The hierarchical logic of the Chinese language

What number is halfway between 1 and 9?  Is it 5, or 3?  I have a graduate degree, and I’ve read The Black Swan, so I’m quite comfortable answering 3.  This also a natural answer for children, traditional peoples, and animals, according to researchers at MIT.  But logarithmic thinking is apparently driven out of people with an intermediate level of education. How could one go about teaching logs without scary multiplication tables and the constant e?  One of the best ways I could think of would be the Chinese language (as an example of fractals in general, but again those can be scary for kids.) For instance, take the pictogram for heart.

心

This character can be used separately, or in combination with other characters to form ‘words’ (which were not really a concept in Chinese at all until outside contact was established.)

心里

Literally, “inside the heart” = psychology (or just “inside the heart”).  But the character can also be squeezed into portions of other characters, as a “radical.”

情  患  恭  必

So shish kebab (I’ll let you figure out which one that is) your heart = disaster or anguish.  But then there’s chengyu, another level above words consisting, typically, of four characters, generally with some logic to their placement.  For instance:

心上心下

“heart goes up, heart goes down.”  Sometimes, chengyu also have history behind them, something like an inside joke (although the heart character doesn’t lend itself to good examples of this, as far as I know.) So the Chinese language is built around this concept of nested levels, of the type you get by using power laws, very different from the Western logical, grammatical mindset.