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miri makes things

Book words, topology words

Published: 2023-7-25

I like to make books sometimes. Pictured above is the first book sewing pattern I ever made myself, and the book that resulted from it. I have a plan. It involves making a little digital tool so that I can do stuff like design more sewing patterns without running out of mechnical pencil lead.

This will require me to figure out some stuff that involves how book sewing structures work, and that means looking at how thread works, too, and how knots work. This means working with topology and knot theory, which I am extremely familiar with on a practical level and extremely unfamiliar with on an academic level.

But here’s something cool: a mathematical knot is contiguous. As far as I understand, if you held one in your hands, started at a certain point on it, and kept on going so you touched every part of it, you’d always get back to where you started.

And that’s also true of the thread in the book I made above, if you were to rip all of the thread out of that book and hold it in your hands, which, please don’t do that.

A disclaimer: I’m not a topologist or a mathematician. I’m also a hobbyist bookbinder, not a professional one. What this means: I’m almost certainly going to use at least one term wrong at some point. Just roll with it and/or consider these terms idiosyncratic by default.

So, let’s define some terms.

Some book terms

  • Sheet: You know this one.
  • Signature: Several sheets stacked and folded together.
    • The book pictured above has five.
    • Metonymically named for the marks binders put on them to keep track of their order and/or origin.
  • Station: Take a needle, put thread on it, poke a hole with it through the cover. That hole is one station.
    • There are technically kinds of stations that have more than one hole but I’m using a simplified definition here.
  • Sewing (n.): In a book sewn with one continuous piece of thread (like with the picture above), I’ll be using the word “sewing” to refer to the gestalt of the stations, holes, thread, and knots that tie the thread to itself.
  • Sewing pattern: The reproducible steps one takes to produce a sewing.

Some math terms

  • Plane: Per Wikipedia, “A flat two-dimensional surface that extends indefinitely”.
    • Because paper is expensive the planes I will be discussing are not infinitely large.
    • If you would like to fund me making an infinitely large book please contact me.
  • Vector: A line segment with a direction. This means it has:
    • A tail / start point.
    • A head / end point.
    • An orientation.
    • A magnitude (how long the line is)
      • The magnitude can be 0, in which case we’re talking about a point that’s technically going somewhere but also never getting there.

In book topology terms: if you take a threaded needle, poke it into a piece of paper, and then back out the other end, the length of thread in between the two holes can be represented as a vector.

Which means I’m pretty sure I’ll be able to get away with treating each book sewing as fundamentally being an ordered array of vectors. There are a lot of exceptions, but that’s for the next post. I’ll also talk about how a book is a planar sandwich, so, get stoked.