Foundations

Everything has foundations. Have you thought about that?

If you've undergone formal education, you've heard a professor mention the importance of foundations. In fact, math curricula are built that way: you learn the basics of arithmetic before you jump into linear algebra or group theory.

The core value proposition of foundations is that they help you learn well: learning foundations implies easier progress. 

Sometimes it's hard to see what builds upon what. This happens often, especially as a field of knowledge matures.

What's interesting is that each layer of foundation does not necessarily stack on top of each other. While analogies are great for initial intuition development, they can lead us astray in our search for truth. I've heard expressions along the lines of “building the roof before the walls” when emphasizing the role of foundations. But, this assumes knowledge is linear—which is wrong if you look at the history of human discoveries. What many consider useless may turn out to be extraordinarily useful and vice versa. But figuring out what has value and what has not is hard.

For example:

  • Understanding the Internet will help you grasp other kinds of interconnected systems.
  • Writing well will aid your thinking
  • Drawing improves your memory (which can improve many other things).

Foundations stacking on top of each other is useful to understand the utility of core skills (better learning), but it may be erroneous to think of knowledge as bricks. At that point, we've overextended the analogy. What happens if you have knowledge that is interconnected? In that case, there is no single piece on top of another piece; both are valid pieces of knowledge. The analogy breaks particularly as the number of pieces increases.

At that point, it's more useful to think of human knowledge as a graph—or, if you want to be pedantic about it, a hypergraph.