Hacker News Reader

Comment by Terr_ | Hacker News Reader

I think I avoid imposter syndrome in some areas, but Not Enough Real Math is definitely a weak spot.

When people start talking about eigenvalues, I'm just a business-rule caveman with a little discrete-math unga bunga.

This kind of statistical stuff falls somewhere in-between.

Eigenvalues are a topic in linear algebra. They're coefficients you can put in front of some matrices or vectors that change their magnitude.

Linear Algebra was the most useful and fun math class I took in college. Highly recommended if you ever wanna do gamedev. It's more approachable than you probably think.

For me, when people start talking about differential equations, specifically the symbols you'll see in a wikipedia article about Navier Stokes equations, I'm just a business-rule caveman with a little linear algebra zug zug.

> Eigenvalues are a topic in linear algebra. They're coefficients you can put in front of some matrices or vectors that change their magnitude.

Multiplying a vector or a matrix by any nonunit scalar changes its magnitude (hence scalar!! i.e. something that scales). Not all scalars are eigenvalues. So this isn't quite right

Think about it geometrically instead. A linear operator transforms a space. Geometrically the transformation can be one or more of stretching, compressing, or rotating (taking shearing to be a kind of stretching). The directions in the space which remain the same other than having been scaled by some factor are the eigenvectors of the transformation. The scaling factor of one of those such directions is its eigenvalue.

> when people start talking about differential equations

It's not like you are going to solve those analytically.

Implement a couple numerical solvers for things like Navier–Stokes and you'll see that differential equations is just obscenely compressed code.

Studying more statistics is often clever. Although in this case Mr. Miller led the the most important part - if there are two numbers (like 7 and 5) in a statistical context they might be the same number. That throws a lot of people into such a tailspin that they never really recover after making the obvious mistake of thinking they are different.

The powerful heuristic for the less technically inclined is to say "well, this evidence isn't conclusive until someone who knows statistics has tried to shoot it down".

I'm probably like you, haven't taken the time as an adult to really rub these things in, but I find it helpful to sometimes throw up a P5.js and do some high school or early uni exercises graphically. JS can be a trivial language and doesn't get in the way and it gives a draw loop for free, including a global frame count you can pull from when you need some integers to juggle.

For me it teaches differently than trying to follow video lectures.

Then definitely what 3Blue1Brown's video on eigenvalues and eigenvectors. [1] That's when I clicked to me! His entire series on Linear Algebra is incredibly well produced.

[1] https://youtube.com/watch?v=PFDu9oVAE-g

Reply on news.ycombinator.com