Bounded in a Nutshell

So I've been asked to review a paper for a journal. This is not, in and of itself, a first; in fact, it's the fifth such request of me in the past two years.

The journal making this request of me, however, enjoys a very good reputation in my field: if not one of the top two or three prestige-wise, then certainly in the top ten. Further, this is the first time that I know any of the authors (I know three, out of six); they, too, all enjoy very good reputations in the discipline.

I can't help but think of this as a catastrophic reversal of the natural order of things.

Anyone else notice that I mainly seem to update this site on Tuesdays?

I got a paper through our library's wonderful Document Delivery Service today. Rather than actually passing pieces of paper around, we get our documents on a website, which contains scanned images of the journal pages from wherever. (In this case, "wherever" is Fullerton, California; why the Cal State campus there is the most convenient library from which to get a twenty-odd-year-old article from an obscure Indian journal is left as an exercise to the reader.) This makes good sense to me.

I was hoping to just read it on my screen, but that turns out to be impossible; when I scroll past the cover page to the first page of content, I find myself looking at up-side-down text. Not feeling up to reading math up-side-down, I give in and print it out...

...to find that the second page of content is right-side-up... that is, up-side-down with respect to my inversion of the stack of paper. And the pages alternate thereafter.

While I admit that this makes sense in some ways, it's a little annoying.

Clevermonkey pointed me to the Safari Bookmark Exporter, solving the main issue I was having with switching from Safari to Firefox. Huzzah!

So now I'm-a using Firefox. The great advantage it enjoys (aside from apparently being much less of a resource hog) is that Firefox exists cross-platform, and so all of a sudden things on the web look very, very different as I surf to sites with various enhancements. (For instance, the aforementioned Google Maps, which is indeed pretty sweet.)

As far as drawbacks go... the Firefox downloads manager is pretty stupid, at least as compared to its Safari counterpart. On a Mac if you download a file to a place where a file of that name already exists, the result is a file that looks something like filename-1.ext, and successive files get successively higher numbers. Safari will reflect this in the list of downloaded files; Firefox will not, and so if you try to open the file from Firefox you get the file of that name which was already there to begin with.

Some of the keyboard shortcuts don't make as much sense to me in Firefox, though that could just be because I'm used to the Safari shortcuts. (I'm thinking specifically of navigating between tabs here; commands that use the left and right arrows seem more intuitive than ones that use Page Up and Page Down, even though I can see the logic in the latter.)

My first cup of kawphy in any given day is a freebie. Well, I still have to pay for it, probably, but I don't have to exert myself unduly to get it.

If it develops that further kawphy is warranted, necessary, or just plain desirable, then I am required to walk for at least twenty minutes, that I might deserve it. (I say this now, since it's such a nice day outside. The radio's been threatening 3-5 inches of snow accumulation tonight, so it's possible that this rule will be suspended until real spring.)

Further cups of kawphy beyond the second will require proportionately greater effort.

Note that, for the purposes of this rule, "kawphy" is defined as a caffeinated suspension: coffee, tea, hot chocolate, etc. I suppose I should really count caffeinated soft drinks (the only ones I generally drink these days, since good ginger ale doesn't exist in this country), so let's do that too.

An exception is made for weekends, when a bodum of coffee or pot of tea in a day is considered free.

As I've mentioned before, I work on a G5 iMac. Supposed to be blazingly fast, right? I mean, reasonably good processor, reasonably sleek OS, what's not to like? And yet, I'm constantly seeing delays when switching between tasks. It could be argued that this is because I routinely have eight or more applications open at once, but these days who doesn't?

I've figured out a couple of the bottleneck applications. The MS Office Suite is a problem sometimes, often taking longish periods to come to full consciousness. (Excel is a little worse than Word in this respect, but then I use Excel much more frequently so that's a big problem.) My TeX editor seems suprisingly bloated. But recently I've been forced to conclude that the worst, most consistent offender is Safari: the web browser done it.

My main evidence for this is that switching to and from Safari takes a lot of work, even when there's but a single web page (that doesn't "do" anything) open. By contrast, switching between iTunes and iChat, or MSN Messenger and Terminal, takes about as long as it takes me to hit Apple-Tab. OTOH, this varies with how long Safari's been open, so it might just be a case of bit-rot or something.

In any event, between this small epiphany and Elbie pointing out the existence of Google Maps -- which does not, right now, support Safari -- I figured that it was time to take Firefox out for a spin.

So, my first complaint about Firefox: while it claims that it will import your bookmarks etc. from IE "and other browsers", the other browsers in this case seems to mean "Netscape". Won't import Safari bookmarks; if you tell it to import from a file, and point it at the .plist file from Library/Safari, it'll blithely ignore you. And there's no obvious way to export bookmarks from Safari into, say, and HTML file like Firefox expects.

Damn it.

So I signed up for GMail some time ago. And I got three invitations I could send out; I think I used two of them. After sending out my second, I got five more invitations; these have all been happily idling away in whatever conceptual space they live in.

I check my account today (for the first time in a little while), and find out that I now have 50 invitations available.

So if any of my Loyal Readers want a GMail account... or two... or five...

I was working on a research problem in between watching my room full of students struggle with histograms and standard deviations, and then I suddenly saw it.

The particulars of the "it" in question are probably of no interest to most of my readers, and little enough to the rest. Hell, in the "of great mathematical significance" sense, it's not even very interesting to me. It's not a solution that's going to save the world or make me rich or anything.

But the reason that we do mathematics -- at least, the reason that I do, at least sometimes -- is to catch these little moments when the clouds clear away and one can apprehend a Pattern in its purest form. When things, against all expectations, make sense.

The hard part, now, is to take the vision of How It Works and turn it into words and other symbols. I'm firmly in the camp that has mathematicians as explorers rather than inventors: the things that we discover are already, in some sense, there. I can see the pattern for this particular family of structures, and its construction makes it clear (to me) why it's correct. Justifying it is going to be a bit of a pain.