How the program works

Understanding a subject tends to move through five stages. Naive realism takes appearances and inherited assumptions at face value: the world is as it seems. Skepticism sets in once those assumptions collide with a contradiction, an anomaly, or a better argument, and the learner starts doubting them on purpose. Formalism answers that doubt by building an explicit, symbolic system, logical or mathematical, that explains the observations and can be checked. Abstraction is noticing that the same structure recurs in a different formal system and asking where the analogy holds and where it breaks. Intuition return is the point where the formal work has been internalized enough that judgment on new cases is fast again, but it can still explain itself and survive an objection, unlike the naive judgment it replaced.

The cycle is a way to organize study and self-testing within each topic. Fields rarely moved through these stages in a straight line, and nothing here claims they did. The table below turns each stage into something you can check.

Study happens through books, including primary sources where they are readable, online courses, papers, experiments you run yourself, and small projects, mixed as each topic demands. Free and open resources are preferred throughout; a handful of classic texts are worth buying or finding as PDFs where no open edition exists.

The goal is breadth across many domains plus real depth in one chosen specialty, a generalist who is not shallow everywhere. David Epstein's Range collects evidence that people who sample widely before specializing tend to do well in domains where feedback is slow or ambiguous. This curriculum adds one deliberately deep specialization on top of that breadth. The aim is to move between domains, see shared structure, and act competently and honestly in at least one of them.

This is written for motivated adults with a secondary-school education, including basic algebra, and no assumed university training. Readers with prior technical training, in engineering or a science, will find some subsections easy; the right move is to attempt that subsection's checkpoints first (section IV) and skip ahead on whatever you pass cold, banking the time saved for what is new to you. Sections A through F organize the material by domain; G is a capstone that draws on all of them. Section III gives the order in which to study them.

Each subsection that follows opens with a status line giving its phase, an hour estimate, and its prerequisites, then body prose that moves through the topic's history and resources, then a Checkpoints paragraph whose sentences are each tagged with the cycle stage they test. Footnotes point to the References section at the end.

Treat each subsection's Checkpoints paragraph as a gate you can fail. This section describes the general tools behind the checkpoints.

The most direct is a problem set with solutions, attempted closed-book, checked only after a genuine attempt, with errors logged by type: concept, algebra, or misread. MIT OCW's "SC" courses provide this format with full solutions, as does Hammack's Book of Proof for proof-writing and OpenStax's end-of-chapter answers for the sciences; the Nand to Tetris hardware simulator checks your chip designs automatically. This is the main test of formalism.

For abstraction and intuition, use the explanation test: write about 500 words explaining one idea to a specific non-specialist reader, with the source closed, then mark every sentence where you hand-waved and go back to the source only for those. This is in the spirit of Feynman's teaching rather than a technique he named himself.

Formal knowledge decays without use, which is what retrieval practice and spacing are for: 15 to 20 minutes a day of flashcard review, in Anki, for definitions, dates, formulas, and derivation steps you already understand once, not new material. Dunlosky et al.'s review of learning techniques rated practice testing and distributed practice as the only two of ten techniques with high utility, and rereading and highlighting as low utility; Michael Nielsen's essay on using Anki for research-level material is the practical guide to doing this well.

History, philosophy, and the social sciences have few ready-made problem sets, so writing for critique substitutes: short essays, posted somewhere a genuine critic in the field will read them, with a steelman requirement, meaning you state the opposing view well enough that someone who holds it would accept your summary. This is the check on skepticism and intuition that a closed problem set cannot provide.

Replication means re-running the historical experiment where practical, a pendulum measurement of g, Eratosthenes' shadow measurement of the Earth's circumference, a pinhole camera, and re-analyzing real data such as John Snow's 1855 cholera tables or the public datasets at Our World in Data, so that you check the textbook's result yourself.

Finally, cumulative review: at the end of each phase, re-sit a sample of earlier checkpoints cold, and put anything you fail back into both the problem queue and the Anki deck. This is also where the running knowledge journal lives: one place for baseline notes, error logs, and written explanations, kept across the whole curriculum rather than per section.

Assume 12 hours a week, 46 working weeks a year, about 550 hours annually. Each week splits into three tracks that run in parallel: a spine track of mathematics and computation (about 5 hours), a domain track for whichever science or social-science subsection is current (about 5 hours), and a reading track for history, philosophy, and primary texts that don't block anything else (2 to 3 hours). The reading track carries slow material (world history, philosophical primary sources, art, questions of meaning) in the background for years without holding up the rest.

A few prerequisites are worth stating up front, since the phase table alone can mislead: mechanics needs derivatives and basic integrals; electromagnetism needs multivariable calculus and benefits from differential equations; quantum mechanics needs linear algebra, complex numbers, and probability; psychology (D.1) needs statistics through hypothesis testing; economics and strategic interaction (E.2) needs calculus for optimization and basic probability; complex systems (E.3) needs differential equations and programming; control theory (E.1) needs differential equations.

Add it up and breadth, phases 1 through 6, comes to roughly 3,200 hours of study plus about 10% for review, call it 3,500 hours, which is about six years at 12 hours a week, five at 15, or seven and a half at 10. The capstone adds another 1,000 to 2,000 hours, two to four years depending on the field. Total: eight to ten years for the whole path. There are exactly three honest ways to shorten it: test out of a subsection via its checkpoints and skip what you already know, mark optional items as skipped rather than compressing everything, or accept a lighter breadth target from the start. Skipping checkpoints to go faster only postpones the cost. At 6 hours a week, double the phase durations.

Find a reading group or a study partner, at least for the writing-for-critique method in section IV. Explaining yourself to someone who will push back is most of the value of that exercise, and it is hard to do alone.

Alternate breadth and depth on a schedule: a stretch of new material, then a stretch spent consolidating what you already have.

Expect real difficulty. Dense proofs, unfamiliar formalism, and stretches of confusion are ordinary parts of the cycle described in section I.