Feeling a little grab-baggish today.  First things first, watch this.  Shut up and do it, dammit, it’s Saturday and you can spare eight bloody minutes:

You didn’t watch it, did you?  Jerk.  Fine, I’ll sum up:  the fella in the video is a British physicist, and he demonstrates a couple of interesting properties of infinite series: first, that the sum of 1 -1 +1 -1 +1… out into infinity is actually one half.  Then, to further screw with our brains, he demonstrates that the sum of the series 1 + 2 + 3 + 4 + 5… is negative one twelfth.  Which is completely absurd, but the demonstration he works through is elegant and relatively simple even for non-mathematicians (which, for the record, is a category I’m including myself in) so long as they have some recollection of how algebra works.

I came across this here, at Phil Plait’s awesome Bad Astronomy blog.  The article touched off a bit of a shitstorm in the comments and elsewhere on the Interwubs for what is probably a perfectly obvious reason; it doesn’t make a speck of logical sense.  The math concepts being applied are apparently actually useful in string theory.  The problem, of course, is that most of the people involved in the argument don’t have the faintest goddamn idea what they’re talking about– which, surely, is the first time something like that has ever happened on the Internet.  This makes the argument not terribly enlightening.

Me, I’m inclined to trust the experts– while I agree that neither answer makes a drop of intuitive sense, I’m also sympathetic to the counter-argument that infinity itself doesn’t actually make a drop of sense to our non-infinite brains and that therefore “this doesn’t make sense” isn’t actually a valid knock against the math.  In fact, if I’m being honest, I find that argument fascinating.(*)  The guy in the video also points out that you’re right that if you stop at any point along the sequence, yes, you’re going to get a certain number, either 1 or 0 in the first instance and something really big in the second– but that if you extend the series to infinity, a concept that doesn’t rightly fit in our brains, you get these wonderfully unexpected results.  It’s cool.  And he’s kind of adorable.  So go do what I said and watch the video, because I know you didn’t watch it the first time.

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Complete change of subject: I need a feminist, or at least someone with a bigger vocabulary than me, to ‘splain me something, and to do it out of the goodness of her or his heart, because I’m perfectly aware I can research this myself but I’d rather ask the Internet for some reason:  is there a specific term for a society that is patriarchal in practice but not by law, other than “de facto patriarchy”?  Like, a single term?  The example I’m thinking of is America, obviously, where there are no longer any laws preventing women from, say, high office, or corporate boards, or other offices of high power that are currently occupied either nearly exclusively or literally exclusively by men, but that nonetheless all or nearly all of those offices are occupied by men.

To phrase it differently, I’m looking for a term or set of terms that distinguishes what I’ll call for the sake of argument a “hard” patriarchy– where women are literally not allowed access to positions of power via specific religious or legally enforceable and punishable prohibitions, from a “soft” patriarchy where the barrier is culture and not law.  Note that in a practical sense the effects can be exactly the same, which is why “de facto” and “de jure” would work if they weren’t phrases and not individual terms.

And maybe also you can see why I’m not trying to stuff this into a Google search, too.  🙂  Anybody got anything for me?

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(*) We’re gonna leave my inconsistency re: theology there aside, although now that I’ve noticed it I may think about it harder later.