Any compact space is coarse equivalent to a point. ℝ is coarse equivalent to ℤ. The universal cover of a compact manifold is coarse equivalent to the fundamental group.
John Roe
seen from Norway

seen from Norway
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seen from United States
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seen from Malaysia
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seen from United States
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seen from Malaysia
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seen from United States
Any compact space is coarse equivalent to a point. ℝ is coarse equivalent to ℤ. The universal cover of a compact manifold is coarse equivalent to the fundamental group.
John Roe
Mona Baker’s 5 levels of equivalence
Once again, no fancy theories or sophisticated vocabulary. Let’s get down to business. Mona Baker, the author of “In Other Words,” has explained the concept of “equivalence” in a way that might help us, language learners, understand how our target languages work.
What’s equivalence in translation?
Simply put, it means "the best translation of a word/phrase/concept." A concept expressed in your native language is expressed by a concept in your target language so, they evoke the same emotions, mental pictures, and adhere to cultural standards.
Simple example:
A car – big, small, red, 4 wheels, a windshield, Toyota, etc.
Samochód – the features I stated above apply to samochód as well.
They’re equivalents.
Difficult example:
Święcenie koszyczka (a Polish thing. We do it for Easter.) = Basket Blessing
“What the hell is Basket Blessing?” That’s what non-Polish people usually ask me when they learn about our Easter traditions.
Święcenie koszyczka has special connotations in Poland. It’s a Catholic tradition that people like. There are some preparations for it like decorating boiled eggs, etc.
Basket Blessing is a literal translation. The target audience is usually confused and doesn’t feel anything while reading this phrase, no sentiment, no mental pictures, nothing. Just a fun fact. It’s not the best equivalent, but you can’t go with anything else because there’s no other way to translate it. You can replace it with a local custom (you’ll get people sentimental), but you’ll change facts. Is it a good choice? I don’t know. It depends on what you want to achieve.
Fun Fact
Equivalence is not about word-for-word translation (just like in a dictionary). It’s possible to achieve equivalence, but you need to remember that there are so many people in the world and each of them creates different mental pictures when they hear a word. They feel different emotions, and that alone makes achieving the perfect, the ultimate equivalence impossible. That’s why linguists and translators have been studying equivalence for a while now. They keep working and looking for the answer to “How can we achieve the best equivalence?”
To the point!
Mona Baker talks about 5 different levels of equivalence:
Equivalence at word level and above word level (2 levels) – we’re trying to translate words only or phrases, collocations, idioms, etc.
You might not be able to translate a word because you’re dealing with:
Culture-specific concepts which are expressed through one word only.
There is no such thing/action in your target language/culture.
Your native language is more specific, and the word you want to translate refers to one thing only. Your target language, on the other hand, refers to many things, and it uses one word for a lot of objects. (skówka na długopis, zakrętka, zatyczka = a cap).
Differences in physical or interpersonal perspective (words such as come/go, take/bring, arrive/depart).
Different connotations (some words are neutral in your native language, but some are very emotive in your target language).
Affixes (prefixes and suffixes). English "–ish" (greenish) is applicable to many words. It’s almost impossible to render it into Polish.
Some words can be translated (have equivalents), but they’re not used as often as they are in the target culture/language.
How can I deal with that?
Use more general words, less expressive words.
You can always describe the thing, provide an explanation (translation by illustration).
You can omit that word if it isn’t necessary and won’t cause any problems with understanding.
Paraphrase.
Borrow the word and provide its explanation.
Cultural substitution (instead of święcenie koszyczka use a custom common for your target language’s culture).
Grammatical equivalence – differences in grammatical constructions (they might be difficult to translate as well). Catford’s translation shifts overlap with Mona Baker’s grammatical equivalence.
Number (plural/singular)
Gender
Person (I, You, He, She, It)
Tense and aspect (perfective and imperfective)
Voice (active/passive)
Textual equivalence – differences in text organization and structuring (word order, cohesion, word choice, paragraphs, etc.)
It’s most visible in languages such as Japanese, where the topic and the subject are two different concepts.
In Polish, the word order is very flexible unlike in English. The Japanese always finish their sentences with verbs.
Some languages prefer nominal structures. In Polish, we like to use verbal structures. (jakie anime planuje się stworzyć = upcoming anime releases)
Pragmatic equivalence – how it is that we understand more than it is actually said.
Implied information – you know, all those little things that tell us that our speaker meant something completely different or meant to insult us in a non-straight-forward manner using culturally specific words and concepts. (Forrest Gump is a good example of such implied information. You need to be familiar with US history and culture to fully enjoy the movie).
So, how this knowledge can help you?
1. It will help you ask better questions in class. 2. Understanding how your native language works will speed up your learning process tremendously. 3. If comparing languages is your favorite language learning method, Catford’s and Mona Baker's translation theries can give an idea where to start and what to notice. 4. If you’re a teacher, it can help you explain some grammatical phenomena. 5. If you help others learn your native language, you’ll be able to explain grammatical issues, or at least give examples. 6. You’ll speed up your translation abilities.
Bourgeois society is ruled by equivalence. It makes dissimilar things comparable by reducing them to abstract quantities... anything which cannot be resolved into numbers, and ultimately into one, is illusion; modern positivism consigns it to poetry.
Max Horkheimer & Theodor W. Adorno, Dialectic of Enlightenment
“Equivalences”
© Henri Coudoux
An Archive of Our Own, a project of the Organization for Transformative Works
Chapter 8 of Equivalence is up, though literally anyone here is going to be here from that fic in the first place so this is kind of pointless but
Expanded Equivalence [1.12.2]
Ссылка на источник: Читать дальше »
The Three Meanings Of E=mc^2, Einstein's Most Famous Equation
“Even masses at rest have an energy inherent to them. You've learned about all types of energies, including mechanical energy, chemical energy, electrical energy, as well as kinetic energy. These are all energies inherent to moving or reacting objects, and these forms of energy can be used to do work, such as run an engine, power a light bulb, or grind grain into flour. But even plain, old, regular mass at rest has energy inherent to it: a tremendous amount of energy. This carries with it a tremendous implication: that gravitation, which works between any two masses in the Universe in Newton's picture, should also work based off of energy, which is equivalent to mass via E = mc^2.”
When it comes to equations, few can lay claim to being ‘the most famous one’ of all time, but right up there is Einstein’s greatest and simplest: E = mc^2. Yet it doesn’t simply state that mass and energy are equivalent, or that the relationship between them is given by the constant c^2. Sure, it says those things, but there’s also a vital physical meaning behind them. Understanding E = mc^2 has led to a variety of tremendous discoveries and breakthroughs, from nuclear power to the creation of new particles in particle accelerators. It even led directly to discovering that Newtonian gravity was theoretically unsound, ushering in the era of General Relativity, as well as the fact that any theory of gravity needs to include a gravitational redshift/blueshift.
How did it all come about? Find out the three meanings of Einstein’s most famous equation, and what it means for our Universe.