The collection

Every essay

One idea per essay, ordered so that the earlier ones set up the later ones — but nothing here depends on being read in sequence.

What cloth is

A fabric is a structure before it is a material. Interlacement, the draft as a matrix, and the question of whether a cloth holds together at all.

Weaves

Plain, twill and satin, and what actually separates them — float length, interlacing count, and a satin that cannot exist on six ends.

plainfloat 1 · 8 interlacingsfirmness 1.002/2 twillfloat 2 · 16 interlacingsfirmness 0.505-end satinfloat 4 · 20 interlacingsfirmness 0.40a filled square means the warp is on the facecounted from the matrices, not from the pictures

Plain, twill and satin

Three rules, and everything else in weaving is a variation on them. What separates the three is not appearance but one trade — how often a thread changes face against how far it runs when it does not.

10 figures
5-end satinwarp floats of 4weft floats of 120 markedruns measured round the repeatfloat 4

The float decides

How far a thread runs on the face before it goes under is one number, and it sits behind lustre, drape, snagging, abrasion, tear strength and how densely the cloth can be set. Almost nothing else in the subject has that reach.

7 figures
ordermoves that give a satinhow many3 endsnone — every step shares a factor with the order04 endsnone — every step shares a factor with the order05 ends2 326 endsnone — every step shares a factor with the order07 ends2 3 4 548 ends3 529 ends2 4 5 7410 ends3 7211 ends2 3 4 5 6 7 8 9812 ends5 7213 ends2 3 4 5 6 7 8 9 10 111014 ends3 5 9 114enumerated from the coprimality condition, not recalled3–14

There is no satin on six ends

Weavers have known it as a rule for centuries. It is a theorem with a one-line proof about common factors, and it rules out four ends as well.

6 figures
weaveinterlacingsdensest settingplain1.0020 per inch2/2 basket0.5027 per inch2/1 twill0.6724 per inch2/2 twill0.5027 per inch3/1 twill0.5027 per inch5-end satin0.4029 per inch8-end satin0.2532 per incha geometric jamming model, circular sections, yarn diameter 1/40 inch

Interlacings and firmness

Every time a thread changes face it has to bend, and a bend takes room. That one sentence decides how densely a cloth can be set, how firm it feels, and why the two run in opposite directions.

6 figures

Setting and geometry

Yarn diameter, crimp and cover. How close threads can be set, why thread count is not what it is taken for, and which model produced any number.

Knits and other structures

Loops rather than crossings. Why a knit stretches without a bias, why stockinette curls, and why a dropped stitch runs while a woven cloth frays.

Mechanics and drape

Cloth as a mechanism rather than a material. The bias, the angle at which threads jam, and why a flat sheet cannot cover a sphere.

Pattern and colour

A draft is a periodic plane pattern with two states, so the symmetry is two-coloured. Colour order, and the things the eye reliably gets wrong.