Here’s a tidbit of science that I should have written about a long time ago. Last month, there was a surge of excitement in the particle physics community when the ATLAS detector team announced that they had pretty much conclusively observed the Higgs boson decaying to tau leptons for the first time.

Now, you might be forgiven for thinking “what’s the big deal? I thought we already found the Higgs boson?” Well yes. A year and a half later, physicists are fairly confident that what they found is the standard model Higgs boson. But back in July 2012, when the discovery was first announced, all anyone knew was that ATLAS and CMS had discovered a previously unknown particle with a mass of \(\SI{126}{GeV}\). It wasn’t clear just what kind of particle it was: the standard model Higgs boson, another kind of Higgs boson, or something else entirely. That question would be resolved by gathering more data on how the new particle interacts with other, known particles, and that’s what this most recent bit of news is about.

The Higgs search: a year in review

To understand all this in more detail, let’s back …

Evidently my post from a week ago on the rate of fires in Tesla electric cars compared to gas cars couldn’t have come at a more appropriate time. People are still harping on the recent string of Tesla Model S fires, despite the fact that — as I showed in my last post — there’s no evidence to suggest that the fire risk in a Tesla is any greater than that of a regular car. In fact, if anything it seems to be slightly less.

In my last post I kind of hinted at the fact that the rate of fires isn’t the whole story. Even if a fire does happen, your risk of getting injured or killed is different in a Tesla than a normal car. Something similar goes for other types of accidents. So if you want to tell whether Teslas are safe, what you probably should be looking at is the overall rate of injuries and fatalities for Tesla drivers and passengers, compared to the equivalent for gas cars. And that number tells a very interesting story: Tesla CEO Elon Musk has written a new blog post which emphasizes that not one person has ever been …

About a month ago, this happened: a Tesla Model S (electric car) ran over a large piece of metal which punctured its battery compartment, and the car caught on fire. It was a big deal because, according to CEO Elon Musk’s blog post (first link above), that was the first time a Tesla has caught on fire.

Since then there have been two more similar incidents in which a Tesla was involved in an accident and caught fire. Naturally, people are getting concerned: three high-profile fires in one month is a lot! But these incidents get more than their share of attention because electric cars are new technology without a proven safety record. So the question we all should be asking is, how does the fire risk in a Tesla compare to that of a regular, gas-powered car?

Most of Elon’s blog post about the first incident discusses how well the safety features of the car performed after it did catch on fire, and how this would have been a catastrophic event if the car were gas-powered like a normal car, and now we should all be driving electric cars and so on. My interest here is purely …

Everyone — and by “everyone” I mean anyone who analyzes discrete random processes on a regular basis (quite an inclusive group, I know) — knows that the statistical error in a random count of events is the square root of the count. (For those of you not in the know, when you’re examining some process in which events occur at random intervals, e.g. the decay of radioactive atoms, if you count the number of events that occur in a minute over and over again for a large number of minutes, you’ll have some average number of decays per minute, and the distribution of counts will have a standard deviation of the square root of that average.)

But what happens when the quantity you’re really interested in is not the count itself, but something proportional to the count? What’s the statistical uncertainty in that? It’s actually fairly simple to figure out based on the usual formula for error propagation. If the quantity you’re measuring is denoted \(I\) and it’s related to the count by

where \(A\) is some constant (or anything independent of the count), then