What on earth are successive approximations? Learning some, backing off, learning some more, backing off again, etc. Eventually, with enough of these reiterated cycles, you can accumulate quite a bit of knowledge. I find that this is in fact how I learn languages. Rarely do I just charge in, learn everything from lesson 1, and just keep on in a straight line until achieving a reasonable command of the language.
Although I had had this up-and-down experience with language learning several times before, it had always felt like the wrong way to go about it. I really should just plow on through. The only reason I did not was lack of diligence on my part, I thought. There might be something to this, but in fact, I think it is a behavior pattern that is rooted in common human nature. One day, I think it was when I was taking an anthropology class at SIL, I heard an account of the Indian groups who live along the jungle-lined rivers of Venezuela. Many tribes live along these rivers, and they regularly intermarry. Children grow up learning the language of each of their parents and bits of other languages spoken in their villages. As they grow, they gradually learn more of each of these secondary languages. By they time they reach middle age, they routinely have a good command of 7-10 languages. But they don't learn them by steady study of one at a time. They learn them by this process that I have labeled successive approximations.
After hearing about this, I felt "legitimated," so to speak, with regard to my own experience. I have felt good about it in the 25 years or so since taking that anthropology course. And I have continued learning languages in this way. Now that I am in my forties, I can see the benefit of this approach. I have gained sufficient ability in reading French that I can easily read the technical books and articles needed for my graduate studies. I have learned to read German well enough to at least plod through articles without getting lost in the deep forest of grammatical trees. My knowledge of Greek has likewise progressed in fits and starts to the point that I can now read the book of Hebrews in the New Testament with little difficulty, in spite of its Greek being the most complex in the NT corpus. And so on and so forth.
I am glad to be where I am, though it has taken much effort over many years. Given a couple thousand more years, who knows? I might actually get the sort of knowledge I would like in all the languages I would like to have it in! But in the meantime, it is nice to be able to read a lot of materials, even if slowly, that would have been all but impossible for me to handle ten or fifteen years ago.
So, those few of you who may actually read this blog, take heart. Don't beat yourselves up over your slow, often interrupted progress in learning the languages you want or need to know. Just keep on plugging away in those successive approximations and you will see plenty of good results as the years go by.