The image is not mine. It is a fantastic creation bybigblueboo that has caught some attention outside of the usual math tumblverse. You should definitely check out eir blog and if you like this post you should (also?) reblog the original. With that out of the way:
Linear Algebra. Linear algebra is the study of vector spaces, which are “flat” structures that have a notion of addition and dimension.
L^2(S^1) is the space of “square integrable functions on the circle”. Every continuous function from the closed interval [-π,π] is in L^2(S^1), but the space also includes some functions which have discontinuities, so long as they are not too extreme.
bigblueboo’s image happens to be an excellent source of mathematical content: this post is final post in a series in which I discover some of its secrets. In the first post you can see a derivation of its symbolic equations of motion, and part two contains a sweet characterization. The third post, which explains that the non-constant speed in the gif is not (entirely) a result of the viewing angle, and the fourth post quantifies the variation.
I have some more questions about HTPs; there are certainly natural questions to look at. Therefore, I am planning on doing an epilogue post which will lay out some of the questions I have. If you have any questions you’d like me to share, please reblog and I’ll (probably) include them! However, that post will not be written in fancy images like usual but I’ll just do the best I can in plaintext so that it can be a legitimate reblog of the OP (hopefully he’ll see some of the work that his wonderful piece inspired!)