Linear algebra explains why some words are effectively untranslatable

This is also why lawyer speak is so particular. Language is fuzzy in most cases. Only language that relates to discrete physical objects gets closer to the binary state of exactness described in the article.

But that's true of any language. Not only that, but English uses loanwords heavily which are often Anglicisations of words from other languages, which may not in themselves be just one word.

"Ho ho ho", the flag-waving Little Englander types say, "Gaelic is such a stupid language, they don't even have a word for 'television', they just say 'television' in a stupid accent!"

But English also has no word for "television". Worse, the word "television" isn't even just a loanword, it's two words from two different languages, "tele" from Greek and "vision" from Latin. What a bodge job! Imagine letting something like that slip through to production use!

The hypothetical Catalan-Hungarian inventor of it in another leg of the trousers of time may have called it llunylátás, and then where would we be?

Well, most languages would have some variant of that word to mean "television", as they do now, I expect.

The English word "galore" (meaning "sufficient" shading towards "more than enough") comes from the Gaelic words "gu leòr", (goo lyaawr, the grave accent above the o makes the vowel sound longer). What a silly language English is, doesn't have a word that means "more than you're ever likely to need", has to steal one from Gaelic and then spell it wrong.

Oh, they use this word "whisky". You know what that means? It means "uisge beatha" but they only say the first word, in a silly accent because they can't pronounce it properly.

Quite often there's no single word for a thing you're trying to translate but that doesn't mean it's untranslateable. English has only one single word for rain, for example, but Gaelic has about half a dozen of which the only ones I can reproduce here are "uisge" (that word again) which just means "water", and "fras" which is more like a gentle shower. The rest of the words in the Gaelic of the North-West of Scotland that refer to rainy weather are, of course, profane in the extreme.

You're forgetting about synonyms. The common adage that English has the largest vocabulary stems from the fact that it often has multiple words for the same thing. Sofa, couch. Autumn, fall. Etc etc. Other languages generally don't do this. I've never heard anyone suggest that English has words for more concepts.

Even if the number of words in a language were finite we wouldn't have a reasonable way of counting them. There are too many kinds of fuzziness involved in deciding what counts as a "word" and you can't ignore the borderline cases because the borderline cases vastly outnumber the straightforward cases.

I think people don't realize how weird language is. Like you could look at Chinese and call each sentence a "word" as there are no spaces. What's the difference between that and a compound word like "nighttime" or the whole German language where you got words like Krankenwagen ("patient" + "car").

Now this doesn't mean there aren't words or phrases that aren't translatable. But the thing is we can always translate the words themselves. What we can't always translate is the meaning behind them. I think the best example of this comes from Star Trek and the Tamarian Language[0,1]. "Sokath, his eyes open!" The problem with communication is not that the words don't translate, it is that the meaning behind them doesn't. Just as people struggle with idioms when learning American English or why someone might be confused about why someone "shit in the milk" or "fucked the dog". Words are an embedding. A compression.

The thing people are constantly forgetting, but is more important than ever in a globally connected world, is that words are not perfect representations of thoughts. We compress our thoughts into them and hope the person on the other side can decompress them. It is why you can more easily communicate with your close friends who have better context than you can with another person that natively speaks your language and is why someone that learns a new language can speak perfectly well but still struggle to communicate. Language is not just words, it is culture[2]. So in a much more connected world today we have these disconnects in culture and thus interpretation of what people say. I know every one of you has been told to "speak to your audience" but how do you speak to your audience when your audience is everybody and when you don't know who your audience is? The new paradigm requires us to be much better interpreters than we were before. Least everyone is going to sound crazy, other than those you frequently talk to and have that shared understanding.

[0] https://memory-alpha.fandom.com/wiki/Tamarian_language

[1] https://www.youtube.com/watch?v=3-wzr74d7TI

[2] This is, btw, why people argue for embodied AI being so critical. Not because LLMs can't appear to grasp the language, but because we as humans have embodied our language so deeply you probably didn't even realize that I used the word "grasp" to refer to an abstract concept and not something you can actually touch with your hand.

In another blog post where he uses "shibui" as an example of an untranslatable word, he says, "Saying shibui like that, in a mere second, conveys what would otherwise make a clunky and unnecessarily long digression."

At the root of nearly all the blog posts like this one (basically explaining why they don't agree with a widely held belief) is a redefinition of a term or word into something very specific that contradicts the common definition.

So in this case, I see the diagrams as representing the boundaries drawn when projecting / quantizing complex ideas into a set of central points that are insufficient for catching all of the nuance of the original. How well can you adapt a nuanced idea to a different space?

If Language A has an idea that exists at one point in space, which is the closest word in Language B that might be used to represent it? A Voronoi diagram is one possible way of illustrating it.

Tangent on your tangent: this GDC presentation from 2016 is probably my favorite real-world application of Voronoi Diagrams, and uses them for N-player split-screen camera control: https://www.youtube.com/watch?v=tu-Qe66AvtY&t=1594s

I have a lingering dream in the back of my mind to make a single-couch Liero-style casual game for N-players with good dynamic camera support using this technique.

I'm not quite sure I understand this—I do have mental sensations/processes sans language, but I would not characterize them as "thoughts". To me, a thought is inherently linguistic, even if they relate to non-linguistic mental processes. So to me, learning a new language is very literally learning how to think differently.

    Each language is a lossy approximation of all conceivable thought...

The same process that allows two speakers of the same language to communicate adequately allows one to translate from one language to another. If it were truly impossible to translate from one language to another, we would be unable to perceive this and argue about it. The recognition and correction of errors is part of the process of translation just as it is part of the process of communication in a single language.

That indeterminacy of translation isn’t mentioned is a huge shortcoming of this article.

We can look no further than English: "man can do something," "man can do not do something" (i.e., can do but does not have to), then pretty straightforward "man can not do something" and, all of sudden, to express that man cannot decline some obligation, we say "man can not help but do."

It is not translation per se, but shows that some parts of language were evolved to tiptoe around non-customary things, in this case, double negation. And double negation is very easy in some other languages.