Anybody out there?

Since hardly anybody knows I have a blog, I assume that hardly anyone’s reading this. If you’re reading this, and I don’t know it, post a comment to let me know you’re out there. I’ll be much more motivated to post things if I think anyone’s watching.

Also, in case you’re wondering, I really enjoy playing Dr. Science, so if you have any science questions you think I might be able to answer, drop me an e-mail. I’ll answer here on the blog if I can. My main areas of expertise are big-bang cosmology and relativity, but you can try me on other topics in astrophysics and physics too.

The End of Cosmology?

According to Scientific American, it’s coming. The fact that the Universe’s expansion is accelerating means that we gradually have less and less access to information about the Big Bang. This is true in principle, but it’ll take billions of years before there’s a significant loss of information.

I guess we should increase cosmology funding now: We need to find out all we can before the information goes away!

Mercury

I’ve enjoyed seeing the pictures of Mercury from the MESSENGER flyby. (If you haven’t already seen it, you should definitely check out pictures of the spider.) So far, the news accounts don’t seem to do a very good job explaining the scientific importance of the results. Here’s an article that gives quite a bit more detail about the sorts of questions that can be addressed with these data.

At this stage, not surprisingly, the data have raised a lot more questions than they’ve answered. It’ll be a lot of fun to see what comes out of the rest of the mission.

By the way, here’s a nice introductory physics puzzle: Why is it hard to get to Mercury? Obviously, it takes a lot of energy to get to the outer planets, since you have to go “uphill” against the Sun’s gravity. But Mercury’s dowhill from us, so it ought to be easy to get there.

More on electability

There seems to be more and more talk about which Presidential candidate is most “electable,” at least on the Democratic side. As I noted in an earlier post, the political futures market gives a way to assess electability. Here are some graphs showing what the market has thought about the electabilities of the two leading candidates in each party over the past few weeks.

First, the probabilities of winning the party nomination:

Nomination Probability

(Click on the images to get better-looking versions.)

Next the probabilities of winning the Presidency:

election.gif

The ratio of these two is the electability (probability of a candidate’s winning the election given that he or she gets the nomination):

electability.gif

By the way, I think that the big jump in Romney’s electability in the last couple of days is probably just a fluctuation. The other big features you can see here are South Carolina on the Democratic side, Florida on the Republican side, and the current uncertainty in interpreting Super Tuesday on the Democratic side. Perhaps the most important thing, from the point of view of voters concerned about electability, is that Clinton and Obama are consistently very close to each other.

In the end, what you make of these results is up to you. Some people seem to attribute to the futures markets an almost magical “wisdom-of-crowds-style” ability to discern the Truth. It’s certainly possible to exaggerate that sort of thing, but at the very least what we’re looking at here is the average view of a community of people who pay a lot of attention to this subject and who are willing to put money behind their beliefs. If the numbers here strongly disagree with what you think about the candidates’ electabilities, then I have two questions for you:

1. Are you confident that you know more than this group of people?

2. If so, why don’t you bet on it?

After all, if you think that the probabilities shown here are wrong, then you can place bets on the futures markets (specifically, Intrade, which is where the above data comes from) where the odds are weighted in your favor.

Why doesn’t the Sun have an iron core?

The Q+A column in today’s New York Times is uncharacteristically weak. The question was “Why doesn't [the Sun] have a core of heavier elements that sank to the center?” The main problem with the column is that it doesn’t really answer the question. Here’s what I’d say.

Although the Sun is made mostly of hydrogen and helium, it does have trace amounts of heavy elements. These do not settle to the core but are distributed throughout the volume of the Sun. The reason is temperature: there is enough thermal energy in the solar interior to keep the heavy elements bouncing around. As an analogy, consider the Earth's atmosphere. Although carbon dioxide molecules are heavier than nitrogen molecules, there's plenty of thermal energy to keep the CO2 from settling at the bottom of the atmosphere.

The article also presents the impression that the Sun will produce its own heavy elements later in its life. The Sun will produce only helium, carbon, and oxygen. Elements heavier than oxygen are produced only in more massive stars.

I sent the Times a letter to this effect, but I don’t know if they’ll care.

Update: They didn’t.

Electability

I’m not going to write about politics in this blog — there’s plenty of that out there already. And I’m certainly not going to engage in any sort of political advocacy. But I thought of an interesting application of probability theory to the upcoming election, and I thought I’d summarize it here.

Remember back in 2004, when it seemed like every Democratic voter was basing his or her choice on which candidate was most “electable”? People’s gut feelings about this sort of thing are generally pretty unreliable, so it’s kind of interesting to look for a data-based answer to the electability question. It occurred to me recently that the various political futures markets provide a good way to answer that question for the upcoming election.

For those who don’t know about the political futures markets, they’re basically a way that people can bet on various political events, including the upcoming US Presidential race. Slate has a good description with lots of nice graphs. The odds on all of these bets can be interpreted as giving the probabilities of various outcomes in the race, as estimated by the community of bettors. These probabilities give enough raw data to measure each candidate’s “electability.”

By electability I mean the probability that a candidate will win in the general election, given that he (or she) gets the nomination. One of the futures markets (Intrade) lets people bet on both who will get the nomination and who will win the general election. The ratio of these for any given candidate is the electability. It’s just Bayes’s Theorem:

P(Hillary wins the presidency) =

P(Hillary gets the nomination) * P(Hillary wins the presidency | Hillary wins the nomination).

[In case it’s not familiar notation, P(y | x) means the probability that y occurs given that x occurs.]

The last factor on the right is Hillary’s electability. The futures market tells us the other two probabilities for each candidate. So we can find the electabilities of all the candidates by simple division. Before looking below, take a guess about which leading candidates in the two parties are most electable.

Continue reading Electability

Some good web sites

Ned Wright’s Cosmology Tutorial: A great resource for all sorts of cosmology news and information.

Frequently Asked Questions about Black Holes (shameless self-promotion!)

John Baez’s web site, which is full of information about a lot of different topics in mathematical physics. The parts I’m most interested in are the ones about general relativity and gravity (and not just because I co-wrote some of it.)

For technical articles about astrophysics and cosmology, the place to go is the astro-ph arXiv.

For great astronomy pictures, you can’t beat NASA’s Astronomy Picture of the Day.

Update: These are now listed on the blogroll (over on the right), which is where they belong.

Hello!

This blog is for discussion of my scientific interests, which mostly focus on big-bang cosmology and general relativity. I’ll let you know what my research students and I are up to and comment from time to time on news in astronomy and cosmology. If you have anything you want to say, leave a comment on the blog or send me e-mail.