Monday, July 11, 2011

Natural Beauty

I came across this interesting video where 365 layers of makeup is applied in one day.

Lernert & Sander: Natural Beauty on

Some stats from the page:
Production time: It was a relaxed shoot but it took us nearly nine hours non-stop to apply all the layers to Hannelore’s face.

Magic ingredients: Seven bottles of Foundation S103; two bottles of Creamy Eyes E107; three Milky Lips L205 pens; and two bottles of Blush S301. All together 228.40ml of makeup.
Could we make some guesses as to which layers are represented by the several clips that ended up in the video? How would we go about making an estimate? How thick was the make up? Assuming they applied the makeup at the rate shown at the beginning of the video, is the data provided above on time spent applying makeup reasonable? Is there evidence they accelerated the process by applying more than one layer's worth of makeup at a time?

Any other questions we can ask?

Friday, July 8, 2011

Go and Komi

In the game of Go, just like in Chess, there's a first-move advantage. To compensate for this difference, points (called Komi) are added to the second player (white) to offset this advantage. For the longest time, komi was set at 5.5. It means that the first player (black) has to win by 6 to win the game. Komi has recently been changed in Japan (2002). Watch the video below:

(Clip is from Hikaru no Go's anime series on hulu)

How would you go about deciding if komi is too high or too low? How many games of Go must be played before you decide with some confidence whether the komi is too high or too low? Is the first-move advantage static or changing over time? What are some sources of this variation?

Thursday, July 7, 2011

Zeno's Paradox in Ancient China

While I was having some High Mountain Oolong Tea with my parents, the topic of the diversity of the philosophies of ancient China made its way into our conversation. I grew up in Brazil so I missed out on most of the Chinese history that, as a student in Taiwan, I would have gotten in school. I've always enjoyed these topics whenever they came up in our conversations.

Our conversation started with the Hundred Schools of Thought, a Golden Age of Chinese philosophy near the end of the Zhou Dynasty (Eastern Zhou). The slow death of the Zhou Dynasty is divided into two periods: the Spring and Autumn period and Warring States period that ended with Qin Shi Huang's (the first emperor of China) unification of the Warring States.

The topic turned to the Chinese philosopher Zhuang Zi (4th century BCE) of Warring States period who, according to my parents, is considered to be Taoist in the Chinese tradition. In the eponymous work Zhuang Zi, he often engaged in dialectic with Hui Shi, who is more closely associated with the School of Names. As best they could remember, the major figures of the School of Names, by virtue of their verbal prowess, created paradoxes and exploited ambiguity in language that led to "ridiculous" results like "white horses are not horses" to confuse and defeat others who engaged them. It reminded me a little of the Sophists of ancient Greece. It piqued my curiosity and my parents urged me to do a little digging online.

I found this article on the life of Hui Shi and several translations of Zhuang Zi [1]. Looking for the original Chinese text and reference to Hui Shi, I came across this article on chapter 33 of Zhuang Zi. In it, Zhuang Zi criticized Hui Shi for his penchant for verbal sparring. According to him, Hui Shi delighted in his paradoxes and would engage with others in what Zhuang Zi considered to be pointless discussions. Among the many examples Zhuang Zi offered is this one:
which I translate clumsily word for word here to:
One meter/foot (or the ancient Chinese version of it) short stick, daily take half of it, ten thousand generations will not end
A little digging online I find the following translation of Zhuang Zi by Herbert Allen Giles (of Wade-Giles romanization system). His translation:
That if you take a stick a foot long and every day cut it in half, you will never come to the end of it.
There are some slight differences [2], but they essentially mean the same thing. After his translation, Giles gives the following suggestion on page 453:
Compare " Achilles and the Tortoise," and the sophisms of the Greek philosophers.
So I followed his suggestion and looked at the 3 versions of Zeno's Paradox listed in Wikipedia:
Achilles and the Tortoise
In a race, the quickest runner can never overtake the slowest, since the pursuer must first reach the point whence the pursued started, so that the slower must always hold a lead.
Dichotomy Paradox
That which is in locomotion must arrive at the half-way stage before it arrives at the goal.
Arrow Paradox
If everything when it occupies an equal space is at rest, and if that which is in locomotion is always occupying such a space at any moment, the flying arrow is therefore motionless.
I definitely noticed the similarities. So I read Giles' translation further to see if there was a solution provided in Zhuang Zi. Continuing with the translation by Giles :
And such was the stuff which dialecticians used to argue about with Hui Tzu, also without ever getting to the end of it.

Huan T'uan and Kung Sun Lung were of this class. By specious premisses they imposed on people's minds and drove them into false conclusions. But though they won the battle in words, they did not carry conviction into their adversaries' hearts. Theirs were but the snares of the sophist.

Hui Tzu daily devoted his intelligence to such pursuits, purposely advancing some preposterous thesis upon which to dispute. That was his characteristic. He had besides a great opinion of his own wisdom, and used to say, "The universe does not hold my peer."

Hui Tzu makes a parade of his strength, but is devoid of any sound system.
Just like in ancient Greece, this paradox wasn't resolved in ancient China, at least it seems that the solution was not known to Zhuang Zi (or author(s) of Zhuang Zi [4]). Zhuang Zi's citation of the paradox in his criticism of Hui Shi would seem to suggest that the paradox had no solution in his time. It wouldn't make sense for people to argue with Hui Shi incessantly on it if a solution were known, unless such were the dialectic prowess of Hui Shi that he could take a question with a known solution and twist it into a paradox.

The resolution of paradox using the mathematical solution by infinite geometric series would not come until the advent of limits and convergence of a geometric series, topics students study in high school Calculus today. I've read of a possible mathematical solution by Archimedes but I can't find a source, maybe someone can point me in the right direction. There is a reference in the Wikipedia article to the formula of a finite geometric series in Euclid's Elements Book IX Proposition 35. It seems likely that Archimedes, known for his use of method of exhaustion, would have been able to find a mathematical solution to the paradox with the formula for geometric series.

Hui Shi's version of Zeno's Paradox does allow us to ask a question that doesn't come up with the other versions. It brings up whether matter can be split forever and whether there is a smallest unit. My question is: What would happen if we divided a meter stick by half everyday for 10,000 years? Is it even possible? What other information would we need?

  1. Zhuang Zi is romanized in Pin Yin. It is romanized as Chuang Tzu in Wade-Giles.
  2. One difference you'll notice is that I used ten thousand generations where Giles says there's no end. This is actually typical of Chinese language. When describing a very long time, there is a tendency to use ten thousand (萬) to describe something large. The Japanese Banzai derives for this usage.
  3. Hui Shi who is sometimes referred to honorifically as Hui Zi, would be translated by Giles as Hui Tzu using Wade-Giles system instead of Hui Zi in Pin Yin.
  4. There seems to be some contention about the authorship of Zhuang Zi the book.

Monday, July 4, 2011

Prime Number of Links #1

Here are some links I'm saving (I want to say for this week but I don't want to commit to a fixed schedule). The number of links is arbitrary. Posts will be published whenever (most likely when there's too many tabs in my browser).
  1. Ignoring Past Warnings
    In 1904, a report was published by the Mosely Educational Commission to the United States on a number of observations and comparisons between schools in the United States and in England. The report was based on visits by twenty-five Commission members the preceding fall. The members were all distinguished educators in England at the time.

    It's interesting to read from a perspective that is more than 100 years old regarding the disdain for an educational system (their own) driven by testing and their appreciation for the American system that did not rely on testing. Here are two excerpts from the study:
  2. The 44 Chromosome Man
    A doctor in China has identified a man who has 44 chromosomes instead of the usual 46. Except for his different number of chromosomes, this man is perfectly normal in every measurable way.

    His chromosomes are arranged in a stable way that could be passed on if he met a nice girl who had 44 chromosomes too. And this would certainly be possible in the future given his family history.
  3. Of the Algorithms, by the Algorithms, for the Algorithms
    So, why is an algorithmic solution for congressional redistricting such a pipe dream?

    In part it's because it is surprisingly hard to define, or at least reduce to a set of rules, what a "gerrymandered district" is. Writing a formula for drawing districts requires us to define how funny-looking is too funny looking. And what is funny, anyway?
  4. Has any author's reputation fallen further or faster than Dostoevsky's?
    Still, the 24-year-old Fedya D was suddenly feted everywhere as the new literary genius of St Petersburg. It went to his head and he soon became insufferable, alienating all his new literary "friends", who revenged themselves when he published his second novel, The Double. Not merely trashed, the book was denounced. Dostoevsky became a bad joke.

    What I didn't know until now was the length of time between his moment of glory and terrible downfall. Authors then wrote much more quickly than they do today, and some of those impossibly fat 19th-century mega-books were composed in a quarter of the time it takes Milan Kundera to crank out a boring late novella. Bearing that in mind, take a guess: how long did Fedya D last as a cause celebre? A year? Nine months? Six? Three?
  5. Stephen Fry Kinetic Typography - Language

Friday, July 1, 2011

Chat Noir

Chat Noir (French for "Black Cat") is a nice little game from Gamedesign. The goal of the game is to fence in the black cat. The game reminds me of Go (game). It's probably what it would be if it were played in a hexagonal packed game board instead of square grid. Here's a video of me solving one of the levels.

Can you come up with an algorithm to solve this game? Are all games solvable? Are all games solvable if the board were empty at the beginning? If the board extends indefinitely, would it be possible to fence in the cat? What's the smallest number of steps to win a game?

Have fun! Click here to start.

Experimental Design & Scatterplots (Coffee & Caffeine)

Nice little video on the story of coffee.

(h/t John D. Cook)

I did a little additional reading after the video. Here are some lesson ideas or activity that could be developed.
  • The first one is on LD50 or Median Lethal Dose.
    The LD50 or Median Lethal Dose of a toxin, radiation, or pathogen is the dose required to kill half the members of a tested population after a specified test duration. LD50 figures are frequently used as a general indicator of a substance's acute toxicity. The test was created by J.W. Trevan in 1927.
    We could use the value from the video of 150mg/kg to create chart with weight of a person as the independent variable and dosage as the dependent variable. Sketch the graph and interpret the results. One extension would be to get students to select their favorite drink and find the caffeine content and do some additional activity with it. Even though the video explains there's no recorded deaths from caffeine overdose from drinks, I have some reservations about this since I'm working with teenagers.

    We could alternatively do a similar activity, but focus on rats instead of humans, grab the data from the table of LD50, which lists 192mg/kg (data from rats that were administered orally), to create a table and interpret results. We could also discuss about how this data would be obtained and why the Fixed Dose Procedure is being recommended as an alternative.
  • The second idea is to build off of the assertion in the video about caffeine's (coffee and tea) role in the Enlightenment. Discuss the possibility of alternative explanations such as coffee/tea houses bringing of people together in these "penny universities" in an alert state so that ideas can develop, spread, and flourish. Perhaps use this as an introduction to the lady tasting tea (there's a book with same name by David Salsburg, I won't link it here) and the birth of randomized experimental design by Sir Ronald Fisher.
  • The third idea is a more boneheaded extension of the above to achievement of students in international tests due to coffee consumption. Students would create a scatterplot from data about coffee consumption per capita and plot it against either TIMSS or PISA scores and interpret the results in context. What are some assumptions made? What conclusions can we draw? What are some possible confounding variables? Are there outliers? Which is a better predictor of achievement in these tests: GDP per capita or coffee consumption per capita?
  • The fourth idea is to discuss this little gem found by John D. Cook about why headache is often listed as a side effect in drugs. Be sure to also read the comments on his blog.
    In an interview on Biotech Nation, Gary Cupit made an offhand remark about why so many drugs list headache as a possible side-effect: clinical trial participants are often asked to abstain from coffee during the trial. That also explains why those who receive placebo often complain of headache as well.
    Use this as an opportunity to discuss experimental design.
  • The fifth idea is to discuss the flawed study about the link between coffee and lung cancer. The page at Google Books only gives a generic example, I was hoping to see an actual study referenced. The closest I can find after a bit of searching is this article about cancer myths. Maybe someone can point me in the right direction.
Comments, suggestions, and/or corrections are welcome.