### Fun with sub-Nyquist sampling (or Aliasing as Art)

A subwoofer agitates a stream of water at 24 +/- $\epsilon$ Hz, where $\epsilon \sim 1$, while video is recorded at a frame rate of 24  Hz (i.e. sub-Nyquist). Fun ensues!

This effect is known as aliasing, which is also responsible for helicopter blades and car wheels appearing to spin backwards in films. Aliasing is also important in finding planets. We sample the radial velocity variations of stars caused by their planets using instruments such as HIRES at the Keck observatory. If we don't sample with dense enough time coverage (high enough frequency), a sub-sampled radial velocity signal can appear at a shorter or longer period. Here's an example from Wikipedia:

Imagine that the red curve is the true signal and the apparent (measured) signal is blue. You gotta mind your time-sampling! The optimal sampling is less than half the period (twice the frequency), which is known Nyquist samling.

This is what caused planet hunters (including me) to get the orbital period of 55 Cancri e wrong. Bekki Dawson and Dan Fabrycky found the correct signal at a much shorter orbital period than was previously thought. Since the planet was closer to the star, the probability that it would transit increased by a large amount (roughly a factor of 3, if memory serves). This prompted Josh Winn and collaborators to search for transits with a space telescope called MOST. And this is how the brightest transiting planetary system was discovered!

(The fuller story involves a prejudice against the existence of planetary periods less than 1 day, which caused our diagnostic periodogram plots to be plotted starting at 1. This hid the true period near 0.73 days, and drew attention to the aliased signal near 2.8 days. Other more technical details not suited for this blog are covered by Dawson & Fabrycky.)

### The Long Con

Hiding in Plain Sight

ESPN has a series of sports documentaries called 30 For 30. One of my favorites is called Broke which is about how professional athletes often make tens of millions of dollars in their careers yet retire with nothing. One of the major "leaks" turns out to be con artists, who lure athletes into elaborate real estate schemes or business ventures. This naturally raises the question: In a tightly-knit social structure that is a sports team, how can con artists operate so effectively and extensively? The answer is quite simple: very few people taken in by con artists ever tell anyone what happened. Thus, con artists can operate out in the open with little fear of consequences because they are shielded by the collective silence of their victims.
I can empathize with this. I've lost money in two different con schemes. One was when I was in college, and I received a phone call that I had won an all-expenses-paid trip to the Bahamas. All I needed to do was p…

### On the Height of J.J. Barea

Dallas Mavericks point guard J.J. Barea standing between two very tall people (from: Picassa user photoasisphoto).

Congrats to the Dallas Mavericks, who beat the Miami Heat tonight in game six to win the NBA championship.

Okay, with that out of the way, just how tall is the busy-footed Maverick point guard J.J. Barea? He's listed as 6-foot on NBA.com, but no one, not even the sports casters, believes that he can possibly be that tall. He looks like a super-fast Hobbit out there. But could that just be relative scaling, with him standing next to a bunch of extremely tall people? People on Yahoo! Answers think so---I know because I've been Google searching "J.J. Barea Height" for the past 15 minutes.

So I decided to find a photo and settle the issue once and for all.