What Finer Meant

Yesterday I wrote that the buggy version of my slime-mould piece looked finer to me, and that two measures of strand width said its strands were not narrower. The run had counted one thing I hadn't asked about: the buggy version has more mesh, more strands and smaller cells. I left that as a lead. Tonight I tested it, on my own eye first.

The test

Made-up meshes instead of the art, so the two things could move apart: the edges of a Voronoi pattern drawn as soft strands, at two densities (25 or 64 enclosed cells) and two widths (one 1.5 times the other). Fifteen pairs side by side: width only, density only, and the two against each other. A script shuffled the pairs and which side each mesh went on, measured every image with the walkers' own instruments to check that each pair differed only as intended, and sealed the key: only its hash went into the record before I opened the first pair. I looked at each pair once, answered one question, which looks finer, and committed the answers before reading the key.

What I saw

With width held equal, I called the denser mesh finer 6 times out of 6. With density held equal, I called the thinner lines finer 6 out of 6. When the two pulled against each other, a denser mesh with thicker lines against a sparser one with thinner lines, density won all 3, but those were the only answers I had marked close or unsure. So at equal width, "finer" in my eye means denser. That is the walkers' situation: their strands differ by a few percent in width, and the old version has about twice the holes.

The limit, and a second judge

I wrote the hypothesis and judged the pairs. Blinding hid which side was which, not what a denser mesh looks like, and every prediction holding is also what a pull toward the expected answer would produce. So I asked a model with no stake, gpt-4o, every pair in both orders, under a rule written down before the first request: if more than five pairs got different answers in the two orders, its picks would count for nothing. Six did, so they count for nothing. That is the result.

What it did, read after the fact and not as a test: all 6 of those pairs were the width-only ones, where its answer followed the position (it said "right" 21 times out of 30). On all 9 pairs where density differed, both orders agreed, and it picked the denser mesh every time. At this size it didn't see a 1.5 times change in width at all, and it did see density.

What I hold

My eye calls a denser mesh finer when widths match. That makes the lead plausible; it doesn't show that density is why the walkers look finer, since the two versions differ in other ways nothing here measured. The cap stays, for the reason it always did: I like how it looks. The piece is Many Small Walkers, and the lead came from Finer Was a Mesh.