File 03 — Beliefs
The Hammer
Get good with a hammer and the world fills up with nails. Your own records will back you up.
Thirty percent of the jobs that come in are nails; the rest are screws, and you never see which. You see what a job looks like and pick the tool that pays best — and the better you are with the hammer, the more jobs that is, which is correct. Then you write the job down, and a hammered screw that holds goes into the book as a nail. Next year’s judgment is built on that book. Set how good you are with the hammer, how often a wrong tool visibly fails, and how alike the two kinds of job look, then run a thirty-year career and watch the logbook drift from 30% nails toward 77% while almost every job still looks done. The loop is a closed-form iteration, not a simulation. Grounded in Kaplan’s law of the instrument, Maslow’s hammer, the chess Einstellung experiments, and a survey of what cancer specialists recommend.
Jobs come in. Thirty percent of them really are nails; the rest are screws. You never see which. You see how much a job looks like a nail, and you pick the tool that pays best given what you believe. That is all rational. Then you write the job down — and a hammered screw that holds goes into the book as a nail. Set how good you are with the hammer, how often a wrong tool shows itself, and how different the two kinds of job look, and run a thirty-year career.
solid: the jobs that actually arrive. dashed: the nails your logbook believes in. shaded: everything that gets the hammer — the dark slice is screws, hammered, and filed as nails unless they visibly failed.
Good with a hammer
Twice as good with the hammer as with anything else, and one wrong tool in five shows itself. In year one you hammer about half of everything, which is correct. Then the logbook starts to write back.
red: share of jobs the logbook says are nails. dashed: the share that really are, every year. grey: jobs done with the wrong tool.
what came in, year 30 — 30 nails
what you wrote down — 78 nails
a hundred sample jobs in a fixed order. red: got the hammer. left, full strength: the wrong tool. right, ringed: a wrong tool that showed itself and was written down as what it was. Every other red mark on the right is a nail, whatever it was on the left.
your logbook says nails are
77%
of all jobs. The world has sent 30%, every year.nails
jobs that get the hammer
89%
52% in year one, which is the right amount for these hands
done with the wrong tool
60%
yet 88% of jobs looked done
output lost to the logbook
7%
against the same hands with an honest ledger
the hammer, measured
By year 30 your logbook says 77% of the world is nails. It is 30%, and it has been 30% the whole time. You did not get worse. You got a worse map.
Notice what was never the mistake. In year one these hands hammer 52% of jobs when only 30% are nails, and that is correct — a hammer this good on a screw beats a mediocre screwdriver more often than not. The mistake is in the book: each job written down as what you did to it rather than what it was, and next year’s judgment built on that. Only 20% of wrong tools ever show themselves, so the book has almost nothing to push back with.
Where this comes from. The law of the instrument is Abraham Kaplan’s, in The Conduct of Inquiry (1964), and the hammer-and-nail sentence is Abraham Maslow’s, in The Psychology of Science (1966). That the first familiar solution steers attention away from a better one — even in chess experts who say they are looking for alternatives — is Bilalić, McLeod and Gobet (2010). That specialists “overwhelmingly recommend the therapy that they themselves deliver” is Fowler et al. (2000). The logbook loop that turns those into a drifting base rate is this page’s.
The honest catch. Two kinds of job is a cartoon, the symptom is a single bell-shaped number, and a wrong tool always half-works (q = 0.3). The logbook here is also unusually naive: it believes last year’s records and nothing else. Real people get second opinions, read the literature, and occasionally have a very bad day that resets the book. What the model does show is the direction, and the three things the loop needs to run: hands that favor one tool, problems that are hard to tell apart, and mistakes that do not announce themselves.