Answering this is a goal of the Natural Semantic Metalanguage project.

https://en.wikipedia.org/wiki/Natural_semantic_metalanguage

One thing that's confused me about this project is how much they are relying on people's prior human experience to understand the explications -- maybe a question of how much they use extensional or intensional definitions.

https://en.wikipedia.org/wiki/Extensional_and_intensional_de...

I wanted to thank you for mentioning NSM. I hadn't heard of it before and it's quite exciting and interesting research—seems like a fantastic jumping-off point for building a small language!

thanks for this link. I have been thinking a lot about what the language "primes" are, and my approach was looking at chinese writing's "radicals", a small list of symbols that it combines to form every written word.

i wonder also how well you could get language primes to align with the axes of a word vector, as used in word2vec and other neural network based translation engines. what would a pure vector based language look like, I wonder?

APL is a real programming language used in specialized domains like finance since the 70's I believe and can convey a lot of information in a single line of code. It looks like Greek symbols because it was developed by a mathematician. Pretty cool stuff. The primitive data type is the array so it works well with parallel calculations...etc.

This is an interesting question. On the one hand, I think that you could argue that there is indeed some limited subset of words that can be used to say everything that can be said in a given language. One way to prove this, perhaps, would be to count all of the words that are used in the definitions in a given dictionary. I suspect that in most dictionaries, the total number of unique words used in the dictionary definitions is less than the total number of defined words.

This is related to what you wrote, "in practice, words are continually added to a language when new things need to be described". Consider new technologies for which new words are invented: these can generally be defined using the existing set of words in a language. The new word just provides a one- or two-word short form method of referring to that technology.

On the other hand, there are certain things - and I'm thinking specifically of human experiences as one set of those things - which are not easily summarized in a sentence and these get their own words. Consider emotions as one example. As the set of "known" human experiences (emotions, perspectives, etc.) grows, based on a more sophisticated understanding of human nature (via psychology, literature, etc.), new words are needed. Sometimes these words are borrowed from other languages, like "schadenfreude" and "empathy" (I was surprised to read that "empathy" first appeared in English in 1909, based on another German word).

On this basis, it would only be possible to limit the set of possible words if it were possible to limit the set of human experiences, which I don't think is possible. A transhuman/sci-fi example would be if a method was invented to perceive visual wavelengths that are currently outside the human visual spectrum as colours (i.e. infrared and ultraviolet, but perceived directly in the same way we perceive red and purple). I can't currently imagine a way (although perhaps there is one) of describing something like this using the existing set of words.

A minimalistic Turing-complete language is usually not very useful. Nobody seriously programs in Brainfuck.

It is entertaining to look for corresponding patterns between formal languages (programming languages) and natural ones. For example, defining new words is essential and corresponds to procedures. What about templates/generics? I think the concept of adverbs and adjectives comes close. You take a generic word "car" and specialize it "blue car". Natural languages have namespaces, but they are implicit. A jaguar could be an animal or a car depending on context.

If you like thinking about programming languages in terms of spoken ones, check out the book on J, which talks about gerunds, verbs and adverbs http://www.jsoftware.com/help/learning/contents.htm

Isn't the absence of user-defined abstractions the problem here? You cannot seriously program in BF, but you could program in lambda calculus or combinator logic, and it has just two primitives.

Maybe if there existed BF where you had a macro system for user-defined sequences, it would be possible to program in such a language.

I tried it once, it was called m4bf[0] and it abused the C preprocessor.

[0] https://github.com/federicoculloca/m4bf

recursion and embedded structures has been posited by some linguists as one possible explanation for similarities between languages cross-linguistically, however, controversially, Dan Everett's work on Piraha claims that this does not exist in Piraha. The mainstream community disagrees with him however.