Intelligibility in a Piece of Wood
I went on a road trip to see the eclipse. I went to Terre Haute, Indiana, because Teresa lives there now. I brought the family and got there a couple days in advance, just to hang out and spend time together.
The first place we went in Terre Haute was Fairbanks Park: an unimpressive little city park on the bank of the Wabash River, containing a small playground and a short walk along the river. We let the little kids play in the playground while we met and talked with Teresa and her boyfriend. This was the unexceptional scene of my “mystical” experience.
It began with the mulch. You can’t really tell from the Google Street View photo, but the mulch they used for this playground was slightly unusual, and for some reason caught my eye. I noticed it wasn’t shredded; rather, it was chopped and the pieces were rather large, as pieces of mulch go. I don’t know exactly how they produce it, but I imagine it might be a similar process to a diamond cut paper shredder, which produces rhombus shapes (more secure because harder to recombine) by combining strip cutting with a periodic diagonal slash.
Anyway, however the pieces of mulch were produced, the result was not a mess of wood shreds so much as a disorderly pile of almost Lego-like pieces of wood, each one being a similar rhomboid with corners that were rounded due to wear and tear. The shape of these things was the next thing that caught my mind–it reminded me of calculus.
Computations about Wood
I love math; there’s always a small part of my brain thinking about something mathematical. So maybe it was something peculiar to me that cause mulch to recall calculus. But I don’t think I’m entirely weird here; I think a lot of math enthusiasts would could follow along with me here.
In most calculus textbooks, there’s a part where they start having you calculate volumes for odd shapes. The common thread for these problems is that you start looking at volumes as cross-sectional shapes that cut out a volume as it moves through space. Then if you can come up with a formula for the shape at any point along that path, you can just integrate to come up with the volume. It’s a classic math problem, and the rounded-off rhomboid shape of the mulch was reminding me of the sorts of shapes they ask you about in those problems.
I think looked at two pieces of mulch, one leaning on another. And this brought to mind the physics classes I took at about the same time as my calculus. In physics, they have you use similar integration techniques to figure out the center of mass of oddly shaped objects. Looking at the two pieces of mulch, I started reformulating the scene into a physics problem in my mind. Suppose you had the one piece suspended over the other and you dropped it on top of the other, could you predict where that piece would end up, given my small residual knowledge of the relevant physics?
And I thought I probably remembered enough where I could just about figure it out, with difficulty. You’d need to calculate the center of mass of the top piece, so that when it impacted the bottom piece you could calculate a moment arm at the time of impact. Then depending on the angle of the two pieces at the point of impact, the piece would swivel in a predictable direction. The kinetic energy would be calculable (I think) given a known starting location, and then at the point of impact after swiveling, there would or would not be enough energy for the top piece to overcome static friction and start sliding, depending on the coefficient of friction of the wood.
It would not be an easy problem for me, and it would involve a lot of tedious working out, but there was nothing super complicated in the math or the physics–this is all essentially would physics simulators in game engines do all the time nowadays. I felt that, with effort and a little more information, I could explain the relative position of those two pieces of mulch. It was something that could be figured out.
Intelligibility in Many Pieces of Wood
At that point, I leaned back and looked around . . . and here my mind brok a little bit. My eyes now took in the whole of the playground scene in front of me. Two little pieces of wood together had turned into an abstract problem; something that I knew had an answer that I could get to if I wanted. But now? I saw a hundred thousands pieces of mulch on the ground, and I imagined the scene when they were poured out on the ground, thousands at a time, all falling and jostling each other and eventually settling where the laws of physics (and the prudent application of rakes, one assumes) dictated.
And that would be just the same problem that I had been focusing on: just multiplied a hundred thousand times as every little piece interacted with every other pieces, over and over until everything settled into a single local potential energy level minima.
Seeing as I had just been thinking about how I could barely manage to fully grasp the case with two pieces of wood, the sudden apprehension of the larger picture had something like the effect of looking at the qualities of a small rock, then stepping back and seeing that it was actually part of the Matterhorn. I actually became very slightly physically dizzy as I suddenly sensed the gulf between what I did know, and what could be known.