Are they multiplying a 3x3 matrix by a 2 component vector ?
In that one case, yeah; I don't think they're going for anything more than general illustration here.
Linear algebra explains why some words are effectively untranslatable
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Re: Linear algebra explains why some words are effectively untranslatable
#12It'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.
Re: Linear algebra explains why some words are effectively untranslatable
#13Are they multiplying a 3x3 matrix by a 2 component vector ?
Yeah that made me twitch also.
Re: Linear algebra explains why some words are effectively untranslatable
#14The 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…
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.
That's just a difference in orthography. English could easily have had an orthographic standard where we write "compoundnoun" for compounds. This is in contrast with a language like French, where compound nouns are relatively rare. Compare English "Olive oil" and German "Olivenöl" with French "huile d'olive". In French you need to have a preposition to combine the two nouns, whereas English and German do noun-noun composition.
Re: Linear algebra explains why some words are effectively untranslatable
#15The 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…
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.
If you ignore the spaces, the only real difference between German and English compound nouns are the infixes between elements to show bracketing. Case in point: Nomenkompositum
Re: Linear algebra explains why some words are effectively untranslatable
#16The 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…
That isn’t a proof. Synonyms can bolster the enumeration sans augmenting novelty.
That is the crux of the article premise: each synonym conveys similar denotations (principle component is I think what the article called it), but usually with some difference in connotations (the off axis contributions). You can nudge the languages vectors towards each other by adding enough synonyms and modifiers together, but they are always a little bit off even still
Re: Linear algebra explains why some words are effectively untranslatable
#17I 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...
Re: Linear algebra explains why some words are effectively untranslatable
#18Are they multiplying a 3x3 matrix by a 2 component vector ?
In that one case, yeah; I don't think they're going for anything more than general illustration here.
The text that follows does take on a new meaning though, for those that know linear algebra:
If the mere sight of the above is like a punch in the face for you, don't worry.
Almost makes me wonder if it was intentional.
Re: Linear algebra explains why some words are effectively untranslatable
#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 seeing a matrix.
Re: Linear algebra explains why some words are effectively untranslatable
#20Are 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.