I’ve always loved flashlights. Yes FLASHLIGHTS with an A!!! Anyway, apparently not many people share my rather niche interest.
So I ask you, fellow Lemmites, what are your hobbies and weird obsessions that you can ramble on about for hours?
Please feel free to ramble on about your passions here. Maybe you’ll find some likeminded individuals!
Audio engineering. How to take a bunch of tracks that sound like hot shit and make them into beautiful music. How to record an awesome performance, probably in a shit space with shit acoustics and shit gear. How to work my “magic” on a track to somehow do the impossible. More recently, how to analyze and design analog outboard gear and digital plugins that emulate them in real time. I would do it for free if I had the time. I used to mix people’s tracks on Reddit (different username) before I went back to school.
Music, particularly writing and playing
shitty bedroom black metalguitar. So I guess not that weird other than the music choice…Automation, particularly AI and Control Theory. I approach AI from a dynamic viewpoint, i.e. using machine learning to analyze and control systems that “move”. I’m still working on unpacking the mathematical fundamentals of AI, especially because the dynamic applications I’m interested in require much more careful understanding of the assumptions that typical machine learning paradigms make about the input and output signals.
Math. Calculus, linear algebra, dynamical systems, and high- or infinite-dimensional problems. Both theory and applications. I read textbooks and watch open course lectures. I use this math to back up my intuition in all the above subjects. Even people who say they like math find my interest in the subject obsessive.
What the hell would constitute an “infinite dimensional problem”?
Any time you need to analyze or synthesize a function or signal, rather than just a set finite set of values, the problem will in general be infinite-dimensional unless you choose to approximate it. Practically, most physics problems begin as a partial differential equation, i.e. the solution is a signal depending on both time and space. Hopefully, you can use problem symmetry and extra information to reduce the dimensionality of the problem, but sometimes you can’t, or you can use the inherent structure of infinite-dimensional spaces to get exact results or better approximations.
Even if you can get the problem down to one dependent variable, a function technically needs an infinite number of parameters to be fully specified. You’re in luck if your function has a simple rule like f(t) = sin(t), but you might not have access to the full rule that generated the function, or it might be too complicated to work with.
Let’s say that you have a 3-dimensional vector in space; for example, v = (1,0,-1) (relative to some coordinate system; take a Euclidean basis for concreteness). Another way to represent that information is with the following function f(n) = {1 for n=1, 0 for n=2, -1 for n=3}. You can extend this representation for (countably) infinite vectors, i.e. sequences of numbers, by allowing n in f(n) to be any integer. For example, f(n) = n can be thought of as the vector (…,-2,-1,0,1,2,…). This representation also works when you allow n to be any real number. For example, f(n) = cos(n) and g(n) = e^n can be thought of as a gigantic vector, because af(n)+bg(n) is still a “gigantic vector” and functions like that satisfy the other properties needed to treat them like gigantic vectors.
This allows us to bring geometric concepts from space and apply them to functions. For example, we can typically define a metric to measure the distance between two functions. We can typically define a “norm” to talk about the size or energy of a signal. With a little bit of extra machinery (dot product), I can find the cosine between (real) functions and get the “angle” between them in function space. I can project a function onto another function, or a subspace of functions, using linear algebra extended to function spaces. This is how I would actually take that infinite-dimensional problem and approximate it: by projecting it onto a suitable finite basis of vectors and solving it in the approximation space.
Math can be so much fun. I fell in love with math after watching the linear algebra series by ThreeBlueOneBrown. Unfortunately I don’t have much time to do math puzzles, because I’m too busy with programming puzzles, hacking puzzles, arduino stuff or building stuff inside or outside the house.
I highly recommend checking out The Bright Side of Mathematics if you want to learn more about math in some detail. His videos are a lot shorter than typical open course lectures covering the same material, but you still get the major results and important proofs. He has playlists on linear algebra, real analysis, probability, and tons of more technical topics. IMO if I need to learn high-level math in a short time, he’s where I go first.
Also, despite the channel name, he has both bright and dark versions of all his videos so my eyeballs don’t melt.
3Blue1Brown is great too.