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Ask HN: Concepts that clicked only years after you first encountered them?

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Re: Ask HN: Concepts that clicked only years after you first encountered them?

#11

Post by tails4e »

The fourier transform. Encountered it first in my undergrad engineering degree, it was presented as dry mathematics, with no real explanation, just threw complex exponentials at us, and pages of derivations. Years later I actually use it in my job, and through that and other material can see its beauty, and how its actually not that complicated. Some great resources like this helped a lot:

[0] https://betterexplained.com/articles/colorized-math-equation...

Re: Ask HN: Concepts that clicked only years after you first encountered them?

#12

Post by gen_greyface »

linuxlizard wrote: post #10
ergonaught wrote: post #3

Basic music theory. Almost no one I encountered bothered to actually explain anything. They simply regurgitated things and I guess expected me to somehow intuitively understand something or other.

Sadly, mathematics classes are like that as well. Instructors start throwing equations on the board, expecting us to somehow connect it all together. The best math textbook (Theory of Algebra) I ever read had little sections about the person who revealed a particular subject, why they were studying it, and how the subject is used.

Do you remember what the book was called, or the writers.

Re: Ask HN: Concepts that clicked only years after you first encountered them?

#13

Post by btrettel »

It took a couple years in college for me to understand entropy.

Entropy in classical thermodynamics is presented in a mysterious way that leads to confusion.

Entropy in statistical thermodynamics, however, is logical. Once one understands basic statistical thermodynamics, entropy isn't mysterious.

The book in my statistical thermodynamics class was An Introduction to Thermal Physics by Daniel Schroeder, which is an excellent book that I've referred to many times since.

Re: Ask HN: Concepts that clicked only years after you first encountered them?

#14

Post by everybodyknows »

bsuvc wrote: post #2

Unit testing and using dependency injection to write test-able code. I'm not sure if it was years, but it wasn't immediate. I just didn't understand why dependency injection was good at first, and not just someone's weird personal code style choice. I thought it was just people being "Enterprisey" which I'd encountered many times over the years. Once I committed to unit testing, I realized how necessary it is. Unfort…

> dependency injection

The term is unfamiliar to me -- is it related to "fault injection"?

Re: Ask HN: Concepts that clicked only years after you first encountered them?

#15

Post by mumblemumble »

The monitor model in second language acquisition. Or, more accurately, the more contemporary synthesis that it's developed into in the decades since it was first proposed.

The model itself is easy enough to grasp. But concretely understanding what it implies about how I should be studying took much, much longer.

Re: Ask HN: Concepts that clicked only years after you first encountered them?

#16

Post by parasti »

ergonaught wrote: post #3

Basic music theory. Almost no one I encountered bothered to actually explain anything. They simply regurgitated things and I guess expected me to somehow intuitively understand something or other.

I recently learned what solfege actually is from a simple ChatGPT conversation after hearing about it for many years.

Re: Ask HN: Concepts that clicked only years after you first encountered them?

#18

Post by number6 »

bsuvc wrote: post #2

Unit testing and using dependency injection to write test-able code. I'm not sure if it was years, but it wasn't immediate. I just didn't understand why dependency injection was good at first, and not just someone's weird personal code style choice. I thought it was just people being "Enterprisey" which I'd encountered many times over the years. Once I committed to unit testing, I realized how necessary it is. Unfort…

Can you explain the concept? I feel I didn't grok it fully

Re: Ask HN: Concepts that clicked only years after you first encountered them?

#19

Post by sdenton4 »

Lie Groups... I signed up for a grad level course in my second year, and had no idea what was going on. Eventually I did my PhD on algebraic combinatorics, which works with Lie Groups quite a lot, but it took years to internalize all the ideas needed to have any intuition at all.

https://en.m.wikipedia.org/wiki/Lie_group

Re: Ask HN: Concepts that clicked only years after you first encountered them?

#20

Post by closeparen »

bsuvc wrote: post #2

Unit testing and using dependency injection to write test-able code. I'm not sure if it was years, but it wasn't immediate. I just didn't understand why dependency injection was good at first, and not just someone's weird personal code style choice. I thought it was just people being "Enterprisey" which I'd encountered many times over the years. Once I committed to unit testing, I realized how necessary it is. Unfort…

Seven years into my career I'm increasingly convinced that the emperor has no clothes with respect to unit tests that are just transcripts of the code under test with "mock.EXPECT()" prepended to everything - 95% by volume of the unit test code I've ever read, written, or maintained.
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