Measuring the Volume of a Container

My sister was packing for an overseas vacation when she found herself with a small bottle of hand moisturizer. Unfortunately, she was uncertain as to whether the bottle was of a size within the travel limits, which was 100ml. My assistance was sought.

The first and probably the most commonsensical solution I came up with was to compare the size of the bottle with other containers of known capacity, such as my water bottle which has 100ml markings. But this method was unsatisfactory as the precision was poor.

I then suggested to fill the bottle with water, and to then measure the amount of water contained. However, this too was unfeasible, since the container already contained some moisturizer.

Being trained or born with scientific and mathematical thinking, I then came up with a most intelligent approach. First, I observed that the container was almost a perfect cylinder. Thus, using a ruler and the simple volume formula, I was able to calculate that the container was almost certainly a 100ml container.

Basic mathematical knowledge proves to be useful to daily life.

In retrospect, a fourth solution is possible, but this is rooted in more science. We can simply immerse the container in a beaker of water such that it is fully submerged. Then, the volume of the container is simply the amount of water displaced. This solution is clearly generalizable to all shapes of containers, assuming they are watertight.

Auction Game

I am keen on running a game that has some elements of game theory. The particulars of the game are described below.

The game is an auction game, where each player aims to end up with the most amount of money. The items to be auctioned are bundles of money. As with typical auctions, the highest bid win the auctioned bundle of money. However, there are two important differences. Firstly, the auction system is sealed-bid, meaning that each person places his bid in secret. Secondly, the auction is all-pay, meaning that everyone pays the amount they bid, regardless of whether they won anything. Hence, the auction is an all-pay sealed-bid first-price auction.

Thus, the rules are:

1) Each player starts with the same amount of money, S dollars.
2) The X bundles of money, and their denominations, are announced in advance.
3) Each player may place, secretly, up to one bid per bundle of money, so long as the sum of his bids is equal to or less than S. Each bid must be a positive integer.
4) Everyone pays an amount of money equal to amount they bid.
5) After each player has placed his bids, for each bundle of money, the person(s) with the highest bid(s) share the bundle of money equally.
6) Any remaining unclaimed bundles of money are forfeited.
7) The final score of each player is equal to the total amount of money he has; i.e., the sum of money won and money not spent during bidding.
8) The final score is used to rank the players in the game.
9) No communications are allowed between players before or during bidding.

An exception to rule 9 is that before the bidding begins, each player may issue at most one public statement, viewable to all players. The public statements are displayed on a first-post-first-displayed basis.

10) At any point before the bidding phase, each player is allowed to make at most one public statement which is viewable by all players. The public statement will be displayed immediately.

A trial run of the game is provided below.

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Preparation Phase:

There are three players, A, B, and C competing. They have $10 each.

There are 4 items being auctioned. The items are:
#1: $3 note.
#2: $5 note.
#3: $5 note.
#4: $12 note.

Before the bidding begins, it is possible to make public statements. C makes a first public statement, “Hello, I love money.” Everyone is notified of C’s statement.

A also wishes to make a public statement, “I will not make any bids.” Everyone is notified of A’s statement.

B forfeits his right to make statements as he does not wish to make any statements.

Bidding Phase:

The bidding phase begins. Each player independently and secretly makes their bids for the items.

A bids $2 for item #2, $2 for item #3, and $6 for item #4.

B bids $10 for item #4.

C bids $2 for items #1, #2, #3 and #4.

After each player has submitted his bids, the bidding phase ends. Each player pays for his bids. A pays $10 for his bids, and he has $0 left over. B pays $10 for his bid, and he has $0 left over. C pays $8 for his bids, and he has $2 left over.

Settlement Phase:

It is time to settle the auctions, and compute the final scores. Item #1 is won by player C. Item #2 is won and shared by players A and C. Item #3 is won and shared between players A and C. Item #4 is won by player B.

Player A has $5 in the end.

Player B has $12 in the end.

Player C has $10 in the end.

Player B has the most money, and wins.

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If there are any willing participants to try this game, please contact me by some means. I will post more details if/when there is sufficient interest.

At the End of the Road

There is an abandoned temple at the dead end of a road. In that temple, one of the innermost rooms overlooks the river nearby.

It is said that one of the windows overlooking the river is cursed.

One day, three boys decided to test their bravery. When the sun set in the evening, they met outside the temple; they came armed with some joss sticks and candles to provide light. And so, separately, they went to look at the window in the temple room

X went in first. He came out after some time.

He said, "I saw nothing leh".

The second guy, Y, went in after X came back. He too came out after some time.

He said, "I saw my reflection in the window. X, you must be coward lah, didn't even go look right?"

X denied this and claimed he looked at all the windows, but perhaps he got the wrong room.

Finally, it was Z's turn. And so, Z went in. After a short while, Z screamed and came running out.

"Fuck, I saw an old person's face in the window!"

X and Y didn't know whether Z was joking, but Z seemed to be in serious shock. They felt spooked also, so they all ran home.

A few days, then a few weeks passed. Eventually X,Y, and Z came to think less and less of the events of the temple.

Then, a few months later, Y died in his sleep.

It was unusual for a young boy to die while sleeping, though it was not unheard of altogether.

But he died in his sleep with eyes left half-open.

It reeked of a supernatural flavor, but investigators could find no cause other than "natural death".

X and Z were scared, but somehow they convinced themselves that the events were unlinked.

And so, as fate would have it, nothing else seemed to happen. A few years passed, and they both grew up.

X took up a job in a small machine shop, while Z went to the city and had a cushier desk job. Then one day, Z received a call, and then he learnt that X had suffered a most gruesome death. X had apparently had a fatal accident while on his job.

X's head was severed while he was cutting some sheet metal.

The entire head was cut clean off.

Nobody was nearby when it happened, but investigators surmised that he had tripped while operating the rotary saw cutter.

An accident.

But to Z, it was clear. It was unnatural, and it was somehow linked to the events that happened many years ago at the temple. Hurriedly, Z ran to the nearest temple in the city for help. Eventually, he was directed to an elderly Taoist priest with expertise in such matters. Z recounted the events that happened many years ago, and the fates of his friends.

The priest then asked, “Does the temple overlook a river? Is the temple at the end of a road?"

Z was shocked at the priest's knowledge, but he replied in the affirmative.

"Ah ! Then it is clear." The priest then explained.

“A river at the dead end of a road has great spiritual energy and supernatural significance. A dead man walks for 7 days and comes to a river that divides the mortal realm from the afterworld.

Of course, it is not always that when a river meets a dead end that supernatural events occur but the temple, abandoned, may have contributed to matters.

Still, that is only half of matters. The window directly overlooking the river to the underworld offers a glimpse into the underworld. But also, it reflects the view of the dead man before he enters the underworld. In other words, what you see in the window is simply a reflection of you when you die.

Y saw a young boy, and hence he was fated to die at a young age.

X saw nothing, but what he really saw was his headless self.

You, Z, thankfully saw your elderly self. Perhaps it did not seem so then, but it is the most fortunate of outcomes. You will not die, except of old age.”

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The above is the original version of a story I first told over a MSN conversation. I have since written a more complete and polished version, but it is not available to the public eye.

Mother Tongue Reweighing

There has been much furore over the suggested (and later retracted) reweighing of Mother Tongue at PSLE. Much has been said regarding this, but from my observations of forum letters as well as of online views, almost everyone has made a crucial oversight.

The policy, despite being about Mother Tongue, seems almost inexorably argued or discussed in the context of the Chinese language. While it is not wrong per say to discuss one's experiences (which are obviously limited to one's own mother tongue), the apparent lack of consideration or input regarding other languages is disturbing. After all, the suggested subject reweighing affects students of all races and mother tongues, not merely Chinese students.

Despite my hesitance to invoke issues of race or ethnicity into discussions, I suspect that any move to reduce the weighting of Mother Tongue would have a greater negative impact on students of other races and ethnicities than on Chinese students; in general, they have better overall proficiencies in their mother tongues than do Chinese students, and hence would be more likely to be negatively affected by a reweighing.

Of course, now that the policy suggestion has been retracted, the contents of this may no longer be important. However, I do hope that future policies are more considerate of other ethnicities, and are more explicit in such considerations.

Fear of Morbidity

Friends may have heard of my view that I am not quite so afraid of mortality as of morbidity. Death, while being something to be feared as it reduces the value of your life to 0, is more preferable (or better phrased, less undesirable) as compared to morbidity, which may quickly reduce your life to a most terrible state of suffering; if we were to subscribe to a utilitarian framework where suffering and happiness are the key measures of value, a severely morbid life would have negative value.

Death has the elegant property of being an end, at least for you. Perhaps that nothingness is frightening in itself. At the same time, however, death seems more preferable than many other things, particularly if you are suffering from such a thing in the first place. Beyond the most evident problem of pain and massive pain, other forms of suffering are brought about by morbidity; it might be accompanied by loss of body function, thus rendering you all but invalid; it might be accompanied by emotional suffering caused in relation to family and friends. And worst of all, morbidity persists for some time until your ultimate demise.

People do not seem afraid of morbidity, at least not as much as mortality. Perhaps it is because the risk of mortality is more salient, whereas morbidity seems to occur much further along the time horizon. Another possibility is that perceptions are relative and may change with one’s age, and death may eventually become less fearsome than morbidity. I am uncertain; perhaps I will be sufficiently intrigued to study this at a later date.