The Method — Seven Principles 七則

Zhu Xi's gloss is the important part: 溫，尋繹也 — 溫 means to draw out a thread, to re-derive. Not to reread. And the test of real learning is that revisiting old material yields something new each time, so that the knowledge is 在我 ("in me") and 其應不窮 — your responses to unfamiliar positions become inexhaustible. That is explicitly a claim about transfer, not recall.

The science

Cepeda et al. (2008), n≈1,350, mapped the spacing curve parametrically. The optimal gap is roughly 20% of your target retention horizon for horizons of a few weeks — and the proportion falls as the horizon lengthens, to about 5–7% at a year. The absolute gap grows; the fraction shrinks. At a 70-day retention interval, correctly spaced review produced a 111% improvement in recall over none. The curve is a ridge, not a slope — too much spacing hurts as well as too little.

The chess action

Keep a failed-puzzle deck, not a puzzle feed. Every tactic you get wrong enters a queue and returns at roughly 7 days, then 3 weeks, then 2 months. Re-solve it cold from the diagram — never reread the solution. If a re-solved position gives you nothing new on revisit — a second motif, a refutation of the defence, a transposition — you have reread rather than re-derived, and it did not count. Lichess's Puzzle Dashboard does most of the bookkeeping free; the discipline is yours.

憤 is the pent-up frustration of being unable to work something out. 悱 is having something you cannot yet articulate. Confucius withholds instruction until the student has generated the struggle. This is a 2,500-year-old statement of the generation effect, and it is the single most useful idea on this site.

The science

Roediger & Karpicke (2006), prose recall after one week: restudy 42%, retrieval practice 56%. Karpicke & Blunt (2011, Science): retrieval beat elaborative concept-mapping 0.67 vs 0.45 one week later — an effect size of d = 1.50. And the sting: students predicted the opposite, with 75% expecting concept mapping to match or beat retrieval. Fluency during study is systematically misread as mastery.

The chess action — engine off, always, first

The mechanism, in Nate Solon's words: "once you've seen the engine lines you can't unsee them." After engine exposure you can no longer reconstruct your own reasoning — and your own reasoning is the entire diagnostic. Honesty note: there is no controlled study of engine-off-first versus engine-first. It is near-unanimous coach consensus with a coherent mechanism. Treat it as that — and note the one scoped concession the consensus itself makes, set out in full on Analyse Your Games: for blitz, and for players around 1000 whose losses are mostly outright hanging pieces, letting the engine simply name the move is a defensible use of the time. Everywhere else on this site, "always, first" means it.

Zhu Xi: 罔 because 不求諸心 — you sought nothing in your own mind, so you are in the dark and gain nothing. 殆 because 不習其事 — you never practised the thing itself, so you are precarious. Note that he reads the second half as a failure of practice, not of study. Xunzi puts it sharper: 吾嘗終日而思矣，不如須臾之所學也 — "I once spent a whole day in thought; it was not equal to a moment of study."

The science

Chase & Simon (1973). Shown a real middlegame position for five seconds, a master recalls about 16 pieces, a Class A player 8, a beginner 4. Shown a random arrangement, the master's advantage largely collapses. Skill is stored as labelled patterns, not raw memory — which means an unlabelled repetition builds no chunk at all.

The chess action

• Against 罔 (lost): after every missed puzzle, name the motif out loud — "overloaded defender," "back rank," "removing the guard." Grinding puzzles without naming what you saw is the purest form of labour lost.
• Against 殆 (precarious): knowledge never executed under a clock is not knowledge. Hard ratio: no more than one hour of input per two hours of output. Most improvers invert this and wonder why nothing moves.

Context matters. This is addressed to Zilu, the impulsive and overconfident disciple. It is not a general platitude — it is a targeted correction of a specific cognitive vice, and it is the vice that loses chess games.

The science

Bjork's illusions of competence, grounded in the New Theory of Disuse: memory has independent storage strength and retrieval strength. Conditions that feel hard depress retrieval strength while raising storage strength. The corollary is uncomfortable and load-bearing: current performance is an unreliable index of learning.

The chess action

Rate your confidence 1–5 before you check. On puzzles, on opening lines, on candidate moves. What you track is not accuracy — it is agreement between confidence and correctness. Your 5-rated errors are the most valuable training material you own: positions where your pattern library is confidently wrong, which is strictly worse than a blank. Most improvers never find these, because they never separate "I knew it" from "I guessed right."

The second clause is load-bearing and almost always dropped when this is quoted. Bad play is equally instructive — but only when converted into 改之, a specific correction in yourself, rather than contempt.

The chess action

• From every loss extract two things: one 善 (something the opponent did that you will adopt) and one 不善 (a move of yours you will change — stated as a rule, not a regret). "I shouldn't have played Bg5" is a regret. "I do not develop a bishop to a square a pawn can attack with tempo" is a rule. Only the second one changes a future game.
• This extends downward. Analysing a game between two players rated below you teaches you the failure modes still latent in your own play, and they are far easier to see in someone else.
• It extends to whoever is nearest. A slow game against a friend or family member, played properly with a clock and reviewed together afterwards, is worth more than the same game against a stranger — because you will actually discuss the moves.

The stopping rule is what makes this a method rather than a list: 弗措也 — "do not set it aside." You do not advance to the next gate until the current one closes. Cheng Yi, quoted by Zhu Xi: 五者廢其一，非學也 — drop any one of the five and it is not learning at all.

The science — and where gate four comes from

Rohrer & Taylor (2007) is the cleanest experiment on this site. Practice problems, blocked versus interleaved:

The condition that felt worse during practice won by 43 points a week later — a 3.2× advantage. Blocked practice tells you the answer in advance. Discrimination is the skill, and blocked practice deletes it.

The chess action — run every training block through the five gates

And accept the arithmetic that comes with it — 人一能之己百之. The documented range of hours to reach master level is 3,016 to 23,608, an eightfold spread. Someone will need a tenth of your repetitions. 雖愚必明 is the classical answer to that fact, and nothing in the data contradicts it.

A 跬步 is a half-pace — one leg's advance, deliberately the smallest countable unit. And 9.19's point is not "don't quit near the end." It is agency symmetry: 吾止也 / 吾往也 — both the stopping and the advancing are mine.

The science — three independent reasons daily beats weekend

• Spacing is a function of sessions, not hours. Rohrer & Taylor found that doubling massed practice bought nothing — 49% versus 46%.
• Consolidation is sleep-gated. Walker et al. (2002): no significant gain after 12 waking hours, then +20% overnight. Follow-up work: +17.0% after one night, +26.2% after three. Nights of sleep are a training resource that only daily practice buys. Caveat: that study used a finger-tapping motor task. Extension to chess pattern consolidation is a reasonable inference from the wider literature, not a directly demonstrated result.
• 習 is a frequency variable. Zhu Xi on Analects 1.1: 習，鳥數飛也 — "xí is a fledgling bird beating its wings again and again." Practise to the point of 熟 (shú, ripe, automatic), and the pleasure of that automaticity is what makes progress self-sustaining.

The chess action

25 minutes six days a week beats 2.5 hours on Sunday. Not marginally — categorically, for three separate mechanisms. It is also the only version that survives contact with a real life.

And the honest counterweight, which belongs in the same principle

Practice explains about 26% of the variance in games skill (Macnamara, Hambrick & Oswald 2014, 157 effect sizes) and roughly 18–34% in chess specifically. Xunzi is right that accumulation is necessary. The meta-analytic record is clear that it is not sufficient. Analects 9.19 is the correct response to that fact: 吾止也 — the stopping is mine. The variance you do not control is not an argument about the variance you do.