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.
Our family plays "Match Three" during long drives where one person comes up with three words and whoever correctly answers with a word that can complete or precede any of them becomes "it" and chooses the next set.
Homophones and proper nouns are considered acceptable.
So for example: (Fox, Lone, Crossed)
The answer would be: Star
Star Fox - a well known rail shooter originally on the SNES
Lone Starr - the only man who would dare give a raspberry to Dark Helmet
Star Crossed - a Shakespearean reference to two people whose relationship is doomed
Reminds me of https://en.wikipedia.org/wiki/Rhyming_slang: “The construction of rhyming slang involves replacing a common word with a phrase of two or more words, the last of which rhymes with the original word; then, in almost all cases, omitting, from the end of the phrase, the secondary rhyming word (which is thereafter implied)”
Is the example meant to rhyme, or is it an example of a subtle category of "words that only rhyme in some English accents"? "Offle Woffle" is somewhat standard American English, while "Orful Warful" would be British English.
You could add the additional constraint that the words have to insult the guesser based on their unique psychological vulnerabilities. Hope that helps!
My personal recommendation is this game1. Not for travel, but a very good in forcing interesting associations and making you mad at your partner, which is a certified sign of a good game.
If you like codenames, you might also enjoy decrypto [1], it scratches a very similar part of my brain. There's a set of secret words, and the codemaster needs to give clues that are specific enough that if you know the secret words, you can make the connection, but vague enough that you can't guess the secret words.
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.
The classic, "why did the chicken cross the road" also fits into this genre, but nobody seems to understand that "get to the other side" means "to cross over from life to death." Every time I explain this to someone they are shocked that they never knew this meaning.
That's a failure of the joke not to set it up -- one of the "top corners" of the square is missing. Chickens normally don't make an effort to get to the "other side" (as far as we're aware anyway).
To make the square you'd have to do something where the context of "the other side" means past life into death. e.g., "Why did the spiritualist put his ear towards the road? To hear from the other side."
It is easy to find references [1]. I always thought it referred to the Greek mythological river Styx, where crossing the river meant going to the underworld.
Gosh, after all those years I've only just realized the double meaning of "fruit flies". Thanks!
Before that, I just thought it was more of a non sequitur, but still amusing. There was just something inherently funny about imagining a banana hurling through the air in an awkward tumbling motion, right after the sagely abstract concept of time and its elegant arrow metaphor.
"Fruit flies like a banana" is arguably the quintessential example of ambiguity in English grammar. It shows that the grammatical structure of a sentence (which words are nouns, which are verbs, etc.) cannot be reliably recovered even if we know the meaning and possible grammatical categories of every word.
Both ways to parse it are grammatically sound:
(Fruit) (flies) (like a banana)
(Fruit flies) (like) (a banana)
To decide which meaning was likely intended, the listener needs to make a value judgement about the speaker, based on detailed knowledge of the everyday world.
Would marking compound words resolve this? As in germanic togetherwriting of things that form one whole, as in English' noun-that-they-modify-preceding adjectives, or as in some other language: some way of signaling this?
Is it a coincidence though? You could have started with the phrase "outstanding in his field", recognize the double entendre, and simply consider whether it's anyone's actual job to "stand in a field". Scarecrow is one of many possibilities.
It's pretty straightforward, top left "outstanding", bottom left "out, standing" connected as homonym, and then field on the right also homonyms. Both horizontals are phrases.
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.
In "The Man Who Mistook His Wife For A Hat," there's a chapter where Oliver Sacks makes a similar argument about music stemming from the case of two autistic twins who couldn't do arithmetic but played a game with each other where they named increasingly large primes. Basically says that music/harmony is a kind of innate appreciation of the numerical relationship between sounds, much like naming primes is an appreciation of the _lack_ of a numerical relationship between numbers. The experience of a resonance between two different things (frequencies, numbers, and in this blog's case words) can exist extremely strongly outside of the ability to operate on those things in the first place. Interesting read.
I've read that music and dancing memory is mainly handled in the cerebellum, which is separate from many other types of memory. This is also theorized to mostly explain why playing familiar music can help "stabilize" people with dementia who otherwise feel lost (funny enough also something Sacks has talked about[0]), because the cerebellum is typically less affected than the neocortex by whatever process is causing the brain to break down.
> 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!
Fun game! Though I dispute that people are "very close" to achieving a perfect pattern.
To get a "perfect" pattern you'd need to find three 7 letter words that can stack on rows adjacent to each other to form a 3 letter word in each column. Such arrangements do exist, for example:
o p e r a t e
a r r o w e d
r e s e n d s
but they are very rare - I estimate something on the order of 0.002% of combinations of three 7-letter words have any valid arrangements. Assuming that you're using standard ETAOIN letter frequencies, the typical bag of 21 letters will usually have just a handful of combinations of three 7-letter words so a given puzzle has a << 0.1% chance of having a perfect solution.
But there are 12,000x more ways to rearrange 21 tiles within an 8x3 grid, and the word choices are more forgiving as well (if you draw 7 letters from the etaoin frequency distribution, those 7 letters in order are much more likely to form a 3 letter word followed by a 4 letter word than they are to form a 7 letter word). Pretty much every puzzle should have at least some solutions fitting within an 8x3.
Additional note: 3 blank spaces is the best non-perfect arrangement, since the grid is only 10 tiles wide. One blank space could only be achieved by a single 23-letter-long word, and two blank spaces could only be achieved by a 10 letter word next to an 11 letter word, and an 11 letter word would not fit inside the 10x10 grid.
Glad you like it! :) And thank you for your comments, super interesting! Excellent point about the rarity of the perfect arrangement. Perhaps I should throw in a few lettersets that do have a solution, I am intrigued to see if people would discover it.
My other game, https://squareword.org focuses exclusively on perfect 5x5 squares, but here the goal is to uncover it wordle-style rather than arranging it from scratch. There are surprisingly few combinations that have ten unique, common words in a 5x5 letter square!
Puzzles that are always open is exactly what I mean, yeah.
Some "daily" games call this kind of generated puzzle a "practice" mode. But whenever I encounter a daily game, I go straight for that mode, which is what most games would just present as the game itself.
I think in Chinese this is literal for hand made (手工) - the gong 2nd character can also mean work or job I think - but the sex term of art I guess is different there. Haha
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" :-)
> 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.
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.
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).
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.
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.
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 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.
It's a cryptographic mechanism that allows you to see what was there in plain sight the whole time. Merkle-Dåmgard, Diffie-Hellman, cryptographic mechanisms are often named like this
I think Double Categories [1] would be a more appropriate setting: In a double category, the vertical and horizontal arrows are of different types. In usual commutative diagrams, they are of the same type.
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)_/¯
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.
There was a local food-truck operator named "Phở King" and eventually they established a storefront ... well, I see one closed, and another opened up. Formerly known as "Phở King Kitchen" and now there's the "Phở King Eggroll" place.
Fred Armisen did an SNL bit about this, too.
Not far from me, there is a ghost kitchen cluster. It's tucked away in a commercially-zoned neigborhood, and it serves all the food delivery services. Apparently, you can walk in too. I only accidentally patronized them once, when they had some great larb on offer. I think the report says there's 15 different menus and "virtual kitchens" in the building, just turning out food-to-go.
While it doesn't fully describe it, his category theory diagram reference seems relevant to me.
The stricter of the squares seem to be a homomorphism. But the "looser" ones which don't "preserve structure" after the transformation but "find a new structure" are some of the more interesting ones.
Semantic Bayesian hyper-graphs where each of the percepts have strong correlation between each other.
I’d argue you could bind them tighter by giving the corners strong relationships to each other as well.
We find these sorts of dense correlations pleasing because it’s the natural way we discover meaning. Even though in this case the meaning is fairly superficial.
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.
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