Prime Numbers for June 29 to July 5, from today's New York Times. (I don't know if this is a weekly thing; it could be but I don't recall seeing it before.)
The numbers are 46, 62000, 30, 18%, and 30000; each is important to some news story from this week. (If you want to get technical, 62000 and 30000 are approximations.)
Presumably they mean "prime" in the sense of "important". Or in the sense of "composite", but that would be a bit perverse.
06 July 2008
05 July 2008
A couple of links
1. Jordan Ellenberg's review of Andrew Hodges' book One To Nine. Read the review, if only because it uses the word "mathiness". Ellenberg's review seems to imply that the book has similar content to most popular math books; sometimes I wonder how the publishing industry manages to keep churning out these books, but then I remember that the same thing is true in most other subjects and I'm just more conscious of it in mathematics.
2. Open Problem Garden, which is a user-editable (?) repository of open problems in mathematics. Thanks to Charles Siegel, my fellow Penn mathblogger, for pointing this out. The majority of the problems given there are in graph theory; that seems to be because Matt Devos, one of the most prolific contributors, is a graph theorist.
But I have to say that "garden" feels like the wrong word here; gardens are calm and peaceful and full of well-organized plants, which doesn't seem like a good way to describe problems that haven't been solved yet. "Forest" seems like a better metaphor to me -- certainly when I'm working on a problem that's not solved, it feels like hacking my way through a forest, not walking around a garden. Also, the use of "forest" enables bad graph theory jokes -- the problem of "negative assocation in uniform forests", due to Robin Pemantle, in particular sounds like it could be about sketchy people you meet in the woods.
(I gave a talk back in February where I mentioned this problem. I'm glad I didn't think of that joke then, because it's really bad and I would have just embarrassed myself.)
2. Open Problem Garden, which is a user-editable (?) repository of open problems in mathematics. Thanks to Charles Siegel, my fellow Penn mathblogger, for pointing this out. The majority of the problems given there are in graph theory; that seems to be because Matt Devos, one of the most prolific contributors, is a graph theorist.
But I have to say that "garden" feels like the wrong word here; gardens are calm and peaceful and full of well-organized plants, which doesn't seem like a good way to describe problems that haven't been solved yet. "Forest" seems like a better metaphor to me -- certainly when I'm working on a problem that's not solved, it feels like hacking my way through a forest, not walking around a garden. Also, the use of "forest" enables bad graph theory jokes -- the problem of "negative assocation in uniform forests", due to Robin Pemantle, in particular sounds like it could be about sketchy people you meet in the woods.
(I gave a talk back in February where I mentioned this problem. I'm glad I didn't think of that joke then, because it's really bad and I would have just embarrassed myself.)
03 July 2008
Lightning and lotteries
From a rerun of Friends:
Also, Ross is wrong. It seems the record for getting struck by lightning is Roy Sullivan, seven times. So nobody's been hit 42 times, while plenty of people have won the lottery.
I don't know how to calculate the odds that someone gets hit 42 times by lightning in their life; the lifetime incidence of getting hit is three thousand to one, and if you figure that lightning strikes are a Poisson process with rate 1/3000 per lifetime, as this article states, then the probability that lightning hits one person seven times is something like one in (1/3000)7/7!, or one in about 1028. (That's the probability that a Poisson with parameter 1/3000 takes the value exactly 7; I'm ignoring the normalizing factor of exp(1/3000) and the even-more-negligible probability that someone gets hit eight or more times.)
Since the number of people who have existed is much less than 1028, the existence of a person who's been hit seven times is very strong evidence that that's not the right model. My hunch is that events of each person getting hit by lightning are a Poisson process, but with a separate parameter depends on the person. Roy Sullivan was a park ranger.
But the 1 in 3000 figure can't be trusted; the article also claims the annual risk of getting hit by lightning is one in 700,000. People don't live 700,000/3,000 (i. e. 233) years.
Ross: Do you know what your odds are of winning the lottery? You have a better chance of being struck by lightning 42 times.Unsurprisingly, Chandler seems to know that probability doesn't work this way; Joey doesn't.
Chandler: Yes, but there's six of us, so we'd only have to get struck by lightning 7 times.
Joey: I like those odds!
Also, Ross is wrong. It seems the record for getting struck by lightning is Roy Sullivan, seven times. So nobody's been hit 42 times, while plenty of people have won the lottery.
I don't know how to calculate the odds that someone gets hit 42 times by lightning in their life; the lifetime incidence of getting hit is three thousand to one, and if you figure that lightning strikes are a Poisson process with rate 1/3000 per lifetime, as this article states, then the probability that lightning hits one person seven times is something like one in (1/3000)7/7!, or one in about 1028. (That's the probability that a Poisson with parameter 1/3000 takes the value exactly 7; I'm ignoring the normalizing factor of exp(1/3000) and the even-more-negligible probability that someone gets hit eight or more times.)
Since the number of people who have existed is much less than 1028, the existence of a person who's been hit seven times is very strong evidence that that's not the right model. My hunch is that events of each person getting hit by lightning are a Poisson process, but with a separate parameter depends on the person. Roy Sullivan was a park ranger.
But the 1 in 3000 figure can't be trusted; the article also claims the annual risk of getting hit by lightning is one in 700,000. People don't live 700,000/3,000 (i. e. 233) years.
Li's proof of Riemann has a flaw -- but all might not be lost?
Terry Tao claims that Li's proof of the Riemann hypothesis (which I wrote about yesterday) is flawed. (via Ars Mathematica.) But that was, I think, version 2 at the arXiv; the paper is now up to version 4, which apparently attempts to fix the flaw Tao claims in version 2.
Alain Connes has also weighed in at his blog; Li's paper relies on his work.
Alain Connes has also weighed in at his blog; Li's paper relies on his work.
02 July 2008
Obama isn't average -- and that's a good thing.
Someone at the Washington Post is a bit confused about averages.
Basically, Barack and Michelle Obama (you've heard of them, right?) got a mortgage at a rate of 5.625% at a time when the average rate was 5.93% -- and so the Obama campaign finds itself playing defense. But as Nate Silver pointed out, this is evidence that the Obamas have good credit, and as various people commenting there pointed out, it's an average.
Some people get better than average rates. That's true by definition. (Although I suspect that more than half of people get a rate below the mean, because the right tail is probably longer than the left tail.
Personally, I want my presidential candidates to be getting a good interest rate -- because it's evidence that they have good credit, which in turn is evidence for some sort of financial prudence. (Yes, I know, some people with bad credit got there because they got dealt a bad hand. It's evidence, not a proof.) And if someone is good at managing their own money, they might be good at managing the country's money.
And do we really want our president to be average?
Basically, Barack and Michelle Obama (you've heard of them, right?) got a mortgage at a rate of 5.625% at a time when the average rate was 5.93% -- and so the Obama campaign finds itself playing defense. But as Nate Silver pointed out, this is evidence that the Obamas have good credit, and as various people commenting there pointed out, it's an average.
Some people get better than average rates. That's true by definition. (Although I suspect that more than half of people get a rate below the mean, because the right tail is probably longer than the left tail.
Personally, I want my presidential candidates to be getting a good interest rate -- because it's evidence that they have good credit, which in turn is evidence for some sort of financial prudence. (Yes, I know, some people with bad credit got there because they got dealt a bad hand. It's evidence, not a proof.) And if someone is good at managing their own money, they might be good at managing the country's money.
And do we really want our president to be average?
Li's proof of Riemann?
A proof of the Riemann hypothesis, by Xian-Jin Li.
I'm not qualified to judge the correctness of this, but glancing through it, I see that it at least looks like mathematics. Most purported proofs of the Riemann hypothesis set off the crackpot alarm bells in my head; this one doesn't. Li has also stated Li's criterion in 1997, which is one of the many statements that's equivalent to RH, although I don't think it's used in the putative proof, and wrote a PhD thesis titled The Riemann Hypothesis For Polynomials Orthogonal On The Unit Circle (1993), so this is at least coming from someone who's been thinking about the problem for a while and is part of the mathematical community.
I'm not qualified to judge the correctness of this, but glancing through it, I see that it at least looks like mathematics. Most purported proofs of the Riemann hypothesis set off the crackpot alarm bells in my head; this one doesn't. Li has also stated Li's criterion in 1997, which is one of the many statements that's equivalent to RH, although I don't think it's used in the putative proof, and wrote a PhD thesis titled The Riemann Hypothesis For Polynomials Orthogonal On The Unit Circle (1993), so this is at least coming from someone who's been thinking about the problem for a while and is part of the mathematical community.
01 July 2008
Yudkowsky on Bayesian reasoning
An Intuitive Explanation of Bayesian Reasoning, by Eliezer Yudkowsky (of Overcoming Bias fame).
A sequel to this is A Technical Explanation of Technical Explanation [sic].
A sequel to this is A Technical Explanation of Technical Explanation [sic].
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