Meetup summary

2025-01-10 - Knovel knaughts

  • All the introductory reading on formal power series and computation from the classical methods meetup. on formal power series.
  • Review how painful it was to extract coefficients of a composition of power series even in O(n3)O(n^3) time using classical techniques.
  • M. Douglas McIlroy’s Power series, power serious functional pearl from JFP. This is a wonderful introduction to practical computing with power series, which themselves have direct connections to Analytic Combinatorics through generating functions. It shows how lazy (but automatically memoized) stream types (such as Haskell’s lists) make these computations signifcantly simpler than doing things the “direct” way.
  • Spend some time thinking about your novel knot/novel knot integration for show and tell.

Agenda:

  • Novel Knots show and tell. Try to show up with some unique not that you developed or else some unique way of putting knots together in a working, practical system (or aesthetic display). It’s fine if you later discover that your knot or system was already developed elsewhere; the idea is to get the creative juices flowing and explore how knots work.
    • Check out the novel knots or knot systems/integrations everybody has developed over the past few weeks.
    • Critique and enhance each others’ discoveries.
  • Work through the Power Series, Power Serious paper. The goal is to get through all basic series operations (including series composition; the same stuff we did with classical techniques).
    • I don’t expect to get through “advanced” use cases involving reversion, differentiation/integration, or differential equations. We can do a follow-up session on that if there’s interest.
  • Compare the lazy technique to the classical technique from last time.
    • Ease or difficulty of implementation.
    • Understandability (especially for somebody without the requisite background).
    • Runtime and space usage.

Notes:

We didn’t even get to the power series paper and instead spent the whole time discussing knots.

Knots worth mentioning:

  • Reever knot as a binding knot (e.g., for securing shoe laces)
  • Reever knot on a bight. (Technically, on a one-sided bight; one side must have a working end). This knot has many potential use cases, though I haven’t heard of anybody else using such a knot. I took a video of tying it a few months ago but still need to upload it. Link pending.
  • A clever technique for slipping a stopper knot through a rap ring such that you load the main line through the stopper knot and then untie it by pulling on a tag line. Theoretically interesting in the context of doing a long rappel where you need to recover the rope but don’t want to carry twice the rappel length in full-width line. Terrifying practically speaking due to the construction not being inherently secure. (I’m curious if anybody has used similar tricks in practice.)
  • Triple pretzel knot. (Literally in the form of fresh-made soft pretzels—tasty!)

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