> Can a language map all it's concepts to words and other concepts defined by just words.

I don't see why natural language would have this property. It is certainly possible to construct codes such that the distribution over codewords does not have this property.

I also don't see why it would, but then that would of course be a limit to the idea in the paper.

I'm amazed that what the paper shows even works.

It seems extremely unlikely to me that it wouldn't. I conjecture that no such word exists in any widely used human language. This would be a word who's meaning is not contained in the span of meanings of all other words in the language.

Can you think of one in english (or your native language)? You won't find it in any dictionary, since all those words have descriptions in terms of other words.

The example I've been thinking about was 'pain', which, according to Wikipedia, is "an unpleasant sensory and emotional experience associated with actual or potential tissue damage." The native Dutch word "Gezelligheid" has no direct English translation and thus apparently has a wiki page in English [0]. Now I wonder what the relevance is of the distance between word vectors from different languages relating to nearly the same concept (e.g Gezelligheid to Cozyness)

[0]: https://en.wikipedia.org/wiki/Gezelligheid

Gullible?

easily deceived

actually, it's theoretically a hard problem -- https://aclanthology.info/pdf/J/J86/J86-4003.pdf

I would have thought that they needed to 'ground' (https://en.wikipedia.org/wiki/Symbol_grounding_problem) at least one shared reference word/concept so they could proceed to define everything relative to that and thereby communicate effectively and know how to map different languages to the same latent space. But I guess perhaps one can infer/approximate it statistically -- https://cis.upenn.edu/~ccb/publications/discriminative-bilin...