An interesting mail

Subject: Further Maths Question . REALLY HOPE u REPLY ASAP.TQ

It was around 3pm. I knew this wasn't a regular email, and I quickly clicked on it. It was about a question in the Nov/Dec 2006 Paper 1, Further Mathematics. Here's the question:

Derive the Taylor series for e^x expanded at x = 0 and show that
2 < e <3.
[6 marks]
(6 marks would mean 10-11 minutes of work.) And here's my solution:

Any questions?

What is Medicine like?

Hmmm...feeling like writing a bit about how it feels to study medicine...

am
6.00 - Still asleep
7.00 - Last few minutes of sleep
8.00 - Morning face wash, breakfast, travel to uni, etc.
9.00 - PBL tutorial starts, goes for 2 hours
10.00 - Talking in PBL class
11.00 - PBL class over; some pre-reading in library


pm
12.00 - 1st lecture of the week
1.00 - Internet, leisure reading (chill time)
2.00 - HP lecture (the non-scientific side of medicine)
3.00 - lecture over
4.00 - chilling, lunch
5.00 - biking around the park
6.00 - losing some sweat in the gym
7.00 - dinner, to a friend's house
8.00 - trying out friend's 4GB RAM, 1GB VRAM PC
9.00 - still stuck there
10.00 - back home, fumbling through tomorrow's lecture notes
11.00 - reading lecture notes on Krebs Cycle (=TCA/citric acid cycle)

am again
12.00 - reading lecture notes on Fat Metabolism
1.00 - about to go to bed
2.00 - asleep


Based on 2nd week of 2nd semester. The Med website recommends at least 15 hours of "non-contact time commitment" per week for my science subject (NDM), and 9 hours for the non-science (HP2). It's like squeezing the most I can out of what I have.

Picture credit: http://www.germes-online.com/catalog

When I first wept in prayer

A friend requested me to write something "enlightening" today. Here it is.


I was taught how to pray when I was 9 years old. My younger sister was also taught at that time. It was my mom and my dad who taught us.

“Thank You Lord Jesus for [something that happened in the day].
Thank You Lord Jesus for [2nd thing that happened that I could recall].
Thank You Lord Jesus…”

You get the picture.

It was at night, just before bedtime. We would sit on mom and dad’s bed, holding our hands together. We closed our eyes. My parents would start the prayer.

I figured that prayer was directed to God. It was just like we’re taught in Sunday school. Eyes closed, hands locked, to reduce distraction. I learned the “script” off my parents. I had the “feel” of what to mention when we pray. But did I really mean what I said?

On one of those nights, Daddy had just come home from “outstation”. I recall that he traveled to Sandakan, Tawau, Lahad Datu and other places quite often at that time. Nights without Daddy around were quite common.

That night, when it was my turn to pray, I began, “Thank You Lord Jesus for taking Daddy safely home from outstation.” In the middle of that sentence, I cried. I was sobbing. Tears rolled down my cheek. I didn’t know why I was crying. I continued and finished up praying while weeping.

I still don’t know exactly why I cried at that time. I could only give possibilities. Crying means that something touched us deep inside. Humans deeply moved. Overflowing emotions. “It touched my heart.” Came across this before?

“And you shall love the LORD your God with all your heart, with all your soul, with all your mind, and with all your strength.” (Mark 12:30)

I quote this verse as it tells us that all our human dimensions – emotional, spiritual, mental, and physical – should be submitted to God. To worship God means that all our human aspects respond to Him, in spirit and in truth. Crying is a truly human response. Though it’s not the only way to respond, it is one of our unintentional responses to the things that happen to us.

Occasionally, I still cry when I pray. Till today.

Mom, Dad, thank you for teaching me how to talk with God.

Of Microeconomics and Tales of Pirates

I find this book by Gans, King and Mankiw very appealing. Deep in my head, I had always wanted to know what on earth it is that economics has to offer as an academic field (to the extent that it has an honorary Prize in Economics, a Nobel-equivalent).

It starts off with "Ten lessons from economics", divided into three 'types' of lessons. I'll focus on the first one: How people make decisions.

Lesson 1: People face trade-offs
At the most basic level, this lesson is illustrated by my decision whether to play the MMORPG Tales of Pirates or not. Once I decide to play, more trade-offs surface: Should I pick Lance, Carsise, Phyllis or Ami? What stats should I add? What skills to learn? Because I can't be a Lance-Carsise-Phyllis-Ami universal soldier who has maximal stats and knows all skills.

Lesson 2: The cost of something is what you give up to get it
So I selected Lance because I want to be a dual-sword-wielding Crusader. It looks cool. But I start out as a Novice who has no offensive and defensive skills at all! Then I can turn into a Swordsman at level 10. A Crusader is available only once I hit level 40.
To be a Crusader, I need to level up.
To level up, I need to kill monsters (or do quests...but most quests still involve killing monsters anyway. And I want to do this quickly).
To kill monsters more quickly, I can either add strength or agility. Strength increases the damage that I do when I swing my sword. Agility increases my rate of swinging the sword. Every character gets 1 point per level up (5 points every 10th level).
I decide to add my agility first, because the swordsman that I have in mind is a fast-swinging warrior. What I've given up (the opportunity cost) to increase my attack speed is an increase in my other attributes, which are strength, constitution, spirit and accuracy.

The book cover

My crusader

Lesson 3: Rational people think at the margin
Swordsmen have a skill called Illusion Slash. It is an "air wave" to attack enemies from a distance. It increases tremendously if my attack speed reaches 140, and increases even more if it reaches 210 (and no more after that).
I was a swordsman when my attack speed reached 139. My agility at that time was 40, and I had a few points to spare. So I added one more point into agility, and my attack speed reached the magical number 140. The monsters which previously survived 2 Illusion Slashes could now survive only one. By the way, after casting an Illusion Slash, I have to wait for 5 seconds before delivering the next one. Killing rate was significantly increased by just 1 mere status point.
The marginal benefit exceeded the marginal cost.

Lesson 4: People respond to incentives
To be really blunt, the opportunity cost of playing this game is my time. I could be reading. Or writing. Or thinking. Or doing something else other than staying stuck to the computer. But playing this game takes all of that away, and while playing, all I can do is read, write (type), and think within the boundaries of the game. Yes, deciding what monsters to kill and what items to collect are thinking processes.
And all I want to get is a lot of fun. Which usually relates to achieving high levels and getting lots of powerful equipment.
That's why, during the 2x exp event (experience gained by killing monsters is doubled - effectively making leveling up faster), I didn't mind spending one whole day slashing and hacking monsters (also called grinding). I used the mini-amplifier of strive to again double the experience, and partied with a newer character to get the 3x experience boost from Star of Unity. Each level 19 Killer Shroom which would normally give 226 experience points gave me 2,712 instead.
Having 2x, 3x and 4x exp events are indeed incentives to play and level up.

So yes, observing the links between economics and my gaming habit does intrigue me.