That’s Some Board

I just saw A Serious Man, which stars a struggling mathematical physicist plagued from all sides in 1967 St. Louis Park (outside of Minneapolis). It really is a great movie and deserves viewing in its entirety, but I just had to put up this still from the trailer. There’s a better version without all the students in the film, but I couldn’t find a copy of that shot.

Click to massively embiggen. Bonus points if you can recognize everything.

Bad Language

I know I’ve been really lazy about my blogroll, and I should get around to that sometime. But there’s a new one I have to point out right away: The Language of Bad Physics (as noted in the comments, now on WordPress at this address). Like Frank Costanza on Festivus, she’s got a lot of problems with you people (physics writers) and how mathematical terms get mangled and confounded in the physics literature. It’s one big Airing of Grievances, and you’d do well to listen up.

My only complaint is that it’s one of those horrid, ugly Blogspot pages and not a nice -enabled WordPress page. But maybe it’s early enough to get her to switch

So that’s why they stuck me here

Taken from the parking lot of the hotel:

At least it won’t be hard to find it tomorrow morning.

What’s Next?

Last May we started talking about linear algebra, with a little aside into complex numbers and another into power series along the way. Before that all, long long ago, we were talking about single variable calculus. Specifically, we were studying functions which took a real number in and gave a real number back out, and the two main aspects to this study: differentiation and integration.

The first part studied how a function changed as its input varied near a fixed point by coming up with the best linear approximation of the function near that point. Now that we’ve got an understanding of linear functions between higher-dimensional real vector spaces, we can work towards extending this idea of differential calculus into multivariable functions.

The second part studied how to “add up” a continuously-varying collection of values, each with its own (infinitesimal) weight. Again, our new understanding of higher-dimensional analogues of linear spaces and functions will help us find the right way to generalize the integral calculus.

I’m trying to get access to some of my references again, since I no longer have even as much of a mathematical library down the hall as Western Kentucky University provided. So I’ll pick up when I can.

The Unapologetic… Book?

Yesterday some lonely voice on Twitter with the moniker @arthegall (which nickname I simply cannot parse) suggested turning this weblog into a book. The idea has come up before, but it usually has a spirit of “Turning weblogs into books is a Thing That People Do”, and so I might someday follow suit. But to look deeply at this particular weblog and say that it should be done? Clearly there are some problems here.

First of all, is there really a market for it? I flatter myself that there really is a “generally interested lay audience”, but how big is it? Unless one says something controversial — or that some crank thinks is controversial — math, physics, and computer science weblog readers tend to be a rather silent bunch. The obvious exceptions are those who have major corporate backing. Not that I disparage major corporate backing or anything, but it might reinforce my point that I don’t have it already. And even if that’s just the whims of chance, I really have no good way of gauging my current audience, let alone who might be willing to shell out for an honest-to-Gauß book. Without an audience, publishers aren’t going to be interested, and without a publisher I’m left with vanity presses. At which point, what’s really the difference between a vanity press and a weblog anyway?

Second of all.. well, just look at this mess. I can’t even keep my blogroll up-to-date. If you’re wondering why you don’t see your weblog there it may well be that I’m reading it and haven’t updated that thing in over a year. I’m worse with bibliographies. One of the nice things about the weblog format is that I don’t really have to do a lot in the way of referencing my sources, especially since nothing I’m saying is particularly new (unless I’m making it up myself). Ninety percent of what you read would get cited as “[stuff] I remember from graduate school [or earlier]“, with the rest filled in with occasional tokes from old textbooks or Wikipedia to make sure I’m getting the details and standard usage more or less correct. See, I really don’t think in terms of where ideas come from. Once they go into my head they’re churned into a sort of lumpy grey paste. Semantic leveling is great when it comes to pulling out oblique analogies (a useful tool in mathematics, actually), but it’s really horrible when it comes to giving credit where it’s due.

And yet, a book could lead to fame and fortune, and what American doesn’t want that? The tour might not get me on with my mancrush Keith, but Rachel tries to extend overtures to math/science/technology geeks from her policy-wonk side of the room. She even made mention of ∏ Day, which I’m sure could provide a great hook for an interview given my well-established stance. And Stewart and Colbert are wide open. Yesterday Stewart’s featured interview was with a guy who wrote a bio of Henry Hudson, of all things. So.. it might not be a bad idea.

But what would I write about. Just “turn blog into book” doesn’t feel right to me. Terry Tao can just make a tarball of a year’s worth of posts, slap an ex post facto theme on it, and ship it out. He can get away with this partially for the reason he’s got a built-in weblog audience in the first place: he’s got a Fields Medal. Me, I can’t get a proper postdoctoral position to save my life, so I have to work a bit harder on coherence. There’s way too much here, with no clear goal. I have local goals, and longer-term goals, but overall this project is very unstructured. I can hold what attention I do because it’s a nice little snack of whatever I happen to be talking about today. But a book needs to have a theme and, in a sense, a goal. Tangents are acceptable, but even they should clearly tie into the overall narrative.

And then I thought of one topic I’ve covered here, which could be stripped down a bit and rearranged into a single coherent thread: the progression from natural numbers to real numbers, and beyond. Natural numbers are, or at least seem, to be simple and intuitive, but by the time we’re talking about real numbers I don’t think most people have a real sense of what these things are. At the time most people first see them (even under the capable eyes of a good schoolteacher) they probably don’t realize what huge conceptual leaps they’re making. Even their teachers may not really know. Even up through the calculus sequence, which is where even most mathematically-able people stop (going on into science or engineering), it’s never really made explicit what’s going on. The fine details that are essential for making calculus work as it does are swept under the rug. By the time many people are ready to put real thought into what a number is, they’re beyond the point where there’s going to be a class telling them that the question is as deep as it really is.

Now, I don’t think I’d be interested in going in a philosophical direction with this, trying to really answer the question in a deep way, but I’d probably have to brush up on some of that sort of thing to make appropriate mention of it. My concern would be more to explore the progression of notions of “number”, and to explore the structures we encounter along the way. I wouldn’t want to go into nearly as much depth on group theory as I’ve done here, but some mention of it in parallel with the step from natural numbers to integers would be useful, for instance. But I’d need a collaborator — or at least an editor — who can understand what I’m doing and keep me honest about my references.

But given the right support I wouldn’t be against the idea…

Updates

As a much-anticipated visit approaches, my apartment is asymptotically approaching neatness. My former students’ comprehension of the word “asymptotically”, however, remains constant.

And this morning I received the proofs to a paper that was accepted for publication two years ago: “Functors Extending the Kauffman Bracket”. So yeah, I get out with it finally appearing in print, but in the meantime my career is shot.

Sunday Samples 125

I could, in honor of last week’s Indians-Royals game, pull out “I Ran” (by A Flock of Seagulls), but I was reminded of a great selection for my activities these couple weeks.

One of the other people in last week’s class was dragged along with her boyfriend and his father. She kept up pretty well, but spent a fair amount of time saying that she’d rather have gone on a cruise or something for a vacation. One of her consistently repeated phrases got a song stuck in my head, and I realized how appropriately its lyrics could be taken for the whole underground venture. So, from the Talking Heads (and David Byrne in particular), it’s “Once In A Lifetime”

A Quantum Theory of What?

I’ll stick my head out of the ground long enough to link to this, and to remind you that my pictures are going up here, with one more day to go in this first course.

Hiatus

This week’s been hectic, what with interviews (which I can’t talk about but I think went okay) and driving back to Kentucky. And now I’m about to spend two weeks up at Mammoth Cave. I should have some internet access, so I’ll try to keep up with lower-content features, but real mathy stuff is off the table for a while. You can always follow my twitter stream to keep tabs, and find links to pictures I take underground, assuming that the wireless at Hamilton Valley really works. But of course, the best laid plans of mice and men…

Testing

If all goes according to plan, a link to this post should show up on my Twitter feed shortly. Thanks to twitterfeed.