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Toy · 04

Hairy Ball

// comb it flat. all of it. shouldn't take long.

0.0%COMBED
drag the ball to comb · drag the dark to spin
Combedeverything mathematics allows

why can't i win?

you've met the cowlick that won't die. it's not a bug. in 1912 brouwer proved you cannot comb a hairy ball flat: any continuous arrangement of lying-down hair on a sphere has to fail somewhere. push the failure around all you like — it just moves. that failure is the cowlick.

and it keeps books. every cowlick carries a charge: the number of times the hair swirls around it. a whorl is +1, a saddle is −1. poincaré–hopf says the charges on a sphere always total exactly +2. merge your two +1s and you hold one +2. manage to comb a −1 into existence and the ball instantly owes three +1s elsewhere. right now yours reads:

reading the ball…

same theorem, bigger ball: at this exact second there is a spot on earth where the horizontal wind is precisely zero. the atmosphere is hair on a sphere.

want a winnable version? play on a donut. a donut's number is 0, not 2 — its hair combs perfectly flat, nothing owed. nobody ships that game because you'd be done in four seconds.

the fur in there is a real tangent vector field and the score is honest — the last few percent are the cowlick's neighborhood, billed by the theorem. the comb was never going to save you.

// no gravity in here. hair holds its set. the ball remembers.