Dale in Rome

88 and 55, or, The Mystery of Repetition

Tomorrow, Friday, the 30th of July, is the 88th anniversary of the reception of G. K. Chesterton into the Roman Catholic Church. The next day, Saturday, the 31st of July, is the 55th anniversary of my own baptism into the same Mystical Body. I thought this repeated appearance of multiples of eleven to be quite wonderful. Eleven is an interesting number - it is the only prime palindrome which has an even number of digits. (I have a proof for this, but people will moan if I post it here. In other words, "the margin is too small", though it surely is not a problem worthy of Fermat, hee hee. You lit'ry folks can ignore this very "3+4i" math pun. Sorry, I know you EE's call this "3+4j". Ahem.)

Repetition is a curious idea, and it may sound redundant to say that it comes up again and again in GKC's writing. (hee hee) We all know the great law GKC states:

Now, there is a law written in the darkest of the Books of Life, and it is this: If you look at a thing nine hundred and ninety-nine times, you are perfectly safe; if you look at it the thousandth time, you are in frightful danger of seeing it for the first time.
[GKC The Napoleon of Notting Hill CW6:227]

We also recall his triple exemplification with the drama of the spoken word:

[Holbrook Jackson:] XIV. Familiarity breeds not contempt, but indifference.
[GKC] But it can breed surprise. Try saying "Boots" ninety times.
[HJ/GKC Platitudes Undone 15]

There is a truth in talking of the variety of Nature; but I think that Nature often shows her chief strangeness in her sameness. There is a weird rhythm in this very repetition; it is as if the earth were resolved to repeat a single shape until the shape shall turn terrible. ... Have you ever tried the experiment of saying some plain word, such as "dog," thirty times? By the thirtieth time it has become a word like "snark" or "pobble." It does not become tame, it becomes wild, by repetition. In the end a dog walks about as startling and undecipherable as Leviathan or Croquemitaine.
[GKC Alarms and Discursions 30-31]

It may sound strange to say that monotony of its nature becomes novelty. But if any one will try the common experiment of saying some ordinary word such as "moon" or "man" about fifty times, he will find that the expression has become extraordinary by sheer repetition. A man has become a strange animal with a name as queer as that of the gnu; and the moon something monstrous like the moon-calf.
[GKC The New Jerusalem CW20:211]

In previous columns I've mentioned the huge repetitions of three words - "the", "of", "and" - which comprise over ten percent of all GKC's writing. I've also mentioned the deeply mystical and significant repeated phrase within GKC's The Everlasting Man, which I found by applying my extension of DNA pattern-matching software to the text:

"Heaven and earth shall pass away; but my words shall not pass away."
[GKC TEM CW2:327 and 392, quoting Lk 21:33]

Remember, I am not suggesting this statement applies to GKC. No, I think it is clear (even if utterly unintentional) that this repeated phrase of our Lord's own words is Chesterton's signal homage to our Lord's words: the One Who is Engineer ("Bridge-builder") is also Author, for He granted "a real romance to the world". [GKC TEM CW2:380] Or, to take a far more delightful avenue:

We must certainly be in a novel;
What I like about this novelist is that he takes such trouble about his minor characters.
[GKC quoted in Ward, Gilbert Keith Chesterton 63]

An aside: Remember, too, that "The Everlasting Man" is Chesterton's own mystic title for Jesus Christ. For proof, see The Thing CW3:302.

The mystery of repetition is a terribly common one, even if this sounds confusing to some. I mean that most of life is repetition. Not only in the sense that our bodies are built from the same things applied over and over - both DNA and proteins are polymers, though they are built as words are built (or perhaps I ought to say STORIES are built) not by pure iteration of the same letter, but by judicious selection - indeed, authorship. But we need not even delve so deep. Even from the most casual examination of a human face we see repetition - though we must not carry this idea too far:

Suppose some mathematical creature from the moon were to reckon up the human body; he would at once see that the essential thing about it was that it was duplicate. A man is two men, he on the right exactly resembling him on the left. Having noted that there was an arm on the right and one on the left, a leg on the right and one on the left, he might go further and still find on each side the same number of fingers, the same number of toes, twin eyes, twin ears, twin nostrils, and even twin lobes of the brain. At last he would take it as a law; and then, where he found a heart on one side, would deduce that there was another heart on the other. And just then, where he most felt he was right, he would be wrong.
[GKC Orthodoxy CW1:285]

In fact, it is the error of Aristotle and of Marx (and many others from the Dark Side of Thought) who try to apply this apparent repetition to Man, thinking that each human is UNimportant since he is just "yet another" proles - existing merely to give more offspring to the State. This error Chesterton corrects with all the emphatic power of Christianity in a most elegant statement:

For religion all men are equal, as all pennies are equal, because the only value in any of them is that they bear the image of the King.
[GKC Charles Dickens CW15:44]

Wow! High drama, for those who can stand it, and a brutal slap against followers of the Dark Power! It's not that we are (from one perspective) just a duplicate, a penny, a proles, existing only to replicate. No; we are IMAGES OF THE KING and therefore have immense value. But then we were told: "the very hairs of your head are all numbered. Fear not therefore: you are of more value than many sparrows." [Lk 12:7] If this romance-granting Author (Whose image we bear) "takes such care about Him minor characters" that He tracks even the dull details of every one of our hairs, how much more must He care about what we do. And that takes us to the next aspect of today's exploration.

Repetition is a fact of human life, whether it is in cooking yet another meal, washing yet another load of laundry, making yet another part, or whatever task one is employed in doing. It is a puzzle that so many people think that life - and especially work - must somehow be so dynamically variable... it isn't, not for artists or musicians or authors - who MUST use the same pigments, the same instruments and pitches, the same letters and punctuation over and over and over. What is it people think work is supposed to be? I dunno. But here too GKC gives us instruction:

the average man has to obey orders and do nothing else. He has to put one dull brick on another dull brick, and do nothing else; he has to add one dull figure to another dull figure, and do nothing else. ... the bricklayer cannot put the bricks in fancy arrangements of his own, without disaster to himself and others. ... A woman cooking may not always cook artistically; still she can cook artistically. She can introduce a personal and imperceptible alteration into the composition of a soup. The clerk is not encouraged to introduce a personal and imperceptible alteration into the figures in a ledger.
[GKC ILN Apr 7 1906 CW27:161]

Ahem! That was funny, and insightful, and does apply, but that was NOT the quote I wanted. Excuse me just a moment while I berate the programmer: This stupid software, who wrote it? (Well, I'll just take a look at the code.) Gosh, a computer program has the same lines of stuff over and over again, oh my it looks REALLY BORING to write such drivel, and I thought computer software development was supposed to be GLAMOROUS... Ahem!
Ah, here's the quote I wanted:

...there is one thing that no realist, however daring, however frantic, would venture to depict upon the stage. He may make indecencies walk naked in the open day. He may cry from the housetops the things of shame which humanity has kept secret for centuries. But there is one thing that no dramatist dare produce upon the stage. That thing is the thing called " Work." There is no playwright who would reproduce upon the stage the first four hours of an ordinary clerk's day. Nobody would send up the curtain at 8 o'clock on a man adding up figures, and send it down at 10 o'clock on a man still adding up figures. Even an Ibsenite audience would not support the silent symbolism of three scenes all of which were occupied with the same bricklayer laying bricks. We dare not say in artistic form how much there is of prose in men's lives; and precisely because we cannot say how much there is of prose, we cannot say how much there is of poetry.
[GKC "Ibsen" in A Handful of Authors 140]

But if the bricklayer did not repeatedly lay those bricks, there would be no houses, if the dairyman did not repeatedly milk the cows, there would be no milk, if the programmer did not write drivel, there would be no INTERNET and no bloggs - and the same is true for many (if not all) other forms of employment, even those deemed "artistic" and "free" by the Media! Ah. (More on this mystery another day - it ties into an important idea in one of St. Paul's letters...)

But perhaps the greatest of GKC's studies of repetition is the one in Orthodoxy, which comes up in his brilliant study of what is usually termed "the Laws of Nature" in the chapter called "The Ethics of Elfland". I've quoted it here before - this is the one which has the famous "Beach Boys" quote, the three-word cheer used by the sports teams at Chesterton University (er, actually there's only one - Gype)... and we've studied it at length some time ago. But please read it again, and think about it some more:

...the mere repetition made the things [of the natural world] to me rather more weird than more rational. It was as if, having seen a curiously shaped nose in the street and dismissed it as an accident, I had then seen six other noses of the same astonishing shape. I should have fancied for a moment that it must be some local secret society. So one elephant having a trunk was odd; but all elephants having trunks looked like a plot. I speak here only of an emotion, and of an emotion at once stubborn and subtle. But the repetition in Nature seemed sometimes to be an excited repetition, like that of an angry schoolmaster saying the same thing over and over again. The grass seemed signalling to me with all its fingers at once; the crowded stars seemed bent upon being understood. The sun would make me see him if he rose a thousand times. The recurrences of the universe rose to the maddening rhythm of an incantation, and I began to see an idea.
...
A child kicks his legs rhythmically through excess, not absence, of life. Because children have abounding vitality, because they are in spirit fierce and free, therefore they want things repeated and unchanged. They always say, "Do it again"; and the grown-up person does it again until he is nearly dead. For grown-up people are not strong enough to exult in monotony. But perhaps God is strong enough to exult in monotony. It is possible that God says every morning, "Do it again" to the sun; and every evening, "Do it again" to the moon. It may not be automatic necessity that makes all daisies alike; it may be that God makes every daisy separately, but has never got tired of making them. It may be that He has the eternal appetite of infancy; for we have sinned and grown old, and our Father is younger than we. The repetition in Nature may not be a mere recurrence; it may be a theatrical encore. Heaven may encore the bird who laid an egg. If the human being conceives and brings forth a human child instead of bringing forth a fish, or a bat, or a griffin, the reason may not be that we are fixed in an animal fate without life or purpose. It may be that our little tragedy has touched the gods, that they admire it from their starry galleries, and that at the end of every human drama man is called again and again before the curtain. Repetition may go on for millions of years, by mere choice, and at any instant it may stop. Man may stand on the earth generation after generation, and yet each birth be his positively last appearance.
[GKC Orthodoxy CW1:262-3,263-4]

Now that I've quoted that, let me conclude by giving you two mystical excerpts which deal with baptism. There is some wondrous mystery here, a mystery touching "repetition" - but then is not baptism our entry into Life? Is not that Life a form of Work? Are we not bidden to "Do whatever He tells you"? [See John 2:5] Did not Jesus Himself seek to be about His "Father's business" [Luke 2:49] and did He not spend the next 18 years after He said that working in a carpenter shop? He weren't writing no theology journal articles... oh no. He was about His father's business, making tables and chairs and doors and Useful Things... Very Engineer of Him, oh yes, and very Common Man too, laying bricks for hours on end for the sake of His neighbor.

But I promised two quotes about baptism - one about GKC's own, the other in general. They are very Newman - that is, both tech and lit - which is just like being Augustine, very old and very new. It's a Catholic thing, you see... but you may have to read them several times before they sink in.

Bowing down in blind credulity, as is my custom, before mere authority and the tradition of the elders, superstitiously swallowing a story I could not test at the time by experiment or private judgment, I am firmly of opinion that I was born on the 29th of May, 1874, on Campden Hill, Kensington; and baptised according to the formularies of the Church of England in the little church of St. George opposite the large Waterworks Tower that dominated that ridge. I do not allege any significance in the relation of the two buildings; and I indignantly deny that the church was chosen because it needed the whole water-power of West London to turn me into a Christian.
[GKC Autobiography CW16:21]

I know only one scheme that has thus proved its solidity, bestriding lands and ages with its gigantic arches, and carrying everywhere the high river of baptism upon an aqueduct of Rome.
[GKC The Thing CW3:156]

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My Error! Or, "like the Pantheist's Boots"

As you know, this year is the 100th anniversary of GKC's What's Wrong With the World. Allied to this particular title is a rather famous quote - not THE quote (about "when a man stops believing in God") but another, which so far has not been located. It is said that some newspaper or other asked several authors to give their own answers to the question as to what is wrong with the world, and, the legend says, that GKC responded with this:

Dear Editor:
I am.
Sincerely,
G. K. Chesterton

CAUTION: Please note: to our present knowledge, this is legendary, like "THE quote" and we do not know that GKC actually did such a thing. But it does sound possible. (As you see there isn't a bibliographic reference to the above, as I always put on GKC quotes.)

Clearly, there are many things wrong with the world, and, just as clearly, all too often we are the cause of those faults. It is strange, therefore, that when the usual song about "problem solving skills" is sung by the educologs, they omit this important concept. I cannot fault them too much; I've seen it myself in my own discipline. I've seen tenured faculty who use their powerful computers to typeset their journal articles, because they don't know enough about programming to begin to convert their theory into anything at all. I've seen pompous professors who brag that they can "prove" that programs are "correct" but the library software they sell has major bugs of the kind which are most insidiously difficult to detect... all because they prefer the appearance of academic complexity to the usefulness of simple real-world engineering. (To put it into the classical tongue, Conspici quam prodesse.)

Ah, engineering. It provides the bumper, the thick padding, the safety equipment, for science... It is the mental discipline which assumes there are problems, maybe even unforeseen ones, lurking in our world. It is science made practical: it is the professor dragged, kicking and screaming, from the ivory tower and thrust into the mire of the real world. Not that he abandons his discipline - he must apply others in order to augment his skills. There is a very famous line which demonstrates this:

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]

Engineering is the honest man's reply, like GKC's (if he really did say it): Yes, there IS something wrong, and in some cases, it is I who am wrong - but since I am honest, I hope to do something about it, in the hope of keeping it from happening again. It's the point of Christ saying "Go and sin no more". He could have changed the law - sure, He is God and He wrote the law - but it was more Godly to forgive. (If you want to know more about why He didn't, you need to read GKC about fences in The Thing CW3:157.) Now we are to go and do likewise, even if we are not engineers - because we will most certainly deal with mistakes and flaws and crimes and sins and errors... with what's wrong in the world. And sometimes these errors are a bit worse than a mere error of typography that changes "cosmic" to "comic". [As accurate as that error may be. See GKC ILN June 9 1906 CW27:206]

For example. Here is a famous line of Chesterton's which a very serious student has complained about. "Physical science is like simple addition: it is either infallible or it is false." [GKC ILN Sept 28 1907 CW27:558] But as most of us who balance our own checkbooks know, it is easy to make mistakes in simple addition. Is Chesterton wrong?

Maybe that is not a suitable quote. Let me try one with a known error, yes, where Chesterton really is wrong. Oh, are you upset? Well... there are plenty of others, but I don't know why you are whining. Maybe I have to pull that Caesarea Philippi thing [see Mt 16] and ask: "Who do YOU say that G. K. Chesterton is?" Ah, yes. Very good. You are right; GKC is not God. But let us stay on the topic.

For example, in GKC's masterwork The Everlasting Man we read:

Somewhere along the Ionian coast opposite Crete and the islands was a town of some sort, probably of the sort that we should call a village or hamlet with a wall. It was called Ilion but it came to be called Troy, and the name will never perish from the earth.
[GKC The Everlasting Man CW2:211-2]

At one point in my many explorations, I was curious about something else, and pulled out an atlas - and I found that the Ionian Sea is on the west side of Greece, and the Aegean Sea is on the east. Moreover, Troy was, even in legend, assumed to be on the west coast of Turkey, not the west coast of Greece. So that means...

Is this picky? Maybe a little. Chesterton isn't writing orders for a navy fleet, after all, and most people will guess that the Ionian Sea is somewhere at the eastern end of the Mediterranean - as it is. Yes, it would have been more accurate for him to say the Aegean - but the important thing for us to know is not where Troy was located, but that this little "village or hamlet with a wall" has a name with an enduring meaning to human history.

Here is another interesting and elegant statement of Chesterton's. It is important, too, and we'll explore it further a little later, but for the moment, I want you to look at just one little bit:

Ice is melted into cold water and cold water is heated into hot water; it cannot be all three at once. [see below for citation]

Uh, not quite. Water can be in all three states at once, and this is not some dogmatic lunacy of the Catholic Church, either! One of my other projects involves a number of curious facts about that wonderful substance called water, and one of those curious facts tells us that water certainly can be all three - ice, liquid, and steam - all at once! This happens at the temperature called the "Triple Point" of water, which is 273.16°K (0.01°C, or 32.018 °F) at 610 millibars (according to my CRC Handbook of Chemistry and Physics).

All right, Doc. What's going on here?

How nice of you to ask. In this case, as in others of this kind, whether in Chesterton or in other authors, we have to be careful about what we are doing. We are NOT trying to "show up" the author as "wrong" - where we take "wrong" to mean "useless" or "untrustworthy". We are not trying to dethrone him, or put him into a "bad light" - what is sometimes called an ad hominem argument. That's Latin for "to the man" - when you argue against a person himself, rather than against the issue at hand. You may not know how this is done, and since I am from the tech side of the world I don't get to see it very often, but I have seen it done, and it will be useful for you to know. So I will write it up for you, and then you can print it out and have it ready for use should the opportunity present itself:

Dr. Thursday's Guide To... (drum roll)
The Ad Hominem Argument.

This is best done in full academic regalia. So get out your frayed old gown with the little beanie, and get 'em on. Don't worry about whether the color matches your degree, people don't know those color codes these days; most of 'em don't even know what color acid turns litmus paper! If your shoes are scuffed, so much the better, but don't be wearing sneakers which will make you look like a student. Your hair ought to be a bit wind-blown, as if you had just been playing Quidditch (hee hee!) - this is easy enough to effect with your hand (DON'T use a comb!), even if you do not have a broom, or don't know what Quidditch is. Your glasses ought to be at the end of your nose. You can take them off and wave them for emphasis - this looks extremely professorial, and will earn you all sorts of brownie points from any deans who happen to be in the audience. If you don't normally wear glasses, get some to keep with you just for this purpose - but not sunglasses, which make you look like a student.

Next, you should obtain a copy of the offending book. This is where you may wish to use a grad student, assuming you can find one who isn't surfing the net or grading your latest test; grad students are quite adept at finding books in the library, and of course it would not DO to have anyone (like a Dean) see you in the library! If a Dean (or, Darwin forbid, the Provost) sees you in such an odd place, it's easy enough to make an excuse, but be sure to speak loud, look annoyed, and wave your glasses.

Now, once you have the offending book, use a little sticky-note to mark the page (and line) with the error. The grad student can usually help here, since most books are now stored in electronic form, though it may take a bit of searching to find the equivalent place in the actual book, but a stern threat or two will work wonders. Of course in certain disciplines, you won't need to actually acquire the book itself, though in that case you will have to implicitly appeal to Authority - or to Technology, which is the same thing. If you are pompous enough no one will notice your hypocrisy - and you can always wave your glasses.

Have the book in your hand when you are speaking, and wave it. Or hold it up, open to the offending page (the one with the sticky note) and point to it. Wave your glasses.

Now, for the important bit - what to say. Please note it's very important to get all this said in one breath, so you may want to practice it beforehand. Practice keeping your face pompous and magisterial; you are RIGHT about this, so don't let your emotion get in the way. All right, ready? Sya this:

"This author was wrong about this..."

[If the author is present, you may for greater effect revise this to "You were wrong about this..."]

Here you cite the book and page with the error, and perhaps quote the offending text with a very snide chuckle, but don't take too long, since you have to say the rest of this on the breath you started with!

"and so you are WRONG about everything else!"

(Now you can take a breath if necessary, but keep going.)

"I don't CARE how right you are elsewhere. It doesn't matter. You were wrong here, so you're wrong everywhere!"

Then you slam the book down, and walk out of the room. If it was a library book, send a grad student to return it to the library eventually.

There. Wasn't that fun? (Yes, I thought so too, but you see, I have actually been there, and seen how it works, but that was a long time ago, and I've got my degree. I live in the real world now, which has other sorts of problems. Seen any cable TV commercials lately? How about them prerolls, guys? Audio levels balanced? You're not pixelating, I hope... Hee hee!)

If that playlet sounds vaguely familiar, I can assure you, I am NOT quoting from GKC's Thursday. But since I happen to like that bit, I will quote if for you so you can compare:

I made myself up into what was meant for a wild exaggeration of the old Professor's dirty old self. When I went into the room full of his supporters I expected to be received with a roar of laughter, or (if they were too far gone) with a roar of indignation at the insult. I cannot describe the surprise I felt when my entrance was received with a respectful silence, followed (when I had first opened my lips) with a murmur of admiration. The curse of the perfect artist had fallen upon me. I had been too subtle, I had been too true. They thought I really was the great Nihilist Professor. I was a healthy minded young man at the time, and I confess that it was a blow. Before I could fully recover, however, two or three of these admirers ran up to me radiating indignation, and told me that a public insult had been put upon me in the next room. I inquired its nature. It seemed that an impertinent fellow had dressed himself up as a preposterous parody of myself. I had drunk more champagne than was good for me, and in a flash of folly I decided to see the situation through. Consequently it was to meet the glare of the company and my own lifted eyebrows and freezing eyes that the real Professor came into the room.
I need hardly say there was a collision. The pessimists all round me looked anxiously from one Professor to the other Professor to see which was really the more feeble. But I won. An old man in poor health, like my rival, could not be expected to be so impressively feeble as a young actor in the prime of life. You see, he really had paralysis, and working within this definite limitation, he couldn't be so jolly paralytic as I was. Then he tried to blast my claims intellectually. I countered that by a very simple dodge. Whenever he said something that nobody but he could understand, I replied with something which I could not even understand myself. "I don't fancy," he said, "that you could have worked out the principle that evolution is only negation, since there inheres in it the introduction of lacunae, which are an essential of differentiation." I replied quite scornfully, "You read all that up in Pinckwerts; the notion that involution functioned eugenically was exposed long ago by Glumpe." It is unnecessary for me to say that there never were such people as Pinckwerts and Glumpe. But the people all round (rather to my surprise) seemed to remember them quite well, and the Professor, finding that the learned and mysterious method left him rather at the mercy of an enemy slightly deficient in scruples, fell back upon a more popular form of wit. "I see," he sneered, "you prevail like the false pig in Aesop." "And you fail," I answered, smiling, "like the hedgehog in Montaigne." Need I say that there is no hedgehog in Montaigne? "Your clap-trap comes off," he said; "so would your beard." I had no intelligent answer to this, which was quite true and rather witty. But I laughed heartily, answered, "Like the Pantheist's boots," at random, and turned on my heel with all the honours of victory. The real Professor was thrown out, but not with violence, though one man tried very patiently to pull off his nose.
[GKC TMWWT CW6:549-51]

Glorious! Some of the best humor in all of GKC. You see, that is the important thing for us to learn. If Chesterton is canonized, it will be due (at least in part) to his strong lessons about pride and humility - and knowing where we fit into the scheme of things. Please, please, I've told you before - if you have not yet read it, please do read (and re-read) GKC's "If I Only Had One Sermon to Preach" in The Common Man!

What is the point, Doctor? You wonder. Well - we do not throw out the Bible because there are typos in it, or even curiosities of writing caused by an archaic view - the firmament, the motion of the earth, the pillars that hold up the "corners" of the earth and all that. (The correct view was exposed long ago by St. Augustine, but perhaps you think it was Glumpe, and believe in it as much.) I was just struck the other day by the reading where Jesus says "the Queen of the South will rise and condemn this generation". He goes on to say how she came from the "ends of the earth" to see Solomon, yet there is a greater than Solomon here. [Mt 12:42] Do you think that Jesus didn't know the earth was round? Hee hee! Oh my. Do not be confused. I impute no error to our Lord, I am not committing blasphemy. (Compare GKC's famous bit about God writing a book on the Evolution of Grant Allen in The Everlasting Man!) This is a form of talking, and it's obvious to everyone, except the guy in academic robes we heard about a few minutes ago.

Let's try another realm of knowledge. Do you think astronomers get fined for saying "oh what a lovely sunset?" Hee hee! What about Aristotle, that Greek guy that so many people think was so smart. Maybe he was, but you do know what he said? He says that the Milky Way comes from a swamp! Oh yes, it's in his Meteorologica, Book I chapter 8. (See Jaki on this in The Milky Way Chapter 1.) Does that mean we junk all of Aristotle? Not quite - and the same is true for other authors, some of whom have phrases that are just as funny and just as wrong.

But let us resume poking our stick at Chesterton, which is lots more fun - he poked at himself too, you know. So, for a change, let us take an instance where he notes his own error. It is found in the hilarious essay called "The Real Journalist" in the collection of his Daily News essays called A Miscellany of Men. This is a famous case, and I have alluded to it previously. Here is an essay worth study - if not literal memorisation - by every journalist and media-being in the cosmos, as well as every blogger and blogg-commenter. It reveals how easy it is to make mistakes, and how even easier it is to have these mistakes be blown out of proportion. The essay tells the story of how GKC wrote a certain essay, and how, in the heat of the moment, or perhaps we might more charitably say, in the urgency of the situation, he stated that "Shakespeare" had written a certain line of poetry - a line which had, as a matter of fact, been written by "Thomas Gray". (In my own case, several columns ago, when *I* was what is wrong with the world, I had torn the authorship of "Trees" from Joyce Kilmer and assigned it to Rudyard Kipling! Hee hee!)

But GKC's case gets better, and the error is magnified in a way that both Bible scholars and computer scientists can both rejoice in. You see, he tried to "correct" this mistake, and he wrote a letter to the editor in which he made another mistake by spelling the poet's name "Grey".

An aside: Now, if you use just about any form of computer these days, you know how serious the smallest letter, or smallest part of a letter, [see Mt 5:18] can be - when you go to type in your password. It's not only the Ephraimites who can't say "Shibboleth" - see Judges 12:5-6. Ahem!

But that wasn't all that went wrong. This "correction" article was supposed to be titled

"G.K.C." Explains

but it actually appeared under the title

Mr. Chesterton "Explains"

And, as you know about the sometimes emotive use of quotes, that made it far worse! But you'll have to read the essay itself if you want all the details as to what really happened, and why. It is truly funny, and quite instructive as well as admonitory.

Now, I mentioned "engineering", and whined about some abstruse matters of software, and whatever. My point could be brought out by appealing to another sort of engineering, like bridge-building - I might note that John Roebling likely did not envision our modern automobiles crossing his proposed "Brooklyn Bridge" - but he "overdesigned" (as some say) and made the resulting edifice more than sufficiently strong to handle them. (It is worth mentioning here that it is also one of the most elegant of such structures, and well worth your study.) But the point is that in engineering, we must take errors into account. For example: we computer people spend an awful lot of time writing code that (hopefully) will NEVER be used, as it is there only to handle the hundreds of ridiculously unlikely cases of something going wrong! Or, if you don't like that, take your car, and consider that nice smooth paint job, those shiny bumpers... They're not really there to look cool, but to help keep you safe. Or take those circuit breakers... gosh, there are lots of things.

Here's an even more relevant one: you know that roughly every sixth character in all of Chesterton is the BLANK? Also called the SPACE - you know that long thing at the bottom of the keyboard. Don't forget I told you about the smallest letter... in computers, the space is just as important as any other letter or number or symbol, even if you cannot see it! I've told you elsewhere about how the ancient Romans didn't use spaces; they just rantheirwordsupagainsteachother - yeah, EVENONMONUMENTS. Sheesh. But if you have some philosophical aversion to the mystical details of things that no one can see but everyone believes in and relies upon, consider this: Ten percent of Chesterton's total writing consists of three words: "the", "of", "and" - and if you want a quarter of all of Chesterton you can have it with just another handful of words, all very common and boring. Sure, it is rare that any of these working words are critical to the discussion, though I am sure I could find examples where they matter... but the point is that these things are just like the rivets of the Brooklyn Bridge, or those almost-never-used bits of my code. They are there to help hold things together. These tiny things matter, like the space, even if they are almost never seen... BUT if they are gone how quickly will you notice! TRYITAGAINANDSEEHOWMUCHYOURELYONTHATSPACE! It's even worse in speech: try sucking out the silence between words and you get the same effect, like the fine print in a contract... Yo! What did that announcer just say???

The final point is this. It is easy enough to miss such minor details, of spelling, or niceties of grammar, or even more factual matters - (Say, GKC, who DID write "antique roots peep out"? And on what sea did you say Troy was located? How about the Triple Point of water? Hee hee!) The point is to fix such things and go on. We don't deny these things are flaws, but we do not discard the entire work because of them either. We recall the warning about the plank in our own eye, which is too big to be seen. [see "The Three Tools of Death" in The Innocence of Father Brown, also Lk 6:41-2]

And now, since there was something more to that quote about water, I shall give you its conclusion. Since we Chestertonians are always catholic even if we are not Catholic, we ought to consider it very carefully. Dogmatic accuracy is no insurance against a building fire; we need to keep up our study of hydraulics as well as ontology.

Ice is melted into cold water and cold water is heated into hot water; it cannot be all three at once. But this does not make water unreal or even relative; it only means that its being is limited to being one thing at a time. But the fullness of being is everything that it can be; and without it the lesser or approximate forms of being cannot be explained as anything; unless they are explained away as nothing.
[GKC St. Thomas Aquinas CW2:530]

Recall my recent voluminous gurglings about finite state machines? There is here revealed part of the mystery - the mystery of the limitation of being. It helps reveal why a quarter (or more) of Chesterton is working words, and an entire sixth is not even readable at all, being mere empty space. It helps reveal why the Brooklyn Bridge has to be so strong, or why software has so much code that is never executed, or why our bodies are mostly water - though not at its Triple Point, ahem! It even helps explain why God loves us so much, despite our failings, even though we are what is wrong with the world... but there I think I shall let you ponder the matter, and say good-bye for today.

Comment Moderation

Sorry folks, one bad spam-bot apple got past the word verification and created chaos for me. Until Blogger improves their ability to hold off blog spam, I'll have to put this on moderation. Otherwise, you would see some pretty immoral stuff, and that's not what this blog is all about.

This spam bot was awfully clever. It took words either from the post or from the comments already posted, and re-posted them, sounding almost as if they were contributing to the conversation. If it weren't for their "special" user name, I might not have noticed.

Singer Needed for the ChesterTones

From Bob Cook:

Are there any other members of the Barbershop Harmony Society planning to attend the 2010 Chesterton Conference? Or anyone who can, and would like to, sing lead (melody) in a Barbershop Style quartet? We need a lead.

The Chestertones, an as yet unrehearsed quartet, had planned to sing, at least in the hallway, at the upcoming conference. However, due to circumstances beyond our control, one of our members has had to drop out. We need a lead.

We plan to sing only 3 songs. They are: My Wild Irish Rose, Let Me Call You Sweetheart, and a newly arranged version of Beethoven’s Ode to Joy (in Barbershop Style). The words for Ode to Joy are those of G.K. Chesterton’s poem, from The Flying Inn, Song of Right and Wrong.

I can FedEx the Ode to Joy words and music to any volunteer. The other two songs will be recognized by any Barbershopper as Barber Pole Cats, songs all Barbershoppers know. I can FedEx learning tracks and music to any volunteer for the Pole Cats. Also, the Pole Cats (My Wild Irish Rose, Let Me Call You Sweetheart) are immediately available if you have internet access at http://barbershopharmony.ca/LearningLounge/

If you’d like to join us at the Conference for some singing fun, please volunteer. Contact Bob Cook at 740-703-5651 if you can help us out or have any questions.

Just a little more about that secret treasure...

Today we'll finish our little glimpse of automata, those fun games which make computing possible. Of course we have not actually explored the subject, but taken a view of the trails from a lookout. I'm not sure why anyone who likes to read would fear this topic, since the things are so interrelated, but then there are a variety of mental diseases around these days. Speaking of diseases in such discussions, I always like to recall this handy little piece of dialog:

"Well, that's all I can tell you about the new religion," went on Flambeau carelessly. "It claims, of course, that it can cure all physical diseases."
"Can it cure the one spiritual disease?" asked Father Brown, with a serious curiosity.
"And what is the one spiritual disease?" asked Flambeau, smiling.
"Oh, thinking one is quite well," said his friend.
[GKC "The Eye of Apollo" in The Innocence of Father Brown]

In line with this, since we ought to strive for humility even while we are striving to enlarge our knowledge and and wisdom, we must also remember the precision teaching GKC gave on that topic:

Pride consists in a man making his personality the only test, instead of making the truth the test. It is not pride to wish to do well, or even to look well, according to a real test. It is pride to think that a thing looks ill, because it does not look like something characteristic of oneself.
[GKC "If I Only Had One Sermon to Preach" in The Common Man]

The strange thing about automata theory is that it IS characteristic of literature as well as mathematics, since it underlies the whole realm of words and stories - and games - even though it seems to be so intractable a topic...

The principle is this: that in everything worth having, even in every pleasure, there is a point of pain or tedium that must be survived, so that the pleasure may revive and endure. The joy of battle comes after the first fear of death; the joy of reading Virgil comes after the bore of learning him; the glow of the sea-bather comes after the icy shock of the sea bath; and the success of the marriage comes after the failure of the honeymoon. All human vows, laws, and contracts are so many ways of surviving with success this breaking point, this instant of potential surrender.
In everything on this earth that is worth doing, there is a stage when no one would do it, except for necessity or honor.
[GKC WWWTW CW4:69]

Yes, the joy of reading Virgil entails the bore of learning Virgil - which means learning the conjugations and declensions and all that... why then should you refuse the joy of automata? Ah, well - alas, I have no time to make such an intricate argument, especially at this intermediate state of things, so let us proceed.

Last week I said we needed to talk a little more about the game-board. I gave you a little example last time, and as we know, good teachers give examples, and then explain the idea or principle using that example. The problem with giving you almost any example of a Finite State Machine or Automaton - our "game" of last week - is that the example contains many uses of the simple ideas - and they are very simple ideas.

It is the true paradox of such fundamental truths, which is why GKC was so insightful with his "too big to be seen" phrase. For example, when we begin to learn to read we pay lots of attention to the letters and their shapes. We learn them first - but then, as soon as we get started actually reading, we stop paying attention to the letters on their own, and begin to pay attention to how they are arranged - we read words and think about words, not the separate letters comprising each word.

The same thing is true about automata - that is, about the "playing board" for our game. But just like the mysterious method by which letters form words, there is a mystery about the board as well. And now I am going to explain it.

The playing board actually consists of two parts. The first is the "places" where your token may reside. In the actual theory we call these "states". Here we must apply our quote about limitation: there are always a finite number - and that number is fixed - that is, decided upon, and unchanging. You must draw your playing board, and once you've drawn it you must play with it - or discard it and and make another. You aren't allowed to edit your board during play! (Imagine a chess game where one player adds an extra row or column, or a card game where a player comes up with the 13 of ampersands, the 20 of roses, or the senator of clubs! (hee hee) In the real study of automata theory, we call this the "Set of States" - and it is always a finite set. Most often when we do this for real in computing, we simply give each state a number, and call the "starting state" zero - you can call it "Go" if you like, and are willing to risk some sort of copyright infringement. Traditionally, we write states as the letter "q" with an integer as a subscript - perhaps because it begins the Latin word quid, meaning "which" - that is which state we're in. But when we draw these states, we just make circles or ovals, and maybe write their names inside. If you like you can think of them as rooms, rather like that murder game with Mr. Mustard in the Conservatory with the lead pipe... ahem. We'll come back to this idea of rooms shortly. But remember, the set of states is a very simple idea, as simple as the rooms of a house or mansion... it's a real mansion, and it so it has a fixed, definite shape, and finite number of rooms.

The second part of our board is what we'll call "the rules of travel". That is, when you are in any given place (or state, or room), and you take up your next little tile with a symbol on it, you must move based on the possible lines which go out of your room. (Yes, you may end up coming right back to the same place - we permit that, even if it's kind of boring during actual play.) Now here is where we get technical - but just a little. It's not very hard, though.

What is a rule of travel? It simply means that when we are in a certain room and we take up a tile with a certain symbol, we must proceed to another certain room. In the theory we call this the "state transition function": that is given the pair which we'll call "an origin-state and a motion-symbol" there is just one single state which corresponds to that pair. That state is called the "destination state". It's a function, which is just another mathematical object... you know, a fancy kind of box, with smaller boxes inside. We look through them to find one where our given pair is in the left-hand box, and whatever state is in the right-hand box is the one we want.

Yeah, yeah, that's SO technical! you whine. It's not. If I wanted to be technical, I can be, and write

s:Q * A ® Q

which says the same thing and far more tidily. But really, I don't want you to worry about that. I want you instead to think about it like the game board. The "rules of travel" are very simple. All it means is that there are pathways that start in each room, and go to other rooms (or perhaps the same room). Each path has written beside it the characters which permit that path to be taken. So when you play, you take your little tiles one at a time, and you move your token according to the rules. Now, if the game is made correctly, you will always know what to do in every case. In other words, you won't try to move to two places at once, or suddenly find that there isn't any possible path for you to take! You'll cry and moan, and toss the game onto the floor - or, if you're a bit more mature, you'll take it back to the store.

Now, these cases are interesting ones... but here is where I must remind you that this is just an introduction to the topic. If you'd like to know more, you'll have to take a course in Automata Theory. You'll be surprised, since you do NOT need lots of math to deal with it. Nor is it exceedingly complex... at least not for Finite State Automata. Why - because of that self-limitation thing! Hee hee! It's wonderful.

But now for the treasure, which is the really grand part of this.

Every computer that exists, that has existed, or that will exist, is necessarily a finite thing. And that means every computer, and (a fortiori) every conceivable program which runs on such computers, can be represented by this simple little idea called a Finite State Automaton.

As you will learn if you ever take a course in this, these FSA are "well-known". That is, we understand what they do - and what they cannot do. We know them so well we are able to describe them formally using symbols, and explore them... and yet every part of computing, that is or that will be, is contained therein.

You are gagging - you are disgusted with me and this topic. You ought not be. Don't you realize that every possible writing - the Gospels and Chesterton and Marx and Aquinas and Nietzsche and Duhem and Belloc and Hitler and Tolkien, adventures and essays and poems and my own columns - anything and everything, good, bad, dull, instructive, misleading - is constructed from a mere handful of symbols? That does not put a stop to creative writing. You might as well say that God's limiting chemistry to about 100 elements puts a stop to creation!

No... this mystery of limit reveals the parallel truth which we need to ponder, whether we build
automata or mix chemicals or write poems about automata or chemicals - or about poetry:

The more simple an idea is, the more it is fertile in variations.
[GKC ILN Dec 14 1907 CW27:607]

Just for your reference, I will summarize the FSA here, but you may ignore this and go to another site to read about some meaningless sports figure or politician or theologian or playwright.... but remember, as you are using your computer, within it you are depending upon these automata.

A Finite State Automaton is a game (mathematical object)

< A, Q, s:Q*A®Q, q₀, Q_f >

where

1. A is the "alphabet" - a box full of tiles, each engraved with a symbol (like scrabble). Or you can think of these as "motion cards": at each move of the game you take the next one and play it.

2. Q is the "set of states" - the regions on the playing board.

3. s is the "state transition function" - the Rules of Motion. These are the pathways between the regions on the playing board, each of which is governed by some symbol from the alphabet. For any particular "origin state" and any particular symbol in the alphabet, you proceed to the "destination state".

4. q₀ is the starting state - or starting place on the board.

5. Q_f are the "final" or winning states. In order to WIN the game, you must be in one of the WINNING regions when you finish your playing tiles. Otherwise you lose.

And now, since you've been so patient and worked so hard to try to have just a tiny bit of acquaintance with this marvel, I will give you a bonus.

The bonus has to do with the "first" computer game - the real progenitor of just about every video game worth playing. That game is called "ADVENT" (short for "ADVENTURE"). It is a bunch of rooms, and some rooms have treasure, and others have little dwarves which throw knives at you (and sometimes kill you!) and mazes and a pirate and all sorts of other fun things. It had no graphics and was all done by simple text - but it was fun. All modern video games in which you struggle through mazes or complex layers of geography are derived from that game.

BUT...

All of them can easily be reduced to a FSA!!! Yes, think about it: your "states" are the rooms, or locations in the maze. The "state-transition function" is just "rules of travel" - how you may move from place to place. Instead of an alphabet, you yourself are the "input" or playing tiles, since you choose the next move...

Well, what does that mean? It means that in grasping the idea of FSA, you grasp the Ultimate Master Key to all such games. You understand how they exist, and what their underlying structure is... you can in fact write you own games, and you do not even need a computer!

This, of course, is why I said you can make them at home, and they are great gifts... you merely need the discipline and care to make sure you do not build an impossible arrangement.

This, incidentally, gives some insight into plot-design and other topics relating to fiction - and translation:

...no man has ever reproduced the atmosphere and magic of one single word by the use of another word. Nobody could put the exact equivalent of 'revisit thus the glimpses of the moon' into any other English words; and he certainly could not put it into German or Russian or Chinese words. It is this separation that makes necessary such intermediate explanations as these; it may be that the Tower of Babel was indeed the chief tragedy of mankind. But anyhow, it is strictly true that we can translate anything in reason. We cannot translate anything that is beyond reason; like the way in which mere sound and spelling can be a spell.
[GKC Chaucer CW18:317]

I mention translation because one of the three uses of automata is to translate - the other two are generating and recognizing, which we have seen in our example: you win when you recognize a winning pattern. (The changes to make a translator or a generator are trivial, and you might wish to work them out for yourself.)

But I see I am out of time for today, and so I will let you ponder all this until next time.

Remember: with automata theory you are touching the fundamental structure which underlies language itself - and be grateful for this secret treasure!

Let's Play a Game: FSA were made for Man...

I had debated today's topic several times since last week - especially because yesterday was the Nones of July, and that is a very special day for me and a major day in the Saga I am writing... but I must not tease you with that. Also (speaking of Sagas) last evening I watched a movie called "National Treasure" which had some hilarious moments besides some goofy distortions of history and physics... so perhaps maybe there is hope even for my Saga, which distorts geography as well. Mine has some cool hidden treasures too, and very difficult cyphers - and even more awesome history to go with my distorted geography. Ahem.

Having brought up geography, let us therefore resume my distorted literary presentation of automata theory in a Chestertonian style. This may sound like a game - but then it is a game. Most of us know a fair number of games - let us ignore typical sports for the time being, and stick with what are typically called "board games". As I was saying, one of the delights of a childhood Christmas is to receive a new game. You open it - there's the usual board which you unfold and put on the table (after your mom yells to tidy it up first!) Underneath the board is a funny little container, probably plastic, with the various parts in their compartments - and the all-critical instruction book. One or two games might have come with something out of the ordinary - a little egg-timer, perhaps, or something with a spring you wound up, or maybe it needed two batteries. But most of the time there were these things: the board, and the instructions, and the parts - and finally the thing that made it a GAME and not something else: THE PLAYERS. Here, a certain famous line pops into my head - "Tennis was made for Man and not Man for Tennis." [GKC The Thing CW3:168] In other words, there was something which made the game live - the Latins called that the anima or soul. In our modern computer game world, the word "animation" is used to signify that something is in motion. We'll talk about that more in a bit. But for now I want to call your attention as a Chestertonian to something larger.

It is, as I delight in recalling for you, something "too big to be noticed" [See "The Three Tools of Death" in The Innocence of Father Brown.] You may recall that last week I said how the mystery of the box as a container (we tech people call this "set theory") was merely the very curious idea that there is no reason why a "container" cannot contain OTHER containers! And so it is. In our particular idea of some general board game, we have a box - the one you found underneath the Christmas tree and unwrapped and pried open. But within that box we had at least one smaller "box" - perhaps the playing tokens, maybe money or dice or other items used in the game.

But this is not just a box - as if it were a trunk, or perhaps a suitcase. It is (as the Scholastics would phrase it) a thing-in-itself. Granted, it is a complex of simpler items. But the box, as it came to you under the Christmas tree and unwrapped, is a Whole Game. (We ignore for today the possibility that it was defective from the factory, another day we can consider this interesting case, which alters my larger topic from a Scientific into an Engineering Matter.)

Since I am trying to lecture you about something called the Finite State Automaton, which is NOT a Board Game (though it could be, as you will eventually learn), you will want to know what the correct word is for this very special sort of container. Yes, it is a "set" just as your board game is a "box" - but it is a special sort of set, because it contains an organized collection of things. Other experts might use other terms, but I will use the term "mathematical object" - that is nothing more than an organized collection of things. This idea is very simple - just think back to some Christmas gift, of some board game with lots of components - or even one of those awesome "art kits" with all sorts of stuff, all nestled in their little plastic depressions in the box. You have the sense that the box contains an arrangement of items, but they are organized. What a wonderful word!

Why is this word so wonderful? What is the mystery of "organization"? Is it simply a synonym for "order"? Well - no. There's something else added. It's another one of those Greek roots - "erg" - which means work or deed or action. The arrangement is made for the sake of DOING something. This sense is very powerful, and is one of the hidden delights of such diverse things as an orderly kitchen, or workshop, or the glory of the board game or art kit when first opened... everything is there, waiting to be used - to be worked with.

Now, at last, we have our various ideas - all except the last one. If this thing, this finite state automaton, is meant to be worked with, what is it we're going to accomplish when we work it?

Ah. This is the very famous question, another from the depths of the Middle Ages, which I myself learned from my mother: dic cur hic = "tell why you're here". Why do this? What is the Purpose?


We can just as readily ask what is the purpose of a board game - and the simple kid's answer is "to have fun" - but there is a simpler one, which exists at the level of the game, and not at the level of the child. Which is why some kids passionately hate board games, or sports - I think of the famous comic "Calvin" who detested the real game of baseball and favored his variants with 12th base or where the outfielder may tackle the goalie... such correctives would do much to ameliorate the corruption in our world... Ahem. But let us proceed. The point is that the "reason" for the game (to be distinguished from "the reason for John or Sally playing the game") is to find out who wins. And the finite state automaton has the very same reason: it is a device arranged to find out who wins.

This is no mere entertainment - or if it is, then all human actions are entertainment, and we might as well change our species from Homo sapiens (Man, the wise) to be Homo ludens (Man, the player). Sure, we can say this by some awkward analogy: An engineer works to design a bridge to "win" - that is, he wins if it stays up. I think of the fabulous Brooklyn Bridge in New York, opened in 1883, or the even more amazing Roman bridges built about two millennia ago. In order to play that game of Bridge (which is not played with 52 cards and a dummy) you need to know a lot about phsyics and materials and design and things like that - it's not an easy game to play. So let us take something far simpler - an example which you encounter from time to time when you use a computer. You are, let us say, need to tell the computer how many copies of this column you wish to print. There is a little box where you may type the quantity. This is a nice little game, perhaps too simple for you to bother with - but someone needs to bother with it. The milk in your refrigerator had to come from a cow - and someone needed to know about cows for you to get it. In the same way, someone needs to know how to play this very simple little game called "You win if you type in a valid number". Granted, you need to know what makes a "valid" number - but this is lots easier than deciding what makes a valid bridge. Or even a valid cow.

So. Here's our game - the "Valid Number Game". It comes in a box, and we unpack it. What's inside?

Oh boy oh boy!

Let's see. There's a playing board...

And there are a stack of tiles, just like those in Scrabble, but there are all the characters on your computer keyboard, the ampersand and F12 and stuff like that. There is your playing piece... I will let that up to your imagination. Then there's this little instruction book.

1. Draw a series of tiles - choose as many as you like - and put them in a row in front of you face down.

2. Place your playing piece on the blue-ringed starting location labelled "Start".

3. When it is your turn, take the leftmost tile from your row, and turn it over. Depending on what that character is, move to the correct location on the board. You must move your playing piece along the track that leads away from your current location, depending on the tile in play - and leave your piece in the new location as the track may direct. It may happen that you will not move from your present location; this is permissible, but only when there is such a track. After you have moved, you must discard that tile; your row will now be one tile shorter than it had been.

4. When you have no more tiles in your row, you WIN if you are in a green circle, you LOSE if you are in any other color.

And that's all. What a nice little game. It's very kindergarten, yes, of course it is. But we can make it lots more complicated... but not just now.

Instead, let's see what we have in our game box.
(1) a playing board
(2) a bunch of tiles with various symbols on them.
(3) a rule-book
(4) a place to start
(5) and places to win

We shall have to talk more - especially about that playing board - but not today.

You might try playing this yourself - you'll have to make your own tiles, but like Chesterton's Gype, the whole point is that you do it yourself. It's anti-Chestertonian to "buy" such a thing. Which is another reason why automata are so Chestertonian - they are so easy, it is silly to buy them... you might want some assistance if you have a really big one to build, but that's different. Not even the great master-builder John Roebling tried to span the East River by himself.

Hey. If you think all this is not Chestertonian, here are a few quotes which may help out:


"What is the shortest journey from one place to the same place?"
["Homesick at Home" in TCL; also CW14:64

The object of a street is to lead from one place to another...
[GKC NNH CW6:321]


...it is the definition of a story that it ends differently; that it begins in one place and ends in another.
[GKC TEM CW2:378]

For my part, I think it rather more foolish merely to rush from one place to another and back again, and pay money for wind (not to mention dust) than to pay money for wine, with its not quite extinct accompaniment of wit.
[GKC Sidelights CW21:491]


People go from one place to another place; but not from one place to another place on the road to everywhere else.
[GKC Appreciations and Criticisms of the Works of Charles Dickens CW15:344]

The story begins in one place and ends in another place, and there is no real connection between the beginning and the end except a biographical connection.
[ibid]

Celebrating the Fourth on the Fifth

Speaking of "verbal fireworks" - Chesterton would have laughed out loud about the silliness of celebrating the Fourth of July on the fifth of July - so perhaps you will enjoy this excerpt which is quite humorous - but also very thought-provoking.

--Dr. Thursday

Prohibition is a joke; and its most optimistic supporters can only pretend that it is a practical joke. But the absurdity of a foreign nation having to take seriously what the natives take flippantly adds a sort of final flourish of frivolity to this triple tangle of falsity. Take first the case of the Fourth of July. The Anglo-American rhetoric in honour of it has run so long in official ruts that it has become utterly formal and fictitious. We know exactly what the British Minister and the American Ambassador will say about the Fourth of July, and we know, alas! that, considered as history or practical prophecy, it would be more suitable to the First of April. Independence Day is, in fact, the most fantastic of all feasts. The Americans celebrate it because they have forgotten what it meant. The English now celebrate it because they have never found out what it meant. It is comic enough, in all conscience, that an Empire should be called upon to jump for joy because it has lost its largest colonies, and dance with never-ending delight on receiving the repeated news of its own defeat. But it is funnier still that it should show a warm and generous agreement with the ideals of the victors; ideals which, rightly or wrongly, the English disbelieved in then, and mostly disbelieve in still. The orators tell us a hundred times that the English and the Americans had ultimately the same ideal of liberty; which is exactly what they did not have. They had two opposite ideals of liberty, for both of which there is a great deal to be said. One was the aristocratic ideal of liberty, with its sense of humour, its instinct for leisure, its loose local custom, and casual compromise. The other was the democratic ideal of liberty, with its dogmatic abstractions, its generalizations about millions, its universal type of citizen, and its wide level of human dignity. I believe I am one of the very few Englishmen who really do believe in the doctrine of the Fourth of July. That is why I am one of the very few Englishmen who flatly refuse to celebrate it. I have enthusiastic admiration for Jefferson; I have a very warm respect for Lord North. But to pretend that Jefferson, but for a mere misunderstanding, would have been as Imperial as Lord North, is a lie. To pretend that Lord North, but for a mere blunder, would have been as democratic as Jefferson, is a lie. Lord North, as a matter of fact, was a very good specimen of an English gentleman; but the ideal of an English gentleman and of an American citizen are not the same and never will be, and it is nonsense and clap-trap to pretend that they are. I am enough of a democrat to wish seriously that England had developed as a democracy; but I do not think the case is met by America developing snobbery.
[GKC ILN July 31 1926 CW34:134-5]

The FSA - One of the Secret Treasures of Life

Ah, yes - today is the Kalends of July, and also a Thursday. Those of you who are audacious travellers are no doubt busy climbing Sneffels, or, perhaps, already descending into its depths. But I don't know how you could be reading this if you are. Perhaps when you return. Ahem.

Last time I wandered at great length down the middle of the road, trying to suggest an idea about "middle" - and thereby suggest Grammar as a fundamental Problem-Solving Skill. Unfortunately some readers will most likely think I am making a very complex figure of speech from the so-called "Three Ways" (or Trivium) which puts Grammar together with Rhetoric and something else - oh, yeah, Logic - as the first things one ought to learn. Dumb, sir - very dumb. There are other things which must precede these as I shall show... Ahem! But I have no time to debate such trivia today. There are larger things to do, and we ought to be doing them while we can.

Doing what? you ask.

Well - to put it simply, doing automata theory in a Chesterton blogg.

I have been pondering this matter for a little - I've told you I have other things going on, and time seems to vanish past my fingertips - but the thing strikes me as so poetic that I must do it. In fact, the answer struck me as I was searching GKC for a motif-phrase for the next episode of my Saga. I found something, it was quite good, and in fact you can blame it for my resolve to proceed with this topic. Here it is:

"There are two Christian virtues," said Hope with dogmatic emphasis, "the first is unselfishness, and the other is cheerfulness."
[GKC "Wine Of Cana" in CW14:562]

I was told long ago that I think of myself as "God's Gift to Computer Science" - and that is true. We are God's gifts, after all - so we ought to strive to live so as to be worth of that position. But do I keep my knowledge of finite state machines to myself, gloating that I know about them, and YOU don't? Horrors, no! How can I be a Doctor and not teach? (Latin docere = to teach) Or do I find automata dull and boring - and lightyears away from usefulness? Of course not! I like this subject very much, and I wish others to know it and delight in it.

Well - come on, Doctor (you moan) Do you expect the Common Man to prove the Pumping Lemma? Or demonstrate the algorithm to convert a non-deterministic automaton into a deterministic one? No. Hardly. But I told you previously about my friend who said he "knew" 20 or 30 computer languages, and proceeded to list their names. I may be a tech, and only by courtesy a "literary man" since I read GKC. But I know a little about language (English, I mean) and about grammar, and about literature. I can tell the difference between a verb and an essay, or a dependent clause and a metaphor - I even can distinguish a superlative adjective from dramatis personae. If you, O reader, can grasp why Hamlet is not a preposition, and why one cannot conjugate a sonnet, why should you not have a small sense of the far more splendid - and in fact primordial distinctions between sets and variables and functions - or have some insight into the grand device we call a "mathematical object"? Especially when I assure you that all these things are very easy to grasp - simple enough for children to handle, and much less dangerous than certain forms of literature - and that these ideas, as mathematical as they may be, are the strong and elegant foundations - the basement jammed full of utilities - water, heat, lighting and building support - on which most other intellectual work is built.

Oh yes - the Three Ways start in one place - and that place is mathematical. Yet, it is thoroughly literary as well, as you shall see.

Now, my poor distressed and fearful reader, you bring Chesterton against me. I shall quote him for you:

It is certainly time that someone protested, apart altogether from the merits of this particular play, against the absurd assumption which seems to exist in the minds of many people, that any good novel not only may be, but must be, put upon the stage. That a good novel should make a good play is not only rare, it is intrinsically unlikely. If it is a good novel it will probably make a bad play. We should see this at a glance in connection with any other two forms of art. Anybody can see that if a thing is a good sonnet it will probably be a bad song. Anybody can see that if a thing is a good three-volume novel it will probably be a bad epic in twelve books. We all realise that if a thing is a good wall-paper the chances are that it will be a rather loud waistcoat. Nobody proposes to adapt carpets into curtains. Yet all this is in no way more essentially false or foolish than the perpetual assumption that the art of fiction is akin to the art of drama, and that therefore the merits of the former will provide material for the latter.
[GKC ILN June 30 1906 CW27:222-3]

You are right - but I am not doing this. I am not proposing to "mathematize" Hamlet - or Chesterton. I am trying, very poorly, to convey a grand truth from my world by using terms from yours. The Literary Man uses terms to describe and distinguish various kinds of writing and their even more varied components - even though the elements of writing are just a mere handful of things, as simple as the tiles upon a Scrabble Board. But from these profoundly mystical and powerful keys we humans have built so many incredible things - the Psalms, the Divine Comedy, The Phantom Tollbooth - Sherlock Holmes - all made from letters, with a handful of things like punctuation and judicious use of space. A very large part of the art of writing is knowing your medium - your tools. You may not know the name of this pigment or that oddly shaped brush, just as you may not know what a "synecdoche" or a "dependent clause" is - even while you are using them.

That is my point. You can begin to have a basic knowledge of automata - and once you have it, you will begin to see more of even the world of literature.

It will also help immunize you against Stupidity - against claiming powers for a computer which the computer does not have, and cannot have, whether in our present day or at any future time. It will keep you from bringing the wrong measure when you wish to understand something - against applying "reason" to things which are "patterns" or "intelligence" to "computation". You will have some sense of what the computer really is - and it is a very simple thing inside, even though it is large and powerful and useful in some sense, it is small and weak and exceedingly dull in others. Sort of like this:

Who will deny that height, or the appearance of height, is one of the effects of architecture? Who has not read or said or felt that some wall seemed too enormous for any mortals to have made, that some domes seemed to occupy heaven, or that some spire seemed to strike him out of the sky? But who, on the other hand, ever said that his sonnet was printed higher up on the page than somebody else's sonnet? Who ever either praised or disliked a piece of verse according to its vertical longitude? Who ever said, "My sonnet occupied five volumes of the Times, but you should see it pasted all in one piece"? Who ever said, "I have written the tallest triolet on earth"?
[GKC ILN Jul 11 1914 CW30:125]

Did you note the hilarious pons asinorum there? Oh... you didn't. Gosh, and here I thought you were the literary man.

A sonnet is always only 14 lines long, so it's not really possible to have it occupy five volumes of a newspaper. And, in case you didn't know, a pons asinorum is a trick question for some field or specialization which will sound impossibly complex to an outsider but is trivially simple to even a beginner in the field.

So - you see, I am trying to build a very goofy looking simile - and yet it is not goofy at all. Since all our human language is finite, to study Language is to study Automata Theory - and vice versa. And the nice thing is that as you learn more about your own language, you will also learn a little about computers, and begin to realize their proper place in the world.

In order to begin, I must give you some tools. These tools are well-known in my own world, but will probably not make any sense to you literary people. However, you already have very similar tools, and use them constantly - you just don't know they come from my world. Let us start with the very famous little thing called the VARIABLE. Please note I am NOT going to give FORMAL precise statements today. This is just a introduction. We don't lecture on the rhyme schemes of sonnets (versus triolets for example) when we are just beginning to address poetry in the general sense - versus prose, or versus a sentence, or the parts of speech. And with the term "variable" we are at the level of "parts of speech". (Actually I wonder what the generic word is for the other structures within language - what is the general term for "sentence" and "verb" and "essay" and "paragraph" and "phrase" and....? Maybe something like "logoid"? Hmmm, another research problem.)

People get scared with this term "variable" as they get scared with some other words we use. I find it rather sad:

Because I could not bear to make
An Algebraist cry
I gazed with interest at X
And never thought of Why.
[GKC from "True Sympathy or Prevention Of Cruelty To Teachers" CW10:486]

The funny thing about the "variable" in math is this. It has just the same power and use as the word "pronoun" in grammar - and we all know how powerful they are! A pronoun is a name - well, maybe a nickname - for something else. But then that's all WORDS are. "Cow" is not a cow - it is a word that stands for the bovine creature that gives milk, the mystic progenitor of cheese. "It" is an incredibly powerful word, it stands for one thing in one place, and something else in another place - it's tricky that way, even sometimes two different things in the same sentence - but it makes sense when we use it that way. For math people, X is not a number (yes, I know it meant 10 for the Romans!) A variable is like a pronoun: X stands for a number. But for our purposes today, X might also stand for other things - and is far more like a pronoun than the silly term "place-holder" the grade-school teachers use.

Variables, it might be said, are the angelic pronouns. For the pronouns of human language typically vary depending on who is speaking (or writing) - maybe we OUGHT to call them variables, since they vary! I know very little Vietnamese, but I do know that the word for "I" depends on who you are in relation to who you are speaking with: a child calls himself con (son) when he addresses his father, but "anh" (older brother) when he addresses his younger sister - if you don't know the person you call yourself "tôi" (servant), as courtesy demands you honor others - which is why they call the unknown stranger ông (grandfather) or bà (grandmother) regardless of their actual ages, for it is the height of honor to refer to someone as old. (Oh yes.)

A pronoun, after all, is really just a verbal trick of finger-pointing - you indicate who or what you mean by pointing, and we have agreed to let certain sounds (or symbols) stand for the gesture. It permits us to hold onto the things we are talking about - even though the hold is a very loose one. A variable is like a pronoun - it is a way of holding onto something loosely, as if by an angelic glance. And that is the idea I wish you to have. We want to understand that a variable is somehow like a kind of pointer. It points to something. When GKC's Algebraist uses it, as most high school students will grasp, it points to a number. But for us today, it may point to something different.

But what? In order to answer that, we need the second tool. If this "variable" is a kind of pronoun - something that stands for a noun - then we need our box full of nouns. I rather like the word "box" (meaning a carton or container, not the act of fist-fighting) but that isn't the tech term we use. We use one of the most over-loaded words in English - the word "set" - in its sense of "a collection of items". This word "set" has a nasty name, something vaguely despised, almost dated. It is like a "lava lamp" or "tie-dying" or "disco" - people always think of it as "modern" math. But they forget the word "modern" is NOT modern - it was invented in the Middle Ages. And the word "set" is not modern either, even if modern math rather tainted it for too many casual readers. I could try to give a technical explanation but that may be too annoying. Besides, the idea is simple very simple - and you all know what Chesterton said about that sort of thing:

The more simple an idea is, the more it is fertile in variations.
[GKC ILN Dec 14 1907 CW27:607]

You know how some grade school teachers "simplify" the word "variable" to "place-holder". We could "simplify" the word "set" to something even grade school teachers might possibly know: the term "box".

A set is a box. In other words, it's a thing which holds OTHER THINGS.

And these boxes are very awesome boxes. They're like computers - that is, they are MAGIC boxes, because you can produce multiple copies of the things inside them - and do stuff with them.

They are also magic because they can contain the most amazing things. And if you know even a little about computers, you may already grasp this idea - the strange truth that one of the things that a box can contain is ANOTHER box. (In today's computers, a directory can itself contain another directory... but there are other sorts of containing which can go on... er... another time I will tell you a scary secret about this idea, but not today.)

A set is a container for other things, which could themselves be containers. I know that sounds either overwhelmingly simple, or trivially complex - but all you need to think about is moving cartons into which you put several shoeboxes, which contain matchboxes and little candy boxes and stuff like that... Maybe you collect stamps, or tiny shells, or sequins, or pebbles. Or maybe we're talking about one of those COOL Christmas presents like the old "Erector Sets" with lots of metal parts and nuts-and-bolts and wheels and axles and motors - it all came in a really neat box with lots of little indentations where everything fit...

But I have run out of time. I will have to proceed further next time.

Just so you will have a little more to read, I will give you the motivating quote from which I drew today's title. This excerpt will also give you a very good Chestertonian introduction into automata theory - which is really just a very simple and fun game... but I shall let you ponder this until next week.

The ordinary poetic description of the first dreams of life is a description of mere longing for larger and larger horizons. The imagination is supposed to work towards the infinite; though in that sense the infinite is the opposite of the imagination. For the imagination deals with an image. And an image is in its nature a thing that has an outline and, therefore, a limit. Now I will maintain, paradoxical as it may seem, that the child does not desire merely to fall out of the window, or even to fly through the air or to be drowned in the sea. When he wishes to go to other places, they are still places, even if nobody has ever been there. But, in truth, the case is much stronger than that. It is plain on the face of the facts that the child is positively in love with limits. He uses his imagination to invent imaginary limits. The nurse and the governess have never told him that it is his moral duty to step on alternate paving-stones. He deliberately deprives this world of half its paving-stones, in order to exult in a challenge that he has offered to himself. I played that kind of game with myself all over the mats and boards and carpets of the house; and, at the risk of being detained during his Majesty's pleasure, I will admit that I often play it still. In that sense I have constantly tried to cut down the actual space at my disposal; to divide and subdivide, into these happy prisons, the house in which I was quite free to run wild.
And I believe that there is in this psychological freak a truth without which the whole modern world is missing its main opportunity. If we look at the favourite nursery romances, or at least if we have the patience to look at them twice, we shall find that they all really support this view; even when they have largely been accepted as supporting the opposite view. The charm of Robinson Crusoe is not in the fact that he could find his way to a remote island, but in the fact that he could not find any way of getting away from it. It is that fact which gives an intensive interest and excitement to all the things that he had with him on the island; the axe and the parrot and the guns, and the little hoard of grain. The tale of "Treasure Island" is not the record of a vague desire to go on a sea voyage for one's health. It ends where it began; and it began with Stevenson drawing a map of the island, with all the bays and capes cut out as clearly as fretwork. And the eternal interest of the Noah's Ark, considered as a toy, consists in its complete suggestion of compactness and isolation; of creatures so comically remote and fantastic being all locked up in one box; as if Noah had been told to pack up the sun and moon with his luggage. In other words, it is exactly the same game that I have played myself, by piling all the things I wanted on a sofa, and imagining that the carpet around me was the surrounding sea.
This game of self-limitation is one of the secret treasures of life. As it says in the little manuals about such sports, the game is played in several forms. One very good way of playing it is to look at the nearest book-case, and wonder whether you would find sufficient entertainment in that chance collection, even if you had no other books. But always it is dominated by this principle of division and restriction, which begins with the game played by the child with the paving-stones. But I dwell upon it here because it must be understood as something real and rooted, so far as I am concerned, in order that the other views I have offered about these things may make any sort of sense. If anybody chooses to say that I have founded all my social philosophy on the antics of a baby, I am quite satisfied to bow and smile.
[GKC ILN Feb 8 1930 CW35:253-4, emphasis added]

A Postscript:
In case you were wondering, yes - I forgot to explain what "FSA" is. An FSA is a Finite State Automaton - it is the simplest of the kinds of automata, and in the final analysis, the only one which really matters, since we cannot buy infinite amounts of memory. In future columns I will tell you more about the FSA and you'll get to see how much fun they are... they make excellent gifts, and are very inexpensive. And you do NOT need a computer to make them... but you'll have to stop back if you want to know how. It's fun - you'll see.
--Dr. T.