Most language learning resources focus on the process of what YOU can do to learn a language.
But what I'm interested in is how a language is an organic, living, naturally occurring phenomenon, like rivers, trees, and humans, and what that has to do with efficient language learning, as well as what it has to do with the nature of life/God/the universe (as a bonus).
The mathematician Leonardo Fibonacci used a set of numbers (Fibonacci numbers) to describe how rabbit populations expand. The numbers are 1, 2, 3, 5, 8, 13, 21, 34, ... (each number is the sum of the previous two numbers). This "golden" ratio also describes flowers, trees, rivers, seashells, galaxies, and the human face.
Language also grows this way in your mind -- particularly if you're a child. My goal is that it grow that way also in the mind of the adult.
The way it looks is that for every language you grew up speaking there are a number of situations you've experienced in which you used that language. You now draw from those situations and everything in them to speak the way you do today. Each of those situations (or topics) are like branches that grow from a single point -- that single point being whatever language you're speaking.
Each of those situations has its own branches, those being verbs that support the situation. For example when hungry, the verb is 'I want', or 'I need'; when happy, the verb is 'I feel', or 'I love'.
Finally, growing from each verb are vocabulary, such as 'food', 'milk', 'great', and 'you'--that which completes the sentence that the verb started.
At each level, the total number of points increases, the result approximating the Fibonacci scale (See visual aid at the end of this post).
And that's it. It's the tree. It's the way language grew, multiplied in your mind as a child without your consent. It happens as naturally as anything does in nature. It's golden; it's divine.
In terms of practical language learning, it means that if you want to learn a language, you have to cultivate the proper conditions for the language to grow in your mind. This involves sunlight and water (input), it involves roots (thinking in the language), it involves branches (verbs) and leaves (vocabulary). And it involves doing things in a certain order so that the process be in harmony with that golden mean.