• pu pi toki pona: A case study in orthodoxy

    toki pona is a minimalist constructed language, created by linguist Sonja Lang between 2001 and 2014. It features 9 consonants and 5 vowels in its phonemic inventory (cf. most dialects of English at 24 and 14-25), and those 14 phonemes combine into a 123-word vernacular. The standard reference document on the conlang is currently Lang’s book from 2014. There are many things to find fascinating about toki pona, but the one I’d like to explore in detail right now is this: toki pona dedicates one of its 123 words to that specific book, despite not having a word for “book”...

  • Introducing: Comments!

    For a long time, I’ve wanted comments for my Jekyll-based ‘blog. However, the existing alternatives, Disqus and Staticman, were not satisfactory, so I decided to roll up my own implementation. It has certain drawbacks that might make it unsuitable for most applications, but I would like to tell its story here anyway, because it would not have been possible without the ‘blog posts by others...

  • The cheapest path problem and idempotent semirings

    Let me propose a interesting theoretical variant of the shortest path problem. You have a directed graph with source and target vertices, and every edge has a cost to traverse it. However, not every cost is in good old American dollars—some are in alternative currencies, and you don’t know what the exchange rates will be until the day of your trip...

  • Prime Filters in Distributive Lattices III

    Recall from PFDL II, I gave an interesting characterization of Boolean algebras among distributive lattices, using a technique from formal logic. Today I’d like to share some final musings on the topic, specifically in the form of a counterexample to a weakening of the hypotheses...

  • Review of This 'Blog

    This ‘blog has a lot of lattices in it. ¶ Some of them are kinda hard to imagine, like countable boolean algebras, where you have to use your brain and count or something. Some of them are really hard to imagine, like the free modular lattice on three generators, which for some strange reason is finite and proving that requires over a half hour of computations...

  • An excluded subobject theorem for nondistributive lattices

    I gave a talk yesterday at the PMC’s SASMS. I typeset some notes, and I thought I would share them because I drew pictures. This typeset version has more details and less visual intuition than what I presented on the blackboard, which is why the whole thing fit into a half hour. Find a link to the notes and some flavour text under the cut...

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