I have come for division!

One of the sillier "education" notions these days - I mentioned it recently - is the idea that children ought to be taught "problem-solving skills" rather than the ordinary traditional subjects which they will need if they are ever to solve problems. No teacher, no administrator, no "doctor" of education (I use it in quotes since they are rarely PhDs and almost never actually teach, which is what the Latin word means!) - none of these educators actually specifies what skills these are, since the few which I know of (e.g. math induction & recursion, automata, graph theory, force diagrams, dimensional analysis, and so forth) all require the basic tools of learning. Ah, well - you think I mean these things ought to be taught in grade school? Certainly, but not necessarily. I think kids are lots smarter than any educator - or any Media Personage - can grasp, and could be getting far more meat far sooner, if there was discipline (which means living & acting as a student does!) and lots less trash and distractions. But this posting is not on the "Thursday" method of education, as interesting as that might be. Besides there is a better way of showing my point on this topic, and it is quite funny. For at the same time these dear ones are pushing for "problem solving skills" they are rejecting traditional skills - like (don't get scared now) - like "LONG DIVISION".

Now, the funny thing is that long division is a problem-solving skill! It solves the question of how many times some given number (say the number of stars) can be split up ("divided") among another given number (say the number of students in a classroom). If there are 5000 stars, and there are 40 students, then each person gets 125 stars. I know that was an easy one, but I am not lecturing about the technique today. (I can, if you want, but it will have to be on my own blogg. But see below for GKC's comments on the topic.)

These dear educatists will say that we use calculators for chores like long division - but that is like saying we can use bicycles to go around the bases during a baseball game! Sure, we could, and get Home lots faster than running! But as worthy a tool as the bicycle is, it is not admitted to be fair part of the game of baseball.

Nor is the calculator a fair part of the game of long division.

That is because long division is a skill which is necesary for other tasks than getting the result of dividing one number by another. It is a SKILL, writ large as FAther Jaki likes to write, and comes up in a whole range of places in mathematics, computing, and such disciplines. But there is another reason for it, which completely escapes the understanding of these educators.

That is Long Division is a means of teaching something much harder to describe than the very simple idea of getting the quotient. In fact, it exemplifies the First Problem Solving Skill one ought to have.

Oh, Doc! Really?

Yes, my child. Really. It is simply stated, and something I would guess you've heard from your mother, especially if you've ever helped her in the kitchen. It is simply this:

Follow the Directions.

Yes. You see, Long Division is a bunch of Directions - it is a - well, since I am a computer scientist, I should use the word "algorithm" - but I am often a baker (and even occasional cook) so I should use the word "recipe", and I am also a scientist (yes, I have a white lab coat!) and so can use the term "lab protocol"; I have been a musician so I could suggest the term "score", and I have read GKC's plays, so I could call it a "script", and I am also a Catholic so I might use the term "rite" (though that is a bit of a stretch).

Long Division is a lot more interesting than "Long Addition" or even "Long Multiplication" because it contains a "step" we computer people call a "conditional" - that is something with an "IF". That is nothing new to any of the above fields of human activity: recipes often have "if" statements, and everything from lab protocols to liturgical rites contain such things.

Does this division business connect to Chesterton? Sure, and in a startling way. I am sure you know the Gospel lines "Think ye, that I am come to give peace on earth? I tell you, no; but separation." (Luke 12:51) or "Do not think that I came to send peace upon earth: I came not to send peace, but the sword." (Matthew 10:34) which GKC relied on when he writes:

Christianity suddenly stepped in and offered a singular answer, which the world eventually accepted as answer. It was the answer then, and I think it is the answer now.
This answer was like the slash of a sword; it sundered; it did not in any sense sentimentally unite. Briefly, it divided God from the cosmos. ... And the root phrase for all Christian theism was this, that God was a creator, as an artist is a creator. A poet is so separate from his poem that he himself speaks of it as a little thing he has "thrown off." Even in giving it forth he has flung it away. This principle that all creation and procreation is a breaking off is at least as consistent through the cosmos as the evolutionary principle that all growth is a branching out. A woman loses a child even in having a child. All creation is separation. Birth is as solemn a parting as death.
[GKC Orthodoxy CW1:281]

Father Jaki elaborates on this idea in several places, notably in his Genesis 1 Through the Ages where he discusses the Hebrew bara which means "create" but also "divide, hack".

Not that I suggest the learning of Long Division is somehow a part of theological training - but of course it is. Theologians, like Philosophers and Historians and all the Students of Words, no less than the Students of Numbers, need to FIRST learn to think according to simple, easy, formulated rules - in order that they can proceed to examine issues for which there might not be such rules! Yes, Long Division is as important to the most esoteric branches of literature and philosophy as good grammar is to the most esoteric branches of engineering and science and mathematics.

Besides, and you may find this most surprising to learn: there are lovely problems in mathematics that calculators (and even computers) cannot solve, and that is one good reason why we need to learn Long Division. I've seen such things at work, and it was not something esoteric either. But as much fun as it is I cannot go into the math of such things here.

To conclude, I'll let you enjoy the only four excellent insights which I found where GKC uses the term "Long Division". The hilarious thing is that one of them says almost the same thing I've been trying to say - but it's nearly 100 years old. Odd that the modern up-to-date educators are still trying such failed and fusty old methods...

It is unfortunate that common-sense has come to mean almost the contrary of the sense that is common. Indeed, we might say that when men boast of common-sense, it generally means a contempt for common people. A man who will not listen to any evidence in favour of ghosts or witches may (especially in his own opinion) possess sense; but what exactly he does not possess is common-sense. He has no realisation of the common bond of human instinct and experience which binds him to the very varied memories and lives of his fellows. He may be right in saying that he has no nonsense about him; a very lamentable gap in any man's character. But the general impression of a borderland of abnormal experiences is not nonsense. It IS sense, even if to some it seems like the suggestion of a sixth sense. It is not nonsense either in the bad or in the good sense. It is not a confusion of thought or a contradiction in terms. It is not a fantastic form of art or a grotesque form of beauty. Spirit-rapping does not introduce us to the Mad Hatter or the Pobble Who Had No Toes; would that it ever introduced us to anybody so entertaining! On the other hand, it is not nonsense to say that a man's soul went out of his own body, as it is nonsense to say that he jumped down his own throat. It is simply an assertion, true or false, about certain conditions on another plane, which are different from the laws of our planet, but not different from the laws of our reason. It is certainly unknown; it may be unknowable; but it is not unthinkable. It is not like saying that long division is green, or that Wednesday is oblong, or that thought is a molecular movement.
[GKC ILN Jan 12 1929 CW35:21-22]

Shelley invented half a hundred goddesses, but he could not pray to them, not even as well as the old atheist Lucretius could pray to Venus, Mother of Rome. All Shelley's deities were abstractions; they were Beauty or Liberty or Love; but they might as well have been Algebra and Long Division, so far as inviting the gesture of worship goes. In this, as in everything else, what is the matter with the new pagan is that he is not a pagan; he has not any of the customs or consolations of a pagan.
[GKC Jul 5 1930 CW35:339]

A peasant who merely says, "I have five pigs; if I kill one I shall have four pigs," is thinking in an extremely simple and elementary way; but he is thinking as clearly and correctly as Aristotle or Euclid. But suppose he reads or half-reads newspapers and books of popular science. Suppose he starts to call one pig the Land and another pig Capital and a third pig Exports, and finally brings out the result that the more pigs he kills the more he possesses; or that every sow that litters decreases the number of pigs in the world. He has learnt economic terminology, merely as a means of becoming entangled in economic fallacy. It is a fallacy he could never have fallen into while he was grounded in the divine dogma that Pigs is Pigs. Now for that sort of intellectual instruction and advancement we have no use at all; and in that sense only it is true that we prefer the ignorant peasant to the instructed pedant. But that is not because we think ignorance better than instruction or barbarism better than culture. It is merely that we think a short length of the untangled logical chain is better than an interminable length of it that is interminably tangled. It is merely that we prefer a man to do a sum of simple addition right than a sum of long division wrong.
[GKC The Thing CW3:165]


Education is only truth in a state of transmission; and how can we pass on truth if it has never come into our hand? Thus we find that education is of all the cases the clearest for our general purpose. It is vain to save children; for they cannot remain children. By hypothesis we are teaching them to be men; and how can it be so simple to teach an ideal manhood to others if it is so vain and hopeless to find one for ourselves?
I know that certain crazy pedants have attempted to counter this difficulty by maintaining that education is not instruction at all, does not teach by authority at all. They present the process as coming, not from the outside, from the teacher, but entirely from inside the boy. Education, they say, is the Latin for leading out or drawing out the dormant faculties of each person. Somewhere far down in the dim boyish soul is a primordial yearning to learn Greek accents or to wear clean collars; and the schoolmaster only gently and tenderly liberates this imprisoned purpose. Sealed up in the newborn babe are the intrinsic secrets of how to eat asparagus and what was the date of Bannockburn. The educator only draws out the child's own unapparent love of long division; only leads out the child's slightly veiled preference for milk pudding to tarts. I am not sure that I believe in the derivation; I have heard the disgraceful suggestion that "educator," if applied to a Roman schoolmaster, did not mean leading our young functions into freedom; but only meant taking out little boys for a walk. But I am much more certain that I do not agree with the doctrine; I think it would be about as sane to say that the baby's milk comes from the baby as to say that the baby's educational merits do. There is, indeed, in each living creature a collection of forces and functions; but education means producing these in particular shapes and training them to particular purposes, or it means nothing at all. Speaking is the most practical instance of the whole situation. You may indeed "draw out" squeals and grunts from the child by simply poking him and pulling him about, a pleasant but cruel pastime to which many psychologists are addicted. But you will wait and watch very patiently indeed before you draw the English language out of him. That you have got to put into him; and there is an end of the matter.
[GKC What's Wrong With the World CW4:64-5]