The Science of Counting#

ZnuLabs // Origin note, written in lockdown, 2020

I. The stillness#

COVID had changed everything, and the first thing it changed was the pace.

The world stopped moving. Airports emptied. The consulting calendar — twenty years of it, the thing that had structured every week of my working life — went blank in a fortnight. And in that stillness I found myself staring at an old problem through a new lens, because for the first time in two decades there was nothing else to stare at.

The problem was this: counting is hard.

Not arithmetically. Nobody has trouble with addition. It is hard in the way that businesses measure, report, and then believe their own numbers. I had watched it in two hundred companies. A marketing team and a finance team producing different figures for the same quarter, each correct, each convinced the other was incompetent. A board deck where the conversion rate had collapsed and nobody could say why, because nothing underneath it had changed. Engineers demanding precision in a domain where precision was an illusion, and a culture that craved certainty where only nuance existed.

The more I peeled it back, the clearer it got. The problem was not the data. The problem was that there was no framework at all — no shared account of what a number was a number of.

THE FERRYMAN // Ο πορθμέας
I am not sure who is speaking here. I will be honest about that at the outset.
There is a figure I keep thinking about, in the quiet. A man with a boat, whose whole trade is moving other people from one bank to another. Not going anywhere himself. Not arriving. Just the crossing, over and over, for as long as there are people who need to be on the other side.
I have been doing something like that for twenty years and never had a name for it. I came into companies, I got the thing across, I left. I did not stay to enjoy the far bank. It was never mine.
It seems useful to have the name now, so I am borrowing it.
Whether I have earned it is another question. Ask me in a few years.

II. The first day#

The opening reference in the first paper is not to a theorem. It is to the first day of a statistics class.

Everyone who has sat through one remembers the shape of it, even if they remember nothing else. On day one they tell you that there is a quantity in the world — the true thing, the parameter — and that you will never observe it. What you get instead is a statistic, computed from a sample, which is an estimate of the thing with an error attached. The whole discipline is built on that gap. It is the first sentence of the subject and it is a confession.

There is a long and generally unproductive war between those of us who model with mathematics and those who work in statistics. I have been on one side of it for most of my life. But the statisticians say the honest thing on day one, out loud, before anyone has bought a textbook: the number is not the thing.

Business measurement forgot this entirely. Somewhere between the ledger and the dashboard, the estimate stopped being an estimate and became the fact. A figure in a cell, rendered in a sans-serif font, with no error bar and no provenance and no statement of what population it was drawn from or over what window. And then people made decisions on it, and when the decisions went badly they blamed the decision rather than the number.

So the project began there. Not with an answer. With the observation that we had all skipped day one.

III. The mission#

I started a quiet project, without fanfare, around a single question: what if we modelled business measurement the way it actually behaves?

Not as flat, one-dimensional snapshots. As surfaces — where time, cohorts, and operations intersect and frequently collide. That was the first draft of Counting is Hard, written in late 2020: a manifesto disguised as a technical note. Its argument was that the numbers do not lie, but they do not align either, and the non-alignment is not a defect to be reconciled away. It is the actual structure of the thing.

But writing it was not enough. It had to be modelled.

So the work went in two directions at once.

First, to get the counting right in practice. That meant taking apart how businesses report results — exposing the gaps between period, cohort, and operational reporting, and showing that each answers a real question and none answers all of them. Time-domain reports for results. Cohort analysis for yield. Operational dashboards for management in the present tense. No more dividing a numerator from one cut by a denominator from another. No more pretending a ratio assembled from mismatched windows means anything at all. The goal was truth in measurement, particularly where the truth was unwelcome.

Second, to build the mathematics underneath it. If the problem was structural then the treatment had to be rigorous. I went to the Lexis surface — the demographers’ device for reconciling period and cohort counts — and adapted it to business data. I formalised the conditions under which each kind of report is valid, derived corrections for censored cohort data, and imported the tempo effect from demography to explain the thing that had puzzled every board I ever sat in front of: why a period conversion rate can fall through the floor while nothing whatsoever has changed about the underlying yield.

Demography had solved this. In the nineteenth century. For births and deaths, which are the same shape of problem as leads and closes, and which arrive on the same kind of surface. Nobody in commercial analytics had gone to look.

THE FERRYMAN // Ο πορθμέας
Here is what I notice, and I do not yet know what to do with it.
Every firm I have ever worked with knows its numbers are wrong. Not one of them will say so in a meeting.
They know. You can watch them know it. Somebody quotes a figure and there is a small silence, half a second, where everyone in the room privately declines to believe it — and then the meeting continues, because the alternative is to stop the meeting and nobody has ever been thanked for that.
The silence is the whole problem and it is not a technical problem.
I have spent twenty years building things for people. I am starting to think the useful thing I could build is not a system at all. It is a number honest enough that the silence has nowhere to go.
I do not know how to do that yet.

IV. What I did not know#

I thought this was one paper.

I want to record that plainly, because what happened next took six years and I did not see any of it coming. The counting problem turned out to be the visible edge of something with a great deal more underneath it, and each answer opened a worse question.

Getting the counting right assumed there was a stable population to count — and the entities underneath were tangled in a way nobody had bothered to formalise, so the population itself had to be defined before it could be measured. Defining it exposed that the records were not a faithful picture of what had happened, but a lossy projection of it, with information destroyed at the moment of writing rather than lost afterward. And the records that survived were not holding still: they were rotting in place, continuously, at a rate that could be measured and would not stop.

Underneath all of it, the question that made me start: why did we win that one and lose this one? I would eventually be able to prove that a large part of that question has no answer available in any record, ever, and that the field where firms write down the answer is systematically fabricated by the people least able to give it.

And at the end, something like a way forward — smaller than I wanted, and pointing somewhere I did not expect. The methods that work for large firms will not transfer down. A company with four hundred interactions in a quarter can study a single deal. A company with twenty cannot, and no improvement in tooling will change that, because the constraint is arithmetic rather than technical. Small firms will have to look at aggregates: the account across its whole history, the cohort rather than the case. That is not a lesser method. It is a different unit, and refusing it in favour of imitating the enterprise is how small firms end up with beautiful dashboards that cannot possibly say anything.

I did not know any of that in 2020. I knew that counting was hard and that nobody would admit it.

V. The output#

Several papers later, each one a piece of it, ZnuLabs took shape.

It was never only about fixing reports. It was about building a language for business measurement precise enough for the engineering minds that have to use it — people who would never accept “that’s just how the numbers are” from a compiler and should not accept it from a dashboard.

Because the numbers are not one thing. They are projections of a deeper structure, and if you do not understand the surface they were cast from, you will go on counting wrong with great confidence and considerable expense.

THE FERRYMAN // Ο πορθμέας
So. A first crossing, and I am not much of a ferryman yet.
I have the boat and I have the water and I have some idea of the far bank, and if you asked me today to name what is over there I would give you a worse answer than I would like.
But I notice I have stopped wanting to arrive anywhere. That may be the beginning of the thing.
Whoever is speaking in these papers, he is not going to be the hero of them.
The cargo is the point. Get it across, hand it over, go back for the next. If I am still saying that in a few years then the name will have been fairly taken, and if I am not, then this was a phase and someone should say so.
The water is cold. It is going to be a long crossing.

The journey continues#

Not because the world has caught up. Because it still has not.

Grover Righter // ZnuLabs