There is nothing we cant conquer!

Aha, Mr Koh said something today that I think is really inspiring..

If you tell someone, you specialise in this and this area(the more impressive sounding the better), you are bound to elicit wows and praises. It is even more impressive if you tell someone, that you are specialising, but you have not failed to conquer everything that you hated. I suppose its satisfying to know that you conquered this big ugly monster called _____(substitute you most hated subject here). For me, I have so much to conquer!..Self conquer if the first step to conquering the world..

So what's your plan to conquer the world today?

Was watching this show yesterday night about how Britain became a world superpower during the Industrial Revolution. It was an example of how everything links up nicely to give you the most astonishing results. It all started with Isaac Newton. Before him, people did not know why the sun rises and sets, why there were tides, etc. In one fell swoop, Newton published a thick volume known as the Principia that explained why planets move in circles, why things fell to earth, the concept of forces, etc etc. Then after Newton, James Watt and others came up with the concept of steam engine..The concept of forces have led directly to the concept of work done and energy. In the time where England started to industrialise, Adam Smith the pioneering economist published his great work, The Wealth of Nations. In his book, he outlines how an economy should work, in particular, that everyone should specialise to be most productive. His famous concept, the invisible hand, was the framework that allowed the gears of the economy to start moving.

If Newton found the key to industrialisation, and Watt used that key to open the door to industrialisation, then Smith and his 'hand' was the prime mover of the industry, the force that allowed the gears to move, the coal to fire, and belching smoke from hundreds of chimneys in England. Britain became even more powerful when it followed the ideas of free trade, by forcibly using military might to colonise other countries, such that it became a centre for economic growth.

I think there would a lot more meaning to studying our subjects if we could appreciate the history behind it, how it came about, how they shaped the world.

In hoc Signo Vinces. Under the sign of S18 we will conquer.

Order out of chaos

These are pictures that I created with a program called Apophysis. Such pictures are created by mathmatical rules, iterated over and over again, called iterated fucntion systems. The mathmatical rules for created such images involves rotation, scaling, shearing and stuff, basically all the stuff that we have covered for Complex Numbers Loci. See, there is such use for Complex Numbers after all..Though difficult to draw by hand, the computer can draw them much faster.

Friday 13th

Why would we welcome you Gandalf? Lathspell I name you.Ill news is ill guest they say.

I must be having the most severe case of inferiority complex ever so far. With a lousy score for PW, sucky bowling score that does not seemed to have improved, the group of juniors that hardly respect me, physical fitness level that seems to lag behind everyone else, it is extremely difficult for me to keep a rational mind right now. I even seem to be losing my grip on academic subjects.

To my PW group, I would just like to say firstly that I am blaming none of you for my lousy score. You all must be pretty disappointed too(with the exception of the disarmingly tall person, who must be congratulating himself for surviving the wreakage with good luck). It is as much my fault as the initial leader as it is yours. Though I would to say that group work on such subjects definitely does not seem like the forte for you all. I sincerely plead you all, and the rest of the class to participate more in the contribution of ideas. Many of you all are smart people, and might have lots of interesting ideas, but are just unwilling to speak up just because the rest of the class dun wan to speak up.I'm to blame for most stuff, because you all are so silent I cannot be more vociferous than necessary for fear that you all think I smart aleck or sumthing. Definitely not leading by example.

To my little crew of juniors, it is my fault that I am earning so little respect? I never wanted to be SL in the first place. I was elected just so that the section would not die out. I did not even join chess club in the first place because I possess otherworldly skills. I joined chess club because I think I enjoy chess as a leisure game. I did not expect to play at such a competitive level to the point that it is sometimes stressful. Of course, the rest of the people think I am having a super easy cca. In terms of time spent, yes, but I think the mental effort I spent each session is about as draining as a physics olympiad training session.

Am I like speaking in Greek or something? Because I think when I am just explaining what is the most rational thing to do, it looks everyone is looking at me like as if I am the irrational one. Erm..perhaps I should just pipe down next time.

Garh, I dun seem to improve in anything I do, even if i improve, its like a slow crawl upwards. Chess skills, bowling, pool, dota, academic..it takes such a long time for me to improve anything. Diminishing marginal returns? Wow, I am not even near the limit yet..

Random Musings

This serves as a pensieve to hold some of my thoughts so that I can return to them later and not forget all about them.

Quantum Mechanics
Possibility of explanation via standing waves and resonance?
Explanation of Young's double slit with electrons using the Chaos game.

Collatz Conjecture
Solved at last. Bit density. Concept of a dynamic equilibrium. Bring off analogy to the Le Chatelier's Principle. Explore possible variations of this conjecture? Markov Chains?

Chaos Theory
Nonlinearity. Feedback Loop. Causal chains that loop on itself. Feigenbaum universality. Stock market/Weather variation. Leaky Faucet. If a system is completely random, each new bit brings exactly one new bit of information. Exploration of chaos theory as encryption scheme? Chaos game.

Information Theory
Whole universe a computer? Information tells energy how to move, and energy tells information how to compute. Information about information. Energy is information? Afterall its capacity to do work.

Ministerial Pay - Case of tradeoff

There is quite a debate recently on how high ministers' pay should be. Should it be marked up to the level of the top pays of the private sector, or should it much lower?

I think this is a trade off problem, where the solution varies from country to country, situation to situation. Hence you cant take any solution from any country and apply it here.

The strongest argument against high pay for ministers is perhaps the associated lower risks for public sector compared to the private sector. The mental image of a golden alloy rice bowl comes into the mind. Obviously, this applies to some low profile secretary working somewhere with a stable job. And while that rice bowl is iron-like, its certainly not made of gold. For ministers, if you are incompetent, you are fired, after 5 years. Its not any better than other private sector CEOs.

Think of it this way. High pay for ministers is in someway justified because you are investing money for the country's future. But you are not investing in something that results in sunk costs. If that is a piece of wreck, you pull out your money from him, and kick him out.

Now Singapore has quite a unique political scene. Circumstances is such that the private sector looks a lot more attractive than public sector. Mighty think tanks is not exactly built into Singaporeans. Why should we? After all we got a great government that does all the thinking for us.

I think Mr Lee is quite right. We need to look at things in perspective. For the sake of less than 1% of the country's GDP, we are prepared to forsake the possible return of the entire country's economic value. Is that rational? For myself, and the rest the teenagers, I think the thing that we care about before considering going into the public sector would be 'What is the pay?' If I can do better by being a banker or being a doctor, why should I be in the public sector?

Creatio Ex Nihilo, more paradoxes

Proof of the Big Bang and the existence of God

You know the formula: m over zero equals infinity, m being any positive number? Well, why not reduce the equation to a simpler form by multiplying both sides by zero? In which case, you have m equals infinity times zero. That is to say a positive number is the product of zero and infinity. Doesn't that demonstrate the creation of the universe by an infinite power out of nothing?

Aldous Huxley

The Unexpected Examination

On a Monday morning, a professor says to his class, "I will give you a surprise examination someday this week. It may be today, tomorrow, Wednesday, Thursday, or Friday at the latest. On the morning of the examination, when you come to class, you will not know that this is the day of the examination."

Well, a logic student reasoned as follows: "Obviously I can't get the exam on the last day, Friday, because if I haven't gotten the exam by the end of Thursday's class, then on Friday morning I'll know that this is the day, and the exam won't be a surprise. This rules out Friday, so I now know that Thursday is the last possible day. And, if I don't get the exam by the end of Wednesday, then I'll know on Thursday morning that this must be the day (because I have already ruled out Friday), hence it won't be a surprise. So Thursday is also ruled out."

The student then ruled out Wednesday by the same argument, then Tuesday, and finally Monday, the day on which the professor was speaking. He concluded: "Therefore I cannot get the exam at all; the professor cannot possibly fulfil his statement." Just then, the professor said: "Now I will give you your exam." The student was most surprised!