Square Theory
104 comments
·May 27, 2025kelseyfrog
vunderba
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 doomedkelseyfrog
Love it! Does the person who comes up with three words have the connecting word in mind from the beginning, or no?
Someone
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)”
jamiek88
Yep, ‘that’s pony’ means ‘that’s crap’. From pony and trap. You omit the actual word that rhymes.
Nice whistle mate! (I like your suit, from whistle and flute).
It’s fun to figure them out.
Agentlien
A few years ago I did something similar in a group chat with some friends. No rhyme, but video game titles reworded using rough synonyms.
Here are some examples with answers in rot13:
Strange, this reunion = Zntvp gur Tngurevat
Boat pork refuge = Nexunz Nflyhz
Donkeybutt taverns gospel = Nffnffvaf Perrq
Caring for the elderly = QBGN
Belongs to me create = Zvarpensg
Superclock = Birejngpu
Top Stories = Ncrk Yrtraqf
Skyline no morning = Ubevmba Mreb Qnja
finnh
My family calls that game "pink mink"!
jacobolus
As far as I know the most common name is "hink pink", if anyone wants to look this up (or sometimes "hinky pinky"). Here's a 1981 book, https://archive.org/details/hinkpinkbookorwh00burn/ and here's a short description from the 50s, https://archive.org/details/realbookofgames0000unse/page/134... Searching further, apparently Hink Pink was the name of an 18th century pirate ship; I'm not sure if there's a relation to the game.
According to this 1941 Life Magazine issue, teenage girls in Atlanta were making up rhyming pairs like this at the time under the name "stinky pinky". https://archive.org/details/Life-1941-01-27-Vol-10-No-4/mode... Webster's Dictionary from the 60s has the game listed under that name, https://archive.org/details/webstersthirdnew0000phil_l0b1/mo... and that name also seems to continue to today, e.g. by the radio show Loveline.
staffordrj
I made a daily game version of this https://rystaf.github.io/hinklepinkle/
kelseyfrog
Thank you! What a fantastic find. This is exactly the kind of book I would have checked out at the library as a child.
It's possible I found this decades ago and the origin of how I learned this game was lost to time :)
jonny_eh
We call it Awful Waffle, based on a Board Game called Brain Strain. They had "Awful Waffle" as an example.
https://boardgamegeek.com/boardgame/8785/brain-strain
I made a proof-of-concept daily game: https://awfulwaffle.jonabrams.com/
mattclarkdotnet
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.
bdr
Stinky Pinky! https://www.nosupplies.com/play/stinky-pinky
cooperaustinj
Do you know any unfriendly word games I can try?
kelseyfrog
You could add the additional constraint that the words have to insult the guesser based on their unique psychological vulnerabilities. Hope that helps!
kragen
Posting on HN counts.
stronglikedan
Perhaps give the Argument Clinic a call.
null
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gostsamo
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.
gms7777
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.
joshhug
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.
j2kun
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.
wavemode
My understanding is that that interpretation is an urban legend.
Wikipedia attributes the joke to an 1847 article, which is phrased in a way that clearly isn't intended to have some deeper meaning: https://en.wikipedia.org/wiki/Why_did_the_chicken_cross_the_...
j2kun
TIL, thanks!
gwd
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."
jagged-chisel
If you cross the wrong person, they just might send you to the other side.
I don’t know how to make the chicken crossing the road use this meaning, but … well, there it is.
Upvoter33
That is funny. We finally figured out this double meaning a few years ago and I have been on the same quest since.
albedoa
> Every time I explain this to someone they are shocked that they never knew this meaning.
You might have taken this as a hint?
cdkmoose
Also, My friend accidentally drank a bottle of invisible ink... she's at the hospital now, waiting to be seen.
"Waiting to be seen" having slightly different meaning with respect to hospitals and invisible ink.
simianparrot
For some reason this old saying popped into my head reading that. I know it's not related but:
Time flies like an arrow. Fruit flies like a banana.
yojo
My favorite part about that quote is the broken symmetry between the double meaning of the second sentence and the single meaning of the first.
It begs one to consider the possibility of little “time flies” snacking on arrows. Which I guess completes the square?
anyfoo
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.
akoboldfrying
"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.
frogulis
Even spoken aloud, there's a natural-sounding stress pattern that is ambiguous. Love it.
abhpro
I assume stuff like this is why some languages or script can never be deciphered
notfed
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.
thejohnconway
I think the meanings are pretty close though? Not coincidental: to be prominent in an area.
preciousoo
If you use TikTok, search up “to the untrained ear”. You’d love those. Maybe they’re on YouTube too
rlonn
If any good frontend/mobile devs here like crosswords, I need a good frontend for picture crossword designer/generator https://crosswordcomputer.com
varjag
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.
wttdotm
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.
oliwary
> 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!
JoshuaDavid
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 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.
isodude
My first initial thought when I saw the game: spaceword golf.
Like any golf, you start with the smallest square possible and increase it with each level. You get less points for how perfect the the square is.
JoshTriplett
Do you have a version of spaceword that's not a "daily" game? I'd be interested in trying it if so.
oliwary
There is a weekly mode with 63 letters, thinking of adding a monthly mode as well. Or would you prefer puzzles that are always open?
JoshTriplett
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.
cshimmin
My favorite example, which was an honest translation error from a non-native speaker friend: Hand job (he meant to say manual labor)
zahlman
Something similar once famously happened with a Japanese vtuber: https://www.youtube.com/watch?v=UeQ5K5DQiDI
emmelaich
To save everyone a click .. it was 'handjob' for 'handwriting'
tclancy
There’s a joke in The Jerk that uses this same intentional misunderstanding.
keepamovin
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
lubujackson
Heard from a non-native speaker watching a missed basket in a basketball game: "Another rim job!"
lisper
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" :-)
kps
> I hate it when people quote text as images because it makes it impossible to cut and paste.
Yes. In this case the text is in the ALT tag, which would help if browsers exposed it.
robinhouston
> I hate it when people quote text as images because it makes it impossible to cut and paste.
That's much less true than it used to be! I don't know what device you're using, but on my iPhone I can seamlessly copy the text from that image.
lisper
I'm using Firefox on a Mac.
layer8
https://support.mozilla.org/en-US/kb/text-recognition
Doesn’t this work?
bee_rider
Down for lunch?
Down with lunch!
(Breakfast food is yummier).
teach
And "down for" something is very nearly synonymous with "up for" something. (:
andriamanitra
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.
dleeftink
Kind of exciting to see Algirdas Greimas' semiotic square derived from (game) first principles!
SamBam
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.
mellosouls
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.
noirchen
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'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.