Experiment № 087 · The story
Keep the Farthest
Why I picked it
A lot of this collection has turned out to be about deciding what to throw away — Huffman, Burrows–Wheeler, Floyd–Steinberg — but I had never done geometry's version of the question. A GPS track logs a point every second; a country's border is digitised to the metre; and almost all of that is wasted on a screen where three pixels is the finest thing anyone can see. Urs Ramer answered it in 1972 for image processing, and a year later two cartographers, David Douglas and Thomas Peucker, published it with a title that asks for a digitised line's caricature. I loved that a paper full of distances reached for a drawing word. A caricature is exactly right: keep the features that make it recognisable, lose everything that doesn't.
What I enjoy about it
The heartbeat preset. Keeping every eleventh sample treats each point as equally important just because of where it sits in the list, so it steps straight over the tall, narrow spike in each beat — the one feature a cardiologist actually looks at. Douglas–Peucker can't miss it, because the only question it ever asks is "what is farthest from the story I'm telling so far?", and a spike is, by definition, far. I also like pressing play and watching the first three or four splits: the island is already recognisable after a handful of points, and the remaining hundreds are just decimals being filled in.
The guarantee is what makes it feel honest. Every point it drops was checked and found within ε of the chord that replaced it, so the worst miss can never exceed the dial. Turn the corridor on and you can see the promise: the faint line never leaves the violet band.
Something you might take away
A good summary isn't an even sample; it's a promise about the worst thing you left out. "We kept ten percent" says nothing — ten percent chosen evenly can lose the spike that mattered. Say your tolerance out loud, then keep exactly the points that would break it, and spend your detail where the shape actually turns. It's a decent rule for notes, reports and maps alike: ask not how much a summary kept, but how far it's allowed to be wrong.