Forget
A dark plate that cannot keep what is written on it. Draw, and the heat equation begins forgetting your mark at a rate fixed by mathematics: every spatial detail decays exponentially, the fine ones fastest, and nothing brings them back. The page watches its own forgetting. From one look at the blur, never told the clock, it estimates how long ago the writing happened, and prints that guess beside the truth. When too little survives to know, it says so instead of guessing.
the age read blind
The right column is estimated from the 8-bit frame alone, by comparing what survives of each spatial frequency with what was written, mode by mode. The estimate is never shown the clock. As the blur ages, the legible modes thin out, the estimate leans on fewer witnesses, and eventually the honest answer is that there is no answer.
This closes a triptych about one operator. Hear asked what the Laplacian's frequencies can say about shape, and the answer was: not everything, two different drums can sound identical. Reply listened in time instead, and the echoes located every wall. Forget is the third face. Run the same operator as a diffusion and it becomes an eraser: each eigenmode of the plate decays exponentially at its own rate, the sharp details orders of magnitude faster than the broad ones. The picture does not fade uniformly. It forgets its fine structure first, the way a memory loses the words before the shape of the afternoon.
The blur on this page is not an effect. The heat equation is stepped live on a 384 by 384 plate, by the same code that passed a pre-registered gate board: modal decay matching the discrete closed form to twelve digits, a maximum principle that never once overshoots, heat conserved except for exactly what the boundary drinks, and the blind dating estimator recovering hidden ages of 40, 200 and 800 steps to within half a step on drawings it had never seen, then declining to answer at 40,000. The display applies a stated tone curve for the eye; the estimator reads the same 256 gray levels the screen carries.
The button tries the impossible thing. Rewinding heat means multiplying each mode back up by the amount it decayed, and for fine detail that number is astronomical: rewind 260 steps and the sharpest recoverable structure must be amplified ten-billion-fold, so the quantization dust in the 8-bit frame amplifies with it. Press once and the broad strokes return, blurry but true, while the unrecoverable modes are dropped and counted rather than invented. Press again, and again, and the reconstruction drowns in amplified noise. That is not a rendering choice. It is the ill-posedness of the backward heat equation, performed on your own drawing.
what the plate cannot say
The estimator works because the page remembers what was written; it dates the distance between then and now. A stranger arriving at the blur alone, with no template, could date almost nothing, which is the real shape of lost time: to know how much has been forgotten you must remember something yourself. And past a certain age even memory does not help. Every legible mode slips beneath the quantization floor, the witness count in the panel reaches zero, and the plate holds the only honest position left: it has been forgetting for longer than it can measure.