Instruments, standard units, controlled comparison and publication, then the laboratory and statistics.
Turn observation into numbers.
Needs first: Glass (Materials), Machine tools and precision (Tools), Printing
Fix the units, hold the standards, and make every measurement comparable to every other.
Needs first: Instruments and measurement, Blacksmithing (Tools), Arithmetic for everyone, Standard weight (Economy)
Establish how you decide whether something is actually true.
Needs first: Writing and the durable record, Instruments and measurement, Arithmetic for everyone
Make disclosing what you know the self-interested move.
Needs first: Printing, Controlled comparison and the negative result, Teach the next generation
Run laboratories whose results can be trusted and reconstructed after the investigator has gone: written procedures, calibrated instruments, raw data recorded and archived, quality checked by people independent of the work, hazards controlled by assessment, and competence proven to an outside body.
Needs first: Instruments and measurement, One metre, one kilogram, everywhere, Controlled comparison and the negative result, Priority by publication, Glass (Materials)
Draw samples at random, state the uncertainty of every estimate, fix the plan before the data arrive, read significance tests for what they are, and believe a finding only when it has been replicated.
Needs first: Controlled comparison and the negative result, Arithmetic for everyone, Count before you administer (Society), Priority by publication
Every guide, build, reference sheet and book reached from the steps above.
Fourteen branches, each with the handful of results a civilization cannot rebuild without, and where to learn the rest.
Level 3Force, energy, heat, light, electricity, relativity and the atom: the laws every engine, wire and lens obeys, each with what it lets you do and who first found it.
Level 3The sky as calendar, clock and compass, then orbits, distances and the universe: each result with what it lets you do and who first found it.
Level 2North is written in the sky twice a day and all night. Latitude is one angle measured at noon. Everything else is counting paces and not lying to yourself about the count.
Level 3The results every other science and machine is built on, in the order each needs the last: the formula, what it states, what it lets you do, and who first found it.
Level 3What matter is made of and how it changes: amounts, gases, acids, the energy and speed of reactions, electrochemistry, and the reactions every industry on the ladder runs on.
A glass bead the size of a pinhead magnifies 150–350 times: enough to see yeast, blood cells and the larger bacteria that cause disease.
Two lenses in a tube: a 1-metre objective and a 25 mm eyepiece give 40×, enough to see Jupiter's moons and the phases of Venus.