Friday, December 25, 2015

Astronomy Sketches

Planet original
Last month, I drew a couple astronomy-related pictures using a graphite pencil on a sheet of white paper. The problem with pencil sketching is that it's hard to draw white glowing objects... so I sketched a negative, and then uploaded the images to my computer and inverted them. Then I increased the contrast to improve the black background and enhance the white.

The image at the top of this post is a ringed planet, possibly Saturn. I included three moons and some lighting on the backside from the rings. The whole image was smaller than a dime.

Black hole original

The image below is an imagined view of a black hole. I included high-energy jets of ejected material and an accretion disk. Most black holes are not actively consuming material, and do not have jets. But those are boring to draw.

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Friday, December 18, 2015


Bubbles in space
Imagine the universe is filled with water. Instead of empty space, every inch of it contains pure water. No planets, no stars, only water. What happens? And what would happen if an air bubble formed?

The answer to this question requires a basic understanding of gravity.

Monday, November 9, 2015

Ski Lift

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 greater than the outflow, so the lines would start getting longer. But after a few minutes, the inflow of skiers would decrease (because not as many people would be coming down the mountain), and the lines would stabilize.

The point at which the line stabilizes depends on the number of people on each chair going up.

When I got home, I decided to calculate exactly how many people would be standing in line, based on the number of people per chair. The problem is that there were 2 lifts running, so to simplify the problem, I only looked at a single chair lift: Montezuma Express. I also assumed that half of the people preferred Montezuma Express (rather than the other lift). This makes the total number of people 1250, instead of 2500.

To solve the problem, I started by looking up some details for Montezuma Express. I found the following information at

Type:High-speed quad
Vertical rise:1589 ft
Inclined length:6213 ft
Speed on line:1000 fpm
Number of chairs:168

Now the number of people in line is going to be the total of 1250 minus the number of people on the slopes, minus the number of people going up the lift.

Let x be the number of people per chair. Half of the chairs, 84 chairs, are going to have people on them (because the other half come down the mountain empty). That accounts for 84x people.

Now how many people are skiing down the mountain? Well, that depends on the rate that people are getting off the lift at the top. This, in turn, depends on how many chairs arrive per minute. The distance between the chairs is 6213 ft / 84 = 74 ft, and the speed of the chairs on the line is 1000 ft per minute, so the chair arrival rate will be (1000 fpm) / 74 ft = 13.5 chairs per minute. This means that the number of people getting off the lift at the top will be 13.5x per minute. Assuming it takes n minutes for the average skier to ski to the bottom, there should be 13.5nx skiers on the ski runs.

Using all these new values, there will be 1250 - 84x - 13.5nx people standing in line. How does this affect the minutes spent waiting in line? Just divide by the outflow rate: (1250 - 84x - 13.5nx)/(13.5x).

Ski resort chair lift
Taken Friday at Arapahoe Basin
That was pretty easy. Now let's try plugging in some values. Assuming that the average skier takes 10 minutes to ski down from the top, and that there are 4 people on every chair, the number of people standing in line will be 1250 - 84*4 - 135*4 = 374, and the time spent waiting in line will be 374 / (13.5*4) = 6.9 minutes.

If the attendant only put 3 people on each chair, then there will be 593 people in line, and the wait will be nearly 15 minutes. This is more than twice as long as when there were 4 people on every chair. I think it's pretty clear how important it is to fill every chair going up! (Incidentally, after a few runs, we got tired of the long lines and went to Arapahoe Basin. It wasn't much better...)

Now suppose there's a lodge at the top... and the number of people in the lodge depends on the amount of time spent waiting in line. Suppose that the number of people in the lodge will be 500 + 10t2, where t is the time spent waiting in line at the bottom. How does this affect the number of people waiting in line? I'll leave this for you to figure out!

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Tuesday, October 13, 2015

CGI Sphere

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.

Saturday, October 10, 2015

Lunar Eclipse

Total lunar eclipse

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.

Sunday, August 30, 2015

Word Puzzle

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?

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Monday, August 10, 2015

Things in the Sky

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 you go outside to a dark location, here are a few other things you may see:

Wednesday, August 5, 2015

Which Hurts More?

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:

    (a) Stick your hand in the oven
    (b) Stick your hand in the boiling water
  ... for a period of 10 seconds

    (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 hard. If you have trouble, heat up your oven and boil a pot of water, and see for yourself what hurts more. (NOTE: I take no responsibility for any resulting injury.)

Tuesday, July 14, 2015

Pluto No Longer on the Horizon

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.

Monday, June 29, 2015

Chalk Illusions

I have some crazy news! I was radiated by some radiation, and became radioactive. Over time, my radioactiveness decreased, and as it decreased, my mass decreased as well. I am now a foot shorter than I used to be, and weigh 50 pounds less! At the top of this post, you can see a picture which proves it. In the photo, I'm sitting on a weird box that materialized in the middle of the road...

Monday, June 22, 2015

Golden Flowers

Honey bee on flower
A few days ago I found a field full of bright yellow flowers. It looked kind of nice, so I started taking pictures. My main goal was to get a photo which showed the vast number of flowers, without any extra information that might distract the mind. I ended up with this:

Monday, June 8, 2015

CG Earth

Click to view larger

You may have noticed that my blog background changed a couple days ago. I've been meaning to change it for quite a while, but I didn't get around to it. Then, a few days ago, I had some free time on my hands. Why not create a 3D model of Earth, I wondered? So I pulled up Blender (a free computer graphics program I use) and got to work.

Sunday, May 10, 2015

Overview of Functions

Imagine you have a blender. To your blender, you add a couple scoops of ice cream and some milk. Then you press the buttons on the blender. Soon, you have a delicious vanilla milkshake. Next, you add strawberries and press buttons again. The result is even better than before: a strawberry milkshake.

Of course, strawberries aren't the only option. Suppose that, instead of strawberries, you added cocoa powder and avocado. The result is a chocolate-avocado milkshake. Or you could have added some mint leaves, for a mint milkshake. Or some peaches, for a peach milkshake.

In each of these cases, you pick the ingredient, and get a different milkshake. Whatever ingredient you pick, the result is always a milkshake. In other words, the blender took your ingredients, and returned a flavor of milkshake.

The blender is like a function.

Thursday, April 30, 2015

Is MSG Safe?

Monosodium glutamate, commonly abbreviated MSG, is a very common chemical used to enhance flavors in food. MSG works by activating the "umami" receptors on the tongue, effectively enhancing flavors and making food taste a lot better. This is similar to the way sodium chloride (table salt) works, but MSG is much more powerful, so sodium content can be reduced by adding MSG to food. For this reason, many food companies use MSG as a food additive.

Despite these apparent advantages, most people would agree that MSG is unhealthy and should be avoided. Sensitive individuals even experience negative side effects after consuming food containing MSG. But what exactly is wrong with MSG? If a person is not MSG sensitive, is it okay for them to consume it in their food?

Thursday, April 16, 2015

Nature GIFs

White blossoms animated gif
I recently created a couple of nature-themed animated GIFs. (Click the images to view larger.)

The first image is a blossoming tree. I thought the tree looked pretty, but I realized that part of the beauty came from the gentle swaying in the wind. So I decided to animate the image.

Wednesday, April 1, 2015

Major Change of Ideas

Edit: April Fool's. The article completely fails to answer for the benefits of math and science (including medicine and natural disaster prediction). It grossly exaggerates the negative aspects of math and science. Incidentally, math and science have made a large positive difference in my life.

Good morning, everybody! I decided to write a blog post to say that I will be completely changing the way I view knowledge and the purpose of life.
A horse ranch
Photo credit: my sister
Basically, "higher" knowledge (including logic, science, mathematics, etc.) is completely useless. There is no point in learning these subjects, which is why I have dropped all my college classes and will not be going to school today.

Instead, we should go to the fields, with a shovel and a rake, and grow crops. I will therefore end my blog and begin life as a worker at a ranch in Wyoming.

Saturday, March 14, 2015

5 Methods for Approximating Pi

Animated pi symbol
Happy super-π day! π-day falls on March 14 every year, because the month-day combination results in 3-14, which are the first 3 digits of π. But this π-day is particularly special: include the year, and you get 3-14-15, the first 5 digits of π. We won't get another π-day like this for another 100 years, so you better enjoy this one!

A particularly special time will be at 9:26:53 PM tonight, when we'll get 3-14-15 9:26:53, or the first 10 digits of π.

In honor of the occasion, I'm going to post 5 simple methods for approximating the value of π.

Saturday, February 28, 2015

Snowflake Photos

In this post, I'm including some of the photos of snowflakes I've taken over the past few days. As usual, these close-ups were taken using my macro setup. I did not edit the photos in any way.

Sunday, February 22, 2015

Nature Wallpaper

I collected 12 of the highest-resolution, best-quality photographs of nature I've taken over the past few years, cropped them to highlight the important parts, and then applied JPEG compression. Now I'm releasing them for my blog readers to enjoy as a desktop background.
To download as a .zip file, click here. Note that the photos shown in this post are low-resolution previews. If you have any questions about the wallpaper, please comment!

Tuesday, February 10, 2015

Perlin Noise

Today I finished a JavaScript program that will generate random numbers, and then use those numbers to generate Perlin noise.

Perlin noise is like a sort of organic randomness. First I'll explain randomness with regards to computing.

Friday, January 23, 2015


In the realm of science, there are many things which are not fully understood. The mechanism behind the formation of a snowflake crystal is one of these things.

Thursday, January 15, 2015

Online Snake Game

This is a simple Snake video game I wrote over the past few days. For the graphics, I used my Firetools.js library, which I also mentioned in my Pong post.

To play the game, use the arrow keys on the keyboard (you might need to click on the game to give it focus). The world loops, so you can go out one side of the screen and come in the other. Eat 50 green pellets to win the game. Each time you eat a pellet, you will get longer and your score will go up; the longer you are, the more points you get for each pellet. If you don't eat enough pellets, you'll begin to starve, and get shorter. Cherries make you longer, but do not prevent starvation.

I did not add the ability to track high scores, but I might add that feature later on. Meanwhile, you can post your scores in the comments. Have fun!

Thursday, January 8, 2015

2014 in Photos

The year of 2014 is over; the year of 2015 has begun. Over the past year, I took a lot of pictures - more than 1200 photos of clouds, bugs, plants, rocks, and more. I deleted most of the low-quality and repetitive photos. Then, I selected 20 of the remaining photos which I thought were the most interesting or significant.

In this post, I'll include those photos, in chronological order.