Week 8 Bench: Timing a decay

Measuring how fast a keypad forgets what was pressed on it, and finding the two different moments at which recovery stops working

12 April 2027

Before the Bench#

Nothing to record this week. The supplied sequence is a set of thermal frames of a keypad after a known four-digit entry, timestamped from the moment the last key was released out to ninety seconds. Bring something that can read per-pixel intensity out of an image and plot a series — the analysis is arithmetic, not photography.

In the Bench#

Extract the mean intensity over each key’s area in every frame, and plot the four series against time. Two results come out of that plot, and the second is the one worth the session.

The first is the obvious one: every series decays, so there is a time after which no key is distinguishable from the unpressed ones and the set of pressed keys is gone. Fit a curve and read that time off it.

The second takes more care. The order of the keystrokes is not carried by any single series — it is carried by the differences between them, since the first key pressed has been cooling longest and is therefore coolest. Those differences are a fraction of the intensities themselves, and they shrink faster. Plot the pairwise differences alongside the raw series and find the time at which the ordering can no longer be read out of them reliably. It will be substantially earlier than the first time, and that gap is the week’s finding: a defender who knows only “heat fades in about a minute” has the wrong number for the thing that matters most.

Afterwards#

Keep the fitted decay constant and both windows. Week 10 asks you to put this channel on a common rubric against the other six, and the constant you fitted here is the closest thing any Bench so far has produced to the quantitative claim that rubric wants.

The Channel Report is due this week.