### Resonances

Start with a metal surface attached to an acoustic oscillator (a speaker). Add salt to the surface. Increase the frequency until the plate reaches its natural frequency, at which point standing waves are set up. The salt settles down along the nodal lines on the surface where the plate is relatively still. Similarly, salt grains are bounced out of the regions where the surface oscillates.

(I found this video on ThisIsColossal. h/t Bri for pointing me to the site.)

This is a 2-dimensional analogy of oscillations in the Sun. Hot material just below the Sun's surface rises in convective cells, which then "ping" the outer layers of the Sun. This pinging causes the Sun to oscillate and set up standing waves throughout it's 3-dimensional interior. Some of these vibration modes can be observed by making repeated measurements of the Sun's brightness as its surface oscillates.

 An illustration of spherical harmonics in the Sun's interior. These harmonics can be measured by watching the Sun's (or another star's) brightness oscillate in time.

In principle, one could estimate the density of the plate in the video above by reading off the nature of its natural frequencies. Plates of different densities (made of different materials) will vibrate differently and give rise to patterns at different characteristic frequencies. The same goes for stars. Astronomers can read off the density of stars based on the fluctuations in their brightness, which allows them to measure their mass and radius.

This is one of the major side benefits of the Kepler mission. By making repeated brightness measurements (photometry) of hundreds of thousands of stars, the mission has discovered thousands of planet candidates. For some stars, their natural frequencies show up in the photometry, which enables the detection of planets and a characterization of the host star's physical properties. Science!

### 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.

I then used the basketball as my metric. Wikipedia states that an NBA basketball is 29.5 inches in circumfe…

### The Force is strong with this one...

Last night we were reviewing multiplication tables with Owen. The family fired off doublets of numbers and Owen confidently multiplied away. In the middle of the review Owen stopped and said, "I noticed something. 2 times 2 is 4. If you subtract 1 it's 3. That's equal to taking 2 and adding 1, and then taking 2 and subtracting 1, and multiplying. So 1 times 3 is 2 times 2 minus 1."

I have to admit, that I didn't quite get it at first. I asked him to repeat with another number and he did with six: "6 times 6 is 36. 36 minus 1 is 35. That's the same as 6-1 times 6+1, which is 35."

Ummmmm....wait. Huh? Lemme see...oh. OH! WOW! Owen figured out

x^2 - 1 = (x - 1) (x +1)

So $6 \times 8 = 7 \times 7 - 1 = (7-1) (7+1) = 48$. That's actually pretty handy!

You can see it in the image above. Look at the elements perpendicular to the diagonal. There's 48 bracketing 49, 35 bracketing 36, etc... After a bit more thought we…

### 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…