I number of thoughts ran through my head while preparing for my presentation on Paganism in America for our small groups meeting yesterday. I’m frequently asked how I can believe that stuff, when I’m otherwise so rational... which reminded me of Spinoza, who laid out his philosophy as theorems and proofs, like geometry class... which reminded me of an incident in high school that can help explain “how I can believe that stuff.”
There’s a classic theorem algebra teachers spring on a class that’s getting cocky (which I have to admit we were, hard as that may be to believe), that proves that two equals one. The obvious assignment is to identify the erroneous step. The catch is that there is no error- when you examine one step at a time. It’s an exercise in seeing the big picture; you’re supposed to realize that one step creates a situation in which another step, which would ordinarily be perfectly valid, is rendered indeterminate. Most of the class did not catch it.
But my point is not the math skills of my classmates- the important point is that despite their finding no error in the logic, none of them were convinced that two equals one. Their intuition was that the conclusion of flawless logic was still wrong. When you look at the history of science, it’s a continuous story of not understanding where your logic breaks down, and taking an intuitive leap instead. Socrates believed that heavy objects fall faster than light ones- and why shouldn’t he? A rock does indeed fall faster than a feather; the technology of the day had not produced conditions which would belie that conclusion. Galileo realized that air resistance skewed the results, but his figures broke down when artillerymen started wondering why doubling the charge of gunpowder didn’t double the speed of the cannonball- they had come up against the totally unexpected sound barrier. Newton’s physics were so convincing that even after Hiroshima there were scientists who said it just couldn’t be- it violated the laws of the conservation of energy. And even Einstein’s logic couldn’t explain the quantum world- and now some of the proponents of string theory are calling into question the Big Bang as the beginning of the universe.
Reason is our most important tool in understanding our world- but it is not our only tool. Sometimes, it is not even the right tool... sometimes, a transcendent leap is required; linear logic is no longer capable of explaining what is going on. Two does not equal one. The human heart is one such situation- and that’s how I can believe all that stuff.
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You might find Stephen Barr's review of Dawkin's The God Delusion over at First Things interesting.
A quote below from Barr.
As one moves deeper into nature—to levels about which the natural historian and zoologist can tell us nothing—one encounters not less and less form but increasingly magnificent mathematical structures, structures so profound that even the greatest mathematicians are having difficulty understanding them. This is what Pope Benedict was referring to in his Regensburg lecture when he spoke of “the mathematical structure of matter, its intrinsic rationality, . . . the Platonic element in the modern understanding of nature.” It is what the great mathematician Hermann Weyl meant when he said, “[I]n our knowledge of physical nature we have penetrated so far that we can obtain a vision of the flawless harmony which is in conformity with sublime reason.” It is what the great astrophysicist James Jeans meant when he said, “The universe begins to look more like a great thought than a great machine.”
Thanks for the link, Bill- interesting stuff, to be sure!
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