Yesterday I posed a famous trick question, and we had the shortcut answer, the long “standard” answer, and a particularly elegant solution by commenter meichenl. Turns out he has his own blog called Arcsecond, and it’s really fantastic. He focuses mostly on examining interesting mathematical situations. Check it out!

Some physics news: the perils of the LHC continue. As you have probably heard, the LHC experienced a severe breakdown during some of the early test runs. Aside from the break itself putting the collider out of commission, the particular system that broke was discovered to have a fundamental design flaw. Worse, this system is duplicated several times over the length of the accelerator. As such, that entire system has to be fixed including the parts that aren’t broken. According to press reports, the LHC operators are hopeful that 5 TeV collisions should start next summer, with full power 7 TeV beams following at some unspecified later time – probably in 2010. This is very frustrating. I’m not even a high-energy physicist but high-energy physics is immensely interesting and I’ll be awaiting the repairs anxiously.

Swans on Tea posted this a while back. I’ve seen it before, and it’s great to share here. The guy in the video is singing something backwards, and to prove that there’s no trickery he constantly does things that increase entropy. Played forwards those things are perfectly possible, backwards they’re not. But really nothing he does is truly impossible backwards, just exceedingly improbable. We talk about entropy and the “arrow of time” a lot, but this is a great demonstration in action:

Here’s a particularly interesting post from Dirac Sea about different approached to quantum gravity. An excerpt:

Recall the idea of duality: some notions are not a property of the physics, just of a certain description thereof. Surprising as it sounds, this includes the question of how many dimensions spacetime has. The attempt to derive general relativity from something else, living in the same spacetime, is likely to fail.

Indeed. One subtle mathematical truth discovered by Dedekind is that in fact it is not necessary to use three real numbers to uniquely specify an arbitrary point in 3-d space. One real number suffices to describe any point in n-dimensional space. How? One scheme might be to write a decimal number, every third digit of which corresponds to the successive digits of the x,y, and z coordinates. Like this: if we have the coordinates

x = 0.3333…
y = 0.4444…
z = 0.5555…

Our single number which describes all of them would be

C = 0.345345345…

Turns out this particular scheme is not quite going to do the trick in all cases, but Dedekind’s more complicated method formally works in all cases.

The last two items are politics: feel free to skip.

Earlier in the week a few ScienceBloggers (I saw Greg and PZ mention it) were agitating for federal science teaching standards which would override state and local education standards. Let me get out my little copy of the Constitution and see if that’s listed among the enumerated powers granted to congress…

…well what do you know, it’s not. I am under the impression that one of the Changes that we are supposed to see in the upcoming administration is a new respect for the Constitution. This particular idea is quite the opposite. I’m all for good science teaching standards. I am adamantly opposed to the ever-distending bloat of the three trillion dollar per year disaster we call the federal government. Remember anything the government can do for you it can do to you, and the pendulum will not always be where it will be for the next few years. Four or eight years hence we might have a president Palin or Jindal; it’s unlikely Greg or PZ would like them setting standards. Never throw away long term safeguards in the pursuit of short term gain.

Speaking of politics, you might be interested in the Secular Right blog written by contributors including Gene Expression‘s Razib. It’s a stereotype with a bit of statistical truth that the left leans secular and the right leans religious. There are exceptions: Obama himself is at least to some extent a member of the religious left. Secular Right is, as you’d expect, written from the secular right. It’s a perspective that’s going to have to be a real part of conservatism if it is to become viable again. I myself am not secular in my metaphysics, but I do think government and religion are both badly damaged when they associate.

And that’s all for now. Have a great weekend!