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Indra's Net, Drawn

A 'splainer, drawn from the mathEvery jewel
shows every jewel

Way up yonder, over the palace of the old sky-god Indra, somebody strung a net. It runs on out in every direction and don't quit. At every knot there hangs a jewel, polished so fine you can see the whole rest of the net in it. And every one of those jewels you see is showin' the whole net too. All the way down. That's the picture. Folks have been chewin' on it for better'n thirteen hundred years, and it'll chew back.

or tap any jewel and watch the tremble spread

The whole thing, dirt simple

  1. There's a net, and it goes on forever.
  2. Every knot has a jewel. Every jewel shines back every other jewel.
  3. So every jewel has the whole net inside it — and the net has every jewel.
  4. Tug one knot and the whole thing trembles. Nothin' in it stands off by itself.
  5. That's all. The rest is folks arguin' over what it means — and the math of mirrors that draws it.
2.25reflections deep you can see in the net up top
236,196pearls four round mirrors make on bounce ten
221lamps in Fazang's mirror room within ten bounces
50.45 → 8.82average hops across 1,000 knots when 1 in 100 links goes long

Walk it in order

1 · Where the picture comes from2 · Many ways to read it3 · The math: mirrors in mirrors4 · Touch one, touch all5 · Do it yourselfWordsSources

Why it keeps comin' back

The net is one of them pictures that fits whatever you hold it up to. A Buddhist teacher sees how nothin' stands on its own. A Hindu storyteller sees a god's magic trick. A mathematician sees round mirrors bouncin' circles off each other till they make lace. A fella who studies the internet sees how your cousin's buddy's boss knows the President. Chaos folks see one little nudge that spreads to everything. They are all lookin' at the same net. None of 'em is wrong about their jewel. Here's sixteen of 'em, kept short.

Four round mirrors, and every mirror seen in every other, nine bounces deep. Each color is one more bounce. This is the math folks named after the net. · computed here · Nan · hongdam.net · CC BY 4.0
A square room with mirror walls and one lamp, unfolded. The gold square is the room. Every other lamp is that same lamp, seen in the mirrors — dimmer the more bounces it took. · computed here · Nan · hongdam.net · CC BY 4.0