The latest episode of Mythbusters tested a slightly controversial and very physics-related myth: that you can propel a boat forward by putting a fan on the boat and pointing it forward, into the sail. What’s going on here?

First of all, why wouldn’t you expect this to work? Actually, first of all, why would you expect this to work? Think about the naive explanation for why a sailboat moves: the wind pushes forward on the sail, and the sail pushes forward on the boat. So someone who had never heard of physics might think that putting a fan on the boat and pointing it into the sail just gives you a convenient, portable source of wind. Presto, instant speedboat!

But, as explained on the show, that reasoning doesn’t work, because of Newton’s laws of motion. There are actually a couple of different ways to apply Newton’s laws to this scenario:

• Newton’s first and second laws (which are kind of the same thing) say that an object maintains its state of motion unless subject to an external force. The key word there is “external”: if you want your boat to move, you need something outside …

There’s a movement going around on Facebook to bring attention to a plan by the Turkish government to begin filtering internet access within the country. As of August 22, internet service providers in Turkey will be required to make their users choose one of four access plans, each corresponding to a blacklist of websites that will be blocked. For example, the “domestic” plan will block international websites, and “children” will presumably block anything considered to be inappropriate for kids (pornography and such). But the exact blacklists will be maintained by the BTK (Turkish Information Technologies Board, or something like that), and will not be made public. So the government can theoretically add any website to the blacklists, thereby using them to suppress political opposition or whatever they want, and nobody will know. Any time a government agency gets power without explicit accountability like this, there’s a high potential for abuse and people should be concerned. Even if most government workers are really just trying to do what’s best for their country, how much do you trust that everyone who ever works in the information technologies agency will be able to resist the temptation to go too far …

It’s a busy time in the physics/life/web world: Fermilab may have broken the Standard Model (but probably not), Physics Stack Exchange is holding moderator elections, and most importantly, Mythbusters is back on with a new season. But I kind of have to ignore all that since I’m preparing for my comprehensive exam next week.

For those not familiar with it, the comprehensive exam at Penn State basically marks the transition from being primarily a student to being primarily a researcher. Accordingly, I’m starting to get questions about what my research is about — not that people didn’t ask before, but it’s reaching the point where “some high-energy stuff” ceases to be an adequate answer. So I’ve been thinking about how to concisely explain what I’m trying to do with my time. The more I think about this, the more I think it’s a good exercise for anyone in physics to go through; after all, if you can’t summarize what you’re doing at some level to a non-specialist, do you really understand it?

At a high level, the project I’m on right now deals with the rapidity evolution of …

I probably should not have worn my frictionless shoes out last night.

Oddly enough (for the end of March) it’s snowing in State College, which means that the sidewalks are slippery again, which reminded me that I’ve been meaning to follow up my previous post about slippery surfaces with one where I talk about hills.

There were two main points I made in the last post:

1. friction with the ground is what allows you to accelerate (speed up, slow down, or change direction), and
2. friction also helps keep your feet from slipping out from under you when you put them down as you walk.

I used a slightly unrealistic diagram of a foot as a visual aid:

Now compare that to the equivalent diagram for a foot on a hill:

On level ground, without friction, there’s no force pushing you along the ground. But the new diagram shows that that isn’t the case anymore on a hill. With no friction, gravity works to pull you down the slope. So in the absence of friction, you do accelerate — you slip down the hill.

Obviously, this is bad news if you’re trying to walk uphill. Even if …

In the process of graphing some complex valued functions, I figured out a couple of neat coloring schemes that I thought might be worth sharing. Both schemes share the same hue and saturation functions:

They differ in the third component, though. The one which I will arbitrarily designate “color scheme 1” (because I like it better) is defined in HSL color space, and has a luminosity function of

where \(S\) is the saturation value. This maps all real or nearly real numbers to white, all imaginary or nearly imaginary numbers to black, and other complex numbers to varying hues depending on their phase.

The other one, “color scheme 2,” has a value (brightness) function of

This maps all real or nearly real numbers to white, and all other numbers to varying hues, again depending on their phase. Positive imaginary numbers are red, negative imaginary numbers are cyan.

Note that both functions are undefined at \(z = 0\). If you implement these you …