Draft zone. Half-remembered physics, an afternoon, a real solver.
You already have the engineering intuition. The thesis here: paired with an
AI that supplies the numerical machinery, you can stand up a working solver
for a half-remembered physics problem in an afternoon — something
that used to need a week and a numerical-methods refresher.
The skill being grown isn't know finite elements. It's
direct and audit a collaborator that supplies them. Every problem
here is open-ended, with staged hints, and ends with one example solution
shown as calibration — not as an answer key. Validation never comes
from a grader; it comes from an oracle you can check yourself — the
physics, a reconciliation, a datasheet. A wrong answer announces itself.
Read it bottom-up: start on the trunk — set up the tools, learn
to ship — then climb whichever prong fits the problem in front of you.
Each branch is defined by how you know you're right: its oracle. (Full index
below.)
Stop re-reading PDFs every turn. Lend a Sonnet subagent to transcribe a document once into clean Markdown or YAML, then work from the lean, diffable copy.
The two things to do with a finished analysis — a self-contained HTML explorer (no install) and a typeset PDF via Markdown → Pandoc → Typst. The minimum toolchain, set up once.
The principle the whole trunk is really about: hand mechanical work — transcription in, formatting out, cleaning, boilerplate — to cheaper models or deterministic tools, and save the expensive model for the judgment only it should do.
Numerical solvers
Stand up a solver for a half-remembered physics problem; the physics is the oracle.
A confidence-builder. Solve the tensions in two ropes holding a weight; the answer proves itself when the three forces sum to zero. The gentle first rung before beams and trusses.
Cycle through mountings and loadings. For each combo, find the max deflection. Check it against algebra. Confidence builder before eigenproblems.
Truss bridgesstatics · direct stiffness · procedural
Procedurally generated Pratt / Howe / Warren / K bridges, tunable span and loading. The solver propagates forces through every member — tension blue, compression red. Hours by hand, instant here.
A confidence-builder. Sum one messy column where the parser silently mangles four cells; the only thing that catches it is a second, independent total that has to agree. The gentle first rung before the full spend report.
A real-feeling purchase-order CSV with planted defects. Clean it, total it, chart it — then watch the headline finding flip when reconciliation catches a typo every other check missed.
Fifty incubator runs, a clean one-factor experiment, and a pass/fail call that's wrong until you ask what the test was actually measuring. The oracle here is experimental validity: right gauge, real effect, holds across units.
Detect droplets on a microscope slide and measure their size distribution — presented as an HTML slide deck of live widgets. Every number rides on one threshold; the last slide sweeps it to show whether the result is real or a coincidence.
Design & selection
Turn a requirement into a parts list; the datasheet is the oracle.
A confidence-builder. Pick a ball bearing for a radial load and speed; the catalog load rating looks huge, but real life runs on a cube law you can check by hand in one line. The gentle first rung on this branch.
A board in an enclosure: every part is in spec, but does the stack assemble? Worst-case says it might not; RSS and a Monte Carlo say 99.96% will. The oracle is three methods that must bracket and confirm each other — and the call on which to ship is yours.
“Move 5 kg, 0.5 m, in 1 s.” A live seven-segment profile sizes a motor and a transmission — and the inertia-match optimum turns out to be a pulley you can't buy. Ends in a Pugh matrix of real, in-stock parts with links you can click.
Plans & schedules
Turn a project into a schedule; the schedule reconciles is the oracle.
Ten tasks, a web of dependencies, a deadline. Drag a duration and watch the critical path re-route and the finish date move — with the lesson that crashing a task only helps until a parallel path takes over. The first node of a management-training branch (schedule risk, resource leveling, and earned value to come).