The Double-Edged Nature of Hierarchical Knowledge

It's easier to run into roadblocks, but also easier to maintain what you've learned.

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The reason that math is hard for most is the same reason that math is easy for some: dependencies.

To succeed in learning math, you need to learn carefully and thoroughly.

If you skip over material, then you won’t be able to learn anything that depends on that material.

In extremely hierarchical subjects like math, a single knowledge defect can create a total roadblock to learning –

whereas in less hierarchical subjects like history and biology, it’s less of an issue.

But dependencies also mean that it’s easier to maintain existing mathematical knowledge than, say, historical or biological knowledge.

The mathematical knowledge base contains a lot of information stacked on top of itself, and you can review the entire knowledge base by just reviewing the information at the very top of the stack.

By contrast, in history/biology, the information is more spread out as opposed to stacked, so you have to review a lot more information in order to cover the entire knowledge base.

This is the double-edged nature of hierarchical knowledge: it’s easier to run into roadblocks, but also easier to maintain what you’ve learned.

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