Say screw it and publish polynomial article

content/blog/search_polynomials.md

@@ -1,7 +1,6 @@
 ---
 title: "Search as a Polynomial"
-date: 2022-10-22T14:51:15-07:00
+date: 2023-05-22T21:39:00-07:00
-draft: true
 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!