Linguists have some methods to measure the complexities of the grammar of a language. Some linguists may refer to how many grammar rules that language has. some may also refer to how many morphemes a single word has in that language , while other linguists may also refer to how many grammatical cases a language possesses . Okay let's go straight to the point, Polish is hard to learn because it possesses so many grammar rules and word changing, same for czech and Lithuanian . American indigenous and some caucasian languages are hard to learn because they possess so many morphemes in their single word (Abkhaz and Adyghe verbs are perfect examples). While Hungarian, and northeast caucasian languages like Tabassaran, and Tsez are hard to learn because they possess so many grammatical cases, with Tsez being the most extreme with 126 cases ( depending on one's analysis). My question is, What are the best methods to measure the complexity of the grammar of a language ? . What is the hardest language on earth to learn in terms of grammar complexities based on that method ?
I haven't the slightest idea what the answer to you question might be. I think you're wasting your time with such speculations. Basically, I guess, you think the difficulty of a language must be somehow proportional to the length of a grammar book written for that language. I don't think so.
Details of vocabulary are a great labor for dictionary makers and grammar writers, but humans don't learn languages by reading dictionaries and grammars, though those may be helpful. Instead, humans have a fantastic ability to remember such details about words -- it's not hard for us.
Linguists have some methods to measure the complexities of the grammar of a language.
Methods to measure the complexities of different aspects, absolutely.
What are the best methods to measure the complexity of the grammar of a language ?
That's the problem: there is no best method.
It's like asking "which cultures on earth are the most complex?" Different cultures, like different languages, are complex in different ways. Some languages have extremely complicated systems of derivational morphology, others have tables and tables full of inflections, and still others have syntax full of movement rules.
And most importantly—complexity in one of these areas tends to lead to simplicity in others. Languages with complicated inflection systems tend to have a freer syntax, for example, while languages with complicated syntax don't need as many inflections.
Now, it is possible to find a language that's simple in all of these respects: look into the early stages of trade languages and pidgins as they begin their evolution into creoles. They tend to start with very straightforward syntax, and almost no morphology at all. But as time goes on, they tend to start gathering complexity, since deeper syntax and morphology make it easier to communicate complicated ideas. Eventually, they reach the level of other natural languages, and tend to rest comfortably there.
P.S. If someone were to actually make a metric of "language complexity" or "language learnability", specifically excluding orthography (since that tends to come later), I would expect all well-established natural languages to be hovering around the same level. The process of language learning puts strong selection pressures on languages, keeping them complicated enough to express elaborate concepts, but simple enough to be learned by speakers. As a pidgin develops into a proper living language, these pressures are what push it to take on more and more intricacies until it reaches that same vague level.
a) What you exemplify is an inductive argument, you have seen or heard of people who have a hard time learning the grammar, and you assume it were the grammars fault. Native speakers might think quite differently, though. What you are looking for is either a reductive (rule based) argument, which would lead to a kind of Universal Grammar base line type system common to all the languages in comparison; Or a deductive argument based around typology. I hope I did not mix-up the two.
b) In physics there is a duality between Measurement, Control and Regulation. Your question for measurement suffers from a loose definition of the system that you want to measure. In other words, you meant to ask for a definition of grammar-complexity. Since grammar is multi-facetted, there is very likely--in my humble opinion--no lossless projection onto a single dimensional measure. Only Euclidean spaces have the unique norm. However, since there is no concensus on whether language grammar were, in some dark corners, a context-free grammar in the sense of Chomsky's hierarchy, thus NP-complete, and since NP-complete problems cannot be modeled in Euclidean spaces, though they can be approximated e.g. via schema of induction, I would not be too sure that your question has an answer.
Sorry for the rant, I am just trying to show the scope of the problem. Put another way, a language with only two words and a really simple construction rule can have a hell of a run-time complexity, but it's rules are really simple to describe.
One can try to evaluate complexity of a written word by calculating its Shannon entropy. This type of complexity is related to Kolmogorov complexity, they might be equivalent.
One approximate way of doing it is by compressing the text and then calculating its entropy rate. If you want to compare the languages of your choice, then you can skip the entropy parameter and stay with the size of the compressed text file.
- Obtain a corpus of translated works [e.g. legal documentation, official announcements, the Bible, etc.], the files must be fairly large;
- All files must use the same encoding system, with constant number of bits per character;
- Use opensource general-purpose lossless compression algorithms/software to compress those files; do that with the disabled use of system or software dictionaries, those must be generated by the algorithm at work.
- Apply statistics to calculate errors of those measurements.