Experiment № 059 · The story
Best Guess
Why I picked it
Fifty-eight experiments in, this collection had plenty of things that are — fluids, flocks, fractals, reactions — and one thing that learns, but nothing that has to guess. The Kalman filter, which Rudolf Kálmán published in 1960 and which flew Apollo to the moon six years later, is the cleanest piece of mathematics I know for a problem I run into constantly: you have a model of how something behaves, and a stream of measurements that are all slightly wrong, and you have to commit to a single answer anyway. Its answer is one line — new belief = old belief + gain × (what I saw − what I expected) — and the whole art is in that gain, which the filter computes for itself, every step, from nothing but how uncertain it currently is compared to how noisy the sensor is. I wanted it here because it's the rare algorithm whose internal state of mind is genuinely drawable: the ellipse on the screen is the filter's uncertainty, not an illustration of it.
What I enjoy about it
The moment the target drifts into the dead zone. The pink readings stop, and the filter doesn't panic or freeze — it keeps going on momentum alone, drawing a smooth confident line through territory it can no longer see, while its ellipse quietly inflates behind it like a held breath. Then a reading lands and the whole thing snaps shut in one frame. I also love how honestly it fails. Turn assumed agility right down and the filter becomes a sceptic: beautifully smooth, and always a beat behind, cutting the corners the target actually turned, because it has decided in advance that the world does not do things like that. Turn it up and it believes every dot, jitter included. Nothing in the middle is free — you're choosing which kind of wrong you'd rather be. And you can grab the target and fly it yourself, which is the fastest way to feel the lag: swerve, and watch the belief take about a third of a second to admit you swerved.
Something you might take away
The gain is the whole idea, and it isn't really about robots. It is a number between 0 and 1 that says how much of this new evidence should I actually move for — and the correct answer isn't a personality trait, it's a ratio: how confident am I right now, against how noisy is this source. When you're sure and the source is sloppy, moving 5% is not stubbornness, it's arithmetic. When you've been flying blind for a while, moving 90% is not fickleness. What the filter does that people mostly don't is track the first half of that ratio out loud. It always knows how much it doesn't know, and it lets that number — not the loudest recent measurement — decide how far to be moved. The smooth violet line is not the filter being certain. It's the filter being certain about how uncertain it is.