1. 2010

    Velocity addition: a myth?

    On the episode of Mythbusters aired a couple weeks back, Kari, Grant, and Tory set out to test the myth that if you have a car driving forward at, say, 60 miles per hour, and you shoot a ball out the back at the same speed, it will fall straight down. Now, if you know anything about physics, your first thought upon hearing this might have been the same as mine: “huwhah?” The idea that velocities of equal magnitude and opposite direction cancel each other out in this way is a pretty fundamental result…

  2. 2009

    Scaled statistical error

    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

    $$I = A N$$

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

    $$\delta I = A \delta N = A …