The Hadron Collider Physics conference is nearing its end now, and that means one thing: Higgs results! The LHC collaborations have just presented their updated measurements of the Higgs boson candidate whose discovery was announced in July, based on the \(\SI{7}{fb^{-1}}\) of new data that was collected in late summer.

I’ll jump straight to the punch line: what they see is mostly consistent with the new particle actually being a plain old standard model Higgs boson (although it’s not absolutely confirmed yet). Which is kind of disappointing, because it indicates a lack of exciting new stuff to discover. Back in July when the discovery of the particle was originally announced, there were some slight discrepancies between the results obtained by the experiments and the predictions, and a lot of physicists were hoping that was a hint at something new and unexpected, but it’s looking more and more as though that is not the case.

Anyway. On to the results. As in the original announcement, ATLAS and CMS are searching for the Higgs in five different channels: they’re trying to detect five different sets of particles that the standard model Higgs boson can decay …

Have you ever wanted to write notes in the cloud?

No, not that kind of cloud. I’m talking about jotting down thoughts and having them sent to a server somewhere on the internet, to be retrieved and pondered over on any computer, wherever and whenever you feel like it. It’s awfully convenient, and if you’re a creative type of person (like, say, a blogger) or a wannabe creative type (like me), having this ability to immediately record a thought at a moment’s notice is especially handy.

There are, of course, plenty of websites offering “cloud notes,” but it’s only today that I found one that I think really has the “whenever, wherever” aspect figured out. Diigo has a website, browser plugins, Android and iPhone/iPad apps, all of which can access the same store of notes, and a well-documented API so that any random person can tie into the service. All the hallmarks of a useful note-taking application.

Now, when I say “only today,” I really do mean that I have about an hour’s experience using the site and apps, so it’s premature to say that I recommend it, but the signs are …

Now that I’ve finished my quest to identify the misbehaving sinc function, I can bring you the latest news from the Hadron Collider Physics conference in Kyoto, Japan. This is a major conference at which several new results from the LHC experiments are being announced — an exciting time for the physics world indeed!

B meson-muon decay

The most interesting result to come out of the conference so far is an observation by the LHCb experiment of a \(\mathrm{B}^0_s\) meson, made of bottom and antistrange quarks, decaying to a muon-antimuon pair. This is a reaction that physicists have been searching for since 1987. This year, the LHCb collaboration has actually seen it happen — or at least, they’ve collected enough statistical evidence to be fairly confident (\(3.5\sigma\)) that it does happen — for the first time.

It’s not quite as dramatic a discovery as that makes it sound, though; the reason \(\mathrm{B}^0_s\to\mu^+\mu^-\) has never been seen before is that it’s incredibly rare. B mesons are not exactly easy to produce, and then once you’ve got one, the standard model predicts that only one out of every 300 million will …

I’ve been working on some code using GSL and wondering why it didn’t match the results I was getting from Mathematica and other programs. Well, one (of perhaps many) differences is that GSL defines the sinc function as

for \(x\neq 0\), but Mathematica defines it as

The latter is the definition I was using in my math, and I didn’t realize it didn’t match the one in GSL until I broke the code down to individual mathematical terms.

So remember to make sure that any code you use is actually doing what you think it’s doing!

OMG I missed an XKCD!

This was posted a couple months ago, but I don’t remember seeing it until yesterday. The really interesting part is the title text:

FYI: If you get curious and start trying to calculate the time adjustment function that minimizes the gap between the most-used and least-used digit (for a representative sample of common cook times) without altering any time by more than 10%, and someone asks you what you’re doing, it’s easier to just lie.

Sure, it is easier to lie, but where’s the fun in that? Half the point of being a geek is watching the looks of confusion develop on other people’s faces when you start talking about your hobby. But don’t tell them I said that ;-)

No, the more interesting part of this title text is the problem it poses. Naturally, as soon as I read it, I had to figure out how to derive this optimal time adjustment function.

The easiest way to derive something is, of course, to look it up. And the XKCD forum thread for this comic yielded the dirt, so to speak. Tallys Yunes, an operations research expert at the University …

This Wired science article is the latest in a series of reports I’ve seen going around the web lately, saying that for some people, the anticipation of doing even simple math activates the same regions of the brain that are responsible for physical pain. So math anxiety isn’t just something that people make up to make themselves feel better (not that I ever really thought it was); it has an actual neurological basis.

I’ll be honest, I just don’t get math anxiety. I know I have a bit of a tendency to act like it doesn’t exist; for example, this entire blog is meant for people who actually look forward to digging into the math (or other source material) behind an interesting result. I make no apologies for the fact that I use a ton of math here. But this is all just because I would actually like math anxiety not to exist. Whether it’s a matter of education, or cultural bias, or some sort of mental condition that could be treated with drugs or therapy (I sort of doubt that last case, but who knows), I hope that someday we can live in …

It’s Election Day (in the US), and I have a relevant post I’ve been meaning to do for a while.

Suppose you have a binary experiment, one which has two possible outcomes with probabilities \(p\) and \(q = 1-p\). For example, voting. (Pretend there are only 2 parties) Overall, let’s say people vote Democrat with probability \(p\) and Republican with probability \(q\). Now suppose a large number \(N\) of people all go out to vote; what can you say about the results?

In a statistical experiment like this, the possible results are drawn from a binomial distribution, in which the probability of getting \(n\) Democratic votes (and \(N - n\) Republican) is

The probability that the Democrats will come out ahead is just the sum of all the probabilities for all the outcomes where \(n\) is more than half of the total vote: we start at \(n = \floor*{\frac{N}{2} + 1}\), which is the first integer greater than \(\frac{N}{2}\), and add up probabilities all the way to \(n = N\).

Just a quick mathematical observation for today (actually yesterday): suppose you have three points. Any function of the three points which doesn’t depend on their absolute location or orientation only depends on the magnitudes of the vectors joining the three points.

Suppose the three points are \(\mathbf{x}\), \(\mathbf{y}\), and \(\mathbf{z}\). A function that doesn’t depend on the absolute location of the points will only depend on the displacements between them, \(\mathbf{r} = \mathbf{z} - \mathbf{y}\), \(\mathbf{s} = \mathbf{z} - \mathbf{x}\), and \(\mathbf{t} = \mathbf{y} - \mathbf{x}\). And a function that doesn’t depend on the orientations will only depend on the scalar quantities we can form out of these displacements: \(r^2\), \(\mathbf{r}\cdot\mathbf{s}\), \(s^2\), \(\mathbf{s}\cdot\mathbf{t}\), \(t^2\), and \(\mathbf{t}\cdot\mathbf{r}\). But the dot products are actually not independent, because for example

so,

Then you can write \(\mathbf{r}\cdot\mathbf{s} = s^2 - \mathbf{s}\cdot\mathbf{t}\) and …

Last year I posted about an infinite sum involving the mean of the harmonic numbers,

The method I used to evaluate this was to approximate the sum by an integral. This is a technique that is used in various places in physics, such as in the computation of the Fermi surface in metals.

In this particular case, we only cared about the large-\(n\) limiting behavior of the sum, namely that it grows sublinearly for large \(n\). But suppose you wanted to know whether there was, say, a constant term as well. Here’s one way to figure that out. Instead of converting the entire sum to an integral, you choose some cutoff value \(a\), and keep the first \(a\) terms in the sum explicitly.

Now you have a value, \(a\), that represents a “break” in your sequence, but it’s an arbitrary …