Field notes on things that run themselves
A Shape With No Address
Stand shoulder to shoulder with a friend under a rainbow and point at it together, and you are not pointing at the same thing. A rainbow has no fixed location in the sky and no material substance at all — it is rebuilt, instant to instant, out of whichever raindrops happen to sit at exactly the right angle between the sun behind you, the rain in front of you, and one particular pair of eyes: yours. Move your head a few inches and an entirely different set of raindrops takes over the job. Your friend, standing one pace to your left, is already looking at a different rainbow, made of different water, and has been the whole time.
The angle is the whole story. Sunlight entering a raindrop bends once on the way in, bounces once off the inside of the drop’s far wall, and bends again on the way out — and that round trip reliably redirects the light back toward the sun at very close to one fixed angle: about 42 degrees for red light, 40 degrees for violet. Every raindrop in the sky is performing this trick constantly, in every direction, but only the drops sitting on that one precise cone of directions — measured from the point exactly opposite the sun, called the antisolar point — happen to send their light back into your eye instead of past your shoulder. Different wavelengths bend by very slightly different amounts on the way through the drop, a splitting effect called dispersion; that couple of degrees of disagreement between red and violet is the entire reason a rainbow has color at all, instead of being a plain bright ring.
Which means the rainbow isn’t sitting anywhere — it’s a cone, with its point at your eye and its rim wherever raindrops happen to intersect that 42-degree surface, opening away from the sun. Nudge your head and the whole cone swings with you, because its apex is anchored to you personally, not to any patch of sky. That’s why you can never walk closer to a rainbow, let alone reach its foot: the “end” you’re chasing is a location defined relative to your own eye, and your eye is still walking toward it. It’s also, more strangely, why no two people ever really see the same one. Someone standing a few feet away has a different antisolar point, so their cone catches an entirely different population of falling raindrops than yours does — and if you could measure finely enough, even your own left eye and right eye, a couple of inches apart, are looking at two very slightly different rainbows at once.
That makes a rainbow the purest case this publication has found yet of a pattern with no fixed thing behind it. A candle flame at least occupies a location in a room; a phantom traffic jam at least sits on a real stretch of highway. A rainbow occupies no location — it’s a set of angles, not a set of coordinates — and even the raindrops “inside” it aren’t standing still. They’re falling, each one lit for the fraction of a second it spends crossing the correct slice of sky, then dropping through and going dark, instantly replaced by whatever drop falls into its place next. A rainbow can hold rock-steady in the sky for ten minutes at a stretch, and not one molecule of the water that appeared to make it up a minute ago is still there.
The tidy version of the history credits René Descartes with solving the rainbow in one stroke, and in 1637 he did supply the geometry that finally pinned the number to 42 degrees, tracing rays through a water-filled sphere using the era’s new law of refraction. But three centuries earlier, working independently of each other and unaware either existed, the German friar Theodoric of Freiberg and the Persian scientist Kamal al-Din al-Farisi had each already worked out the qualitatively correct mechanism — one internal reflection for the bright bow, two for a fainter, wider second one — by testing light through a water-filled glass flask standing in for a single raindrop, building on optical groundwork laid generations earlier by Ibn al-Haytham. And even Descartes had nothing correct to say about color: it took Isaac Newton’s prism experiments, decades later, to show that the rainbow’s single angle is really a nested stack of angles, one for every wavelength, red on the outside and violet on the inside.
Look above a bright rainbow sometimes and you may catch a second, fainter one about 51 degrees out, its colors running in reverse — red on the inside this time — because that light bounced twice inside each drop instead of once. Between the two bows, the sky is measurably darker: no raindrop geometry can send light back to your eye from that particular band at all, since it belongs to neither cone. Alexander of Aphrodisias, an Aristotelian philosopher, wrote the dark gap down around 200 AD, recognizing it as a real, repeatable feature of the sky roughly eleven centuries before anyone could explain why it was there.
So the next time you can’t quite reach the rainbow’s foot, or the pot of gold keeps retreating exactly one step ahead of you, that isn’t bad luck. It’s the geometry working precisely as it should. There was never a place to arrive at — only an angle, held open by the sun at your back and however much rain happens, this instant, to be falling through the one particular slice of sky that belongs to nobody’s eyes but your own.
One loop I’m watching
Next: many orb-weaving spiders don’t patch a torn web overnight — they eat it, silk and all, then spin an entirely new one by morning, in close to the same size and shape as the one before, from a spider that has never once watched another web get built.
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