Cosmos Computed

Keystone on opening day Keystone Ski Resort just opened for the ski season on Friday. I went up to the resort that same day. There was only one run open (not including the beginner area at the top of the mountain), but it was awesome nevertheless! One of the main downsides to skiing on opening day is the number of people. There must have been about 2500 people on the mountain at the same time as me (not including the people snacking in the lodge). To keep the lines moving, the lift attendants made sure that the lift was completely full, with 4 people per chair. Even so, the wait to get on the lift took a long time. At one point when I was standing in line, a thought came to mind: the line was constantly being filled with more and more people, but it never got longer because the chair lift was carrying the people away at the same rate. So what would happen if the lift attendants only put 3 people on each chair, instead of 4? This would disrupt the balance: the inflow of skiers would be ...

Over my fall break (which lasted 1 day), I wrote a JavaScript program that would render a sphere. I thought it would be a fun way to practice math and programming skills simultaneously. As usual, I used my FireTools.js library to help with graphics as well as some other functions. To render the sphere, I wanted to take every pixel on the screen, and calculate the color of the pixel. The color would vary depending on which part of the sphere the pixel was displaying. If the part of the sphere was facing the light source, it would need to be brighter than a part of the sphere facing away from the light source. To find the brightness of each point on the surface, I first calculated the XYZ coordinates of that part of the sphere. This is also equal to the normal vector at that point. I took the dot product between the light source's direction and the normal vector. This is a mathematical operation that tells me whether the surface is aligned with the light source, as well as the percen...

Near the end of last month, the moon passed entirely through Earth's shadow, resulting in a full lunar eclipse. The moon didn't completely black out, due to sunlight scattering through Earth's atmosphere. Instead, the moon had a dim reddish-brown glow. Of course, I took I lot of photos of this celestial phenomenon. I started taking photos during totality. I kept taking photos a couple times per minute, for a period of about 1.25 hours, until the moon was fully lit. My goal was to put the photos together, for an animation of the moon passing through the shadow of the Earth. "Fake" crescent One thing I thought was pretty neat was when the partial lighting of the moon formed a perfect crescent. The crescent looked a lot like the waning crescent phase of the moon, but there was something strange about it. It reminded me of the artificial images of the moon that you'll see when you use a star-mapping program. The reason is this: for a real crescent moon, the lighti...

I'm thinking of two common English words, W1 and W2. W1 is half as long as W2, but has twice the syllables. When combined, the two words form a phrase that can be used to refer to a nonspecific stage of a meal. The letters in these two words can be rearranged to form two new common words: W3, and W4. W3 is half as long as W4, and it also has half the syllables. The two words, when combined, may be used when telling somebody to draw with a certain art medium. What are all four words? New posts every month - subscribe for free !

The Perseid meteor shower is coming up! After midnight on Tuesday, and again on Wednesday, an observer under a dark sky may see up to 100 meteors per hour - an average of nearly 2 per minute. If you live in a city, the light pollution will wash out most of the meteors, so the countryside or mountains will be a much better place to watch them. Meteors start as small bits of material floating in space, usually dropped from comets that passed through the area. At this stage, they are called "meteoroids". When the earth passes through a cluster of these particles, they hit our atmosphere and burn up as meteors, and we have what's called a meteor shower. If you're looking up at the sky, and you see a streak of light zip a short distance and then disappear, this is a meteor. One of the best things about this particular shower is that the moon won't come out all night, so the sky will be darker than usual - making it possible to see more meteors than in most showers. If ...

212° F Let's play a little game. I'll list a bunch of possible actions. Each action will have 2 variations, (a) and (b). You choose either (a) or (b), depending on which would be safer (or less painful). Each of the questions will involve an oven hot enough to bake a cake (350° F), and a pot of boiling water (assume we're at sea level). So... would you rather: 1.     (a) Stick your hand in the oven     (b) Stick your hand in the boiling water   ... for a period of 10 seconds 2.     (a) Leave a fork in the oven     (b) Leave a fork in boiling water   ... for a period of 15 minutes. Then hold the fork tight with your bare hand. 3. Fill a jar to the top with cool tap water. Then:    (a) Place the jar in the oven    (b) Place the jar in the boiling water   ... for a specific, but unknown, period of time. Then remove the jar and put your hand in it. First see if you can figure these out yourself. They shouldn't be too...

This morning, New Horizons became the first spacecraft to make a flyby observation of the Pluto system. During the mission, the spacecraft captured the most detailed photographs of Pluto's surface we've ever had, and possibly ever will have. It also found many new properties including size, mass, atmosphere, and surface composition. In a period of a few hours, we discovered more about Pluto than we've found in the 85 years since Clyde Tombaugh captured its first photograph. Before After  (images credit: NASA) To complete this mission, the spacecraft flew for more than 9 years through the emptiness of space. This may sound like a long time, but it's actually amazingly quick. In fact, New Horizons set the record for the fastest speed at launch, and during the flyby, the spacecraft was moving at a rate of over 30,000 mph, or roughly 50 times the speed of sound. Picture an object twice as heavy as a grand piano moving 25 times faster than a bullet from a gun. Yikes. The man...