Tuesday, June 07, 2005

The Division of the Waters (Part 2)

(This is excerpted from my The Everlasting Detective - a collection of unpublished essays)

One of the recent proposals for the abolition of mental prowess of children is to cease teaching long division. This fiendish torture has been discovered to be useless in adult life, and takes too much time to learn - time which (it is claimed) should be spent on acquiring problem-solving skills. Besides, almost everybody has a computer (or at least a calculator) now, and so the quotient is merely a keystroke or button-press away.

I have to challenge this proposal with all of my background and credentials in computer science. The reasons given are not true. As an adult, I have used long division in study and at work, when factoring polynomials, converting numbers on a computer, integrating by partial fractions, and in Galois Field Theory (an exotic branch of mathematics which underlies error-correcting codes used in compact disks).

A rather serious point, far from obvious to some, is the interesting fact that computers and calculators don't grow on trees. Some human has to know how to perform long division in order to give that ability to computers. Sure, long division is an easy program to write, and it is often taught in introductory programming courses. But there is a reason why it is easy: nearly everyone already knows how to do it, since it is one of the very first algorithms learned in school.

One learns how to perform long division in order to learn a technique, not to get answers to some arithmetic problems. In order to perform long division, a student needs to be able to multiply, compare, and subtract numbers. But the student must also acquire the more complex skill of following an algorithm - a series of steps to accomplish a solution. It is an excellent example of this abstract problem-solving method: the use of several simpler steps to perform a more complex task. This is a valuable lesson in learning how to perform long division, not counting the acquisition of the useful ability to divide.

The Ability to Divide

As is so often the case, a careful reading of the Gospel will show Christ performing all kinds of normal human activities - activities which are startling to see as one of the divine occupations. But Christ, as Master of the Mathematicians, challenged the world: "Do you suppose that I am here to bring peace on earth? No, I tell you, but rather division." [Lk 12:51] That division is to be the last and final division, that of the "sheep" and "goats" foretold in Mt 25:33. Paradoxically, that division will also bring peace to the sheep, for, "they will never hunger or thirst again; neither the sun nor scorching wind will ever plague them, because the Lamb who is at the throne will be their shepherd and will lead them to springs of living water, and God will wipe away all tears from their eyes." [Rv 7:16-17, emphasis added] That "living water" is the One Who Divides, Jesus Himself.

"Divider" is not a term commonly applied to Our Lord, though quite apt, as we shall see. It is linked to the slashing, hacking verb bara - the verb used in Genesis for God's act of creation. [The Hebrew bara is discussed in S. L. Jaki's Genesis 1 Through the Ages 5,295] It is a fundamental element of the creed to state that God and creation are two separate things:
Christianity suddenly stepped in and offered a single answer... 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. That transcendence and distinctness of the deity which some Christians now want to remove from Christianity, was really the only reason why any one wanted to be a Christian.[GKC, Orthodoxy CW1:281]

There is a striking association here, an association between the act of division, the act of creation, and Jesus Christ. It is found within an everyday substance; a substance which is common, necessary, and unusual; a substance which is the divider of natural life and the symbol of the Divider of supernatural life. It is water.
(to be continued)


At 18 June, 2005 09:48, Blogger Bob the Ape said...

Just found this post. Have you ever read Isaac Asimov's "The Feeling of Power"? It's a short story that puts an interesting spin on the issue of paper-and-pencil arithmetic vs. calculators.


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