- The article seems to think that a word is untranslateable if there is no single word in the target language. If I'm not misreading the article, then this is completely obvious -- just consider the number of words in English and the number of words in almost any other language, and you will find that there are more English words than the other language. It is now clear that there exist English words that don't correspond to a single word in the other language.
- I think a succinct way to describe my thoughts on linear algebra/language is that language has high dimensionality (ie many different basis vectors that may not necessarily be orthogonal) and that individual languages use a unique coordinate system to express thought. Each language is a lossy approximation of all conceivable thought and some languages can more efficiently represent the “all thoughts” vector space because they have basis vectors that point in more uncommon directions (like the go to japan example). So while you can more or less point to any thought in any language, some thoughts are easier to express in certain languages, which the post (and me) agree to be untranslatable words.
I tried to find the really interesting article about language and color that describes how some cultures use different naming schemes for colors but couldn’t find it. It talked about how back in the day we don’t know orange as a color, we just thought it was red-yellow and only after the fruit was distributed did the word for the color catch on. Here’s the best article I can find that talks about this phenomena https://burnaway.org/magazine/blue-language-visual-perceptio...
by epistasis
2 subcomments
- > If the mere sight of the above is like a punch in the face for you, don't worry. I'm not going to math you to death in what follows. I will only remind you of a tiny basic part of it that I think relates to languages.
Yes, that mathematical expression is like a punch in my face, but not for the reason you think. I am offended that the rank of the matrix does not match the dimension of the matrix, not that I'm seeing a matrix.
by yubblegum
4 subcomments
- Interestingly enough for this morning's walk I was musing over the tension between the hypotheses that: 'LLMs can map between languages in the vector space' (thus languages are ~equivalent); and 'Language affects thoughts' (as in German is good for Philosophy and English for getting things done).
If both these thoughts are true, then it would appear that languages have topological characteristics. We can (topologically) map from one to another, 'thoughts' (that is a complex of words) form 'paths on the language manifold' and certain paths may be more 'natural' in one topological form than the other.
- My personal analogy, useful in my early days: Translating is like finding a vector in another space that points in the same direction or carries a similar magnitude of meaning.
In other words:
The source sentence is a vector in “language A space.”
The target sentence is a vector in “language B space.”
A good translation finds a vector that has the same direction (same meaning, intent, tone) even though it lies in a different coordinate system (the new language).
- > I hope these rather unorthodox leaps between linguistics and mathematics helped make it almost obvious that some words and ideas are untranslatable in practice. I also hope you don't take the analogy too seriously, because it won't go much further than this.
Phew! Thanks for clarifying.
- Are they multiplying a 3x3 matrix by a 2 component vector ?
- There is a better thesis coming from the late philosopher W.V.O Quine: indeterminacy of translation [1]
[1] https://plato.stanford.edu/entries/quine/#IndeTran
- Big claim but not much substance. They should try to really understand linear algebra first, and also linguistics a bit. Semantic domain (from linguistics) is a better way to describe it, where using sets (from math) might better convey what they want to say.
- The word 'word' is polysemous, and also vague. Polysemous: it can refer to written words or spoken words (or signed words, in sign languages).
Vague: does it mean all the inflected forms of a word, or just the stem without inflection? Example: is (are?) 'walk', 'walked', 'walks' and 'walking' four words, or one? What about "stand/stood"? (And languages where the bare root or stem can't appear by itself, like verbs in Spanish.) Derived words, like 'push' and 'pushy'.
Do compound nouns count as a word, or do only the parts count? Example: 'doghouse' (or 'dog house'). What about idioms? Example: 'to crane his/her/my/your/our neck(s)'.
What about different pronunciations? Is 'roof' pronounced to rhyme with 'aloof' the same word as 'roof' pronounced with the vowel of 'put'? And different spellings but same pronunciation: 'bear' vs. 'bare'.
What about words with different grammatical categories, like 'push' as a noun ("I gave her a push") or a verb ("I pushed her"). Or the same word with virtually unrelated meanings, "I pushed her on the swing" vs. "I pushed my ideas."
by throwaway81523
0 subcomment
- > a gentle, poignant sadness or pathos felt in response to the transient nature of all things, a deep awareness of their impermanence that evokes a subtle, bittersweet sorrow and a profound, quiet empathy for their passing.
https://en.wikipedia.org/wiki/Saudade ?
by rich_sasha
0 subcomment
- It's a tenuous analogy, but if you along with it, you can take it further.
You could consider the "cost" of expressing a word as some kind of metric or norm on the vector. What in one language/basis is a simple Kronecker delta, in another is a very complex vector (of course if it were the same vector in two bases, it would have the same length, but we could rather think of translation as an affine transformation, say).
And finally, with two bases, they need not span the same vector space. You can have a three-coordinate vector space all you like, if you have only two basis vectors you ain't spanning it. At best you can hope for an orthogonal projection from one to the other, and lose some nuance.
Eventually, with bilinguality, you learn not to translate words. Concepts live in different languages and describe a reality. Usually you can describe that reality in two different languages, but sometimes not.
- There's one aspect that I think the article starts to hint at, but doesn't quite make the jump to is that words in a language just map to a subset of concepts that don't necessarily have the same subset boundaries in other languages.
If you think back to the meme from a decade or two ago about how men and women perceive colour [1], where e.g. "pink" to a man covers a whole range of colours to a woman, then that kind of hints at the idea.
One example back in the realm of vocabulary is the English word "happy". This embodies a range of meanings from joy, willingness, pleased, contentment, satiation, etc. There might be some overlap in some of these meanings with other words like "joy" or "excited", that don't have the same overlaps in other languages. E.g. "happy" might be translated to French as "heureuse" for the senses of pleased or content, but not for willingness sense.
Similarly, the French word "dommage" can be translated into a whole bunch of English words that aren't normally synonyms of each other - pity, damage, shame, harm.
This kind of nuance can lead to two opposite problems when translating - when the meaning is limited to a subset of possible meanings by context, and the wrong one is chosen in the foreign language, and when the author's meaning embodied multiple meanings and the chosen translation doesn't cover all of them.
Some of these features can lead to the humour in subtle jokes being lost in translation, e.g. "he'd be late to his own funeral".
[1] e.g. https://www.psychologytoday.com/us/blog/brain-babble/201504/... or https://digitalsynopsis.com/design/male-vs-female-color-perc...
- Communication/language depends on shared context. The more context you share the shorter the trigger for evoking that thing and that context. And if you share no context communication becomes very difficult.
I wasn't aware that that idea was in dispute.
- Tangent: I really like vornoi diagrams and part of me thinks there's a hidden, precious concept they represent. I didn't get their relation to the article but was wondering if they have applications in engineering/sciences.
- Just read Wittgenstein (The Blue+Brown Books / Philosophical investigations), and this confusion will go away. The difference between translation, definition, and explanation needs to be understood.
by decimalenough
0 subcomment
- 上京 jōkyō is less a regular word and more a form of written shorthand. It would not be used in speech, and even in writing it's ambiguous: not only does 京 kyō simply mean "capital", but there's a district of Kyoto that's also 上京, only read Kamigyō.
The closest English equivalent is abbreviations like "PC". They're perfectly usable in context, but if you see one standing alone it's not clear if it's personal computer, politically correct, Peace Corps, etc etc.
by triclops200
2 subcomments
- This article assumes that concepts are somehow precise coordinates within a single language; that's not the case, at best, speakers of a language mutually approximate a relatively consistent representation, but like, look at a word like yeet or whatever: we decided as a society on its meaning while it was being developed, as it were. Furthermore, it never rigorously defines what it means by translation. It claims 上京 is a single basis meaning moving to Tokyo, for example, but that isn't even an accurate translation: the individual components represent superior/greater/above and Tokyo and as an idiomatic phrase it represents the concept of moving to the capital for a better life. Something like "moving on up" or the like in some vernaculars of English, and idioms translating to idioms is a form of translation. It's disingenuous to represent the first concept as a single basis but not the second.
Similarly, it claims mono no aware (物の哀れ) is unable to be translated, but, again, more literally "translated" is saying "the sorrow within things" character by character, and, only as an idiom has the full contextual understanding. It's not really a single point even if it's rather accurately located in a hypothetical embedding space by Japanese speakers. Imo, an English translation of the concept is "everything is dust in the wind", only 2 more individual conceptual units than the original Japanese phrase, and 3 of them are mainly just connecting words, but it's understood as a similar idiom/concept, here.
Concepts are only usefully distinguished by context and use.
By the author's own argumentation: nothing is translatable (or, generally, even communicatable) unless it has a fixed relative configuration to all other concepts that is precisely equivalent. In practice, we handle the fuzziness as part of communication and its useless to try and define a concept as untranslatable unless you're also of the camp that nothing is ever communicated (in which case, this response to the author's post is completely useless as nobody could possibly understand it enough internally for it to be useful. If you've read this far, congrats on squaring the circle somehow)
- What a trendy article, in tune with our recently linear-algebraic turn in how we see language thanks to LLM's.
But I think this exposes an even greater problem, where words thought to be direct translations will always drift in vector value as they are weighted for attention within their respective corpora. Are we on the brink of translation-nihilism?
This isn't even limited to complex phenomena or shades of snow. Even "I like" is a different construction in many languages, in an unexpected way to new language learners.
- I like this as an analogy but not as an explanation. In fact, if you’re unfamiliar with linear algebra, this might be a nice way to think about projection onto a different set of basis vectors. But even the best human translators can be deeply at odds over what translation is appropriate for a term in its context. There’s never a right translation, let alone a uniquely right translation.
by miltonlost
1 subcomments
- Reading any poem that makes use of extensive wordplay within a language shows why there will always be some untranslatable aspect. You can't create all the exact shades of a single pun if all those shades aren't in a different language.
Go translate an ee cummings poem and make sure to retain all its meanings.
- From the title, I thought he was going to explain "eigenvalue".
- It could be the case that it's not even "effectively", "in practice", etc.
N^{any constant} is not bijective with a single R.
- I cannot take seriously an article that presents a 3x3 matrix being multiplied by a 2-vector as an example of linear algebra. Gibberish.
- Another physicist who thinks he can solve problems in a domain he knows nothing about with linear approximations.
There's an xkcd devoted to this problem, even using computational linguistics as an example, IIRC.
- [dead]
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