all question, hold sway for an enormous period of the world's history, from the times that we describe as ancient down to times that may fairly be called recent. The conception of the innocent and hilarious life of shepherds and shepherdesses certainly covered and absorbed the time of Theocritus, of Virgil, of Catullus, of Dante, of Cervantes, of Ariosto, of Shakespeare, and of Pope. We are told that the gods of the heathen were stone and brass, but stone and brass have never endured with the long endurance of the China Shepherdess. The Catholic Church and the Ideal Shepherd are indeed almost the only things that have bridged the abyss between the ancient world and the modern. Yet, as we say, the world does not like to be reminded of this boyish enthusiasm.

But imagination, the function of the historian, cannot let 60 great an element alone. By the cheap revolutionary it is commonly supposed that imagination is a merely rebellious thing, that it has its chief function in devising new and fantastic republics. But imagination has its highest use in a retrospective realization. The trumpet of imagination, like the trumpet of the Resurrection, calls the dead out of their graves. Imagination sees Delphi with the eyes of a Greek, Jerusalem with the eyes of a Crusader, Paris with the eyes of a Jacobin, and Arcadia with the eyes of a Euphuist. The prime function of imagination is to see our whole orderly system of life as a pile of stratified revolutions. In spite of all revolutionaries it must be said that the function of imagination is not to make strange things settled, so much as to make settled things strange; not so much to make wonders facts as to make facts wonders. To the imaginative the truisms are all paradoxes, since they were paradoxes in the Stone Age; to them the ordinary copy-book blazes with blasphemy.
[GKC "A Defence of China Shepherdesses" in The Defendant]
Huh? you ask. What does that have to do with integers that have no integer divisor other than themselves and one?


"...the function of imagination is not to make strange things settled, so much as to make settled things strange; not so much to make wonders facts as to make facts wonders."

Even if you are not a mathematician, there ought to be a wonder about primes (which are perhaps very dull facts), even little ones... But this is nothing more than the song of the old Psalmist, as orchestrated through the classical trivium and quadrivium: "The heavens declare the glory of God..." For it was the arrangement of the quadrivium (by at least some medievals) to begin to organize the idea of number and its application: hence:

number in itself is arithmetic
number in time is music
number in space is geometry
number in space and time is astronomy

We'll talk about this arrangement another time. Right now it's lunchtime and then I have to go see if my computer deserves another "Good Boy!"


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