Monday, September 20, 2010

Mid-Autumn Festival Math and Science

Like most ethnic Chinese, my family celebrates the Mid Autumn Festival. It is a harvest festival celebrated on the 15th of August in the Chinese/Lunar Calendar which coincides with a full moon. In most years, August 15th of the Chinese Calendar happens around September or October of the Gregorian Calendar.

Side note: Chinese holidays, weddings, and ceremonial dates are celebrated according to the Chinese Calendar. Prior to marriage, it is customary to check the compatibility of the groom and bride by looking at their Bazi (literally 8 letters/characters) (Year, Month, Day, Hour of birth) based on the Chinese Calendar, not Gregorian Calendar. For business, the Gregorian Calendar is standard. We conduct our lives using 2 calendars.

On Mid-Autumn Festival, it is customary to eat mooncakes.
Typical mooncakes are round or rectangular pastries, measuring about 10 cm in diameter and 4-5 cm thick. A thick filling usually made from lotus seed paste is surrounded by a relatively thin (2-3 mm) crust and may contain yolks from salted duck eggs. Mooncakes are usually eaten in small wedges accompanied by Chinese tea
The standard mooncake looks like this.
(CC Attribution 2.0 Generic Image by Kansir)

A vegetarian version with bean paste or jujube paste is also popular.
(CC Attribution 2.0 Generic Image by enixii)

Like many Chinese festivals, there's an interesting folk tale involved. It tells of Ming revolutionaries' use of mooncakes to smuggle messages to overthrow Mongol rule in China.
Mooncakes were used as a medium by the Ming revolutionaries in their espionage effort to secretly distribute letters in order to overthrow the Mongolian rulers of China in the Yuan dynasty [ed: better known by its founder Kublai Khan and his grandfather Genghis Khan]. The idea is said to be conceived by Zhu Yuanzhang (朱元璋) and his advisor Liu Bowen (劉伯溫), who circulated a rumor that a deadly plague was spreading and the only way to prevent it was to eat special mooncakes. This prompted the quick distribution of mooncakes, which were used to hide a secret message coordinating the Han Chinese revolt on the 15th day of the eighth lunar month.

Another method of hiding the message was printed in the surface of mooncakes as a simple puzzle or mosaic. In order to read the encrypted message, each of the four mooncakes packaged together must be cut into four parts each. The 16 pieces of mooncake, must then be pieced together in such a fashion that the secret messages can be read. The pieces of mooncake are then eaten to destroy the message.
So to celebrate, my family and friends created a batch of homemade mooncakes.

We used red food coloring to indicate the fillings. Some had dots. Others had stars.

Here are the essentials to celebrating Mid-Autumn Festival. Typically we would drink this outdoors and look at the full moon while our elders would retell the story of Chang-E (嫦娥). If we were in Taiwan, we'd sit on the rooftop and just look up at the moon. With West Nile identified in mosquito populations locally, it seemed like a good idea to stay indoors this time.

Clockwise from the top. A decanter to hold tea after infusion (high grade teas should be infused for a proper amount of time, 10 seconds short or long ruins the tea) and a strainer (to filter out the dregs and small bits of tea). A pear-shaped snifter cup (to smell the aroma after pouring the tea into a drinking cup). Mooncakes in small wedges on napkin. Drinking cup (this particular one is hollow so it's less likely to burn the fingers). Longan fruit. Clay teapot. In the center is a cylindrical snifter cup.
This was a prime opportunity for me to snap some pictures for the math and science teachers.

In this first picture, I poured the tea from the snifter cup to the drinking cup.

Notice a small amount of tea remaining in the snifter cup after I pour the tea into the drinking cup. This is hot tea, and the snifter cup was preheated in a bath of hot water to raise its temperature.

Here are some pictures of snifter cups.

I'm going for the more obvious math and science questions. There's probably plenty to talk about in terms of molecular gastronomy, but I'm not going there.

PS: Harvard now has videos of its Science and Cooking lectures on youtube. (via @jybuell,

Sunday, September 5, 2010

Starcraft 2 Wings of Liberty and Calculus: UPDATE 1

Starcraft 2 Wings of Liberty and Calculus
Starcraft 2 Wings of Liberty and Calculus: UPDATE 1
This is an update to an earlier post.
Let’s see if we can get some information from the graph. Below is a screenshot of the GeoGebra applet.

Here’s a few questions:
  • Which approximation gives the best estimate of total resource collected? Why?
  • If the graph represents the instantaneous resource collection rate (in the context of this game), which sum will provide the best approximation?
  • If the graph represents the average resource collection rate, which sum will provide the best approximation?
  • The red line shows an increase followed by a decrease, what does that mean in context?
  • What happens to the approximation as the number of columns is decreased? What happens when it is increased?
  • Is there information that can help us determine if the graph displays instantaneous collection rate or average collection rate?
  • Whats your best estimate about the amount of resources collected?
Below are 2 screenshots that show the amount of unspent resources by each team on the top right and the amount spent resources in the menu on the top left.

Let’s check our answers:
  • Which sum provided the best approximation?
  • What are some sources of error?
Now let’s connect the graph to what’s happening:
  • Why does the graph of resource collection rate rise and fall?
  • Why does the graph have humps and plateaus? What do they represent? (hint)
  • How did the red player have a steeper rise on the second hump (after first plateau) than the blue player? (hint)
  • What caused the drop-off in the red graph near the end? Does the drop off mean the red player is losing resources or gaining less resources?
  • In the beginning why did the blue graph have dips in its graph? (hint)