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Authority vs. Personal Judgment

Posted by C Moon on February 27, 2008

After the World War II was over, there was a fervent discussion on whether human is by nature “evil.” Holocaust by the Germans and Rape of Nanking by the Japanese are only a few examples showing how cruel people can be to other people who do not belong to the “Us” group, the in-group. While many people asserted that there was something wrong with the Germans, there is an experiment that makes us ponder on whether we can blindly accuse Germans on their wrongdoing: Stanley Milgram’s experiment on “The Perils of Obedience.” To learn more about Milgram, read “The Man Who Shocked the World“.

Milgram’s design is quite ingenious, though controversial on some ethical grounds. The experiment proceeds as follows:

(1) A subject who is selected from the volunteers is told that he will have an experiment on whether punishment will improve one’s performance.
(2) The subject and the researchers’ confederate decide who will be the teacher and who will be the student by drawing a lot, but it is predesigned to make the subject the teacher.
(3) The subject, or the teacher, accompanies the student, who is being tied down to the chair.
(4) The teacher is asked to give a more severe electric shock every time the student gets the question wrong.

While the procedure seems simple, there is a constant pressure given to the subject: The pre-taped voice of the student is played, shouting out to stop or giving no response as the level of the electric shock increases, and there is a person asking the teacher to continue on giving the shocks. Interestingly, most people, in fact, more than half of the subjects, go on to give the highest level of the shock 450 volts (consider that the domestic electric supply of USA is 110V, of UK 240V, and of Korea 220V), labeled as “xxx,” meaning lethal. If you were thrown into such situation, what would be your decision?

Below, I am attaching a video that I’ve recently encountered: A recent recreation of Milgram’s 1963 experiment.

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Photo Credits: “Electric Char – Andy Warhol” by fibonetti on Flickr

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Self-Deception?

Posted by C Moon on January 7, 2008

Human brain seems to be self-deceiving.

After reading a blog post from Zero Divides, a math blog administered by a college student, I had some time to think of the deceptiveness of memory. The part that provoked my thoughts reads as follows:

…, while I may struggle for hours, or days, with a certain theorem, as soon as I know for sure that I’ve proved it, it immediately seems trivially easy. If anything was hard, it was undoubtedly my head, for not noticing this elegant solution sooner.

Well, I often heard that memory and time combined make even the most terrible hardship a “beautiful” recollection. I also read a study reporting how a leading question can “forge” an eyewitness’ testimony, I, who is interested in criminal justice, am worried about the future of the field. Maybe as Gil Grissom said in CSI-Las Vegas, we should “Concentrate on what cannot lie. The evidence…”

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Photo Credits: “The Median Vacuum Semiotics” by jef safi on Flickr

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Predicting Mathematical Ability?

Posted by C Moon on December 7, 2007

According to Keith Devlin in his post Predicting Mathematical Ability, it seems that the psychologist Daniela O’Neill recently proposed that we can predict the mathematical ability of a 3- or 4-year-old pre-schooler.

The interesting aspect of this research is not that we can predict the mathematical ability of a toddler, but the way in which we can predict it. O’Neill says that while the arithmetic skill may reflect child’s future mathematical ability to some extent, it is the narrative skill that actually help people to predict child’s future mathematical ability. For a long time, people thought that math/science and literature/art were relatively exclusive (e.g., Many friends of mine oftentimes say that they are not math persons but literature persons.). This finding seems to propose a thread to the connection between math and literature, logic and emotion, and experiment and imagination.

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Photo Credits: “The Number Eight” by Lab2112 on Flickr

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Rejected Articles Can Be Rejected Again!!!

Posted by C Moon on December 7, 2007

While surfing around the internet, I’ve found an interesting posting. Have you heard of Rejecta Mathematica?

It seems that there are many steps that a mathematics article has to go through in order to be published. And in the process, many articles fail to survive the intense reviews from peer mathematicians. Only selected few get to see the light. Rejecta Mathematica is a new home for the “abandoned” papers. They are revived to see the world.

In order to be published in Rejecta Mathematica, the paper has to satisfy several requirements. First, the mathematician has to include a letter describing the reasons why the paper was rejected and any other flaws the paper might have. Submissions are not peer reviewed, and results are required to be neither correct nor new. But if the paper is considered to be either incomprehensible or not mathematical, the submission can be rejected. What a tough world!
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Photo Credits: “College Math Papers” by sweatpea.loty30 on Flickr

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GEO-4 Calls for Real Action to Curb Climate Change

Posted by C Moon on December 7, 2007

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GEO-4 (Global Environment Outlook 4 by United Nations Environment Programme) provides hesitant nations such as USA with scientific evidence that the sharply rising trend in global warming is ascribed to human activities. Unfortunately, prior to GEO-4, USA has been one of a few advanced countries refusing to ratify Kyoto Protocol, insisting that there is no clear evidence that global warming is man-made. Now, with the publication of GEO-4, both advanced and developing countries should get together, executing a real plan for action. Read the progress on the issue at the post by Andrew Revkin, A 4th Climate Warning. Anyone Listening?

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Photo Credits: “I’m Melting!” by dru! on Flickr

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Superstring Theory

Posted by C Moon on December 7, 2007

Though Quantum Mechanics and Theory of Relativity describe well the nature from the micro and macro perspectives, respectively, they fail to coexist, or fail to explain the other side. Super-string Theory is one of the attempts to explain all the particles and fundamental forces of nature in a unified theory by modeling them as vibrations of tiny super-symmetric strings. Detailed explanation can be found in the 3-hour-long lecture from PBS. (They designed this lecture based on Brian Green’s fascinating book, The Elegant Universe.)

The model requires us to recognize up to the 11th dimension. We live in the 4-dimension world, with length, width, height, and time, the first three of which we can control and the last of which we cannot control. Exploring the internet, I was able to find a video describing up to the 10th dimension. I hope this video will enhance your understanding of the current state of the super-string theory.

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Photo Credits: “ZeroEqualsOne-D” by vaXzine on Flickr

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Math Is Highly Addictive?

Posted by C Moon on December 6, 2007

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Faces of Math is a quite interesting post and I am eager to share some quotes from this post with you.

* Math is highly addictive, and many users spend most of their free time looking for another way to find more of it.
* Math is a stimulant that can speed up one’s heart rate.
* Indications of math use: Has your teen stopped showering? Has she lost interest in grooming? Does he no longer brush his teeth?

If you want to read more amusing thoughts on Math, follow this link. Do you feel something is wrong? In fact, the author of that post simply lists some interesting misreadings. Whenever he sees the word “meth” in print, he mistakes it for “math.” Well, as a person who enjoys math, I totally understand his confusion there : ]

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Photo Credits: “Math books” by Peoria Pundit on Flickr

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Every Even Number Greater than 2 is the Sum of Two Primes

Posted by C Moon on November 23, 2007

Every even number greater than 2 is the sum of two primes.

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The above proposition is notorious Goldbach’s Conjecture, which remained unsolved for two hundred and fifty years. We can check empirically that the proposition holds for small even numbers.

4=2+2
6=3+3
8=5+3
10=5+5
12=7+5
14=7+7
16=11+5
18=11+7
20=13+7
22=11+11
24=13+11
26=19+7
28=23+5
30=23+7
32=29+5
and so on.

But unless we prove it for all even numbers, we cannot call it a theorem. There are always possibilities that it holds for small even numbers and fails to hold for extremely large even numbers. Then, can we prove it definitely?

Uncle Petros and Goldbach’s Conjecture is a mathematics novel. But it does not require mathematical knowledge in enjoying it. The plot evolves around Goldbach’s Conjecture and a mathematician, who devoted his whole life in trying to prove it. Through Uncle Petros’ life-long devotion to this seemingly simple proposition, the novel reveals the passion, tolerance, and efforts that mathematicians pour into their studies. Uncle Petros, a key figure in the novel, is in some sense a tragic hero who is hubristic. He thinks that mathematics is only for the “talented,” and deters his nephew from becoming a mathematician. He is bewitched by the Conjecture and continues to search for a solution, but he does not cooperate or share his byproducts with other mathematicians, believing he alone will be the one to prove it. In his early 20s he was praised as a genius, but in later years his pride made him an isolated mathematician with no tangible mathematical exploit. He became exhausted and died with his works unpublished.

The following is part of a short posting that I’ve found on the internet, reflecting the book’s charm.

Name a book you own that you think no one else on your friends list does: Uncle Petros and the Goldbach Conjecture(Apostolos Doxiadis). I’m hoping this will change, though. Cool Math novel!

The author himself is a mathematician, but he does not talk about details on Goldbach’s Conjecture. Rather, he hints that the proof on Goldbach’s Conjecture may not be possible by introducing into the story Kurt Godel’s Incompleteness Theorems that some mathematical problems can never be resolved. Difficulties in seemingly simple propositions are the charm of mathematics. I am especially moved by the sentence, “Every person has the right to expose himself to whatever disappointment he chooses.” As far as I understand, the author asks us to aim high rather than take an easy path.
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Photo Credits: front cover of Uncle Petros and Goldbach’s Conjecture, taken by myself

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Friendship Math?

Posted by C Moon on November 22, 2007

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These days people try to explain everything through mathematics, technology, and science. I recently encountered with an interesting post, featuring a topic called “Friendship Math” (in the velocity section). Can everything be explained with these objective tools?

No doubt that math is the most elegant, perfect language, successfully explaining many subject matters in an objective and concise manner. It is imperative that scientists attempt to explain everything including human behavior through mathematics. The post says that “The hardest part about mathematically describing friendship is constructing a good model.” However, for the time to come the so-called good model is expected to be deficient in measuring the intensity of the emotion, which differs from individual to individual. The simple model includes variables such as “positive affection” and “negative affection,” whose measurement is still hard to establish. As we all know, human behavior is oftentimes irrational and unpredictable.

Even though everything around us may not need to be explained scientifically, scientists will surely endeavor to explain everything scientifically. Yet, there are many things that we cannot explain well with science, such as love, friendship, and affection. But, on the other hand, we shouldn’t be saddened too much by science’s failure in decoding love, friendship, and affection with sufficient explanatory power. The universe is full of odd bumps and twists. And the unexpected make life interesting.

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Photo Credits: (1) a drawing of characters in “Saiyuki” by my friend 🙂

(2) “Math on the Wall” by alist on Flickr

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