Wednesday, October 24, 2007

Research updates

I seem to have resolved, affirmatively, an open question I'd posed in Sec. 6.5.3 of my thesis -- namely, whether for (just about) any mixing matrix there's a measure achieving those mixing coefficients. I haven't written up a proof yet, but looks like it'll make a cute little result. Here's a very short writeup (no proof); let me know if you want to hear more.

Got an interesting conjecture regarding mixing coefficients of random fields. I can see this one having far-reaching implications but unfortunately see no proof...

[Update: that random field mixing conjecture is wrong. Maximal graph degree is too crude a measure of connectivity -- seems like some sort of path counting is necessary...]

Sunday, October 21, 2007

Bemused metablogging

So Scott calls Al Gore "the Churchill of climate change" -- this despite the fact that the fact that Gore's science is so shoddy that a British High Court ruled that his film can't be shown to schoolchildren. I would love for this to be a bad case of a malfunctioning irony meter (mine), but I fear the worst. (Was Churchill also a shameless hypocrite?)

Then sneaky old Aaronson goes ahead and links to a something this, thus ensuring that readers like me will continue to return and wade through the standard liberal tripe for the occasional (well, ok -- frequent) gem.

[Update: Seems I've been sloppy, both in facts and in rhetoric. The above was meant as a friendly jab (didja notice the not-so-veiled compliment?) though I can see how it might be taken for an ad hominem attack. Also, as Kenny and others point out, my claim about the film not being allowed to be shown isn't accurate. See here for more information.]

Saturday, October 13, 2007

How to Win a Nobel Peace Prize

Glad to see the prize regain its old prestige. Can't we separate the prizes in category #1 from #2 and #3?

Update: C'mon, people. This is an article bashing Al Gore. And the whole Peace Prize sham. Isn't anyone going to get pissed off enough to react? Or have I scared all those types away a long time ago?..

Wednesday, October 10, 2007

More math psychology

Did I really let almost a month elapse without posting? Must be because my life is so wild and exciting. Um, yeah.

Here's a question that's been occupying me for a while -- non-mathematicians' perception of probability. What does a man on the street mean when he says a coin has a 50% chance of landing on heads?

The most likely interpretation is frequentist: if you flip the coin a whole lot of times, you'll see heads about half the time, on average. (How many times is a lot? What does on average mean here? Read my thesis -- at least the section on the Law of Large Numbers.)

But what about one-time events? What does it mean that there's a 30% chance of rain tomorrow? (Tomorrow will only happen once, so any talk of averages is meaningless.) Heck, what does the meteorologist mean by that probability?

Cosma helped me resolve the latter quite satisfactorily in private correspondence (so satisfactorily, in fact, that I feel dumb ever having asked the question). But I turn to the readers:

1. can you make rigorous mathematical sense out of the meteorologist's 30% chance of rain prediction?

2. can you ask your non-mathematician friends what that prediction means to them?