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" :-)
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
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.
> 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!
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.
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!
I struggled on a few days' puzzles under the assumption that there _was_ a perfect solution possible -- It may be worth noting in the "help" that not all lettersets can be solved perfectly.
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.
You could add the additional constraint that the words have to insult the guesser based on their unique psychological vulnerabilities. Hope that helps!
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)”
for the record, i can't find any combination of those words in my transcriptions of loveline shows, although i don't have them all, and it is possible there are up to 50% transcription errors. there is 1 reference to "Stinky Linky" but it appears unrelated, "what's the linky?" "freckles" - i got excited that i found it but looking at the context it was in vain.
i have five clean references to "as a mason jar" so my collection is fairly complete ;-)
Oh, then i concur with your prior statement that it "continues [...] today"; i define "LoveLine" differently. Someday i'll find the time to get "fills" - i only have 5.5 years fully transcribed.
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.
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.
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
Thanks yeah it's a very fun game! When you're creating a new "match three" on the fly, I find it's easiest to start with a common word and work your way backwards until you've got three that fit.
There have been occasions where the answer was not the intended one, but it still fits all three and that's considered fair game!
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.
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?
It would definitely help with written English, but I can't see it helping with spoken. (Is there some rule in German that disambiguates togetherwritten nouns when spoken?)
I actually wrote about speech but thought it distracted from the question and removed it again
No, in speech we seem to get by without spaces, and that's in every language that I'm aware of, but then we also don't have commas, parentheses, apostrophes, or capital letters. Somehow, intonation and emphasis must replace these (or rather, writing encodes our speech somehow) but I'm not sure how they map exactly. Question marks indicate a rising tone for example, that's about the extent of what I know
As a child learning to write, I had a phase where I put whole sentences together because that made sense to me as the next step after we learned to write letters together to form words. It took quite some convincing before I believed that adults don't secretly do this and they're only telling us to add space because they think we're not ready for the next step. I guess I innately thought words belong together and we only add a pause between sentences
There is one speech pattern where spaces can be heard though. Like in English, when you enunciate very clearly because the person isn't understanding (for example, if their English is very poor, or when you're shouting across a long distance), similarly in germanic languages I'd add time between each word, and nearly none if it's a compound word. Like how you'd pause between "get" and "out" if you want to make yourself extremely well understood, but afaik not/barely between "handy" and "man" or "quag" and "mire" because the parts haven't the same meaning, or aren't understood at all anymore, in isolation
Now I'm curious actually, might English native speakers also add less time between compound nouns/adjectives in this speech mode? So not like "quag" and "mire" but something that's commonly written apart, like "bottle cap". Do they (you?) identify and indicate things that form one concept also by separating them less, and only the written encoding is different between the languages, or do they feel like the words are fundamentally separate things in the same way that "go" and "home" are separate parts of speech?
The only pattern I know for sure is that compound words in English tend to begin their lives in hyphenated form (news-paper, life-style, e-mail) and then the hyphen gradually disappears over time. Old enough newspapers still show these words with hyphens in.
I think the hyphen removal follows the typical speech pattern in which the syllables are rushed together just like the syllables of other words, but I'm not sure.
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.
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.
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.
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.
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.
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
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)
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.
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)_/¯
143 comments
[ 2.9 ms ] story [ 177 ms ] thread> 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" :-)
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.
Doesn’t this work?
Down with lunch!
(Breakfast food is yummier).
Yes. In this case the text is in the ALT tag, which would help if browsers exposed it.
Which attractive terrorists?
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.
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.
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!
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.
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:
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.
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!
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.
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.
Nice whistle mate! (I like your suit, from whistle and flute).
It’s fun to figure them out.
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.
It's possible I found this decades ago and the origin of how I learned this game was lost to time :)
i have five clean references to "as a mason jar" so my collection is fairly complete ;-)
note: ripgrep 4.079s wall; ag (silversearcher) 5.916s wall; grep 6.940s wall
Sorry about that.
https://boardgamegeek.com/boardgame/8785/brain-strain
I made a proof-of-concept daily game: https://awfulwaffle.jonabrams.com/
1 https://boardgamegeek.com/boardgame/178900/codenames
[1] https://boardgamegeek.com/boardgame/225694/decrypto
Homophones and proper nouns are considered acceptable.
So for example: (Fox, Lone, Crossed)
The answer would be: Star
There have been occasions where the answer was not the intended one, but it still fits all three and that's considered fair game!
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
"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.
"Waiting to be seen" having slightly different meaning with respect to hospitals and invisible ink.
The success of that initiative remains to be seen.
Is what you reminded me of. Technically first it was "fuckin' Mitch!" Because Hedburg sprayed reappearing disappearing ink on someone's shirt.
Time flies like an arrow. Fruit flies like a banana.
It begs one to consider the possibility of little “time flies” snacking on arrows. Which I guess completes the square?
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.
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.
No, in speech we seem to get by without spaces, and that's in every language that I'm aware of, but then we also don't have commas, parentheses, apostrophes, or capital letters. Somehow, intonation and emphasis must replace these (or rather, writing encodes our speech somehow) but I'm not sure how they map exactly. Question marks indicate a rising tone for example, that's about the extent of what I know
As a child learning to write, I had a phase where I put whole sentences together because that made sense to me as the next step after we learned to write letters together to form words. It took quite some convincing before I believed that adults don't secretly do this and they're only telling us to add space because they think we're not ready for the next step. I guess I innately thought words belong together and we only add a pause between sentences
There is one speech pattern where spaces can be heard though. Like in English, when you enunciate very clearly because the person isn't understanding (for example, if their English is very poor, or when you're shouting across a long distance), similarly in germanic languages I'd add time between each word, and nearly none if it's a compound word. Like how you'd pause between "get" and "out" if you want to make yourself extremely well understood, but afaik not/barely between "handy" and "man" or "quag" and "mire" because the parts haven't the same meaning, or aren't understood at all anymore, in isolation
Now I'm curious actually, might English native speakers also add less time between compound nouns/adjectives in this speech mode? So not like "quag" and "mire" but something that's commonly written apart, like "bottle cap". Do they (you?) identify and indicate things that form one concept also by separating them less, and only the written encoding is different between the languages, or do they feel like the words are fundamentally separate things in the same way that "go" and "home" are separate parts of speech?
I think the hyphen removal follows the typical speech pattern in which the syllables are rushed together just like the syllables of other words, but I'm not sure.
0. https://en.wikipedia.org/wiki/Garden-path_sentence?wprov=sfl...
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."
I don’t know how to make the chicken crossing the road use this meaning, but … well, there it is.
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_...
You might have taken this as a hint?
[1]: https://en.wiktionary.org/wiki/other_side
[1]: https://ncatlab.org/nlab/show/double+category
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.
[0] https://www.youtube.com/watch?v=8HLEr-zP3fc
[0] https://link.springer.com/article/10.1023/A:1008290415597
The "Grubhub" square fits some other alternatives: "Grubclub", "Bitesite", or "Eatmeet" (but eww).
[0]: https://en.m.wikipedia.org/wiki/Semiotic_square
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...
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.
Read until sleepy. Sleep until ready.
https://store.steampowered.com/app/1814170/Lingo/
SATOR
AREPO
TENET
OPERA
ROTAS
(Very easy to commit to memory too since most of the letters are right there in the name!)
https://www.thaifoodnearmenyc.com/
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.