Some reflections on my "work" at NUS, Centre for Quantum Technologies.

I hadn't realised it then, but coming up with something there is quite a difficult thing to do. I'm not sure if those people that my prof had previously recruited before they started uni had produced anything, but it is not a nice feeling to hang around at a place for five months without much idea of what's going in. I guess an analogy would be like being employed by a greek company in greece, with all the books(except maybe one) that teach greek also written in greek.

To be more specific, my journey started with my prof asking me to do the exercises in Griffith's Intro to QM (or as the taiwanese grad student would call it, the 猫书), and learning about Perez-Horodecki's criterion for separable states. Then he taught me about pure states and mixed states. One week later, I was given one 4 page paper, which supposedly requires me to understand a 90 page review paper on quantum entanglement before I could appreciate it. I got stuck on the fifth page, i.e, when the first mathematical equation appeared (the definition of a separable state). It was written in Dirac's notation and made use of the tensor product symbol. It was around that time when I started chapter 3 in the 猫书, where Dirac's notation was taught in one page. (I don't think I'm the only one who can't learn Dirac's notation explained in one page) But there wasn't any mention of tensor products, so I tried to learn about it on Wikipedia, which was a really bad idea, since I followed every link, hoping to be able to understand this one by following the next... but it somehow got into group theory and abstract algebra. Having learnt nothing about tensor products (except the fact that it's a bilinear map), I tried to see if it was related to tensors. I didn't manage to learn much about tensors. After two weeks of struggling with Dirac notation and the elusive tensor product, I asked my prof what a tensor product is, and he gave a really simple explanation. Lesson learnt: don't know, ask. Around this time, a teacher happened to ask me how I was doing, and he recommended me Susskin's lecture and Cohen-Tannouji's textbook, which were really helpful.

Around this time, my prof asked me to help him write some lecture notes for grad students, and I got really excited, cos it made it sound like I was very zai. I came up with the first set of lecture notes, but honestly, I don't think I really understood the material well enough to write notes about it, so my notes were quite crap. Perhaps his intention was to make me think hard about what I was learning. But a nice side effect was that I got introduced to LaTeX, which is NOT user friendly at all.

Just when I thought I could be helping those after me to learn about quantum information, I realised that Nielson and Chieng's textbook of quantum information was better than what I could ever write in the next few months, so the notes I wrote was quite redundant. Also, in the last week there, I realised that measures of quantum entanglement had to be associated with some application for it to have any physical meaning, and so far I had learnt nothing about the application. There have been a few instances when people asked me "can you explain in lay-man's terms what is it that you do?" and I couldn't. At the end of it, I didn't even understand half of that 90 page review paper. That sucks.

But oh well. At least I learnt some LaTeX and linear algebra. And I finally have some idea of what a matrix determinant is.

令堂甚肥 -  具落雁之地心引力矣！

Once one proceeds from Descartes’ global scepticism, one either has to contend with solipsism, or presume that our sensory experience alludes to some underlying consistency in what really exists out there. I personally can find no rational justification to favour any particular ontological theory over another, but I have placed my faith in Materialism (as opposed to Dualism and Idealism) for its congruence with all my other beliefs.

It thus makes sense for me to induce that all events proceed either deterministically or probabilistically from their prior state. Given also that laws of nature do not change, there appears to be no way that one’s consciousness can have any influence in the outcome of things.

I used to think that belief in free will is a hindrance to true understanding of people, and that psychological egoism and utilitarianism combined would be superior to belief in free will in its potential explanatory power. But there are many problems with that approach – we don’t know the relevant coefficients, it requires too much tweaking of coefficients to work, scaling up to more than one person changes mathematical relationships dramatically, and it’s simply not practical because people are not good at calculations the way computers are (just like computers aren’t good at recognising human faces or associating emotions with facial expressions the way humans generally are).

So due to our biological-endowed strengths and weaknesses, our intuitions about ourselves and others based on free will are, for practical day-to-day purposes, the best things we have to understand ourselves and others (though sociologists are probably encouraged to use computers to simulate human behaviour). But recognising that free will is merely a heuristic that we are forced to employ due to our inabilities ought to make us more cautious about drawing conclusions from such intuitions and “off-set” them with science where necessary.

Thus, in our day-to-day interactions, it makes sense to talk about “self-restraint” and “conscientiousness”. It also makes sense to judge people as agents who know “right” from “wrong” and can choose as appropriate, and take responsibility for “their” actions. While it does get a bit grey when nature and nurture come into play, nobody really doubts the existence of a self that one has substantial control over under normal circumstances.

“Substantial control” is still not total control, though. Self-control seems to slip out when emotions rise, so control of emotions is important. I used to believe that I have been keeping my emotions under control, but now it seems to me that I just haven’t been feeling my own emotions strongly. Somehow, people realise that I am happy or angry or sad before I do. And upon reflection, it does seem that my facial expressions and body postures change to reflect my emotions outward before I am aware of it. Perhaps, I may even I have said and done things in an emotional state without myself realising it. Maybe I can overcome this by being more conscious of my facial expressions and body posture, infer my own emotional state, and thereby maintain greater control.

Control over thought seems to be more difficult, though(“Don’t think about a pink elephant”, for example). To me, studying involves looking at a piece of paper/website, and I either understand it or I don’t. Sometimes it takes longer, sometimes it happens instantly, sometimes it feels like it would never happen, but “I” have no control over it. As I walk along, thoughts just appear in the form of voices and sights and sounds (which I can thankfully distinguish from real sights and sounds). It might be possible for me, under the influence of a particular train of thought (caused by a certain book, for instance), to alter my environment that produces a certain way of thinking to attain a certain outcome (such as setting a goal, writing it down and displaying it at a prominent place). But still, that just makes my current self the outcome of a previous train of thought.

Streams of consciousness produce such erratic trains of thought, but perhaps it is only the self-enforcing ones that define a person. From my perception of other people’s intuition, people are supposed to be stable over time, that perhaps, there is a “self” to be found somewhere in consistent behaviour. But maybe this intuition is wrong.

It seems that stable and consistent thoughts and behaviours are created from trains of thought that lead to self-reinforcing thoughts and behaviour – and these sets of thoughts and behaviours become one’s identity. So, perhaps, personal identity is also merely a heuristic for “selves” to make sense of their own thoughts, behaviour, subjective perceptions and interpretations of their surroundings. Without a stable personal identity, it might not make sense for one to make promises or to set goals or to plan for the future.

I realise that my “time-slice” heuristic is only practical and consistent when combined with theories of stable personality traits (because otherwise whenever I try to plan something for my future, I wouldn’t have any way to tell if I might still want it in future). Then again, if I test my own personality to help me decide how to plan for my future, isn’t it just a train of thought that leads to self-reinforcing thoughts and behaviour, thereby leading to a “personal identity”? I’m not sure if I want a “personal identity” created this way – somehow it just doesn’t seem quite right. 

Oh gosh, I haven't blogged for so long throughout this eventful period. In case in future I do want to know what I've been doing so far, here goes:

- Performed salsa on stage for Jitterbugs Studio Recital as part of a student team. I was strangely calm on stage - more calm than I usually was during rehearsals, and as I performed I felt as though I wasn't there. It was the same feeling that I had during National Science Challenge. After that, I went to cafe iguana with the girls for a post-performance chill-out! They were gossiping about the instructors and the good-looking guys at the recital, and they didn't seem to mind my presence. Much of their info was obtained from facebook, and the nicknames they give to some of the guys are really amusing! Like, there seems to be this agreed-upon ranking of which guys are most good-looking, and since nobody knows the name of the number two guy(everyone was too shy to ask), he's code-named "second choice". Among themselves they really refer to him that way, like,

"Eh, I saw second choice on the MRT just now!"
"Really, where!"

And apparently there is also a mutually agreed-upon ranking for the girls among the girls too. Discussing and ranking of people according to looks seemed like something that girls would do in secondary school, but they are all around mid-twenties. I remember that even among the 07S06D guys there was an agreed-upon 四大美女 within the class, so hearing them gossip somewhat reminded me of the first 3 months in RJ.

- Learnt how to use the Dirac notation in quantum mechanics. Gosh. Now that I think back, what I've learnt in those three weeks isn't that hard after all! Why did it take me three weeks then? I suspect that treating quantum states as vectors is very unintuitive. And then there is still index notation and tensor product and unitary transformations before I can understand the second page of the 100 page primer to the 4 page primer to the research proper.... it reminds me of the time in sec 3 I asked Chandru about motion under air resistance. He wrote 10 lines of solution, pointed to the first 2 lines and said, "This is the Physics." Then he pointed to the next 8 lines and said, "And this is the Mathematics."

- Went to China. The driving is insane. Also, we went there as guests to a wedding, of whom the bride's family is from UK and the groom's family is from China, so being bilingual Singaporeans, we offered to help translate! Though towards the end, we felt a little under-appreciated.

- Applications. After getting rejected by so many unis and colleges, I felt a bit like I had to settle for NTU. When I went to check my status online, I was just thinking of getting over with with whole US apps thingy, so I was really really surprised to see the acceptance by Princeton. Even though I showed the page to my family and they were all really happy for me, it still felt a bit unreal then. Right then I wanted to share the good news with all my friends who have supported me in my application. But at the same time, I wondered if sharing the news would sound like showing off if they didn't get into the universities they wanted. So I only told a few people then. But, the other thing I hadn't expected was how sincere zi lin was when she congratulated me. It's definitely not that I thought that she was an insincere person, but it's the first time I've ever received congratulations that really made me feel that the other person was happy for me rather than something that you are expected to say in accordance to social norms. To me, those were the three best things that happened to me that day: Princeton acceptance, Princeton financial aid, and a sincere congratulation(s?).

Oh man, the studio recital is coming up so soon... which means that rehearsals would be ending.

When I started out at the rehearsals, there seemed like so much to do; every weekend was occupied. But now that I'm getting more familiar with the dance routine (and that the music has been sped up substantially), six minutes of performance feels like such an awfully short time. And I suspect that after the performance, it would take me a while for me to get used to being free on weekends again. I think, what I'll miss most is the times I spent hanging out with Jake, Patricia and Aretha before and after lessons.

Somehow, I'm looking forward to the next rehearsal more than going to NUS. Weekends used to be something between weekdays; now it feels like the other way round.

Ten years ago:

I would not have imagined myself in RI.

I would not have imagined myself representing RI.

I would not have imagined myself representing Singapore.

I would not have imagined myself firing a rifle grenade.

I would not have imagined myself being an army officer.

I would certainly not have imagined myself dancing salsa and doing hiprolls on the SCGS stage.

No, not even in my wildest dreams.