I'm a big fan of killing time on long drives with friendly word games. One of my favorites is a mix between rhyming and square theory. Here's how it works: one player picks two words that rhyme perfectly. Then, for each of those words, they choose a clue word, usually a synonym, but any kind of related word is fair game. They say those two clue words out loud, and the other players have to guess the original rhyming pair.

What makes it fun is trying to reverse-engineer the original rhyme from the clues. It's like solving a little logic puzzle. It's easy to come up with new puzzles, but cracking them can be surprisingly tricky. Still, the structure gives just enough to keep it solvable most of the time.

1. Somewhat described here https://bestlifeonline.com/jeopardy-rhyme-time-opera-version... It's actually quite difficult to find a description of the category many of us are already familiar with.

The part about dad joke square theory got me thinking about this classic scarecrow joke, which feels like an example from some higher order version of square theory:

"Why was the scarecrow given an award?"

"He was out standing in his field."

The fact that a scarecrow's job is to be "out standing in his field", and that excelling at one's job can be phrased as being "outstanding in his field" is an incredible linguistic coincidence.

Leibnitz once famously said, "Music is the pleasure the human mind experiences from counting without being aware that it is counting". Perhaps solving crosswords is the pleasure mind experiences from doing group theory.

> If you’ve ever tried to construct a crossword, you’ll find that the framing of a crossword grid under square theory feels right. When you’re nearing the end of the grid-filling process, finding valid crossings of words to fill that final corner of a grid, there’s a satisfying “clicking” feeling—a sense of magic—when it all fits together, analogous to the wrapping-around feeling of completing the square.

If you enjoy this feeling, I think you would like my word game https://spaceword.org. The goal is to arrange 21 letters in a square that is as tight as possible. No one has achieved a "perfect" pattern yet, but people are very close, often leaving only 3 spaces blank!

Aargh! I hate it when people quote text as images because it makes it impossible to cut and paste.

> Jet black/Jet Blue ... catnap/dognap

My favorite examples are how prepositions can change the meanings of idioms. For example, to be "down for" something and "down with" something mean the same thing, but to be "down on" something means the opposite. (And going down to X means something very, very different from going down on X. That last example is also interesting from a geeky HN point of view because the preposition imposes a type constraint on the binding of X, which is why I had to use "X" instead of "something" :-)

My favorite example, which was an honest translation error from a non-native speaker friend: Hand job (he meant to say manual labor)

This is clever, and I want to spend some more time thinking about it. In a sense, I think this is basically saying that you can put the standard SAT-style analogy questions ("Lumen : Brightness = Inches : Length") in a square, and that most crossword clues could be represented as weird SAT analogies. Or maybe I'm stretching the analogy.

But I think that the "Diagonal" that the author suggests for the connection between "Donkey" and "Elephant" and "Party" isn't quite correct. The key is that both the Donkey and the Elephant are a "Party Animal." You can't ignore the "Animal" part, it describes them: they are each the animal that represents their party, the "party animal."

I'm not sure the correct way to represent this in "Square Theory," but it's not just linking "Party" to the animal in question.

Kind of exciting to see Algirdas Greimas' semiotic square derived from (game) first principles!

[0]: https://en.m.wikipedia.org/wiki/Semiotic_square

What a lovely post.

The "Grubhub" square fits some other alternatives: "Grubclub", "Bitesite", or "Eatmeet" (but eww).

> But here’s what I think makes squares special: a square is the simplest polygon that has non-adjacent sides. In a triangle, each side is adjacent to the other two sides. But in a square, opposite sides have no points in common, which makes any connection between them feel surprising, like a coincidence. In pentagons and beyond, this still holds, but the extra sides add complexity that make them feel slightly less elegant. Nevertheless, other shapes can be interesting too, but I see them as the exception, not the rule.

I bet that you could fit the "clever bits" of writing of quite a few literary classics into more complex shapes. Especially when it's the ons that only people who really like literary classics like. Like, say, a story with five main characters who all turn out to be connected in one way like how one might create a five-pointed star with one piece of string and five push-pins, and in a completely different unrelated way like a pentagon made by the same arrangement of push-pins.

Nice article! It feels like there should be something AI-zeitgeist-related in there referencing word2vec or similar.

OT: Going by the url, link here on HN and slightly adjacenty vibe I got to the bottom and signature before realizing this wasn't Shtetl-Optimized finally made mobile-friendly.

one of my favourite english curiosities follows this structure - "outgoing" and "retiring" are both perfect antonyms (enjoying or not enjoying socializing) and perfect synonyms (leaving a political office or job)

This is not surprising at all if you know:

1. Cryptic crosswords (1920s) - the only interesting crosswords.

2. "Metaphors We Live By" Lakoff & Johnson (1980), or perhaps just "Roget's Thesaurus" (1805) long before that (synonyms, antonyms), and obviously homonyms.

3. A little bit of Category Theory, but not too much, just the amount that occurs to you after 1 & 2. An alternative entry point might be knowledge graphs (1990s).

> However, there’s nothing about the square structure that dictates the edges must represent phrases and synonyms.

I got there and thought "Category theory", and, lo, that's the next paragraph.

> Let’s talk about Scrabble, one of the seven most important games [link to review of Seven Games book] https://www.nytimes.com/2022/01/25/books/review/seven-games-...

Seven Games was mentioned in another HN discussion last week, by 'danvk talking about his Boggle solution: https://news.ycombinator.com/item?id=44084022

HN hasn't yet taken an interest in that: https://hn.algolia.com/?dateRange=all&page=0&prefix=false&qu...

The obvious question to ask is could you take it to the third dimension and make a cube out of double-doubles? What about other shapes, perhaps a pyramid or a tetrahedron? Squares are simple enough that it's still easy to come up with examples, but I think a graph with higher edges-to-vertices ratio would be even more satisfying.

There are a number of comedic sketches based on the linguistic similarity of "booty call" and "butt dial."

what a lovely Baader-Meinhof for Ricki Heicklen's delightful "Unparalleled Misalignments", which showed up on HN not too long ago!

This reminds me of the so-called "heartless couplet" (无情对) in Chinese. Every pair of words in the couplets are synonymous or anonymous, and yet the meanings of the couplets are completely unrelated, often in a humorous way.

I came up with a (lambda? Triangle?) loop a few days ago.

Read until sleepy. Sleep until ready.

GrubHub is certainly a good name, but if I came across an app actually named "Food Central-Place" I would have no choice but to install it on the spot. It just has a certain anti-ring to it.

https://en.wikipedia.org/wiki/Commutative_diagram

If any good frontend/mobile devs here like crosswords, I need a good frontend for picture crossword designer/generator https://crosswordcomputer.com

The author of this post would love the video game Lingo:

https://store.steampowered.com/app/1814170/Lingo/

This is pretty cool. I wonder what logic/math describes it?

Huge fun. Besides mixing/matching like this I mix across languages and that give an extra dimension to create such fun phrases.

This feels a little over blown, but on the other hand, you've got to have an angle and I think this is the right angle.

Great article, but I can't believe it didn't mention the sator square!

SATOR

AREPO

TENET

OPERA

ROTAS

(Very easy to commit to memory too since most of the letters are right there in the name!)

How can someone hate "étui" so bad !?

Fun read. As they say in New York, Arigato!

A matrix is a matrix, namely two triangles reflected about a diagonal. No wonder they are frequently used in computer science and general problem-solving ¯\_(ツ)_/¯

Something similar is going on with https://xkcd.com/1645/ . They even both mention platonic solids:

>Platonic solids for my real friends and real solids for my platonic friends!

Definitely gonna be mentally yelling "THAT'S A SQUARE" every time I see a clever pun or a satisfyingly constructed theme from now on

Wordcels discover category theory lol