The Machine's Work Is Countable
The clock lesson gave the machine its metronome: one action per tick. Today that austere rule pays an unexpected dividend — it makes the machine's labor measurable in principle, exactly, action by action. This closes the first tier of consequences and hands the course the currency in which all its future economics will be priced.
Start with the question
"How much work did the machine do?" For most labor the question is muddy — how much work is writing a letter? But for our machine the question has an answer of crystalline exactness, and it costs one sentence to derive:
Every run consists of actions taken one per tick (clock rule) from a small fixed repertoire (processor rule). So a run IS a finite sequence of actions — and the work of a run is simply its count: this run took 47 actions; that one, 3,000,012. Not "about", not "it felt long" — a definite whole number, as countable as steps on a staircase.
Two ancestral rules, one new instrument. Notice what the count deliberately ignores: how fast the ticks come. A quick machine and a slow machine performing the same run do the same 47 actions — in different seconds but identical work. The count measures the labor itself, not the laborer's speed; separating those two will shortly prove to be the smartest accounting decision in the field.
The decisive step: from counting to comparing
Counting one run is bookkeeping. The instrument becomes a science with one further step — and the previous lesson supplied the reason it is needed: paths depend on data, so the count depends on the data too (the failing student was graded in fewer actions than the excellent one). One number per run, different numbers for different data — how then to speak of a PROGRAM's cost?