maximum versus maximal

So I know I learned this at one point, but I can’t rederive the logical argument explaining when to use the words “maximal” and “maximum.” Certainly maximum is both an adjective and a noun, and maximal is just an adjective.

One explanation I remember was that there can be many maximal things, but only one maximum thing. I know that you call it a maximal ideal in algebra, and it need not be unique (unless it’s a local ring?), but then why say “local minima” if a minimum is unique?

I just noticed I’m a bit inconsistent in my usage in this paper I’m writing, and I can’t tell if I should call it the “maximum probability of error criterion” or the “maximal probability of error criterion.” I was leaning to the former, but now thinking about it has got me all muddled.

IEEEtran BibTeX annoyance

I’m busy as a bee writing two papers for ISIT 2007 (in Nice, woohoo!) and as usual I find myself at odds with the IEEE Transactions style formats. The BibTeX format by default puts the bibliography in order of how references are cited, and as far as I can tell there is no option for putting things in alphabetical order. One option is of course to use the \nocite command before any of the other text. This will put the citations in the bibliography without anything in the main text — a handy feature for sneaking in references that you don’t need but should cite (perhaps to appease reviewers). But that hack defeats the purpose of BibTeX, which is to stop you from futzing with your bibliography by formatting the thing in the correct manner, be it APA, MLA, ACM, or IEEE.

I understand that for a survey paper it would be advantageous to list references in the order that they are cited. That way all the papers on topic A will be in a big block together in the bibliography, and the cite package provides a nice shorthand that will list the references as [1 – 5] instead of [1][2][3][4][5]. For conference papers, which often have fewer than 10 citations, it seems that the aesthetic benefits of an alphabetized bibliography outweigh the minor inconvenience in typesetting. From looking at existing published papers, it seems that the IEEE isn’t particularly insistent on making the bibliography in citation-order. So why not provide the alphabetical option?

Perhaps its because the entire LaTeX package system is being maintained by Michael Shell, who I’m sure has better things to do with his time, like a real job. It almost boggles the mind that so many people in the IEEE use this LaTeX package and the Institute doesn’t really support it in the way that the AMS supports AMSTeX.

HD-DVD copy protection

Apparently the HD-DVD copy protection system has been compromised. Is this really a big surprise? I mean, if you actually go and talk to the engineers who designed AACS, would they think it’s totally unbreakable? Behind all the PR and marketing hacks who don’t know the first thing about cryptography are the people who actually designed this system, and I’m sure they would list a load of standard caveats like “assuming a bounded-complexity adversary” But even then, perhaps twixt design and implementation someone screwed up and weakened the protections.

The whole approach to copy-protecting media via controlling the hardware is a little odd to me. Its like having a secret decoder ring made of a piece of red cellophane. If you make a media format which is useful for carrying data and holding movies, you’re inviting attacks far more complicated than those envisioned by scenarios in which you have an average user buying a player and plugging it into their TV. Is it really that the design specs were for the latter and didn’t even think about what would happen if someone popped the disc into their computer?

Personally, I thnk these guys knew it would happen all along and were surprised at how little time it took. The truth is probably that people in the company who were ignorant of the technology ended up approving something that was a lot weaker than it should have been, and not that the guy who hacked the standard was somehow a super-genius. This is not to take away from his accomplishment, but it seems like you can either build a watertight security system or one that leaks like a sieve, and this is more of the latter.