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  • Writer's pictureDr. Benjamin J. Williams

10 Apologetic Arguments - Regularity and Mathematics

Why are we able to do mathematically based science?

If we drop an apple from a tree, we can, with accuracy, predict not only that it will fall instead of rising, but also the rate of acceleration toward the earth and, if the height is known, the time it will take for the apple to reach the ground.

However, there is no reason it should be so. We have seen it happen so often that we have forgotten that the regularity of nature – that the apple always falls – is itself an inexplicable fact. That the entire material world should behave in a predictable, repeatable, and discernible pattern is true, but not necessary. We can imagine a universe where nothing happens the same way twice. Why isn’t reality more like that, whimsical and unpredictable? As G.K. Chesterton beautifully explains in a chapter titled, “The Ethics of Elfland,”

These men in spectacles spoke much of a man named Newton, who was hit by an apple, and who discovered a law. But they could not be got to see the distinction between a true law, a law of reason, and the mere fact of apples falling. If the apple hit Newton’s nose, Newton’s nose hit the apple. That is a true necessity: because we cannot conceive the one occurring without the other. But we can quite well imagine the apple not falling on his nose; we can fancy it flying ardently through the air to hit some other nose, of which it had a more definite dislike. … The man of science says, “Cut the stalk, and the apple will fall”; but he says it calmly as if the one idea really led up to the other. The witch in the fairy tale says, “Blow the horn, and the ogre’s castle will fall”; but she does not say it as if it were something in which the effect obviously arose out of the cause. Doubtless, she has given the advice to many champions and has seen many castles fall, but she does not lose either her wonder or her reason. She does not muddle her head until it imagines a necessary mental connection between a horn and a falling tower. But the scientific men do muddle their heads until they imagine a necessary mental connection between an apple leaving the tree and an apple reaching the ground. They do really talk as if they had found not only a set of marvelous facts but a truth connecting those facts. They do talk as if the connection of two strange things physically connected them philosophically. They feel that because one incomprehensible thing constantly follows another incomprehensible thing the two together somehow make up a comprehensible thing. Two black riddles make a white answer. … It is not a “law,” for we do not understand its general formula. It is not a necessity, for though we can count on it happening practically, we have no right to say that it must always happen. … All the terms used in the science books, “law,” “necessity,” “order,” “tendency,” and so on, are really unintellectual because they assume an inner synthesis, which we do not possess. The only words that ever satisfied me as describing Nature are the terms used in the fairy books, “charm,” “spell,” “enchantment.” They express the arbitrariness of the fact and its mystery.1

The keen observation that Chesterton is making is that we should indeed marvel that science works at all. It is entirely dependent on the regular and orderly behavior of nature, a fact for which we have no explanation at all. Gravity works the same whether in Chicago or Checotah, but there is no intelligible reason it should be so, no matter how often it is demonstrated or described.

One could respond that this is merely the consequence of the mathematical laws of nature, but there again two words have been joined together that deserve consideration. What does the field of mathematics have to do with nature? Mathematics is an abstraction of the mind. Nature is a physical reality. The abstract world of mathematics has shown such remarkable success in describing physical reality that we have forgotten to be surprised that it is so. The famous investigators of physical phenomena were not so quick to overlook this curiosity. Physicist Werner Heisenberg described his feelings when he discovered quantum mechanics:

I could no longer doubt the mathematical consistency and coherence of the kind of quantum mechanics to which my calculations pointed. At first, I was deeply alarmed. I had the feeling that, through the surface of atomic phenomena, I was looking at a strangely beautiful interior, and felt almost giddy at the thought that I now had to probe this wealth of mathematical structure nature had so generously spread out before me.2

Heisenberg also records a conversation with Einstein where they discussed their shared sense of wonder:

If nature leads us to mathematical forms of great simplicity and beauty – by forms, I am referring to coherent systems of hypotheses, axioms, etc. – to forms that no one has previously encountered, we cannot help thinking that they are “true,” that they reveal a genuine feature of nature … You must have felt this too: the almost frightening simplicity and wholeness of the relationships which nature suddenly spreads out before us and for which none of us was in the least prepared.3

Simply put, this sense of wonder at mathematical success and the beauty of natural regularity is well deserved. The power of mathematics to describe in detail a wonderfully ordered universe is inexplicable outside of classical theism. Only with the premise of an intelligent creator do you simultaneously arrive at the conclusion that the universe would be orderly and that the human mind would have the prowess to assess its innermost workings through the use of mathematical abstraction.

  1. G.K. Chesterton, Orthodoxy (New York: Dodd, Mead, & Company, 1908), chapter IV.

  2. As cited in S. Chandrasekhar, Truth and Beauty: Aesthetics and Motivations in Science (Chicago: The University of Chicago Press, 1987), 65.

  3. Ibid.

Ben Williams is the Preaching Minister at the Glenpool Church of Christ and a regular writer at So We Speak. Check out his new book Why We Stayed or follow him on Twitter, @Benpreachin.

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