Staircases and Diagonal Lines

There are a pair of linked paradoxes that tend to do the rounds on the internet: one that proves that pi is equal to two, and one that proves that the square root of two is equal to two. Obviously this isn’t true which is why they are called paradoxes. What follows is my rather small addition to the paradox.
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Dyson Spheres and the Speed of Light

Many years ago when I was living in Switzerland, one of my co-workers and friends there was almost as much of a physics nerd as I would like to think I am, and we were wondering about different ways to shoot things off at the speed of light. As it turns out, you can end up in some pretty impressive energy realms when you start moving things really fast (for instance: Oh-My-God particles that are cosmic rays (subatomic particles) with kinetic energies similar to macroscopic objects like baseballs!)
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Celebratory Gunfire in Tripoli

There was a letter this morning in our local newpaper (the Calgary Herald) from a reader concerned about all of the celebratory rounds fired off in Libya after the death of Gadhafi and if anyone was killed by those rounds falling back to earth [1]. I was curious if this was a realistic worry, so here’s my incomplete, extremely rough analysis. Continue reading