checking a card number or an IMEI in your head: double every second digit from the right, then add
Built as a memo rather than a table: the thing worth hanging it up for reads across the room, with the full reference in smaller type below it.
Three sizes in one archive — from a sheet on the fridge to a poster on the wall.
A shaded box marked “×2” is a digit to double; the bottom row is what goes into the sum. The number on this sheet is made up.
Hans Peter Luhn of IBM filed on 6 January 1954; patent US 2,950,048, “Computer for Verifying Numbers”, was granted on 23 August 1960. What it protected was not a formula but a hand-held mechanical device: a pencil is drawn down a slot beside each digit, and a wheel adds up the motion. A valid number shows 0.
Why the numbers can be trusted. Every countable number here is computed from data rather than typed in, and the sheet must pass 3 independent checks before it is allowed to build — how many items there are, the order they come in, and the claim in the highlighted box itself. If one fails, there is no file.
ten tasks, the year of each, the system, the figure — and the human it was measured against
all 128 positions: the column is the three high bits, the row is the four low ones
who published each standard, when, what it does to the sound, and how many bits per second it allows
forty bits to a quantum: five bytes, eight characters and five padding cases