Opposite problem—I know pretty much what an imaginary number is, and even some applications of i. Numbers can have real and imaginary elements, fine. But I have no idea why they have an application here.
That said, this post makes a lot of intuitive sense to me, a humanities graduate, so this series is off to a pretty good start. If Eliezer’s good at one thing, it’s explaining complex-seeming things I know a little about in a very sensible and useful way.
Then I actually read the article from the comment above (to refamiliarise myself with the maths), and was quite surprised to find that the article makes this relation very clear.
Oh my god...imaginary numbers...they make sense now!
Seriously, thank you for that link. I’ve gotten all the way through high school calculus without ever having imaginary numbers=rotation explained. Looking at the graph for 10 seconds completely explained that concept and why Eliezer was using imaginary numbers to represent when the photons were deflected.
Opposite problem—I know pretty much what an imaginary number is, and even some applications of i. Numbers can have real and imaginary elements, fine. But I have no idea why they have an application here.
That said, this post makes a lot of intuitive sense to me, a humanities graduate, so this series is off to a pretty good start. If Eliezer’s good at one thing, it’s explaining complex-seeming things I know a little about in a very sensible and useful way.
Actually, I was in exactly the same position.
Then I actually read the article from the comment above (to refamiliarise myself with the maths), and was quite surprised to find that the article makes this relation very clear.
Worth a look. :)
Oh my god...imaginary numbers...they make sense now! Seriously, thank you for that link. I’ve gotten all the way through high school calculus without ever having imaginary numbers=rotation explained. Looking at the graph for 10 seconds completely explained that concept and why Eliezer was using imaginary numbers to represent when the photons were deflected.