I've watched a few videos from the Cracking the Cryptic channel, which is mentioned in the article. I've only ever solved a few easy sudokus myself, but for some reason it's really satisfying to...

I've watched a few videos from the Cracking the Cryptic channel, which is mentioned in the article. I've only ever solved a few easy sudokus myself, but for some reason it's really satisfying to watch a master solving fiendishly difficult ones. My favorite video of theirs that I've watched has to be this one, which features an anti-sudoku. The puzzle is constructed such that normal sudoku rules cannot apply. I think it's one of, if not the longest solve on the channel.

I think it ties into what the article is saying about ontological remodeling. You can tell how hard it is, even for a very skilled solver, because none of the usual tricks apply. But you can also watch the pure joy as Simon figures out some unstated rules that follow from the premise, but are not explicitly stated.

Like I said, I don't really solve sudokus. But I do solve a lot of chess puzzles, and there's definitely some overlap with what the article is talking about. My least favorite type of chess puzzle is pawn endgames, because I'm so bad at them. Seemingly, they should be the easiest kind of puzzle (except maybe trivial checkmates), because there's so few pieces on the board. Only kings and pawns. No tricky knights jumping around or queens that can whizz around the board. But they're actually really, really difficult. Often they require you to calculate many, many moves down the line very precisely. They are much trickier than many positions that have a bunch of different pieces on the board.

However, there are many, many different techniques that apply to such seemingly simple positions. Sometimes, solving a puzzle can be fiendishly difficult if you haven't internalized the pattern, but if you have, it's only a matter of recognizing it, and then the actual solve is a straightforward application of a memorized pattern. Things like triangulation or corresponding squares. These concepts are nowhere to be found in the rules of chess - yet they follow logically from them. You need a new vocabulary to describe them.

This is the hallmark of problems solved by ontological remodeling. You don’t want to say they’re tricky, exactly, because the new framework makes them feel pretty approachable. But without the new framework, they’re basically impossible. Trying to describe the difficulty of these problems is something of a trap, because so much of the difficulty depends on the description. Instead, you need to play around with new forms of expression and see which patterns are easy to describe with those forms.

The sheer simplicity of Sudoku makes it an excellent example for how powerful ontological remodeling can be even when it seems obvious which form to represent things in. Even if your generating rules are all related to rows, columns, and boxes, they can interact in such a way that you need new language to describe the interaction. In fact, this has become something of a sport on the channel, with puzzles like this one that start by showing a computer solver unable to solve a classic Sudoku logically (only getting the solution through brute forcing all possibilities), then setting a human loose on the puzzle to discover the hidden trick.

I've watched a few videos from the Cracking the Cryptic channel, which is mentioned in the article. I've only ever solved a few easy sudokus myself, but for some reason it's really satisfying to watch a master solving fiendishly difficult ones. My favorite video of theirs that I've watched has to be this one, which features an anti-sudoku. The puzzle is constructed such that normal sudoku rules

cannotapply. I think it's one of, if not the longest solve on the channel.I think it ties into what the article is saying about ontological remodeling. You can tell how hard it is, even for a very skilled solver, because none of the usual tricks apply. But you can also watch the pure joy as Simon figures out some unstated rules that follow from the premise, but are not explicitly stated.

Like I said, I don't really solve sudokus. But I do solve a lot of chess puzzles, and there's definitely some overlap with what the article is talking about. My least favorite type of chess puzzle is pawn endgames, because I'm so bad at them. Seemingly, they should be the easiest kind of puzzle (except maybe trivial checkmates), because there's so few pieces on the board. Only kings and pawns. No tricky knights jumping around or queens that can whizz around the board. But they're actually really, really difficult. Often they require you to calculate many, many moves down the line very precisely. They are much trickier than many positions that have a bunch of different pieces on the board.

However, there are many, many different techniques that apply to such seemingly simple positions. Sometimes, solving a puzzle can be fiendishly difficult if you haven't internalized the pattern, but if you have, it's only a matter of recognizing it, and then the actual solve is a straightforward application of a memorized pattern. Things like triangulation or corresponding squares. These concepts are nowhere to be found in the rules of chess - yet they follow logically from them. You need a new vocabulary to describe them.

From the article: