Why building substitutes for progress: a first-principles analysis

Also in 中文. Three-part series: The pattern · Why it happens · How to judge.

I once wrote an essay arguing that building substitutes for progress. That was an assertion — it hands you the conclusion and asks you to nod. This is the derivation: start from a few premises that are hard to deny, and force the conclusion out of them, one step at a time. Along the way it settles the two things the essay waved past — where preparation ends and procrastination begins, and when to switch phases.

If the derivation holds, then “build less” stops being advice and becomes a theorem.

I. Formalize the problem

Everyone who does things is solving the same problem: maximize an objective under finite resources. It has three parts — the objective, the resources, and the decision of where the resources go.

Almost every “should I do this” knot is one of those three confused for another: a means mistaken for the objective, a renewable resource lumped in with an irreplaceable one, or effort poured where it cannot change the result. Pin the three down and the conclusions grow on their own.

II. Five axioms

These are premises, not opinions. Challenge any of them you like — but once you accept them, the rest is not up to you.

• A1 (single terminal value). The system has exactly one end. Everything else — tools, process, skills, “the foundation” — is a means, with no value independent of the end.
• A2 (two resource classes, one conserved quantity). Resources come in two kinds. Renewable: money, materials, code, knowledge — they regenerate, or can wait, or sit untouched without decaying to zero. Conserved: your irreversible time and attention — the moment spent on A can never be spent on B. In a single-agent system there is exactly one conserved quantity: your attention.
• A3 (the bottleneck law). A system’s output is set by its tightest constraint. Relax a non-bottleneck constraint and the output does not move.
• A4 (valuation of a means). The net value of a means = (its marginal contribution to the current bottleneck) × (probability it pays off) × (time discount) − (cost to maintain it). Drive any leading factor toward zero, or the maintenance high enough, and the net value goes to zero or below.
• A5 (feedback structure). Different actions sit at different distances from reality answering back. Some return a definite signal in minutes (did the code run); some take weeks, and the answer is often silence or rejection (did a real outcome land). The nearer the feedback, the more controllable the action feels, and the faster it delivers a sense of certainty.

III. Derivations

Theorem 1 — a means has no standing priority

By A1 the end is singular; by A4 a means draws its value from its contribution to that end (through the bottleneck). So to call a means “a priority” without naming how much it currently contributes is empty. The moment a means begins demanding investment for its own completeness or elegance, it has violated A1 — it has promoted itself from servant to end. ∎

Theorem 2 — spending the conserved quantity off the bottleneck is pure loss

By A3, work on a non-bottleneck leaves output unchanged (expected gain: zero). By A2, that work spends the one resource that does not come back. Zero gain in output, paid for with an irreversible resource — a negative net. Note this has nothing to do with how well the thing is done: do it beautifully, and as long as it is off the bottleneck, output still does not move. ∎

Theorem 3 — why building is systematically over-chosen (the core)

This is the key step. People over-choose building not because its A4 (contribution) is high, but because its A5 (feedback) is near.

The brain has no direct readout of A4 — “how much does this contribute to the final end” is both delayed and blurry. So it falls back on a proxy to approximate the feeling of progress: the speed and certainty of feedback. Code that runs at once, a structure that visibly tidies up — that immediate, certain payoff gets logged as I am making progress.

But feedback speed (A5) is not contribution to the bottleneck (A4). And building happens to be the class of action with the nearest, most controllable feedback, while the work that actually moves the goal has the farthest and least controllable. The result is a systematic valuation error: the proxy (fast feedback) gets substituted for the truth (real contribution), so investment keeps flowing to what feels like progress rather than what is.

This is the exact meaning of “building substitutes for progress” — not a failure of character, but a valuation bug that mistakes a proxy for the quantity it stands in for. And it self-reinforces: the more anxious you are about the slow-feedback thing, the more you crave fast feedback to soothe it, the harder you bolt toward building. ∎

Theorem 4 — the boundary between preparation and procrastination

The same act of building — when is it preparation (do it) and when is it procrastination (avoidance)? By A4 and A5:

The test is whether it shortens the distance to the decisive feedback — the real answer (the far end of A5) that tells you whether the end is reachable.

• Shortens it → preparation. It clears an obstacle in front of a committed, scheduled real action; finish it and you reach reality sooner.
• Doesn’t, or pushes it away → procrastination. Finishing it only unlocks the next round of building and shoves the real answer further out.

The practical handles all unfold from that test: Is there a line called “enough”? Is a real action waiting behind it? Does it clear the current bottleneck or an imagined future one? Does it get you to reality sooner or later?

It yields the symmetric, honest conclusion too: over-preparing (loitering at the near end of A5, avoiding) and under-preparing (skipping the near-distance work that was actually needed, recklessness) are opposite diseases. The optimum is not “don’t prepare” but calibrating preparation to the minimum that reaches the decisive feedback. ∎

Theorem 5 — phase and timing

By A3 the bottleneck is not a constant but a function of the stage — call it B(t). Since the optimal move is “act on B,” the optimal decision varies with t. There is no constant answer, only answer(t).

And the migration of B(t) — the old bottleneck clearing, a new one surfacing — only happens after you have genuinely worked the current bottleneck through, and only then is it observable. Two corollaries:

1. Timing is not chosen; it is made, and then revealed. Work the current phase to the wall, and the next bottleneck shows itself.
2. Switch on an observable signal, not on the calendar or your mood. The calendar (“it’s been six months”) has nothing to do with the bottleneck; the mood (“I feel ready / I want to build”) is exactly the bias of Theorem 3 talking — it makes the builder switch early, systematically. The remedy: write the signal down in advance, then at the wall just check whether it has fired. ∎

Corollaries — sunk cost is irrelevant; freezing is the optionality optimum

• Sunk cost is irrelevant. A4 contains only forward terms (marginal contribution, maintenance cost); past investment is not among them. The only test is: starting from zero, given the current B(t), would I invest in this?
• Freeze beats delete or keep-building. Under uncertainty, deleting destroys the future option, building on burns the conserved quantity (A2), and only freezing avoids both — it is the dominant move when information is short. ∎

IV. Compress it into a decision function

For any candidate action x, run the gate in order:

1. Does x point at the end, or is it a means? (A1) If a means, ask only its current contribution.
2. The current bottleneck is B; does x act on B? (A3) If not → value ≈ 0, stop.
3. Does x spend the conserved quantity or a renewable one? (A2) Conserved → scrutinize hard.
4. Does x shorten the distance to the decisive feedback? (A5 / Theorem 4) No → suspect procrastination.
5. Would the minimum reversible version capture most of the value? (A4 maintenance) Yes → do the minimum version.

Pass all five, and only then is it worth the conserved quantity. This is equivalent to the line worth carrying: “This hour — can it move the outcome I actually care about forward this week?” It is just the five gates, compressed.

V. Falsifiability

A derivation has to be refutable, or it is only rhetoric:

• If A2 fails — if you can buy back unlimited equivalent attention with money — then Theorem 2 and the “conserved” corollaries collapse, and parallel investment becomes reasonable.
• If a given action’s fast feedback is in fact strongly correlated with its contribution to the bottleneck (A5 ≈ A4) — then the bias of Theorem 3 disappears, and building more is no longer an error.
• If the bottleneck is constant and does not migrate with the stage (B(t) = const) — then Theorem 5 fails, a constant optimum exists, and “choosing the timing once” is enough.

Each names the world in which I am wrong. In the world we actually inhabit — attention conserved, fast feedback ≠ real contribution, bottleneck moving with the stage — none of those antecedents hold, so the conclusions stand.

VI. Reconciling two proverbs

• “Sharpen the axe and you won’t delay the chopping.” True — but its hidden conditions (the axe is actually blunt, and you are actually about to chop) are precisely the test in Theorem 4. Sharpen an already-sharp axe a tenth time, or with no wood in front of you, and the sharpening is the delay. The proverb does not oppose this essay; it is the folk version of Theorem 4.
• “Move fast” / “speed is the only thing that wins.” The half it gets right is A5 — shortening feedback is a real edge. The half it gets wrong is assuming any fast action shortens the distance to the decisive feedback. Doing irrelevant things quickly is just faster waste (Theorem 2 stacked on Theorem 3). Be fast toward the decisive feedback, not fast where the texture feels best.

Building substitutes for progress because the brain approximates how much something contributes with how fast it answers back — and the two are not equal. Puncture that substitution and the rest is corollary: spend your one conserved resource only on the bottleneck; tell preparation from procrastination by whether it shortens the distance to the decisive feedback; decide when to switch by an observable signal, not a mood. Everything else — the seductive, controllable, fast-answering build — gets frozen.