Study the basics of science and math before higher-level theories

Part of ‣.

I first learned this from Naval Ravikant. The rule is that if you notice that you are trying to apprehend some theory that rests on some other theory which you don't really understand, you should start learning that basic theory first, or abandon learning (or forming) a high-level theory at all and keep relying on practical heuristics.

To focus on the most fundamental pieces first is also one of the ‣ (by Scott Young's account in ‣).

In ‣, Richard Hamming puts this principle like this:

Get down to the basic to find connections between fields. You need to know the fundamentals very well; the fancy parts then follow easily and you can do things that they never told you about.

He also writes,

Pasteur says, “Luck favors the prepared mind”. Study the field fundamentally to discover anything new in it.

This heuristic doesn't mean, however, that one must always start with physics when trying to learn anything about nature, for example, biology or geology. Sometimes, there are solid levels of description (i. e., levels of Emergence) that make it unnecessary (and often ineffectual) to go deeper. For example, Darwin didn't need to know genetics (and biology in general) on the modern level to explain the peculiar features of animals on remote shores because he found a solid framework that emerges from genetics and the biology of species: the theory of evolution and natural selection. By the way, evolution emerges not only in biology, but also in memetics, in computing, and, perhaps, even in cosmology, so it shouldn't be even considered a part of biology. Cf. ‣.

If a theory directly uses some math, e. g. calculus or linear algebra, you have to understand that math before studying the theory, there is no way around it. You fool yourself if you try to learn a theory without understanding the math employed by this theory.

I don't know any specific criteria for deciding whether the emergent abstractions are robust enough so that one doesn't need to study more foundational theories, as well as for deciding whether one understands the basics well enough to proceed with studying or making high-level theories (what does it mean to "understand" something, and what are the degrees of understanding, is a big separate topic). But since the principle of "focusing on the basics of science and math" is just a heuristic, I would also use a vague, yet practical criterion: you should try to reflect honestly whether you are bullshitting yourself or not when you think you understand a high-level theory.

Studying the fundamental science and math before higher-level theories is also an effective strategy of dealing with runaway knowledge growth. The "outer surface" of science expands much quicker than the essential core. Moreover, understanding the core math and science allows you to quickly grasp the essence of many high-level theories if and when you will need to learn them. Thus, prioritising learning the basic science before higher-level theories could be seen as the 80/20 principle applied to learning.

Sociology and anthropology often include a good deal of story which the author wants the readers to believe, e. g. similar to politics in macroeconomy, as Naval writes.

Part of ‣ and ‣.

To study the basics of the science is to ‣.

To focus on the fundamentals of science is the learning analogy to the engineering principle Bottom-up design is more robust than top-down. Study the basics ("bottom") before studying or forming higher-level theories ("top").

More concretely: