Future, Present, & Past:

~~ Giving itself latitude and leisure to take any premise or inquiry to its furthest associative conclusion.
Critical~~ Ready to apply, to itself and its object, the canons of reason, evidence, style, and ethics, up to their limits.
Traditional~~ At home and at large in the ecosystem of practice and memory that radically nourishes the whole person.

Oυδεὶς άμουσος εἰσίτω

Saturday, February 23, 2013

Is it even "down" all the way down?

There is a story told about Wittgenstein, that one day someone remarked to him about the folly of those who had believed the sun went around the Earth. No doubt, Wittgenstein is said to have replied, they were certainly wrong. But what would it have looked like to them if they had been right?

The punchline is implicit, as is often the case with philosophy, which, as Wittgenstein said, ought not to wish to spare people the trouble of thinking for themselves.

I had a rather analogous moment the other day when someone asked me, What was it the ancients thought the world rested on? Wasn't it an elephant? Or a turtle or something? I responded with a reference to 1 Samuel 2:8, a locus classicus regarding the "pillars of the Earth." And what were the pillars "set" on, my inquirer wanted to know?

Those silly ancients!

So ask yourself about scale. Not what the earth stands on, but what is it made of? Duh, molecules! And Atoms! The periodic table of elements! Yes, yes, and the atoms? Despite the etymology, atoms turn out to be divisible into smaller things with, famously, "mostly empty space" between the smaller things. And, indeed, so on and so on. But not ad infinitum, at least not according to current scientific consensus. Indefinite divisibility would seem to leave us with a paradox, but so too does any really indivisible "atom," at least when you try to visualize it. Heisenberg recounted that a bad explanation in an elementary physics book in his youth depicted atoms "latching together" via hooks and eyes, in an analogy whose poor quality made him furious, since it was plain that if an atom could have a hook or an eye, it was not indivisible. In fact, the puzzle isn't about the atoms but about space. Imagine this tiny atom let's make it a sphere, indivisible. Imagine its surface. Imagine a dotted line on its surface demarcating its equator. Per hypothesis, the atom is not "made of" anything (it is indivisible and has no parts), but then what does the dotted line indicate? The puzzle of course means that the idea of space has broken down with the idea of the indivisible. And indeed, this is what happens even when we have surrendered the indivisible atom for the play of fields and forces in quantum mechanics, for, we are assured, at scales smaller than the Planck length, scale itself makes no sense to talk about. Let the performative contradiction here stand aside for the moment. the thing to notice is that in order for our usual explanations of "what things are made of" to work, we have to agree to come to a point where they don't work anymore.

But this is of course what was already at play with the pillars of the Earth, or indeed with the elephant or the turtles or the vast sea with the lotus floating on it and the world in the center, or the great tree Yggdrasil whose roots are gnawed by the Midgaard Serpent. We are imagining vast distances, far "below" or "beyond" our usual ken, and there is no reason to assume that our ordinary experiences are any guide to what we would find there if, per impossible, we were to climb down the trunk of the World Ash Tree or shimmy down onto the actual turtle's fluke.

It was absolutely understood that the terms "pillars," or "tree," or "elephant," was not what we usually meant by such terms, and yet in some manner analogous. Pushing that analogy into the literal in order to force a reductio, ("turtles all the way down" or whatnot) is like painting the dotted equator or putting a hook-and-eye mechanism on an atom. (This is not the same as saying the terms were "symbolic" as if there could be a literal, non-symbolic gloss.) By the time Archytas imagined standing at the edge of the universe and throwing a spear, we had come very far towards losing the sense of this analogical structure.

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