[meta] Leitmotif

[maradydd]

It occurred to me that I should say a little about the common thread that underpins pretty much everything I've written here since lifting radio silence, and will continue to do so for some time.

So I alluded to the whole aspie thing 1 a few posts back. The interesting thing there is, when I first decided to look into the various non-normative

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[michiexile]

So Fink & Mao published a few articles back at this past «mille anni passi sunt»; using ideas from statistical mechanics (read combinatorics) to figure out a classification of possible tie knots for formal neckties.

Turns out that what they did was to articulate a formal grammar for tie-tying. Once you've started tying your tie, it basically builds up a Y-shape across your front.

So you can describe a tie-knot by the sequence of areas (right/left/center) that the active end moves into. Fink&Mao explicitly signal which area you move to, and which orientation your tie has -- but also articulate axioms for their language that reduces it to basically free strings in the alphabet { Clockwise, Anticlockwise } with added decorations to show how and when you push the tie underneath itself. Not only that, but checking whether you can dissolve a tie (pull out the passive end and it unknots itself) can be determined by using a few simple rewriting rules on your tie description string. If the string vanishes under these rules, it will unknot itself, if not, then not.

Together with Anders Sandberg and Primoz Skraba I'm working on an extension of their work that demonstrates this reduction, and studies tie knots that fall outside their (too narrow) demarkations.