pchem 3 textbook

The students of pchem 3 created this textbook for the course. It contains the lecture notes of K. Nelson and the problem sets handed out last year. It is really nice.

Some more data from the US house representative since 1942

The black dots in the figure stands for the election result of US house representatives since 1942. Note that the slope seems to be not so dramatic like the presidential election.

Election as a titration process (revised)

The basic idea is that the current election based on the new electoral system is very similar to the US presidential election - winner of a state get all the electoral votes of that state. So I expect I can get useful information from the data of US presidential election.

So I define x as

Fraction of electoral votes = electoral votes obtained by republican's presidential candidate /Total electoral votes

and y

for US election as

Fraction of popular votes = popular votes obtained by republican's presidential candidate /Total popular votes

but for Taiwan election as

Fraction of seats = seat obtained by KMT /Total seats

As an example, the US presidential election in 2000, (Bush vs. Gore), we have

Popular votes: 50456002(Repulican) , 50999897 (Democrat)
Electoral votes : 271 (Repulican), 266 (Democrat)
Thus, in this case, I have
x=50456002/(50456002+50999897 )=0.497
y=271/(271+266)=0505

I plot the fraction of electoral votes vs. popular votes using the data of US presidential election since 1932 (blue circles in the figure). The result can be fitted by a hyperbolic function: y=tanh(x). There are fluctuation, of course. That was the reason why G. W. Bush got elected, even though Gore got more popular votes.
Additionally, I have also tried to write this function in the form of Henderson-Hasselbalch equation in order to make a connection to the titration curve most chemists are familiar with.

What surprised me was that data from the Taiwan's past 縣市長 election (red solid squares) and result of current election (單一選區, red solid star) roughly fall on this curve given by the US presidential elections! In the figure, I also drew another curve generated by four data points (triangles) taken from previous 立委選舉. Apparently, the slope of this curve is smaller.

This kind of behavior is very similar to phase transition in natural science. I am not sure whether it is possible to work out a theory for this kind of behavior or not.

Election as a titration process

Election is similar to a titration process if we choose a suitable coordinate system.

Quantum weirdness

Quantum weirdness is so counterintuitive that to comprehend it is to become not enlightened but confused. As Niels Bohr liked to say, "If someone says that he can think about quantum physics without becoming dizzy, that shows only that he has not understood anything whatever about it."

In Murray Gell-Mann, The Quark and the Jaguar. New York: Freeman, 1994, p. 165. Bohr liked to joke about the difficulty of expressing quantum precepts in ordinary language by telling the following story: "A young rabbinical student went to hear three lectures by a famous rabbi. Afterwards he told his friends: ´The first talk was brilliant, clear and simple. I understood every word. The second was even better, deep and subtle. I didn't understand much, but the rabbi understood all of it. The third was by far the finest, a great and unforgettable experience. I understood nothing and the rabbi didn't understand much either.' "

http://www.stanford.edu/dept/HPS/WritingScience/Ferris.htm

Bose-Einstein condensation

In 1924 Satyendra Nath Bose from Dacca University, in what was then India, wrote to Einstein asking for his help in getting a paper published. Bose had already sent it to the Philosophical Magazine, where it had been turned down. The paper showed how Planck's distribution law for photons could be derived from first principles. Duly impressed, Einstein translated it into German, and the paper was published in 1924 in Zeitschrift für Physik.

As a result, Einstein temporarily turned away from his dogged but unsuccessful search for a unified theory of gravitation and electromagnetism and started work on the quantum theory of radiation. Thus was born the concept of "Bose-Einstein" statistics for quanta ("bosons") carrying an integer value of intrinsic angular momentum (spin). There is no limit to the number of bosons that can simultaneously occupy any one quantum state.

Einstein noted that if the number of such particles is conserved, even totally non-interacting particles should undergo a change of behaviour at low enough temperatures - Bose-Einstein condensation. Bose had not predicted this because he was looking at photons, which can simply disappear when the energy of the system is decreased.

The condensation that Einstein predicted derives from the fact that the number of states available at very low energy becomes exceedingly small. With less and less room for all of the particles when the temperature is decreased, they accumulate (condense) in the lowest possible (ground) energy state.


From CERN COURIER
Dec 4, 2001
Bose-Einstein condensation revisited

I can safely say that nobody understands quantum mechanics, Feynmann

There was a time when the newspapers said that only twelve men understood the theory of relativity. I do not believe that there ever was such a time. There might have been a time when only one man did, because he was the only guy who caught on, before he wrote his paper. But after people read the paper a lot of people understood the theory of relativity in some way or other, certainly more than twelve. On the other hand, I think I can safely say that nobody understands quantum mechanics.

-- Chapter 6, "Probability and Uncertainty"