How to Understand Things • Hacker News Board

Re: How to Understand Things

#111

Post by closeparen » Sun, Jul 12, 2020, 7:01 PM UTC

RedShift1 wrote: post #2

Heh I get this a lot in my daily sysadmin/developer duties. When you need to turn on a knob somewhere you don't just wanna know that you have to turn it on, you want to know why you need to turn it on and follow the chain up until you get to facts you already know. But it's not always possible to get that far, there's too many layers of abstraction, the source code is not available or you just don't have the time.

Swimming in uncertainty and (conditionally) trusting abstractions is one of the skills I have to teach my interns. I love their desire to understand and I try to be careful not to kill it. But at the same time, software engineering in the real world means contributing to a picture that is larger than will fit in your head.

Re: How to Understand Things

#112

Post by agucova » Sun, Jul 12, 2020, 8:11 PM UTC

lightfooted wrote: post #62

The points about education really resonate with me. In my engineering undergrad, it was frustrating to see in our applied math courses that the mechanical plugging and chugging of equations was the approach that most of my peers took in their studies. They got better grades than me. I wanted to understand concepts more deeply, but there was no time, and the tests rewarded those who could simply go through the motions…

I'm a first-year engineering undergrad, last Friday I finished the last Calculus 3 exam on the semester.

I spent 2 days studying with friends just to see they would blindly memorize formulas with no regard whatsoever for what they were actually doing. "I'm not the understanding type", they said unironically.

Do you think this happens more often in engineering than other disciplines? Some people believe that applied science or mathematics means that just learning formulas is enough

Re: How to Understand Things

#113

Post by jairofloress » Sun, Jul 12, 2020, 11:38 PM UTC

refrigerator wrote: post #6

Great post. Personal anecdote: I don't think I really understood anything in school, but I was decent at going through the motions of carrying out certain methods and recalling certain facts when I needed to. I went on to study Maths at university, and for most of my first year, I had the same surface level "methods + facts" knowledge that got me through school. After some studying, I could recite definitions and the…

I always remember the exams frustration of remembering the exact page of some graph but being unable to get it back. I hated it!

Re: How to Understand Things

#114

Post by iambrj » Mon, Jul 13, 2020, 12:13 AM UTC

nqureshi wrote: post #8

refrigerator wrote: post #6

Great post. Personal anecdote: I don't think I really understood anything in school, but I was decent at going through the motions of carrying out certain methods and recalling certain facts when I needed to. I went on to study Maths at university, and for most of my first year, I had the same surface level "methods + facts" knowledge that got me through school. After some studying, I could recite definitions and the…

OP here -- that is a fantastic anecdote! Do you have an example of a "drawing" of a theorem, in this context? (I've seen these for fairly trivial theorems but not for more complex ones, so I'm curious.)

I think a good example would be Lagrange's theorem[0]. Once you have this[1] picture in mind, it becomes trivial.

[0] https://en.wikipedia.org/wiki/Lagrange%27s_theorem

[1] https://i.stack.imgur.com/w2GfA.png

Re: How to Understand Things

#115

Post by [deleted] » Mon, Jul 13, 2020, 10:46 AM UTC

[deleted]

Re: How to Understand Things

#116

Post by codersteve » Mon, Jul 13, 2020, 10:57 AM UTC

drorco wrote: post #50

knzhou wrote: post #41

Earlier quoted context omitted.

> says you need to master each step on the track before moving onto the next one. this is poisonous and borderline evil What’s wrong with it? You do need to understand calculus before classical mechanics, classical mechanics before quantum mechanics, quantum mechanics before quantum field theory, and quantum field theory before the Standard Model. I’ve seen tons of people disregard this and the result is always confu…

Some people like to work their way in reverse. I'd often pick a really complicated subject I'm after like "stellar fusion" and then work my way downwards and learn whatever I need to learn in order to understand it. If I had to start from differential mathematics, without knowing why I need it, I'd probably give up.

This is the big problem I had with engineering in school, so much was based on faith that you needed it. And just now as I'm writing this, I realized that's completely counter to my personality.

side note: I remember Einstein needed to learn particular math skills to help prove his ideas and sought out to learn it.

Re: How to Understand Things

#117

Post by kenny87 » Mon, Jul 13, 2020, 2:56 PM UTC

Sharing one of my favorite quotes on this topic that James Clerk Maxwell was said [0] to tell his students:

"In this class I hope you will learn not merely results, or formulae applicable to cases that may possibly occur in our practice afterwards, but the principles on which those formulae depend, and without which the formulae are mere mental rubbish. I know the tendency of the human mind is to do anything rather than think. But mental labor is not thought, and those who have with labor acquired the habit of application often find it much easier to get up a formula than to master a principle.”

[0] https://www.youtube.com/watch?v=v40OcJ7rfSE&t=788s

Re: How to Understand Things

#118

Post by cbsmith » Mon, Jul 13, 2020, 6:00 PM UTC

afarrell wrote: post #20

> This quality of “not stopping at an unsatisfactory answer” deserves some examination. > This requires a lot of intrinsic motivation, because it’s so hard; so most people simply don’t do it. It also requires self-confidence, persuasiveness, and social power. Without these traits, your attempts to really understand something will be dismissed as "overthinking things" or "trying to understand the universe". Those arou…

Yeah, there's a bunch of caveats here. You also need to be reasonably quick to understand things, otherwise you'll be spending a lifetime trying to understand some pretty basic concepts and never get to anything interesting.

In general, there are a bunch of starting conditions necessary for this kind of approach to glean value.

Re: How to Understand Things

#119

Post by arendtio » Mon, Jul 13, 2020, 8:11 PM UTC

> Another quality I have noticed in very intelligent people is being unafraid to look stupid.

At school, there was a guy who used to ask questions which made him look stupid, at first. After discussing said questions for a few minutes, it often became apparent that those questions were in fact at the heart of the topic.

Re: How to Understand Things

#120

Post by cutemonster » Thu, Jul 16, 2020, 8:29 PM UTC

BeetleB wrote: post #53

afarrell wrote: post #20

> This quality of “not stopping at an unsatisfactory answer” deserves some examination. > This requires a lot of intrinsic motivation, because it’s so hard; so most people simply don’t do it. It also requires self-confidence, persuasiveness, and social power. Without these traits, your attempts to really understand something will be dismissed as "overthinking things" or "trying to understand the universe". Those arou…

There are both extremes, and best not to be at either one of them. Example: I forget the name of the principle, but in mathematics the statement "P implies Q" is considered true if P can never be true. As an example, let P be "George Washington was a woman" and Q be "Queen Elizabeth is a man". Then the statement "If GW was a woman, then QE is a man" is considered to be a true statement. I have a friend who refuses to…

Actually there were women who dressed like men, pretended to be men -- and if it, surprisingly, turns out this was the case with GW, then that won't make QE a man.

I have to agree with your friend :-)