Week 2: A number is a chain, not a guess

Why breaking a quantity into parts beats guessing it whole, and why defining the target is part of the estimate rather than a preliminary to it

1 March 2027

Open the slides

Asked for a number they don’t know, most people produce one anyway — a single figure, arrived at somehow, defensible only as a whole. Challenge it and there is nothing to point at. The author can restate it more confidently or abandon it. There is no third move.

Decomposition is the alternative, and its advantages are not about accuracy.

Four things a chain gives you that a guess doesn’t

Assumptions become inspectable. A guess fuses every judgment its author made into one figure. A chain lays them out as separate links, each a claim you can examine on its own terms. Nothing about this makes the individual links better; it makes them visible, which is the precondition for anything else you might want to do to them.

Unit errors become visible. Every link carries a unit, and every step has to produce the unit it claims. Stops-per-route times routes gives stops. Stops-per-route times suburbs gives a quantity with no meaning — and the fact that it has no meaning is legible on the page rather than buried inside an intuition. This check costs nothing and catches a class of error no amount of careful thinking will.

Disagreement becomes local. This is the one that matters in a room with other people in it. Two people who disagree about a single guessed number can only trade intuitions; there is no surface to disagree on. Two people who disagree about a decomposed estimate can almost always find the one link they differ on, and then the argument is about something specific and often resolvable. A chain turns an unproductive disagreement into a located one.

The target has to be defined. You cannot decompose a quantity you have not pinned down. The moment you try to break “how many bus stops” into parts you are forced to decide whether you mean poles, shelters, boarding points, or places a bus pauses — because the sub-quantities differ depending on the answer. A guess lets you skip that decision without noticing you made one.

The definition is part of the estimate

That last point gets treated as throat-clearing, and it is the one that most often makes two careful estimates disagree.

Until the target is pinned down, there is nothing definite enough to be wrong. Two honest people can produce very different numbers for the same question and both be right about their own question — and no amount of checking the arithmetic will surface it, because the arithmetic is fine. Only comparing definitions will.

You will hit this today against a real dataset, and the official figure will turn out to be less definitive than it looks. Not because the agency was careless: a count is always a count of something, and the something is a choice somebody made and did not necessarily write down.

What this is not

There is no probability here. No error propagation, no independence, no formula for how uncertainties combine. That machinery exists and this course does not use it, because what matters here comes earlier than any of it: build a structure you can point at, and be able to say what you were counting.

Outline