Hi everyone,

hope you guys had a good and restful weekend after the promos exams. and NOW.....

time to work on your PW.

- PW teacher, Miss Ng

Sigh, to think I can actually slack after exams. I guess I definitely do not get to play after exams anyway :(

The irony of examinations...

Before exams, you play.
After exams, then you study.

I had a stomachache this morning. Quite a bad one because I have never felt so pain in a long while. It was as though I have not eaten for 10 years. So I was tolerating the pain all the way until I reach the canteen, and after eating, I was feeling alright.

But that feeling was just temporary. 1 hour into the maths paper and I was feeling terrible. Yeah I needed to go to the toilet, but not in the middle of exams right? Otherwise there will not be enough time to finish the paper. So perhaps I will just hold for another 120 minutes.

But after around 30 minutes of solving problems and holding back shit, I could not take it any more. I rushed to the toilet while still thinking about the permutation question so that I save time.

When I came back out from the toilet, I met Lincon along the way. We had a brief conversation...

[Lincon]: Hey
[Me]: Sigh I have diarrhoea.
[Lincon]: ... oh shit!

Yeah, literally.

The Diminishing Marginal Returns relationship implies that as more of some inputs is being sold, the value of that item decreases. For example, if there is only 1 iPod in the world, that iPod is sold at a very high price. However, when there are more iPods around, each iPod will cost lesser.

Similarly, the value of a secret is very high. If you hold a secret about yourself and nobody knows about it, its value is priceless because only you know it. When you tell one of your good friends the secret, they 'bought' the secret from you at a high price, but in actual fact you do not gain any money. A special kind of bond exists between your good friend and you - it is like investment. You invest in the secret using faith, trust and friendship.

Let's say more people know about the secret, either through the first person or through his/her good friend. The value of the secret diminishes greatly until there comes a point whereby it holds no value. Both parties' (the first person and the friend) investments fail. Faith, trust and friendship drop. Both will invest less into each other's secrets again. Another case of the Diminishing Marginal Returns relationship. All that is left is just memories of the secret itself which hold no value, and the trails - lack of faith, trust and friendship.

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It is a wonderful day today. I can finally go back to school to take my economics promotional examination, after being cooped up at home for 4 days. I was stunned at the first question though, but as I wrote and wrote I realised that I had more points than the number of marks allocated for the question. Time was no problem though, because I have been training my writing speed. There was even this question on price discrimination. I am glad that it came out because I studied so hard for it. First degree price discrimination is when a buyer is charged the maximum price that he is able and willing to pay for each and every individual good that he purchases. Just like this post, there is some form of first degree (non-price) discrimination because only the smarter ones can understand this post. Second degree price discrimination is block pricing...

Oh yeah, I just remembered that I don't take economics. I woke up at 12 noon today anyway. Ah yawn...

I just had Science Practical Assessments (SPA) for both Physics and Chemistry on Skills C and D.

I guess since I stepped into VJC, the Physics experiments that I have been doing are only on oscillations. Ok maybe not forgetting some of the other minor experiments like messing with electrical circuits... They have very interesting, or should I say innovative ideas about oscillations. In secondary school, there is only one type of oscillation: left-right oscillating a spherical mass suspended by a non-elastic string. In VJC, there is left-right oscillation of mass stuck to a piece of triangular cardboard paper, up-down oscillation of mass suspended by springs (varying the number of springs suspending it too), front-back oscillation of ruler suspended by a strip of writing paper, with additional weights on the ruler, up-down oscillation of metre rule with one end clamped and with masses suspended on the other end, up-down oscillation of metre rule with one end pivoted and the other end suspended by a spring, front-back oscillation of a metre rule, and yesterday... left-right oscillation of a perfectly horizontal metre rule! I mean, it's really so creative that they can try for Guinness World Records: most number of oscillation experiments ever come up by a college. Well that was Physics.

Chemistry is even more interesting. It is so interesting that no one bothered to do the experiment (from my class, that is). It's more of an eyes-on practical assessment rather than a hands-on one. The apparatus given is just for our viewing pleasure only. Too bad I was writing from the start till the end, if I had more time I would have actually try burning the propanol given, just for the sake of doing the experiment. I mean, you are supposed to do the experiment, right?

But oh well I am glad that one more round of SPA is over. Maybe there will be around 2 to 3 more next year. SPA is really a way to get 20% easily.

Here are the answers to the previous post.

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1) The answer is that switching will ensure a 2 in 3 chance of winning the grand prize. The key thing here is that the host KNOWS which door contains the grand prize, so whatever door he opens will definitely be the door with nothing behind. So you have 2/3 chance of choosing a wrong door initially. Of the remaining 2 doors, he will open the remaining wrong door, so switching will definitely get you the grand prize. However, in 1/3 of the cases, you may choose the correct door initially. The host can open either of the remaining doors, but it does not matter, if you switch, you are going to select the wrong door. So switching will fail you only 1/3 of the time.

If you are still not convinced, consider this variation: You have to choose 1 door out of 1000 doors, in which only 1 of the doors has the grand prize behind it. You select one, the host opens 998 other doors which do not have the prize behind them. So you are left with your own door and another door which he did not open. Are you going to switch?


2) The chances of the other being a boy too is 1/3. Consider her having 2 kids, so 25% of the time she will have 2 girls, 25% 2 boys, and 50% 1 girl 1 boy (GG, GB, BG, BB). We discard GG because we know that at least one of them is a boy. As for the other 3 cases which have equal probability of happening (GB, BG, BB), only 1 of the cases means that the other child is a boy too.


3) This one is easy. You know that there are 2 kids, an older and a younger one. The gender of the younger one is not influenced by the gender of the older one. So the answer is 50%.


4) This is my favourite. The answer to part a is 1:1 ratio of boys to girls. Subsequently, the answer to part b is also 1:1. This is due to the fact that a woman gives birth to a boy 50% of the time (and a girl 50% of the time too)

You can consider this ratio because you only determine the number of children in that household. There can be one boy only, or there can be 100 girls with 1 boy. You are not changing the gender of any children, nor are you killing boys. If the question were to be changed to: girls are killed 50% of the time... then of course the answer will be different because you already determined that some girls will be killed (and not boys). But this is homicide so maybe not a good example, but the idea is there.

If you are still not convinced, consider an infinite number of children standing in a row. A household will pick children first in the row until it reaches a boy, in which it will accept. The next household will pick children after that doing the same thing. Of course some households will end up with 1 boy only, with no girls. The boy:girl ratio is hence 1:1.

Some probability problems to think about.

1) Suppose you are on a game show. There are 3 doors, one of them revealing a car behind it, or 1 million dollars, or anything you like. The other two have nothing behind them. You can only pick a door. So you pick a door, let's say door A. The host, who knows which door has the grand prize and which doors do not, then open one of the other 2 doors, either B or C, which has nothing. He will always open a door which has nothing behind it. So the question is, should you stick with your original choice, or should you switch, or it does not really matter? What are the chances of you winning the grand prize if you do not switch? Could it be 1 in 3, because your original choice was a 1 in 3 chance so whatever the host does, does not make a difference, or could it be 1 in 2, because now you have 2 choices, either your original door or the door that is left?

2) Suppose you know this woman who has exactly two children, but you do not know their genders. You ask, "Is one of them a boy?" She replies, yes. What are the chances of the other child being a boy too? Suppose that a woman gives birth to a son 50% of the time and a daughter 50% of the time.

3) Suppose you know another woman who also has exactly two children. You do not know the gender of the younger one, but you know that the older child is a boy. What are the chances of the younger child being a boy too?

4a) Suppose in this country, there is a strange rule. women are to give birth, and they have to give birth until 1 and only 1 boy is born. This means that if a woman gives birth to a daughter, she will have to continue giving birth until she gives birth to a son, then she stops. Or if her first child is a boy, she stops giving birth. Suppose that a woman gives birth to a son 50% of the time and a daughter 50% of the time, what is the ratio of the number of boys to the number of girls after all the families have 1 son each? Do not factor in the number of men and women, only count the offsprings.

4b) The offspings grow up and get married, and they follow the same rule in the country. Then the new generation does the same. After many generations, what is the theoretical male to female ratio?

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If you have not tried those problems, please give yourself at least 5 minutes thinking through each problem. They are mathematical problems, there are no tricks involving words so pardon me for any bad english if any.

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(Answers coming out soon)

I think I will do a short follow-up post on one of my previous posts about relationships.

In a relationship, you want the bond between both the guy and the girl to be strong and everlasting. However, what kind of bonds are we talking about? If you say 'ionic bonds' or 'covalent bonds', then I congratulate you because I see some potential in you scoring well for your chemistry examination. But in this context, you deserve only half the credit. Yes, ionic (and covalent) bonds are strong, but what is lacking is the substance, the quality of the bond. You do not just form bonds with any other person like how atoms or ions do, right?

It is important that in a relationship, nobody should be too dominant. In this post, my definition of 'dominant' will mean that someone tends to gain control of the relationship too much. It can also mean that the other person is (sometimes purposely) not doing enough and constantly hiding behind his/her partner. Take note that I used 'too much'. The guy should be more dominant than the girl in a sense, but nobody should be dominating too much.

Why is it that the guy has to be more dominant? Firstly, the guy is physically built this way to protect the girl. As a general trend, guys have more muscles than girls. That brings me to a point that it does not mean that guys are the only gender suffering. Yes, guys have to torment all the physical tortures because guys are supposed to be like this. However, girls do have to suffer more emotional hardships than guys because girls usually have lower Emotional Quotient than guys. Girls also have to suffer pains which guys do not have to suffer such as labour pain and menstrual cramps. All in all, members of both genders are built such that each gender has to suffer some pain, but mostly distinct kinds of pain from the other gender.

Secondly, guys are... well, guys. They are meant to lead. They have a higher reputation to uphold than girls. When girls take the lead, people will think that the guy is not doing his job. He is being a sissy who hides behind his girlfriend, following her footsteps. There is not really much explanation for this. Perhaps from the past, it has always been the guy going out to brave the storm.

In my point of view, when I say nobody should be too dominant, I will want to mean that the guy should do something to control it. This is because usually the guy has much greater power in a relationship than the girl. He can choose to exercise it up to his own free will, and he can choose how much to exercise. However, sometimes it also depends on the case. We look at 3 cases.

1) The guy is too dominant. This happens either when the guy does not think for the girl, or the girl refuses to match up to the guy in terms of taking control. For the former case, it is usually very hard for the guy to realise, until or unless the girl reminds him. Since the guy tends to be more dominant than the girl (as explained above), he may overdo it. For the latter case, the girl may just like to follow the footsteps of the guy. This is all right, but I feel that in a relationship, love should be both ways. The girl should not just let the guy make all the decisions. The girl should play a part too. This is what I mean by strong bonds.

2) The girl is too dominant. This happens when the guy is naive in nature. The girl may just exert her power a little and the guy will just follow. The guy may get bullied in this case, which should not happen in a relationship. The girl can be too dominant too when the guy wants to please the girl too much. In this case the girl actually is not being 'too dominant'; the guy is being too recessive. Just like what is explained earlier, love should be both ways. The guy should not just do everything for the girl because it is not love. If you look at the girl's point of view, the girl can only be grateful to the guy for everything he does for her, but where is the love? The girl will feel awkward when everything goes in her way.

Also, love fades over time, so what happens when the love starts to fade? The guy will get tired of doing things for the girl. This is dangerous because usually a breakup may occur when both are tired of each other. When one is tired of the other but the other is not, the relationship can still sustain through; perhaps later the one who got tired of the other may start to find an interest in the relationship once again and continue it confidently. However, in the case I was discussing about, the girl does not feel anything for the guy in the first place, so it will 100% that the relationship will end when the guy feels tired of the girl after a while.

3) None is too dominant than the other. This is the ideal situation based on the discussion above.


I am sorry that my post has no examples owing to the lack of experience. Also, this post may appear very confusing. I just hope that you get my idea lah haha.