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Comment by lordnacho | Hacker News Reader

Maybe the way I'd phrase it is the knowledge you learn at university, to the extent that it's applicable, is actually just indexing.

So for instance I figured out that numerical methods are a thing that you can use to approximately solve differential equations, which often don't have a nice analytical solution.

Can I solve differential equations? Not anymore. Can I solve one by the end of this week? Definitely.

What you do in college is a bit of intellectual tourism, looking at wide variety of topics briefly. There are natives who depend on the tourists for part of their living, who know every nook and cranny of PDE solvers. But like in the real world we're mostly at home in one place and tourists everywhere else.

The other answer to your question is that you build up an intuition for where the dragons are. The more tourism you do, the more you come to suspect there are other continents in certain places.

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I largely agree with your points, but i'd say it's more "intuition building". To make a silly example, I don't know C# at all, in fact I have never written a single line of C#, but I'm very confident I could get up to speed relatively quickly because I know Java fairly well. This is simply due to the fact that after a while you just "get" how things work.

Similarly, even though I'm by no means a mathematician, I feel, at least to a limited extent, like I "get" math.

This kind of intuition, innate feel for how things work in a certain field of study lasts way longer than the details of a specific proof or the code for a specific algorithm, and I feel it's the actual output of higher education.

I was able to build a decent intuition in both maths and programming before going to university. It's not something specific to higher ed, just experience.

> numerical methods are a thing that you can use to approximately solve differential equations

indexing of knowledge is useful for certain fields, but without in-depth understanding, you can never apply this knowledge in ways that hasn't been imagined before.

I am reminded of the story of Feynman and the Connection Machine, where there was a need to figure out how much traffic CPUs would generate for the router they designed. If you weren't fluent in differential equations analysis, you would never have thought of using this method to perform the analysis.

Search for "By the end of that summer of 1983, Richard had completed his analysis of the behavior of the router" in https://longnow.org/essays/richard-feynman-connection-machin... to find the relevant section about this.

> without in-depth understanding, you can never apply this knowledge in ways that hasn't been imagined before.

Sure, sure. But the hard truth is that I’m not getting paid to do so.

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