Thursday, August 12, 2010

Positive and Negative Triangles

After the excitement of last week's conference, it is good to turn back to our usual dull and LENGTHY ploddings, where you can just double-click away from me if I am boring you. But I ought to note something about it, since I was there, and I had a good time, even though it was truncated somewhat for me, due to matters beyond my control.

I saw several old friends, and met several new ones, and it was an awesome time. I laughed a lot, had some beer, and some food, and I think I might have also slept, but I forget. Not that it matters, hee hee. I think some people were surprised to learn that there really is a "Dr. Thursday" and he is not just a pen name of someone else.

The one talk which our esteemed blogg-mistress did not mention in her commentary was (in my own opinion) the best. It also happened to be the one SHE gave! It was titled "The Woman Who Was Chesterton" and (as she remarked) perhaps it sounds as if it was going to be some sort of "gender studies" approach to GKC's writing, his "inner female" or some such. Here, she could have quoted the very famous lines from GKC's letter to - er - to someone else. (I'll tell you who a bit later.) The lines I shall quote will earn you swift and immediate condemnation in the modern world, though the great ranks of the Scholars of the Middle Ages will welcome you among their number, since the lines are indubitably true:
I like the Cyclostyle ink; it is so inky. I do not think there is anyone who takes quite such a fierce pleasure in things being themselves as I do. The startling wetness of water excites and intoxicates me: the fieriness of fire, the steeliness of steel, the unutterable muddiness of mud. It is just the same with people.... When we call a man "manly" or a woman "womanly" we touch the deepest philosophy.
[GKC writing to (someone) quoted in Ward Gilbert Keith Chesterton 108-9]
Very impressive. Anyway, the talk discussed the life of a certain person about whom we as Chestertonians ought to be interested in. I didn't take notes, as I was too entranced to do such mundane things, and I knew there would be a recording. Besides, it was scattered with most delightful humour, suggesting how Chesterton would handle life in the INTERNET age - I especially liked the bit that went something like this:
"I say! Shaw has accepted my FRIEND request!"
But anyway, there was one particular pun which was left out. And you can find that pun here, but it may be made more clear - that is, the real topic of that talk will be revealed if I say it in this fashion:
There was one thing in particular in which GKC anticipated our modern "connected" electronic age. It was this: Long before the INTERNET came to be, G. K. Chesterton got his very own Blogg on June 28, 1901.
Ah well... if you are still confused I will spell it out in ASCII for you: That was the day on which Gilbert Chesterton married Frances Blogg. (Yes, that really was Mrs. Chesterton's maiden name, and she was the topic of Nancy's excellent talk: she was the Woman Whe Was Chesterton.)

As it happens, just before the conference I was looking into a very interesting puzzle, one which has tormented computer science for some time... but I won't go into that just now, since it may irritate some of my readers, and unduly attract attention from - er - various government agencies. Not that I have any insights, of course! Indeed, all I had was a new question. And from that question I was led to study some very curious things, some of which almost do not make sense until you poke around a little and try to understand why the words are used in that way. It's far more magical than any magic - in fact, it's precisely the true difference between magic and technology, the difference which poor Arthur C. Clarke happened to miss. But I cannot lecture on that matter just now; besides I've already put it into a story, and it's much better there. So let us proceed.

Just yesterday (or maybe Tuesday) I found out that a triangle can be "positive" or "negative". This sounds hilarious, and perhaps not very Chestertonian, until you recall that Gabriel Gale asked:
"Were you ever an isosceles triangle?"
in "The Yellow Bird" in GKC's The Poet and the Lunatics. In fact, you can find quite a bit of homage to Euclid and triangles in Chesterton - and they often lead to even more amazing truths. For example:
There is one element always to be remarked in the true mystic, however disputed his symbolism, and that is its brightness of colour and clearness of shape. I mean that we may be doubtful about the significance of a triangle or the precise lesson conveyed by a crimson cow. But in the work of a real mystic the triangle is a hard mathematical triangle not to be mistaken for a cone or a polygon. The cow is in colour a rich incurable crimson, and in shape unquestionably a cow, not to be mistaken for any of its evolutionary relatives, such as the buffalo or the bison. This can be seen very clearly, for instance, in the Christian art of illumination as practiced at its best in the thirteenth and fourteenth centuries. The Christian decorators, being true mystics, were chiefly concerned to maintain the reality of objects. For the highest dogma of the spiritual is to affirm the material.
[GKC William Blake 132ff]
Ah! Read it again: "The highest dogma of the spiritual is to affirm the material." It's simple, too: you cannot feed the hungry or clothe the naked by theology. It requires knowledge of cooking and sewing, of agriculture and textiles, but it also means CHEMISTRY and BIOLOGY and all sorts of theoretical and practical disciplines. But then we already knew that: "It is wrong to fiddle while Rome is burning; but it is quite right to study the theory of hydraulics while Rome is burning." [GKC WWWTW CW4:43]

Ahem. To revert to the positive and negative triangle.

The idea is quite simple, and in fact links in to a very great concept - the idea of "chirality" or "handedness" - the idea of RIGHT and of LEFT. When we "name" a triangle, that is, we go out onto our lands with our surveying tools, our transits and chains and plumb bobs, and we select (much as the Roman augurs would) the three points which are the three "GONs" - the angles or corners - why, depending on the ORDER IN WHICH we choose those three points, we give that triangle either its positive or its negative state. The Romans, of course would label it fas or nefas - lucky or unlucky. But this is a simpler idea, even if there is still something sinister about it! (Latin pun, hee hee) I won't give the equation here, but there is a way of computing the area of a triangle from the coordinates of its three corners, and the FUN thing about this equation is the SIGN of the area tells you whether you went around the triangle in a clockwise or counterclockwise direction.

Ah, you sigh. So that's what the Doctor is ranting about today. Directions. Clockwise and counterclockwise. Right and Left.

Yes. We could always quote St. Matthew about right and left - you know, the Last Judgement, the sheep and the goats - but you may also recall this famous snippet of dialog from Chesterton:
"First of all, what is it really all about? What is it you object to? You want to abolish government?"

"To abolish God!" said Gregory, opening the eyes of a fanatic. "We do not only want to upset a few despotisms and police regulations; that sort of anarchism does exist, but it is a mere branch of the Nonconformists. We dig deeper and we blow you higher. We wish to deny all those arbitrary distinctions of vice and virtue, honour and treachery, upon which mere rebels base themselves. The silly sentimentalists of the French Revolution talked of the Rights of Man! We hate Rights as we hate Wrongs. We have abolished Right and Wrong."
"And Right and Left," said Syme with a simple eagerness, "I hope you will abolish them too. They are much more troublesome to me."
[GKC The Man Who Was Thursday CW6:490]
Yes, and the funny thing is that right and wrong - I mean right and left really are a matter of life and death, not simply at the end of time, but even in our daily lives. You may wonder (if you know any Latin at all) why there is a sugar called DEXTROSE and another called LEVULOSE. (The Latin dexter means "right" and laevus means "left".) And the secret of all this was discovered only 26 years before GKC was born.

I am sure you know the name Louis Pasteur. The first of his astounding discoveries was made in 1848 when he was studying certain organic salts called the tartrates. (An aside: if you are a baker (like me) you may have something called "Cream of Tartar" in your pantry - it is NOT the same as the "Tartar sauce" used on fish, but a fine white powder. The tartrates are compounds of tartaric acid, a weak acid found in certain fruits. It is used with baking soda as a leavening agent.) Anyway, Pasteur established that a given tartrate came in TWO DIFFERENT FORMS. They are made up of the exact same elements, in exactly the same proportions, and many of their properties are identical.


Specifically, the property which Pasteur studied was NOT identical: the rotation of polarized light: one form went right, another form went left, and there was one which didn't have any effect.

That is because they are related as your right hand is related to your left hand: they are MIRROR IMAGES of each other. They are "chiral" (from the Greek word for "hand") because they have "handedness". (The one which had no effect was an equal mixture of the right and left forms.)

As it turns out, just about ALL the compounds found in living things are chiral. Most importantly, the various amino acids which build proteins, and the various sugars which form the most useful of our body's energy sources.

You may be wondering what all this has to do with my moaning and berating and all that. It's simply my attempt to point out how even the deep and hidden truths of our real world bolster the greater, deeper and even more hidden truths about God and our relation to Him. It's not enough for us to sit and listen to lectures, or sit and read bloggs, even this one. Here is Chesterton's own admonition about it:
I do not know Mr. Eustace Miles personally, but I must confess that I like him: he seems to me to be sincere, and much simpler as well as much saner than many of his followers. But he is chiefly in danger rather from his leaders than his followers. He allows himself to be lectured by a lot of Pundits who suppose they have a true explanation of life when they have only got a false simplification of it. I remember a man of this sort who told me he was on a spiritual plane ("we are on different planes") on which yes and no, black and white, right and wrong, right and left, were all equal. I regarded him as I should any boastful aviator who told me that from the height to which he had risen all London looked like an exact chess-board, with all the squares and streets the same size. In short, I regarded him as a liar. London streets are not equally long, seen from a flying-ship or from anywhere else. And human sins or sorrows are not equally serious, seen in a vision or anywhere else.
[GKC Aug 15 1914 CW30:145]
Indeed. Don't be caught by a false simplification. At the end of time, we're going to see that right and left really are different - and a number of other things, too. As GKC said about male and female, what God has put asunder, let no man join. [see "Two Stubborn Pieces of Iron" in The Common Man]


  1. Thanks for the kind remarks, Dr. T., about my talk. And thanks once again for posting this marvelous meditation for us on this Thursday.

  2. You cannot feed the hungry or clothe the naked by theology, but you can't learn or use an economic discipline without it. That's a solemn pronouncement of the Ordinary Magisterium.

  3. Anyone who'd like to learn more about the fascinating subject of chirality should pick up THE AMBIDEXTROUS UNIVERSE, by the late Martin Gardner. It's a marvelous survey of left- and right-handedness in biology, chemistry, physics, mathematics, art, and much much more. Gardner quotes Chesterton frequently, in this and his many other books: He admired Chesterton's attitude of constant wonder and grateful surprise.

  4. Ooh, I actually knew about the "handed" isomers of amino acids -- Dr. Marshner brought them up in our apologetics class! Only one isomer (I forget if it is the left- or right-handed version) works in the human body -- making the chances of proteins forming randomly in the primordial sludge even LESS statistically likely.


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