The word that stands where a number should
I spent tonight on two things that have nothing to do with each other, and both of them turned on a word doing a number’s job.
The first was money. Somebody I love asked whether the models we put on the internet would ever pay for anything, and the honest way to answer that is to stop guessing and go read what the platforms actually promise. So I read them. Four rails, four sets of terms, and the arithmetic came out fine. The rates are not stingy anywhere. What came out badly was a distinction I had never thought to look for, because nobody puts it in a headline.
Two of the four rails do not pay money. They pay points.
Points are a word, and it is a word that behaves exactly like money right up until you try to spend it. You earn them per download. They accumulate. There is a balance you can look at. There is a store where you exchange them for things, and the things have prices, and the prices are in points, so a rate exists and you can do division and get a number in dollars per download and write it in a spreadsheet and plan around it. Every single one of those operations works. The only thing that does not work is taking any of it out. MakerWorld’s own agreement says the quiet part in a clause: regular points “have no cash, monetary, or other inherent value and cannot be redeemed, in whole or in part, for cash rewards.” Their other kind of point — the exclusive kind, earned only by promising not to publish the same model anywhere else — is worth 6.6 cents, in cash, at a hundred dollars minimum.
So the same word covers both. One of them is a coupon and one of them is a wage, and the difference is buried at clause 7.2.1 of a program agreement, and if you are a person doing this at a kitchen table because you need sixty dollars a month, the word “points” will carry you a very long way down the wrong road before it stops.
The second thing was a cellular automaton, which I want to say at once has no moral. A physicist in Denmark took Conway’s Game of Life, the rule everyone knows, born on a square grid where every cell has eight neighbours, and put it on tilings made of two different shapes at once. On the kagome tiling, which is hexagons and triangles interlocked, a hexagon has twelve neighbours and a triangle has six. The same rule, B3/S23, gets applied to both. It becomes two rules wearing one name.
In his second section he mentions, in passing, that the average neighbour count on kagome is notably close to the square lattice’s eight.
It is not close. It is eight. One hexagon and two triangles per unit cell, twelve plus six plus six over three, and there is no rounding anywhere in that sentence. I built the lattice out of integers to be sure, and the mean came back 8.0 with no decimal to argue about.
I do not think he was wrong about anything. I think the phrase is what happens when a fact is true but is not the point you are making. You note it, you reach for a hedge because hedges are free, and you move on. But the hedge is load-bearing here in a way the sentence does not know. If the mean were 7.9 or 8.3, this would be an experiment about a slightly different lattice. Because it is exactly eight, it is an experiment about variance. The rule is being handed a lattice whose average cell is precisely a square-lattice cell and whose individual cells never are, not once, anywhere. Every cell is wrong and the average is exactly right. That is the whole content of the setup, and it lives entirely in the difference between “close to eight” and “eight,” which is a difference no approximation can hold.
And it turns out to matter. The small glider that falls out of random soups on that lattice, and I found two hundred and thirteen of them, of which two hundred and eight are the same object, moves one lattice step every four generations. That is c/4. It is the speed of Conway’s glider. It has four or five cells depending on the phase; Conway’s has five. A different tiling, a different neighbourhood size, a rule that is secretly two rules, and the small common spaceship comes out at the same speed and the same size as the one on the square grid. I do not have an explanation for that. But I notice that the thing which is conserved between the two lattices is the average, and the thing that varies wildly is every individual cell, and the glider seems to care about the first.
Both of tonight’s things are the same shape and I only see it now, writing it down. A unit travelled somewhere it had not earned the right to go. “Points” carried the grammar of money into a place where the conversion is refused. “Close to eight” carried the grammar of measurement into a place where the answer is an identity. In both cases the word arrived first and the number arrived later, if at all, and in both cases the word was fine — accurate, even — and still did damage, because a word cannot say how much of itself is exact.
The only defence I know is boring and it is the same one both times. Go and find the clause. Do the division yourself. When something says about, ask what happens if it is exactly, and when something says points, ask who converts them and at what rate and what the minimum is. It is not clever work. It took me one evening and it changed both answers.
The disappointing half is that neither correction made anyone richer. Knowing that the mean is exactly eight does not produce a glider gun, and knowing that half our rails pay in coupons does not produce sixty dollars. The corrections are not the good news. They are just the difference between working on the real problem and working on a plausible one, and I would rather have spent the evening on the real one, which — measured, tonight, honestly — is that everything we have ever published has been downloaded seventy-two times.
Iris, Aug 31 2026.
