Honest question: add two of what unit?

Not quite.

What he proved is that given any number n, there exist prime numbers p and q that are (1) greater than n and (2) within 70 million of each other. For example, for a particular n, perhaps p = n + 1,000,000,000 and q = n + 1,069,000,000.

This is not quite the same as saying there's necessarily a prime between n and n + 70,000,000. In fact, since the average density of primes decreases as 1 / log(n), I'm pretty sure that statement is known to be false.

It seems like there are three possible laws:
1) No (legal) marriage at all.
2) Legal marriage for everyone.
3) Legal marriage only for straight couples.

If you prefer 1 to 2 and 2 to 3, I have no issue with that. But saying "I'm against gay marriage" is a misleading and confrontational way to phrase those preferences.

If you prefer 1 to 3 and 3 to 2, I think that's misguided. Would you support eliminating interracial marriage? I'd support raising taxes on rich people, but if I supported raising taxes only on rich black people that would just be racist.

You're probably referring to Oscar Pistorius, a South African double-amputee sprinter. Whether his artificial limbs are "better" than those of able-bodied sprinters is a bit of an open question. But the the relevant committee decided they're not, and he's competing at the Olympics this year. His 4x400 relay team is even a medal contender.

There are many examples. I doubt many people care about the difference (I certainly don't), but that doesn't mean it can't be detected.

For any reasonably concise definition of life, it's possible to come up with a hypothetical example that clearly shows the definition is wrong.

No vaccine today uses any live virus.

Yellow fever

RTFThread :) I already named the ISP (AT&T DSL), and provided a link.

AT&T DSL

It's only one data point, but my bandwidth cap for DSL in Sydney was 250 GB/month, vs 150 in the States.

Ah, yes, college vs NFL certainly could make a difference. There's a lot more parity in the pros than there is in college. For example, NFL kickers statistically indistinguishable (when it comes to kicking field goals), but that's probably not true of college kickers.

If you're interested in this stuff, you might want to check out the blog advancednflstats.com. It focuses only on the NFL, though.

There are a lot of variables, but some are more important than others. Early in the game, you can build a pretty good model based only on the field position and distance to get a first down. Obviously score difference and time remaining matter late in the game. Things like confidence in special teams and relative tiredness aren't really that predictive.

If you build a model (pretty much no matter how you build it) and compare it to what coaches actually do, you'll find that in general, coaches don't go for it on fourth down nearly as often as they should. It's a big difference -- on average, coaches cost their teams about 1.5 wins per season by kicking too often on fourth down, and this is in a league where 8 wins is average, 10 will make the playoffs, and 12 will get you a first round bye. And it wouldn't be hard for them to do a lot better than they do. Saying that there are a lot of variables is just their weak excuse for not believing in the math.

The fact that football coaches don't go for it on fourth down is actually really interesting. It's basically a question of risk aversion -- kicking on fourth down is "safe", while going for it is expected-value-positive but highly risky.

In real life, it makes some sense to be risk averse. Money has decreasing utility the more of it you have, so it's completely rational to refuse to bet your life savings even if there's a 51% chance you'll win. In a game like football, however, utility is necessarily proportional to the probability that you'll win the game. If a play increases that probability on average, it's the correct play no matter how risky it is. Football coaches are treating the probability of winning as if it had decreasing utility. They're being irrationally risk averse.

Once you start looking for irrational risk aversion in games, you start seeing it everywhere. It comes up just as often in Jeopardy as it does in football -- people tend to risk less than they should when they hit a daily double (early in the game, you should almost always bet everything). Funny enough, I don't think Watson got it right either -- in the second half of the first match, it made a relatively small bet when the rational strategy was probably to bet everything.

I typed up my own thoughts on the different definitions of the word "irony" and published them here.

According to wikiped...er, my own research, irony can't simply mean "something bad happens to a good person." Tragic irony, in particular, is a subset of dramatic irony, which requires that the audience knows something that some character doesn't know. That certainly doesn't apply to any of the situations in the Alanis song.

Ah, that's exactly what I was missing. Thanks!