The Necessity of Grinding Through Concrete Examples Before Jumping Up a Level of Abstraction

If you go directly to the most abstract ideas then you're basically like a kid who reads a book of famous quotes about life and thinks they understand everything about life by way of those quotes.

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Many learners fail to understand that grinding through concrete examples imbues you with intuition that you will not get if you jump directly to studying the most abstract ideas.

If you go directly to the most abstract ideas then you’re basically like a kid who reads a book of famous quotes about life and thinks they understand everything about life by way of those quotes.

The way you come to understand life is not by just reading quotes. You have to actually accumulate lots of life experiences.

And you might think you understand the quotes when you’re young, but after you accumulate more life experience, you realize that you really had only the most naive, surface-level understanding of the quotes back then, and you really had no idea what the hell you were talking about.

It’s the same way in math. In general, the purpose and power of an abstract idea is that it compresses a zoo of concrete examples. But if you haven’t built up that zoo of concrete examples then you miss out on that power.

If you shy away from grinding some messy math then you will never truly know what the hell you’re talking about.

Skipping the concrete examples is a one-way ticket to existential crisis.

If you’ve lived and breathed concrete examples, they’ll get compressed into tangible, meaningful abstractions that inject you with a dose of vitality every time you work with them – but if you haven’t, then the abstractions will feel dull and lifeless, and you’ll constantly wonder what’s the point of pushing meaningless abstractions around in arbitrary patterns of allowed manipulations.

For instance, a company’s balance sheet can tell an incredibly interesting story if you have visceral experience with success and failure in business – but if you don’t, then analyzing financials will make you feel like a robot checking whether numbers match semi-arbitrary conditions for being “good” or “bad”.

Grinding the concrete examples is NOT about turning yourself into a robot and shielding you from intellectual awakening.

It’s the opposite.

It’s about equipping you with invigorating experiences that can live on through the abstractions, empowering you to actually know what the hell you’re talking about.

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