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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

#41

Post by AlotOfReading »

proteal wrote: post #17

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 bec…

    Each language is a lossy approximation of all conceivable thought...
This ultimately boils down to the private language discussion started by Wittgenstein. If you admit public language is a lossy approximation of meaning, you're taking a position on the existence of private languages.

Re: Linear algebra explains why some words are effectively untranslatable

#42

Post by aitchnyu »

bloppe wrote: post #33
seanhunter wrote: post #9

Earlier quoted context omitted.

Not sure this approach really accounts for the difference between a language like German where you have one compound word for a concept that would require multiple words in English. For one good example, the German "Nomenkompositum" is "compound noun" in English.

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…

A couple of ape cubs who learned sign language saw a duck and invented "waterbird". We have to know two dead languages to know if aquaplaning or hydroplaning is the right word.

Re: Linear algebra explains why some words are effectively untranslatable

#43

Post by aitchnyu »

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:_____ ?

Re: Linear algebra explains why some words are effectively untranslatable

#44

Post by HanClinto »

behnamoh wrote: post #10

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.

A Voronoi diagram is created when you color every point on an image according to which discrete point it is closest to.

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.

Re: Linear algebra explains why some words are effectively untranslatable

#45

Post by proteal »

MangoToupe wrote: post #25
proteal wrote: post #17

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 bec…

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

I think we’re in agreement, but I’m afraid I don’t have the philosophical language to precisely pin my mental model into words (what a meta conundrum lol). I’ll try my best here, but I may come back in a few days with an edit if I can more coherently write my ideas.

I take a slightly more narrow definition of “thoughts” that may be more akin to “expressions” - ideas that can be communicated, so excluding non-linguistic mental processes. I think that may be where we disconnect. A lot of my idea about thoughts comes from the Borges story, Funes the memorius (short story about a dude who could not forget - interesting read and really clarifies my feelings on my definition of “all possible thought”). In the story he talks about tree leaves, but instead imagine needing a unique linguistic scheme for every single unique snowflake you ever see. It would be a linguistic nightmare! Therefore language must generalize otherwise it becomes noncommunicable and that generalization to me induces the “lossy approximation” I attribute to language in my prior comment.

So, in my head Funes’s mind represent the abstract space of all possible thoughts. When we use language, we are stacking words/sentences/paragraphs/etc together almost like vector addition trying to reach a particular point in the thought vector space. Some languages have really clean ways of getting to certain thoughts while others take a mouthful and still don’t get you exactly there (物の哀れ example from link).

I agree with your statement on new languages being different thinking. As you follow that vector addition process to get to the “thought,” different languages will take you on different paths to get to your destination thought because languages encode those vectors differently, even if the destination thought is the same. In my mental model, the act of thinking is putting those language vectors together and tracing their path to get to your thought.

And if my comment still makes no sense - I might have to incubate this thought a bit more :) but I do recommend the story- it’s a quick, thought provoking read.

Re: Linear algebra explains why some words are effectively untranslatable

#46

Post by drivebyhooting »

sjducb wrote: post #38
drivebyhooting wrote: post #6

Earlier quoted context omitted.

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

Synonyms rarely have identical meanings for example: Happy: Joyful, cheerful, merry, delighted Or Beautiful: Lovely, pretty, attractive The only truly identical synonym I can think of is flammable and inflammable

Perhaps perhaps.

But what joyful means to you likely differs from what it means to me, simply because we haven’t read the exact same literature and had the same conversations.

Re: Linear algebra explains why some words are effectively untranslatable

#47

Post by yubblegum »

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.

Re: Linear algebra explains why some words are effectively untranslatable

#48

Post by miltonlost »

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.

Re: Linear algebra explains why some words are effectively untranslatable

#49

Post by seanhunter »

bloppe wrote: post #33
seanhunter wrote: post #9

Earlier quoted context omitted.

Not sure this approach really accounts for the difference between a language like German where you have one compound word for a concept that would require multiple words in English. For one good example, the German "Nomenkompositum" is "compound noun" in English.

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 untranslatable but the translation function isn’t one to one.

Re: Linear algebra explains why some words are effectively untranslatable

#50

Post by KolenCh »

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.
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