At MIT I used the xwindows program xmh to read my email. It was a pretty bare-bones program, but had one really great feature. Instead of having to drag a message to a folder to refile it, you could just right-click on the folder title and it would mark it as beign destined for there. Then you could commit all of the moves in one fell swoop. Neither GMail nor Thunderbird nor Mail.app seem to have this feature, which I regarded as a genius piece of interface in what was otherwise a pretty ugle program, all told. Maybe I’m the only one who got a lot of mileage out that feature, but I can’t help but think that our modern mail clients are missing something.
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.