Narrow vs broad cognitive augmentation

Here is one axis I've been paying attention to when thinking about the question of "how to do we make people better at thinking?":

narrow/vertical/specialized: This kind of augmentation looks at a concrete topic and tries to get at its "true nature", and then comes up with tools to help people think specifically about that topic. For instance, Arabic numerals look specifically at numbers, helping people manipulate and think about them. Sure, you might also learn some things about logarithms or Cauchy sequences by studying Arabic numerals, but mostly they only help you think about numbers, not about some completely unrelated topic like linear algebra. (I want to distinguish between how knowing the Arabic numerals helps you do linear algebra because of course you use numbers while doing linear algebra, which seems totally obvious to me, and Arabic numerals actually giving insight about linear algebra, which seems false to me.)
broad/horizontal/universal: This kind of augmentation looks at learning in general, and asks how we can come up with tools that help across a diverse variety of fields. For instance, spaced repetition or the invention of writing are good examples here. Spaced repetition helps you not only learn languages, but also any subfield of math, and chemistry, and physics, and on and on. There is nothing about spaced repetition that is specifically about, say, linear algebra; it's more that spaced repetition is a fact about how the human brain learns.

See also