had the first class of simplicity analysis today. unbeknownst to me, this class is not very simple. i almost forgot i had lecture and immediately jumped into bed to study right before class started. even angel's timetables run late sometimes i suppose. it's just another variable to take into account in this class; it's fascinating, i'll tell you that. this is going to be a very exciting course.

so let me start by introducing the professor. well, he's less of a professor and more of a TA grad student peer reviewed study buddy boytoy. his name is gabriel and the most explicit thing i can say about him is that we study together and i think that my fingers fit quite nicely inbetween his shoulder blades. i had met him before, after i actually enrolled in the class and got a seat, but our meeting was somewhat under different circumstances than lecture, although i think it informed my study in a positive way. i like gabriel and i like that he forces me back into Rn. after working in R2 for so long, it's quite a breath of fresh air. also i like that he takes initiative, so to speak. i find so often that i am the one in the position of choosing things, and while i quite like conducting the orchestra, it's nice to be an instrument and let myself be played.

now that that's covered, let's talk syllabus. it was less of a syllabus and more of a goal, in a way. we're attempting to define a very specific function; we decided to name it s(x), since we believe it might relate to arc length in some sense, no matter how much i dislike the theater of curvature formulas. so s(x). really, it should be a simple goal. we're not even trying to find a taylor series here, we just want to know about it. find its domain, range, kernel, how it interacts with other functions, whether or not it could be an operator. but it's so slippery it's really not as straightforward as it seems.

today was a very interesting lab. our goal was a certain defined output that we assumed the function had based off of its relationship with another actually known function. we were successful in the endeavor, but not by any logical means; we forced it out by overloading the system, so to speak. many of the inputs seemed to do absolutely nothing, and although we weren't able to work with the standard basis we normally chose, we didn't expect to get results this drastically different. it seemed almost as if there was a massive, countably infinite discontinuity that spanned across all of the inputs we would put in. but, i must admit, the output we did get was surprisingly exemplary; i didn't expect to find a pressure volume relation hidden in there, but inexplicably, it was! there will probably be applications of physics to apply this to in the future, but i suspect that'll come in the second half of the course.

we didn't get to experiment enough to see if our results were repeatable, or there were other factors that were contributing to this, but this discontinuity fascinates and puzzles me. i wish to study it more and, since we plan to use s(x) as a known function in the future, potentially find a way to naviagte around this otherwise unwanted result.

oh, i almost forgot to mention. we're attempting to define s(x) in the sense that we have certain stipulations that we're working in that this function needs to exist in (which is mostly what we're in the process of figuring out) but our second step is to find the most efficient definition, the most useful, the most beautiful, the most applicable etc. a host of definitions that each can excel in their own category of applications. to say that in a different light, currently we're trying to understand what s(x)s there are and what we can do with them and how we can make them work for us, then we'll be able to begin work on manipulating them to suit our needs. but i have a sinking suspicion that the first part, the exploration, is going to take a long time.