2008년 2월 29일 금요일

Second person

"I sit here," said the teacher, "and y'all sit there." He did not forget to add, "But don't write y'all in your writing!"

The case of second person plural pronoun in English is the most fascinating. As you know, Modern English uses one word, "you", for both singular and plural form of second person pronoun. I believe I used the plural form in the last sentence. And "y'all" shows desire to make this distinction.

It wasn't always like this. Middle English used two separate words for singular and plural form of second person pronoun. Guess what they were? Singular form was "thou", and plural form "ye". Compare Modern German, which uses "du" and "ihr" respectively. And the distinction was present for many thousand years, since these pronouns ultimately originate from Proto-Indo-European root "tu" and "yus"!

Then how did English come to lose this distinction, that they have kept for such a long time? It is still a mystery to me, but one theory is that "ye" had started to be used as a "polite" form, analogous to French "tu" versus "vous". So for singular form of second person pronoun, "thou" became a "plain" form, while "ye" became a "polite" form. Later, "thou" started to connote contempt, and its use declined. Well, that is the theory. I don't buy it.

It is rather ironic that remaining use of "thou" in Modern English is to address God. "For thine is the kingdom, and the power, and the glory, for ever." Does this mean that we address God in plain, familiar, informal, even contemptous manner? No, it just means that liturgical language simply refuses to change, and that this English prayer was translated from Latin prayer when second person singular pronoun was alive and well.

After all, irregular plural forms are so European. We Koreans simply attach the plural suffix to pronouns. But we do have separate forms for plain and polite usage.

2008년 2월 25일 월요일

Learning and Research

Confucius said: "At fifteen my heart was set on learning" (Analects 2:4). Quoting this, Professor Park asked, "I presume you all are older than 15. Is your heart set on learning?" Silence ensued. Finally, he said, "You are scientists; you should love learning."

Then I said, "Learning is not what scientists do. Scientists learn just enough so that they can do research." The professor thought about it for a while; then he said, "I think such reply is only possible from one who is into the discipline. Thank you."

Is this a difference between scientists and philosophers? Is it a good thing that most scientists don't bother to learn outside of their specialties? Was my reply that unexpected? Science, after all, is about producing knowledge, not consuming it.

2008년 2월 22일 금요일


An innocent-looking exercise in an English writing textbook asks, "Does the universe have an outer edge?". "Such question is meaningless", I instinctively reply. "You are being philosophical" -- the instructor seems to be surprised.

I wasn't being philosophical. By definition, the universe includes all things that exist. There is nothing outside it. Since there is nothing outside, there can't be an outer edge or an inner edge that exists between the inside and the outside.

This seemingly vacuous wordplay actually poses a serious problem in physics. To see why, we need to discuss the interpretations of quantum mechanics.

Digression. The statement, "there is nothing outside the universe", reminds me of the church doctrine, "extra ecclessiam nulla salus", which means "outside the church there is no salvation". As they say, whatever is said in Latin sounds profound. I wonder what would be Latin translation of the statement?

In the book Three Roads to Quantum Gravity, the physicist Lee Smolin includes the statement as one of his four "points of departure". This 2001 book was finally translated into Korean in 2007. The book is accessible yet rich in deep insights; I recommend it. The following discussion draws heavily from the book. End digression.

Quantum mechanics is an extremely successful theory of physics. The theory lets us calculate the probabilities of measurements. For example, one can calculate the probability of finding an electron at a certain distance from a nucleus. But we can't be sure whether we will find an electron or not.

However, when we actually look for the electron -- in other words, when we perform a measurement -- we either find it, or we don't. And after the measurement, any further measurements are consistent with the electron being at the place it was found, not with the probability to find the electron we calculated. It seems clear that the measurement changed "something", but what something is is not clear. This is called the measurement problem.

The Copenhagen interpretation (well, one of Copenhagen interpretations -- there are many variants) says that the probability distribution represents an observer's knowledge about the system. The wave function, a mathematical tool which gives the probability distribution, describes the system. The wave function is not "real", and when the measurement is performed, the wave function "collapses", and the observer is informed.

Now according to the big bang theory, the universe was once small. There must have been time when the universe was so small that quantum effects were significant. The study of such effects are called quantum cosmology.

If we are to accept the Copenhagen interpretation of quantum mechanics, we need to think about the "observer" of this early universe. But since there is nothing outside the universe, this observer must be the part of the universe, not external to it. Doesn't this sound strange and difficult to you?

If you do you are not alone. Hugh Everett proposed that it's the wave function that is real, and there is no collapse after all. The wave function of the entire universe, which is all there is, evolves in a completely deterministic manner according to the law of quantum mechanics. So when the scientist observes an electron that had 80% chance of being there, it's not that the electron changed to 100% being there. Rather, the wave function describing the scientist evolved to the wave function which describes 80% chance of the scientist-who-found-electron and 20% chance of the scientist-who-did-not-find-electron. Bryce DeWitt later named this "many-worlds interpretation", and the name stuck.

Many-worlds interpretation implies that all possible universes should "exist", since all possible universes have non-zero probability and the universal wave function describes such universes. Thus in some universes I have already written this article yesterday and in other universes this article is never written.

Carried to the extreme, consider a person in front of a gun which fires when a radioactive atom decays. A radioactive atom has 50-50 chance of decaying in its half-life. After the half-life elapses, the person is alive in half of universes. But no matter how long he sits in front of a gun, there is non-zero possibility that the atom has not decayed yet. So in some universes he never dies.

Let's wrap up with a little anecdote. Hugh Everett wrote his thesis The Theory of the Universal Wave Function for his Ph.D. For more than a decade, few people paid attention. Disappointed, he directed his talent to applied mathematics of operation research, and earned lots of fortune. Still he believed in quantum immortality, that he will live forever in some universes; but he died in this universe. His daughter committed suicide, before which she said that she was going to a parallel universe, to be with her father.

Reading what I wrote so far, I guess I was being philosophical after all. But it's hard to avoid being philosophical when you discuss the universe.

2008년 2월 15일 금요일

Axiomatic method

This semester, I decided to take a course on Advanced English Writing (this class) and Introduction to Oriental Philosophy. The philosophy class is taught by the professor Woosuk Park. I enjoyed reading his book "Philosophy of Baduk" in the past.

In the Wednesday class, the professor Park raised the issue that the axiomatic method is apprently lacking in the East. He argued that the axiomatic method, examplified in the Elements by Euclid, formed the basis of the scientific revolution in the West. And the lack of axiomatic method is why the West could overtake the East in science. Then he wanted to discuss what role the philosophy played in creating such difference.

I pointed out that the rigorous axiomatic treatment of mathematics is a modern development. He replied that Grundlagen der Geometrie by David Hilbert, motivated by non-Euclidean geometry, may be considered the beginning of the rigorous axiomatic mathematics, but the germ of the axiomatic idea was already present long before. I wasn't satisfied, but I didn't pursue the argument any further at the time.

So here are some of my thoughts. First, Euclid was not rigorous, at least not in the modern sense. Let's look at his first proposition: To construct an equilateral triangle on a given finite straight line. Given the segment AB, two circles, one with center A and radius AB, and the other with center B and radius BA, are constructed. Let C be the point at which two circles intersect. Then that ABC is equilateral follows from the definition of the circle. Now, why should the point C exist? Two circles may not intersect at all, and the existence of the point C is nowhere justified. In general, the Elements is not very careful about between-ness and inside-ness.

Second, it was the analysis, not the geometry, which enabled the development of Newtonian physics and other sciences. And the early analysis was anything but axiomatic. Newton and Leibniz made heavy uses of infinitesimals, treating an infinitesimal as non-zero in one part of the "proof" (where they divide by it), and as zero in the other part of the "proof" (where it is eliminated). The need to prove convergence was not realized for a long time. It was only by the arithmetization of analysis, the 19th century development to found the analysis on the algebra, typified by epsilon-delta definition of limit by Weierstrass, that the analysis became rigorous.

Therefore it seems clear to me, that the axiomatic method is not what made the scientific revolution possible. At the time, the axiomatic method was not applied to the mathematics used by the science, which was the analysis.