Untranslatability And Rubik’s Cubes

Are there really untranslatable words? If so, could a language be entirely untranslatable and if so (again) how? I’ll start with Rubik’s cubes and move on to saudade and sisu.

I never managed to solve the Rubik’s cube. The closest I can get is three sides. I refuse to cheat by reading up on how to do it, and I don’t know how many people who can do the cube have cheated in that way. However, certain things can be seen to be true of the cube which don’t depend on knowing how to do it. One of these is that it’s impossible to do five faces without the sixth also being done. If that were so, at least one face of a sub-cube would have to be the wrong colour for it ever to be complete. That said, there could be other versions of the cube, maybe prank ones, which did have a subface the wrong colour for them to be doable. It’s more than that too. Cubes can be easily dismantled and put back together again, but unless you reassemble a cube in a fashion you know for sure is a possible arrangement of squares you could reach from the completed state, the probability is that you will have put it into a position from which you can’t get back to the original state unless you just take it to bits again and try to put it into such a condition. This is because only one arrangement in twelve can be reached from the perfect starting state. The number of possible arrangements, although vast, is only one of twelve sets of such arrangements, and none can be reached from any of the others. The branch of maths known as group theory can be applied to cube-solving and these permutations, whose sets have been referred to as “orbits”.

Now for language. When one “does” language, one is attempting to express oneself clearly in a way which can be understood by others, or perhaps by oneself although Ludwig Wittgenstein would have a lot to say about that particular idea. It’s a process which reminds me somewhat of Rubik’s cubes, and in fact there are notations for cubes which are rather language-like, though somewhat restricted. They’re not going to be able to describe the world as a whole so much as the very restricted but still gigantic world of The Cube. A string of letters and punctuation, upper and lower case, can be used to describe how to turn the parts of a cube to get it to a particular point, such as F, U, L, R and D for Front, Up, Left, Right and Down, and so on. Other versions exist, such as ones referring to clockwise and anticlockwise rather than using the apostrophe to indicate anticlockwise, but translation between them is easy so this is not what we want. If, however, there’s a way of comparing the transformations of a cube to the communication of ideas, we might be onto something. If there was a scrambled cube in a different orbit and the aim was to get it into a particular pattern which was inaccessible to another orbit, the same string of letters would be fine as a way of instructing someone how to twist the sides, but the end result would be different and communication would have failed. This seems much more promising. Now imagine this. There’s a community of language users whose languages are each based on the cube and how to turn it, and the instructions for getting from the completed cube to the patterns are used as words to describe concepts for which the patterns are metaphors. For instance, twisting the middle layer to produce horizontal stripes from a complete cube becomes a word meaning “stratified” and turning the cube in a manner which produces a chessboard-style arrangement becomes a word meaning “chequered”. A completed cube has a special, simple word and comes to mean “clean” or “perfect”. Nobody from the twelve communities has ever seen cubes from the others, but their language uses the same words. These words will fail to communicate for quite some time, but the set-up is quite artificial and closely resembles Wittgensteins Private Language Argument (PLA).

Wittgenstein often wrote philosophy in quite an aphoristic way. One of the things he asked us to imagine was that we each carry a matchbox with us which contained a beetle which we never show anyone else. For all anyone knows, a matchbox could be empty and when someone says “beetle”, they’re not referring to anything. If we imagine twelve communities each with a differently arranged cube, it does become easier to understand from an outsider’s perspective that “doing the Rubik’s cube” means something both different and the same for each group, and it differs from the beetle in a matchbox situation because everyone in a particular social group can see everyone else’s cubes in that group, so it isn’t the same as a private language. Wittgensteins argument is that an essentially private word which could not be defined in terms of other words cannot mean anything because there’s no way to distinguish between it seeming correctly applied and actually being correct. I also suspect that Wittgenstein is rather too much of a logical positivist for my tastes, something which oddly I haven’t seen anyone else say. That is, he means that meaningful statements have to be axiomatic, logically derived or verifiable by the senses, and in terms of philosophy of mind that would make him a behaviourist, which involves the denial of all purely subjective mental states. That said, he did say useful things and the PLA is not just about logical positivism, and may not even apply to our dozen secret Rubik’s cube communities.

Wittgenstein also said that if a lion could speak, we could not understand him. If you hear a conversation between two people about a soap opera you’ve never come across, you might hear them referring to people like Vera and Ena as if they were real people. I used to have aunts called Ena and Vera. As a child, if I’d never seen ‘Coronation Street’, I might have heard some people on a bus going on about what was happening between Vera Duckworth and Ena Sharples and wonder why I’d never heard of any of that going on between my aunts (and I must admit right now that I’m curious about any story lines which might have involved both of them but I can’t remember). I wouldn’t understand the conversation, but I might think I could. Something even further removed from my experience would be talk of the “offside rule” and the “five-yard line”, which I think is what they call certain things in soccer but I have no idea what they are and I couldn’t participate in such a conversation. Or could I? Is there a way of manipulating talk about those things which means I could fake it? If I could fake that, are there whole fields of discourse which are fake? But leaving that for the time being, the more different someone’s world is from yours, the harder it is to understand what they’re saying, and this seems to be what Wittgenstein means about the lion. It’s been said that the apparent difficulty some non-neurotypical people have in empathising is not what it seems. The process of empathising seems to involve the faculty of placing oneself mentally in the other person’s position and imagining what it’s like for them, and the idea is that a non-neurotypical person doesn’t have difficulty in doing that, but once they’ve done it they’re not similar enough to the other person to succeed in imagining them accurately. It isn’t because they don’t go through the same process as anyone else. I personally tend to think being on the “spectrum” is more about salience than the primary absence of theory of (other) mind(s), but this could lead to such circumstances. In such a situation, you can imagine someone saying “I want to eliminate world hunger” and doing so by trying to wipe out all animal and fungal life on the planet. The initial statement, “I want to eliminate world hunger” is in English, but that doesn’t help most people to understand its full meaning. If everything about that person’s mental world is sufficiently different from our own supposèdly shared one, the fact that they were speaking English wouldn’t even matter, and in a sense it would be untranslateable. But the reason is that it would take too long to outline their assumptions and views for it to be practical. Given enough time, it could be done.

Non-Cantorian set theory was a response to Russell’s Paradox: whether the set of all sets which are not members of themselves is itself a member of itself. This paradox led to older notions of set theory being thrown out, or at least placed into question, and a new set of axioms arose in response aiming to avoid this paradox. All are expressed using predicate and propositional calculus notation and most are quite easy to translate into English. My grasp of maths is rather weak and also patchy. I noticed, for example, that I could often understand the content of the first and final year BSc maths syllabus at my university but not the second year. Nevertheless I don’t have a huge problem understanding Zermelo-Fraenkel set theory. Here’s a fairly easily translatable axiom from that known as the Axiom of Extensionality:


That is, “for any x, for any y, for any x, z being a member of x if and only if z is a member of y entails that x is equivalent to y”. This bare-bones “translation” of the above sequent is of course rather opaque, but it can be disentangled and simplified to read “two sets are equal if they have the same members”. The next few axioms are similarly translatable until one reaches the sixth: the Axiom of Replacement:


This is difficult even to type – I had to resort to using HTML directly to write the above line. It means that the image of a set under any definable function will also fall inside a set. That isn’t an immediately clear thing to say to most non-mathematicians. The above is also an axiom schema rather than just an axiom, meaning that it’s a metalanguage referring to the language used to write the axioms themselves. It also occurs to me that there might be an issue with the use of the cardinal integers in that because Russell’s Paradox is itself applicable to the foundations of arithmetic, so it could presumably be profitably expanded to consistency with Peano’s axioms of number theory. “∀w1∀w2…∀wn” also refers to a countably infinite number of items, so in practical terms this is inexpressible unless you just say something like “and so on, forever” or “ad infinitum“. This kind of thing takes most people into a realm where English, and probably most natural languages, are inadequate to describe something but which is nevertheless not antilanguage. It isn’t anybody’s fault that this can’t be expressed clearly in English as far as I can tell.

Another example of this might be APL – “A Programming Language”. Like my other favourite programming language, FORTH, APL has been described as a “write-only programming language”. That is, it has the reputation of being fairly easy to write but impossible to understand once written. I disagree with this assessment of FORTH because giving words names which make sense and inserting comments, as usual with coding, will lead to code in FORTH making sense to other people. For instance, “: CHARSET 127 32 DO I EMIT LOOP ;” has a series of English words in it, the first just being the label for what you’re going to call that word, which could therefore be named something clearer like “ALLTHECHARACTERSINORDER”. APL, though, is not the same because it uses symbols rather than letters and is very pithy.


will find all prime numbers lower than a thousand. It makes sense if you know APL but wouldn’t be easy to express in English.

Most of the time the problem with setting these over into English or most other natural languages is that they take a lot longer to express when translated. Whereas I’ve described what the above does in APL, I haven’t set out the algorithm using words because it would be much longer and the question of maintaining comprehension arises because of attention span. This feels like a bit of a cheat to me because the weakness is to do with something which could be extended with practice, at which point the sequents would be understood. The idea of untranslatability to me would be a language which simply cannot be translated no matter what, and to illustrate these I can finally get round to talking about the likes of saudade and sissu.

Saudade is a Portuguese word which is often said to be untranslatable, although it can be described roughly as “longing”, “nostalgia” or “missing”. I don’t speak Portuguese but the words used in English are insufficient because they don’t express the strength of feeling involved. I’m wondering if it expresses first stage bereavement, where there’s denial that something or someone is gone for good. Welsh has a similar word, “hiraeth”, and German has “Sehnsucht”, which although it doesn’t strike me as untranslatable, I find myself thinking the word in German rather than English when I try to do it in my head, so maybe it is. This might mean it can’t be translated into English but can be into other languages which do have the same concept.

Sisu is a Finnish word meaning something like “steadfastness” or “perseverence”, or perhaps “foolish bravado”. I’ve only ever puttered around in the foothills of Finnish so I can’t comment much on this. Finnish also has a word for Schadenfreudevahingolino. When coming across words like this, it can be easy to be hypnotised by the pride someone might have in their culture or language which stops one from being able to think of a word. Even so, sisu seems to me to describe the quality one might need to succeed in giving birth vaginally, or perhaps to push through the wall during a marathon. but maybe I’m wrong.

A recent popular word of this kind is the Danish hygge, which I perceive as being a synonym for Gemütlichkeit – a kind of homely cosiness. Other words claimed to be untranslatable include mångata, sobremesa, toska and itsuarpok – Cynthia’s reflection on the water which looks like a street heading towards her (Swedish), the convivial feeling after a meal (Castilian), gloominess/ennui/lugubriousness (Russian), waiting impatiently for something to turn up (Inuit). Considering the first, the idea of multiple reflections on a methane ocean of objects in the night sky of Titan would extend this meaning, perhaps allowing for a whole series of roads to different moons and planets, and I could perhaps invent a word for that but I’ve been able to describe what it would mean already in English. Itsuarpok is a particularly useful word in these days of constant deliveries of stuff we’ve bought online. Could there be an entire language consisting of such words though?

Jorge Luis Borges once wrote a story called ‘Tlön, Uqbar, Orbis Tertius’ which is pretty amazing but rather than go into that now, I want to talk about just one aspect of the story, which is disconcertingly vertiginous and rather like an earworm. The nations of Tlön, which appears to be imaginary in the story, are idealist in the sense that for them the world is not a collection of objects but a succession of separate dissimilar acts. Thus their language is based on verbs rather than nouns, a sample phrase being “hlor u fang axaxaxas mlo” – “upward behind the onstreaming it mooned” or “the moon rose above the river” (Tlön isn’t Earth). In the Northern Hemisphere though, the languages are based on a different principle: that of the monosyllabic adjective. Thus the moon is described as “pale-orange-of-the-sky” and “round-airy-light on-dark” depending on the impression given. Two different sensory impressions can be mixed, such as the cry of a bird at sunset. Hence there is a vast number of nouns, including all those found in English and Spanish in the sense of being direct translations, but none of the speakers gives them any credence as they are transient impressions. Both of these types of language, particularly the second, correspond closely to the idea of untranslatability, although there would be times when coincidentally translatable words would turn up in the languages, and it would be alien to the spirit of the story to exclude such words. Incidentally there’s plenty more in the story than that but I don’t want to veer off-topic.

Dolphins have been said to transmit sound pictures of their perceptions in order to communicate. Although I find it hard to credit that anyone would be able to demonstrate that this is in fact really happening, it’s still an interesting idea, and given that a picture is worth a thousand words, would seem to be untranslatable. A similar idea was pursued by the poet Les Murray in his ‘Bat’s Ultrasound’:

Bat’s Ultrasound

Sleeping-bagged in a duplex wing
with fleas, in rock-cleft or building
radar bats are darkness in miniature,
their whole face one tufty crinkled ear
with weak eyes, fine teeth bared to sing.

Few are vampires. None flit through the mirror.
Where they flutter at evening’s a queer
tonal hunting zone above highest C.
Insect prey at the peak of our hearing
drone re to their detailing tee:

ah, eyrie-ire; aero hour, eh?
O’er our ur-area (our era aye
ere your raw row) we air our array
err, yaw, row wry—aura our orrery,
our eerie ü our ray, our arrow.
A rare ear, our aery Yahweh.

Then again, a series of pictures could just become like a pictographic script with stylised images, although this wouldn’t necessarily impose syntax on it. It might get quite difficult to express certain abstract concepts in it unless a ‘Darmok’-like approach was taken, with abbreviated descriptions of well-known myths and fables. Even in English this could become hard to make sense of. One might say “The Fox And The Grapes”, referring to Aesop’s fable whence the idea of sour grapes originates, and there’s also the concept of “sweet grapefruit”, which is a reversal of the same which however has no associated fable as far as I’m aware. Hence one could proceed to refer to “the hound and the lemon” to refer to a situation where having something which is worthless is subjectively perceived to be of greater value in order to conceal the cost from oneself.

To conclude then, it does in fact seem that several kinds of practically untranslatable languages are possible. There could be languages which refer primarily to experiences which are outside those of most humans, as with the other Rubik’s cube orbits. A species whose dominant sense was smell and whose vision was poor might use a fairly untranslatable language, because for example it would have “insmells” rather than “insights” and wouldn’t “regard” anything so much as “scent” it, and beyond that have a whole world of sensation as rich as our visual one but entirely based on odour rather than light. Or it might have a magnetic sense which could be even harder to relate to. Or, there could be languages which simply take too long to translate for the human attention span, so they could be in principle but not in practice. There could also be languages which have developed metaphors and formed words and phrases as depicted in ‘Darmok’, where the dependence on shared narrative culture is so strong that it’s impossible to make sense of them. Or, there could be languages which combine two or more of these things.

One thing, which I find quite unsatisfactory, is that I haven’t been able to articulate clearly what I would think of as the ultimate case of an untranslatable language – one which does the same job as natural languages as we know them, but based on entirely different principles. The closest to these is the putative delphinese, using sound pictures, but I wonder what else is out there and how it can be made sense of, if at all. Or is it just that the relative obscurity to the Anglophone (or even Pirahaphone or Ubyxophone) mind in which these languages would operate makes them inconceivable to us?

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