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Linear algebra explains why some words are effectively untranslatable

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Re: Linear algebra explains why some words are effectively untranslatable

#61

Post by KalMann »

tptacek wrote: post #28
epistasis wrote: post #19

> 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 seein…

It's a 3x3 matrix with 3 independent rows. The rank matches the dimension.

He probably meant to say "vector" the second time he said "matrix".

Re: Linear algebra explains why some words are effectively untranslatable

#62

Post by nyeah »

wjholden wrote: post #20
d-lisp wrote: post #3

Are they multiplying a 3x3 matrix by a 2 component vector ?

It also has mixed square brackets and curved parentheses. I stopped reading the article when I saw this.

Brackets can be any shape, it's fine. Like (3)*[4] is still 12. But that matrix-vector product is undefined.

Re: Linear algebra explains why some words are effectively untranslatable

#63

Post by bloppe »

seanhunter wrote: post #49
bloppe wrote: post #33

Earlier quoted context omitted.

Some giant portion of English vocabulary actually are compound words. English loves using compound words but only if the roots are sourced from Latin or Greek : words like electrocardiogram ("electronic heart picture", sourced from Greek), agriculture ("field nurturing", from Latin), and telecommunication ("far sharing", a hybrid of Latin and Greek roots). Probably the overwhelming majority of the words in an English…

I wasn’t saying there are no compound nouns in English at all. If you count portmanteau words like “Brexit” and jargon there are a massive abundance of them. All I was saying is the approach would count certain concepts as untranslatable when they clearly aren’t, simply because in one language you have a compound word and in the other language you use several words to express the same concept. It’s definitely not unt…

I think your point basically asks the question "what counts as a word" because clearly German has infinitely more "words" than would ever appear individually in a dictionary. I'm saying that English does, too.

Re: Linear algebra explains why some words are effectively untranslatable

#64

Post by nyeah »

aitchnyu wrote: post #43
voxleone wrote: post #31

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 d…

when did you develop this analogy? Is it well before 2015, when Google demoed a vector model that solved Man:Woman,King:_____ ?

Yeah, I was hoping the article would say something about word vectors and linear algebra.

Re: Linear algebra explains why some words are effectively untranslatable

#65

Post by nyeah »

realusername wrote: post #60
ErroneousBosh wrote: post #58

Earlier quoted context omitted.

> It is now clear that there exist English words that don't correspond to a single word in the other language. 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…

Not to mention that the English dictionary is stuffed with legacy words that no natives understand. Is it even part of the language if no native use it? It's another debate.

It's stuffed with unusual and rare words, and no native speaker understands all of those.

But I think most of those words are in use somewhere, for something.

Re: Linear algebra explains why some words are effectively untranslatable

#66

Post by bloak »

pjsg wrote: post #5

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 corresp…

But perhaps all languages have a countably infinite number of words, in which case that proof doesn't work. (In English we have: legless, leglessness, leglessnessless, leglessnesslessness, ... It's not a great example, but it's good enough.)

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.

Re: Linear algebra explains why some words are effectively untranslatable

#67

Post by grokgrok »

andoando wrote: post #59
yubblegum wrote: post #47

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 (topological…

My take is the human brain learns concepts primarily through differentiation. To a newly born child who has no concept of door or a wall, has no reason to see the two as being different parts. Different languages form different differentiations, but one can always compound concepts, and differentiate them differently.

To extend: there will also be general alignment tendencies towards those readily mapped and expressed concepts within available language. Hard but useful concepts can get mapped to idioms. Modes of categorization will be influenced by these factors, which in turn influences many processes.

Re: Linear algebra explains why some words are effectively untranslatable

#69

Post by drivebyhooting »

nyeah wrote: post #52
drivebyhooting wrote: post #6

Earlier quoted context omitted.

That isn’t a proof. Synonyms can bolster the enumeration sans augmenting novelty.

It kind of is a proof if we assume that single words can be translated at all. Translate a single word from Language X (more words) to language Y (fewer words) and back. I can't uniquely recover all the words in Language X that way.

Does translation have to be a bijection? I don’t think so.

Re: Linear algebra explains why some words are effectively untranslatable

#70

Post by thesz »

yubblegum wrote: post #47

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 (topological…

What is a word in one language is a collocated words in another, possibly context-dependent.

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.

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