Unless they can put forward a viable and concrete plan to change their fortunes without outsourcing everything, putting up dozens of billions of dollars worth of loans may be throwing good money after bad. Unfortunately, the leaders of these companies have mostly focused on threats about what would happen if they went bankrupt, rather than outline changes in long-term policies and priorities that would change their fortune. A lot of people are afraid that the companies might go under, but it looks like they’ve been consistently self-destructing, anyways. It might be a lot better to put the money into infrastructure investments that will pay off economically instead of wasting it on drowning companies that would go bankrupt whatever we do.

It’s a good sign that Democrats are now starting to think the same way, although I think they’re still giving the auto industry too much benefit of the doubt with the way they’re so eager to help the companies. However, I’m not sure it’s a good sign that I’m actually agreeing with the Bush administration on this issue …

If it looks like a duck, swims like a duck, and quacks like a duck, and yet does not act like a swan at all, then it most probably is a duck, not a swan.

(Substitute creationism, vitalism, flat earth, etc. for “it”, myth or fantasy for “duck”, and reality for “swan”.)

The Moon from the Moon Impact Probe

Joining the rank of previous lunar impactors, the Moon Impact Probe from India’s Chandrayaan-1 has successfully crashed into the Moon. Now which country will be next to join the club of nations that have sent probes to the Moon? And how long will it take for India to send a successful lunar lander?

One thing I haven’t heard much about is new scientific results from the impactor. I wonder how they would compare with those that we’ll get from LCROSS next year?

On the other hand, if it’s just a thinly veiled attempt to decry criticisms of Islam, Saudi Arabia would deserve all the scorn it will get. I just hope that this is not the case. I hope the speech is part of his baby steps as he tries to make his country freer. Unfortunately, I do not know about the king well enough to have an opinion one way or the other.

While it’s not the first time that direct images have been taken of planets outside our Solar System, which were in infrared, it is the first time that such images were taken in visible light. Not only that, astronomers have actually managed to see it moving over a two-year interval. Fomalhaut was suspected to harbor such a planet back in 2005 when its lopsided dust belt was discovered, and the Hubble Space Telescope managed to directly observe the planet by blocking out the bright parent star’s light.

Fomalhaut b orbiting its parent star, Fomalhaut

And if that’s not enough to stir some excitement, the Gemini Telescope and the Keck Telescope have for the first time managed to take direct infrared images of a solar system not our own that harbors multiple planets. Initially two planets were discovered orbiting the parent star, but followup observations revealed yet a third planet much closer to the star.

Planetary system HR 8799 showing all three planets

One of the things that direct observation of planets allows is the measurement of spectrographic properties of the planets, which can tell us what kind of stuff they are made of, something that was not very feasible, although not entirely impossible, with indirect methods of observation.

The Mars Phoenix Lander

Due to decreasing sunlight and worsening weather conditions, the Mars Phoenix Lander has finally ceased communications. Given that the lander started to cycle into safe mode only a little while ago, where it put itself into a mode that turned most of itself off in order to conserve power except to send regular signals, it’s not too surprising that it has ceased communications. In fact, it’s incredibly impressive that the little lander has lasted far longer than its original 90-day mission.

Having landed on Mars in May, when the Mars Reconnaissance Orbiter managed to see it during its descent, the Mars Phoenix Lander surprised everyone when it managed to glimpse a patch of ice that was probably uncovered during its landing. And it didn’t take long for it to take microscopic images of Martian dust. And despite its first attempt at scooping up Martian soil for analysis having run into problems when the dirt got stuck on the instrument screen door, it eventually managed to shake it in.

Another surprise was unearthed when the lander dug up the Dodo-Goldilocks trench, where the lander managed to expose water ice buried under the soil. And the water ice evaporated right before its cameras. And it poked a fork into the Martian soil during its first all-nighter.

Unfortunately, the lander’s second attempt to scoop in soil for analysis was thwarted yet again when it wouldn’t even fall down from its robotic scoop. At least the soil eventually managed its way into the instruments before all of the water evaporated away, and in the meantime we got to see a laser light show on Mars thanks to the lidar on the lander’s weather station. Fortunately, later attempts to scoop in soil worked better, with six out of eight of the TEGA ovens having been used in the end. The Mars Phoenix Lander also carried an atomic force microscope, so it got to take a look at Martian dust at truly microscopic scales.

The lander also showed us sights similar to what we can see on our own planet, as it saw frost on the ground and on itself, not to mention clouds in the sky. Altogether, the Mars Phoenix Lander has been fruitful in my humble opinion. And in terms of scientific results, the best has yet to come as us humans back on Earth have only started analyzing the wealth of data the lander sent back. Although I have yet to hear what went on with the supposedly missing water that should have been in the Martian ground.

The presidential dog Barney bit a reporter when approached. This is really a trivial thing, and anyone who watches the news regularly has probably seen this over and over again, but for some reason I have a bit of trouble containing my mirth every time I see the footage.

In the same vein, the 43rd edition of the Carnival of Mathematics is up at The Number Warrior, which has a preponderance of puzzles this time around. Among them is my explanation of a puzzle of chance presented at the Shores of the Dirac Sea.

Let us say that someone gives you a lopsided bet. Say that with probability one gets heads, and with probability one gets tails, and you have to pick heads or tails. You only know the outcome of the first event. Let’s say after the first toss it came out heads. What is the probability that ?

At first glance, the question makes no sense. The outcome of a bet is determined by the probability, so what is it with asking about the probability of the probability? Maybe rephrasing the question might make it a bit more clearer:

Given that the probability of a head is , the probability of a head is . Given that a single toss ended up a head, what was the probability that ?

The first sentence might seem blatantly redundant, and you might be confused about what’s different with the second sentence. If it doesn’t make sense to you, thinking a lot harder is one way to figure out the difference, but another way is to learn about conditional probabilities. For the more mathematically inclined, expressing the problem in formulas makes the difference even more apparent, not to mention explaining the apparent redundancy:

Given this reformulation, all you have to do is to take advantage of the properties of conditional probabilities:

Embarrassingly, my first answer ended up being :

I confused with , which led me to the obvious-looking and yet seemingly wrong answer. (It’s because is such an obvious guess that it seems so wrong, given my experience with conditional probabilities.) The denominator and numerator have to be computed separately, but I foolishly didn’t do so. Since the probability of a head being exactly is , in which case the probability of a head is , the probability of and a head simultaneously is . (Not being a pure mathematician, I’ll live with the bit of fudging here.) And since :

So the probability of the probability of a head coming up being larger than 0.5, given that a single toss turned out to be a head, ends up being 0.75. This probability is much more in line with what I would expect when working with conditional probabilities.

The next time you come across a brand new sort of coin that no one has ever seen before, and a single toss ends up being a head, you can confidently say that it’s much more likely to be biased towards heads. Of course in real life, most of the coins you see will be like every other coin you’ve seen before, and all of them probably turned out to be fair, so all of this doesn’t apply. On the other hand, there are other sorts of practical problems you can apply the same sort of reasoning to.

And now that Obama has all but won the presidential election with McCain having conceded, I feel quite free to list the major things that I think went wrong with McCain’s presidential campaign.

1. George W. Bush. It’s not McCain’s fault that Bush sucked so much that the rest of the Republican Party got dragged down along with him, but it is McCain’s fault for not differentiating himself from Bush sufficiently.
2. The recession. It might not have affected McCain’s chances if it were a gradual downturn, but the bankruptcy of several major financial institutions and the huge bailout bill highlighted the poor performance of the Republican economic agenda.
3. Sarah Palin. While there may have been valid questions about her inexperience when she was nominated, this wasn’t that much of a big deal to me. Then she went and opened her mouth. While she energizes conservative extremists, she was a negative for most of the rest of us.
4. His campaign flailed around like a headless chicken. While not so bad near the end, there have been periods where positions were reversed so rapidly that it made our heads spin. This makes one wonder if they knew what they were doing, and if they were so incompetent during an election, just imagine how incompetent they would be in government.
5. Overemphasis on pandering to the far right. McCain’s pandering to the overly conservative portion of the Republican Party may have been understandable during the presidential nomination, but he seems to have failed to realize that a lot of his base were moderates who were motivated by the Bush years.
6. Lack of a positive message. McCain’s campaign almost exclusively focused on negative attacks against Obama, and far too many of them were extremely dubious, if not outright false. Such negativity could have only turned off a lot of voters, especially since his campaign failed to push a positive message that stuck.

I do hope that Palin doesn’t end up the Republican nominee four years hence. If this happens, that means that yet again we will have a presidential race between a reasonable candidate and a bad one. That would make a vote no choice at all, making me miss another chance to really be part of the democratic process. This election was bad enough in that it didn’t require me to inform myself much at all. Although it might not be the case if the Democratic candidate also sucks four years later, which would be an even worse situation.

Oddly enough, the best case scenario for the next presidential election would force me to spend a considerable amount of effort to ponder who might be the better candidate, with two or more great candidates to choose from. There might be something wrong with me for wishing to pile more work on myself …