A few months ago I finally decided that I'd had enough of repeatedly forgetting most of the Japanese I knew and then spending time getting back to an intermediate comprehension level, and that what I ought to aim for once and for all was to attain native-level fluency, at which point I'd then be able to rely on reading newspapers and listening to radio and TV broadcasts to maintain my newfound proficiency. This effort has thus far been surprisingly successful, in that I can now follow most TV dramas without much difficulty and can now read Japanese newspapers well enough that I regularly see stories in them that are only translated days later if at all, but one fairly obvious point my efforts to reach this level have alerted me to is that by far the biggest obstacle adults face in learning languages like Japanese which have very regular grammars and which are unrelated to the ones they already know isn't mastering grammatical rules but vocabulary: reasonable languages* have at most a few hundred rules of grammar to master, but in order to comprehend most of what people are talking about in a language without continuously reaching for a dictionary, one has to be able to effortlessly recall several thousand terms at the very least.
With languages like German, Spanish and French which are closely related to English, the burden of vocabulary acquisition is not so noticeable due to the huge numbers of terms shared in common, but when one no longer has the crutch of a Germanic and/or Latin inheritance to rely on, the immensity of this task becomes much more obvious. If we define a "word" to mean not just the root term but also all its inflections and derivatives - so that "vary", "variant", "variable", "invariant", "invariably" and "unvarying" all count as the same "word" - the average adult speaking any language probably actively uses something on the order of 5,000 to 10,000 such words in speech or writing, while passively knowing the meaning of perhaps 2 or 3 times as many. Considering that native speakers of a language have had their entire lives to accumulate this store of knowledge, it's hardly surprising that adult language acquisition is so difficult; even if it were not true that children have an innate facility for languages that adults lack, they'd still have an easier time of picking up new tongues due to the fact that no one expects them to be possess fully stocked vocabularies, while the vocabulary gap between them and their peers to whom the new language is native is much smaller than it is with grownups. Adult language learners, on the other hand, must go from being able to use terms like "aesthetics", "itinerant", "peroration" and "luminary" to struggling to learn new ways to say mundane things like "pothole", "engine", "leaky" and so forth.
Now, this is, as I've said, all rather obvious once you think about it, but even so it's still far too vague for my liking: what I want to do is quantify all of the above in at least a half-way rigorous fashion, so that I can try to give an answer to the following question: how many words does one really need to know to be able to call oneself "fluent" in a language, and given the number "X", what does this imply for the number of new terms adult learners must master per day? Obviously this answer will depend in part on what time frame one is looking at to getting up to speed in a language, but there are realistic limits to how many new words anyone can learn in a day well enough to remember them over the longer term, and this in turn will set some hard limits on how quickly one can hope to gain fluency even under the most intensive training regimen.
In planning my "mastering Japanese" program I set myself a base target of 20 new words a day, though I have exceeded this number pretty much every single day, and am averaging about 30-35; as I didn't start from a baseline of zero, this has been sufficient to move me from almost total incomprehension of teenage dramas to a passable understanding of even exceedingly formal NHK news broadcasts, but I'll only know I've reached my goal when it becomes impossible for me to meet my target of 20 new terms a day without resorting to reading highly technical or academic treatises, and it's precisely to estimate how far I am from this endgoal that I need the kinds of numbers I'm searching for. Japanese being a highly inflected (or rather, agglutinative) language, it doesn't require of its speakers nearly as many base "words" as the highly analytic English does, but if this English vocabulary size estimator** were indicative, I'd guess I'm still perhaps 3-4,000 new terms short of where I'd like to be.
*And here I count English as being among the least reasonable languages in widespread use; nearly every possible grammatical "rule" seems to have an exception or other, and usually there are several.
**Native English speakers who are prone to belittling foreigners for having an imperfect command of their language should consider just how basic many of the terms at the 12,000 to 18,000 word level on this test are: if one learnt English terms in their order of frequency, one would still not know the meaning of "adaptable", "capsule", "justify" and "liberate" even after mastering some 12,000 terms! Then there's the hell that is English grammar to consider ...