I abandoned this little blog for a good period of time, and came back to find pending comments, so I guess people are still reading it. In case you’re curious or like what you’ve read, I’ll briefly say what’s been going on with me and what will happen to Gracious Living.

Since my last post in 2011, I made some poor/’interesting’ decisions, entered a dark period of my life, recovered from that dark period, wrote a thesis about model categories, graduated college, and started grad school at Northwestern. I’ve been learning a lot about homotopy theory and algebraic geometry over this first quarter. I’m still the same O. G., confused, thoughtful, struggling, frustrated, excited, and more interested in math than ever. Northwestern’s been treating me well so far and I’m looking forward to the waiting future.

What I wanted to do with this blog — discuss math from the ground up — was ultimately a quixotic task. There is simply too much math, and ultimately the only laypeople capable of reading my posts would be those who are somewhat mathematically-minded already, and accept the mathematician’s abilities to define arbitrary objects, trust in abstract metaphor, and work logically from systems of axioms, and his or her motivations in doing these things. What’s more, a lot of my writing was, in retrospect, very boring — not just because of my tendency to wordiness, but because of the subject matter itself. In order to reach math’s fascinating peaks, you’ve got to traverse a lot of valleys of definitions and technical lemmas, and insisting on doing all of this in the ‘right order’ may not be the best way to communicate. (Not to mention that it takes a hell of a long time.)

This blog’s time has passed, but I haven’t stopped blogging. I currently have two projects ongoing. On my Tumblr, I write sporadic essays about film, literature, music, and philosophy, post typically short and weird fiction, and do the requisite tumblry things what with the gifs and the reblogging. I’ve also just started a new math blog on WordPress with a group of other Northwestern students, intended to be something like the Secret Blogging Seminar. (As I write this, it has exactly one post up, so we’ll see.) I’m expecting the things we write about there to cover a wider range of difficulty levels, primarily either things we know a lot about and want to talk about or things outside of our respective fields of concentration we feel like learning in public, so to speak. As I care a lot about being able to explain my ideas to other people, I’ll probably publish the occasional layperson-level post, and certainly will if someone asks me to, but not with the same Bourbakistic demand for foundations as I had here.

Since people still read this, I’ll check on the comments periodically, but the best way to communicate with me is through either of the other two blogs, or by emailing me at allispaul at gmail dot com. I’m a weird dude but a friendly one and I like corresponding with strangers.

Thank you all for reading and may our paths cross again!

Paul

Filed under: Blog, Math | Tags: algebraic geometry, analysis, blog, category theory, computability, MaBloWriMo, Math, physics, topology

So it appears there’s this thing. It’s inspired by this other thing. As a wannabe NaNoWriMoer (I will have the time someday!), I do find the idea compelling: Siegel’s variation is to write a blog post of about 1000 words every day, on a single subject, ideally something the blogger knows little to nothing about.

So… I’ve been doing posts about every day, and they’ve been over a thousand words in general (going by the WordPress word count, which counts “words” in LaTeX formulas in some weird way). I don’t think this will be that difficult. On the other hand, I’ve been trying to teach math from the ground up, and since writing about a subject new to me will probably require more background than I’ve been assuming, I feel like it would be unfair to my readers, insofar as I hope to attract some.

The subjects I’d want to learn most of all in the context of a project like this are algebraic geometry (for which, small plug, Charles Siegel’s series looks excellent) or category theory (I’ve just gotten started on Mac Lane’s *Categories*). If I wanted to start from a high school background, however, my options are more limited: I feel like I could do some aspect of classical analysis, like Fourier analysis, maybe using Stein and Shakarchi’s *Princeton Lectures vol. 1*, which looks pretty neat. I’ve also just picked up a pretty simple-looking book on computability theory and logic from the co-op’s free pile, which isn’t my favorite subject, but what the hell. Finally, I got (from the same pile) a textbook on thermodynamics, which I know shamefully little about; it’s not really math, but I could give a more mathematical perspective, and it might be kind of fun.

The final option, which I’m leaning towards, is to continue laying the foundations of set theory and topology, but to do so every day. Maybe to work on conciseness and shoot at thousand-word rather than fifteen hundred-word posts. If anyone has any opinions or ideas, let me know!

I’ve added a page listing the topics I plan to cover. As always, I welcome suggestions. The “long-term” section should be interpreted as being pretty long term. It’s essentially the horizon that I’m constantly running towards. There will of course be diversions along the way that don’t have anything to do with those goals: for instance, I’d like to talk about analysis and differential geometry at some point, too.