Music for Oscilloscopes

First, a story:

Many moons ago, before laser pointers were things you could get at your local convenience store for the cost of a few packs of gum, back when lasers were expensive and cool, my friend got a laser. I’m pretty sure it was discarded by some lab. It was a tube about 5 cm in diameter and about 30 cm long and had a large brick-sized power supply. It was fun to play with, but ultimately it’s just a laser making a red dot on the wall. So Phil, for that was my friend’s name, took a speaker from his stereo, and taped a small mirror to the cone. Then, with the lights out, aimed the laser at the mirror and played music. Suddenly, the music came alive on the ceiling where the laser was being reflected. We called it Philsarium, after Laserium, which had been shown in the 1970s at planetariums.

That’s it for the story. Not much of a moral, I admit, but it was more of a trip down memory-lane. Anyway, the reason I bring it up is this week I saw a certain Smarter Every Day video. This video immediately brought that experience back to mind, except this time the laser is replaced by an oscilloscope. Oh, and instead of using regular music, awesome people in Austria craft music specifically to show different things on the oscilloscope. What normally shows sine waves or square waves (or RS-232 signals that Phil and I had to reverse engineer at one point) now shows everything from Tetris blocks to Tyrannosaurus Rexes.

Like Phil’s laser, the oscilloscope also shows a dot. Normally it shows various waveforms for analysis, but really it just shows voltage visually. By splitting the music’s stereo signal into 2 lines (one for the left speaker, the other for the right) and connecting these 2 voltages to the oscilloscope’s two inputs, the oscilloscope’s dot can be moved around the screen based on what the music does. One input (say the left audio channel) controls the horizontal, and the other input controls the vertical, moving the dot around the screen. By adjusting the voltage for the two channels carefully, you can turn the oscilloscope into an Etch-a-Sketch. And by having the sound change the drawing changes, and you can move and change the image. OK, it may be a long way to go for what is today considered mere music visualization, but doing it on a ‘scope is brilliant.

Those wacky Austrians have made albums of music based on this. The music is constrained by it’s primary audience, the oscilloscope, so it sounds somewhat like raw old school synthesizer music.

There’s a lot of trigonometry involved in this, so the next time a student asks a math teacher “when will we use this”, the answer may be “when you form a band.”

Fundamental Equations, Chaos, Fractals, and Leaky Faucets

It’s been a while since I’ve written here. Busy teaching. (I know, lame excuse).

So I go and watch some video on YouTube, and on the side is the list of suggested videos. For a while there’s been this one by Veritasium (Derek Muller). Now, Derek is a fantastic science educator, and is who I want to be when I grow up. One problem is he’s younger than me by over a decade. Hmm. Have to work on that somehow.

Anyway, the video that was just waiting for me to finally click on it was this one. It’s about an equation that will change how you see the world.

The Logistic Map

The math is very simple: x_{n+1}=r x_n(1-x_n) where r is the growth rate. This is a very simple equation with a negative feedback loop.

When you graph r by the equilibrium population, you get this:

from the Wikipedia article on the Logistic Map

What!?

Once the growth rate hits 3, the equilibrium population splits, and oscillates between two values. Then just after 3.4 it splits again. And very soon it becomes chaotic. Oh, and fractal. The chaotic nature was used for pseudorandom number generators.

The Mandelbrot set

Does mentioning fractals make you think of the Mandelbrot set? If it doesn’t, then you have some research to do.

From the Wikipedia article on the Mandelbrot Set

It’s probably the most famous fractal out there. Heck Johnathan Coulton has done a song about it.

But evidently if you somehow rotate the Mandelbrot Set along it’s real number axis, you get this:

From Physics Forum

Look familiar? At this point I started getting a headache, but it was one of those good, excited headaches that come from having your reality twisted about.

Leaky Faucets

Oh yeah, leaks. Derek then mentions that if you get your faucet going drip, drip, drip, and then increase the water pressure just right, it will start doubling: drip drip, drip drip, drip drip. Push it a little more, and you get chaotic behavior.

Of course the YouTube video is so much better than my explanation. Go watch it.

Happy Summer Solstice

How would you like to watch the summer solstice sunrise or sunset at Stonehenge?

The solstices are the two days when the sun is the furthest north or south from the celestial equator. The full path that the sun takes over the year is the analemma. The solstices are the furthest north and south points on the analemma.

Stonehenge is one of the most well known monuments. The ring of standing stones was built between 3000 BCE and 2000 BCE. This English Heritage website is doing/has done livestreams of sunrise and sunset from the site.

Scientists view atomic bonds breaking and forming

Scientists in the UK and Germany have viewed individual metal atoms making and breaking bonds. They used carbon nanotubes as a scaffold to hold the atoms in place. This is with individual rhenium atoms. You can see the distance between the atoms grow and shrink depending on the environment. It looks like this type of microscopy will become important in chemistry.

Which falls faster, feathers or a bowling ball?

Of course, here on Earth, it’s the bowling ball. But why?

The answer is air resistance. Those darn air particles slow down the low mass feathers. They try to slow down the high mass bowling ball, but have little effect. So the feathers take longer to fall.

But what if you could remove those pesky air particles? Well, they did this on one of the later Apollo missions, but you can also do this on Earth. If you have the right equipment. Fortunately, NASA does.

Which way is down?

This seems like a very simple question. But as this video from vsauce shows, it’s anything but. This goes into things way past my middle school classroom, including general relativity, spacetime, and geodesics. Things are simplified in middle school, and it’s still a difficult thing for kids to get. More below the video.

In middle school we’re more interested in the Newtonian view rather than the spacetime view. For us, down is towards the center of the Earth. It’s the same for people on the other side of the Earth (say in Australia (I’m in New Jersey, USA)). For them, down is still towards the center of the Earth, but that’s in a different direction. My down and their down point in close to opposite directions. That’s because the concept of “down” is a local direction, not a universal one. My down is different from the down of my friend who lives in New Zeeland. This can be a difficult thing for 13 year olds to understand. It helps to show it on a globe, with little stick figures drawn on a folded up sticky notes.