The Quantum Theory of Life

In Physics, quantum mechanics is a theory that describes the world in atomic scale. It is probabilistic in construction, and claims that everything is non-deterministic with the famous uncertainty principle. To put things more mathematical, this theory uses wavefunction to describe the wave particle duality behaviour of matter and energy. Any wavefunction can be written in terms of a linear combination of basis state, which resides in the Hilbert space. The modulus square of the coefficients give the probability of that state, and they are normalized. When a measurement is made, the eigenvalue of one state will be observed. I shall not go on to the collapse of the wave-function interpretation as they are highly debatable.

Now if we want to define our life, we can think of it in terms of defining a wavefunction, in a very similar way that we define the state of matter. For example, the languages we speak can form a basis state, with the coefficient representing how well we speak that language. In my case, it can be approximated easily as (using Dirac notation for wavefunctions) |Yun> = 1/sqrt(2) |Chinese> + 1/sqrt(2) |English> . However, this is approximation, as I know a few words of Japanese and German, but they definitely don't count as the coefficient would have at least 20 zeros after the decimal point.

Another interesting basis set we can use is the countries we have stayed in. In this highly globalized world, more and more people are born in one place, raised in another, and working or studying in a third country. Maybe for some none of these are their ethnic native country. Quantum theory somehow can sort of model this highly dynamics society.

So what is your wavefunction?

Physics or Mathematics?

In recent weeks, this thought has been bothering. Have I made the correct decision to study Physics? Or should I have done Mathematics?
Let the story begin in JC. I came across many articles on the development of nano technology. It was a very interesting field with the carbon nanotube and graphene. In addition, fundamental particles were fascinating, and there had been many talks on physics. My inclination was thus pulled towards studying a "Science" subject. Then I graduated and needed to choose something a major. I was pondering between 3 subjects: Mathematics, Physics and Materials Science/ Engineering.
Why I decided against Matierials

• When I applied for NUS, I was not decided between Physics and Materials. Mathematics simply wasn't on my mind at that time. In Singapore, science and maths in general are thought to be for those people who can't get into engineering, and are regarded as lower in status. Business was the hot subject in this "realistic and pragmatic" society. But no matter how small the perturbation is, the effect can be huge when applied continuously on a timescale of years.
• I went for the open house in NUS, and attended some talks on material science. It immediately put me off as there are so much engineering terms such as Young's modulus, toughness and technology transfer.
• I didn't give up Materials totally. I did my pre-departure attachment at IMRE and took Materials Science in Part 1A NST. Both further confirmed that material science is not for me.

The road to Physics

• When I applied to Cambridge, I set my mind to do physics. I was greatly influenced by Dax with whom we were working on a small project at that time. Googling "physics + cambridge" directed me straight to the Cavendish website and subsequently the Natural Science Tripos website. Thus I applied for Natural Sciences.
• On choosing the colleges I read up quite a good deal on Cambridge. Mathematics Tripos featured prominently, boasting a range of famous scientists and mathematicians. I kind of regretted not applying for it, but then it occurred to me probably it is much harder to get in, and considering admission was all important, I was happy with my choice.
• On retrospect, some other factors indirectly pulled me away from Math. I was in SIMO, and never made much progress. This made me realize how difficult math can be and I wasn't really good at it.
• My dad, who is a mathematician, was spending a big proportion of his time in China and not with me, so that source of influence was absent.
• Was applying for astar, and thought Physics would be more "useful" and easier to get the scholarship.

The discovery of mathematics

• The first year physics and mathematics in NST 1A certainly didn't appeal to me. They were tedious and boring. The Mathematics Tripos seemed vastly more interesting.
• At this point I realized I could have pursued Physics under the Mathematics Tripos. This was hugely upsetting as clearly my research earlier on wasn't comprehensive enough. I was too obsessed with searching on tips to get admitted rather than going for a thorough research on the courses.
• Summer internship at DSI was the biggest eye opener. Mathematics had never occurred to me to be so important. Many of the advanced topics in Physics required many branches of mathematics that were not taught in NST.

The point of my internal struggle has been that I closed the door on Mathematics too early by choosing to study NST. I would have made much better judgment if I have gone through the mathematics Tripos. The situation would also have been easily resolved under the American liberal art education system.
It is too late to do anything. Physics may turn out to be alright, but I would have never known if I was better at pure mathematics. This is very close to what I would be doing anyway had I known better. Physics and Mathematics are not hugely different in irreconcilable ways. It will serve as a huge learning point though.

A period of rest

Finally Tiger Storm is over! Actually it was over one week ago but I was lazing around during this well-deserved break. I have been playing Dungeon Siege 2 and watching some old movies such as Saving Private Ryan, just to regain a certain degree of sanity. In the meantime I have attended the Cambridge interview and scored 2130 for my SAT, so I have no matters to bother me at least for now. As I am now back in OETI for BM3 course, life could not have been better. How I wish it will continue like this for the rest of my NS life.

There was a “hype” in the Physics community in Singapore this week. Chen Ying Yang is here for a series of talk and conference to celebrate his 85th birthday. Given his popularity and age, he is worshipped like a star, constantly being swarmed around by students eager to take a photo with him or get his autograph. Of course I took the chance to take a photo with him.

Prof. CN Yang, me and Dax

for langrange and tex

These days I have been writing the physics paper on rolling asymmetrical cylinders. It first seemed an impossible task due to our centre of mass approach, but in the end it still worked out. I learned quite a lot, such as Lagrangian (all thanks to Dax). The most daunting part of the whole thing looks to be presenting (or the typing out) the paper. Firstly, I’ve to learn this LaTEX language, which is really crazy. At first I was using a trial software (for typesetting in LaTEX), and it gives a very good mix of red, blue and black colours when I was typing, which are easily recognizable. But after searching the Internet for hours, I couldn’t find any crack to unlocking the full version. I have an older version, but sadly it doesn’t support pdf so I give up on it also.

As a result, I’ve to switch to WinEdt plus MikTEX, which proved to be more powerful. However the interface of WinEdt is so irritating; it gives at least 5 colours, dark brown, dark blue, dark green, black and purple, all of which look about the same after a while, and spoiling my already 800 degrees eyes. The red colour was assigned for spelling mistakes, which are far less important than formulae mistakes when writing a Physics paper. I still could not appreciate the usefulness of LaTEX, although it's widely popular in the scientific world (ask any science, maybe not bio or engineering graduates they would have used or heard of it).