From 5910ce7980ab6c1d84687d011542ea3ec35563b3 Mon Sep 17 00:00:00 2001 From: Danila Fedorin Date: Mon, 22 May 2023 21:42:32 -0700 Subject: [PATCH] Say screw it and publish polynomial article --- content/blog/search_polynomials.md | 21 +++++++++++++++++++-- 1 file changed, 19 insertions(+), 2 deletions(-) diff --git a/content/blog/search_polynomials.md b/content/blog/search_polynomials.md index 3370121..786f4ba 100644 --- a/content/blog/search_polynomials.md +++ b/content/blog/search_polynomials.md @@ -1,7 +1,6 @@ --- title: "Search as a Polynomial" -date: 2022-10-22T14:51:15-07:00 -draft: true +date: 2023-05-22T21:39:00-07:00 tags: ["Mathematics"] discussionRooms: ["!qLoehEvJNRndNrdlyU:matrix.org"] --- @@ -486,3 +485,21 @@ two trips of equal druation but different length (two-hour trip from A to B followed by a two-hour trip from B to C, or one-hour trip from A to C followed by a three-hour trip from B to C). The first trip wins out, since it requires only \\(3.0\\) units of distance. + +### Anything but Routes +So far, all I've done can be reduced to variations on a theme: keeping track +of some aspects of a trip between cities, using polynomials for structure. +However, that's just the beginning. This sort of trick can be be made even +more powerful by further relaxing the notion of a "polynomial". By doing so, +we can make our polynomials represent arbitrary _effects_ (in the computer +science sense -- things like errors, logging to a console, storing and +accessing information from a database). Relying for just a little longer on +our example of journeys between cities, we might be able to represent trips +with random variation (traffic can be unpredicatable!), or maybe cities where +you will get stuck. But the point isn't routes: the same approach can be +used to represent traversing a binary tree, performing Prolog-like proof +search, or evaluating a non-deterministic program. The sky's the limit! + +Unfortunately, doing so would require even more background and buildup, for +which I just don't have space for in this article. I'll save these +things for next time, though -- stay tuned!