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Friday, Mar 02, 2007 - 02:39 SGT
Posted By: Gilbert

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Method From Madness

So this week's three midterm papers are over and done with. Am I happy with them? Let's start with yesterday's (Thursday's) Microeconomics II - Bad News: stupid differentiation error in Question one part one already, then forgot to sub something in in Question two. At best decidedly average, I suppose. That's the bad news.

Good news: Who cares? It doesn't count towards my CAP. Lalala.

Foundations of Artificial Intelligence module (also yesterday) - okayyyy I suppose. Quick, for six marks out of sixty: Consider a variant of the ancient game of Nim where there are two piles of three sticks. You are competing against another player, each taking turns to remove either one stick or two sticks from a single pile. The player to remove the last stick wins. If you plan to win, should you elect to go first or second? Explain.

Don't be fooled though, this was probably the easiest question out there.

And Monday's Macroeconomics II - Good News: Results are already out on the 26 question MCQ midterm, and I appear to be on track for an A given the lecturer's official curve. 21/26 made the 84th percentile, and one more correct question would have pushed me into the 92nd (A+); Even more incredibly, Macroeconomics I was my all-time worst scoring module.

This has dealt another blow towards whatever tenuous linkage I have struggled to hold on to in the effort-result continuum, given that I was bubbling cluelessly through tutorials (not attempted any beforehand) and prepared for like four hours for half a semester's work - I suppose sticking to the basics goes a long way. What goes in just doesn't relate to what grade pops out. It must be quantum.

Bad news: Who cares? It doesn't count towards my CAP. Lalala.

I wonder what might have been if I got six of these type of modules in a single semester, which doesn't seem that far out as each semester so far has had one or two. That would have been the semester of my life. On the downside, the following semesters would be extremely disappointing.

MCQ tests have the additional bonus of being susceptible to a sort of metagaming - with incomplete knowledge, one can often extract enough information from the options given to deduce the answer, or at least get somewhat closer. Kind of like a simple Mastermind.

Example one: The Solutionless Solution

Which of these are true?

I. something
II. some other thing equivalent to "I. is false"
III. i dunno
IV. hor?

(A) I only
(B) I and II
(C) I, III and IV
(D) IV only
(E) I, II, III and IV

Now, without even looking into the context, we can eliminate B and E, leaving us with three options. Let's say that furthermore, either I must be true or II must be true (e.g. I. XXX theorem is true in all circumstances and II. XXX theorem may be false). Assume that the eventual answer contains all the true statements (and of course only true statements), which is almost always the case partly since question-setters tend not to deliberately set questions with multiple possible answers; Then D is out no matter whether XXX theorem concerns the solvability of n-dimensional Cauchy strange attractors in three-ringed hyperbolic space, or the social habits of large marsupials.

But since D is out, we can deduce that IV is false. Which means C is also out. So we know the answer is A. Without actually knowing anything specific about I, II ,III or IV other than some rudimentary logic.

Clearly (poorly-set) questions like these don't come around often, but when they do, feel free to punish the faulty thinking of the examiners. Hey, they should know better. It is quite common to eliminate a couple of options in this sort of question though, and of course the more one actually knows about the subject, the better the results will be.

This is perhaps a constraint satisfaction problem (CS topic), which was what our guest lecturer expounded on today. He was honest enough to admit that he spent (wasted) years of research on it before realising that other search algorithms were far better - the perennial fear of an academic. There were times when I seriously considered being a researcher, but this possibility of toiling chunks of one's life away without producing anything tangible was one of the greatest minuses - If a research topic is simple enough that one can easily determine what steps to take to achieve success, then likely it is trivial. Unfortunately, if it is not simple enough to be evaluated in this way, then there is a good likelihood that it leads to a dead end. Case in point: Singapore's Biotech Debate.

Example two: The Rereference

Which of these is false?

(A) some other thing from Example one
(B) i
(C) dun
(D) care
(E) really

It is sometimes possible to get information about a certain question in the exam from somewhere else in the exam. Again, don't waste time thinking about B, C, D or E if you are certain about Example one. Shade in A and move on.

In general, one can indirectly learn more (or have one's memory refreshed) about the tested subject while doing the paper itself.

Example three: The Comedy of the Commons

Mumbojumbomumbojumbo

(A) X/Y
(B) X^2/Y
(C) -X^2/Y
(D) Y/XY
(E) X^2/XY^2

This is not foolproof by any means, but if one is running out of time and doesn't know any better, he could do worse than try this heuristic. See that X^2 exising in three of the options? Chances are the right answer has an X^2 term. See that Y is the denominator in three of the options? Likely the right answer has a Y as the denominator. Notice that four of the options are positive (let's say X and Y are positive). Yadda yadda the right answer is probably positive. So pick option B.

The nice thing about this is that you get to feel extra good for foiling the cheap and mean efforts of the question-setter to trap you in a careless mistake, by using statistical analysis to get the marks for free. Be forewarned, though: The smarter lecturers out there are unlikely to blindly apply this technique of generating alternative options, and may exploit this line of reasoning to trap the unwary. But if you've got nothing to lose...

Example four: Some Explaining to Do/Extremely Elegant Elucidation

What is the explanation for "class aptent taciti sociosqu ad"

(A) Proin sagittis metus quis tortor
(B) Vestibulum ante ipsum primis in
(C) Nam semper. In eros turpis, dictum
(D) In eu massa eu diam auctor suscipit
(E) Nam posuere tempor nibh. Phasellus porta mi vitae neque. Phasellus lorem. Fusce tortor dui, dignissim non, commodo eget, congue vitae

Again, not certainly correct, but boy do professors like to give rigorous, complete solutions, if only to prevent hordes of disgruntled students beating their door down in search of restitution. Pencil down E.

That's it for this blog entry, but if anyone wants the complete Gilbert's Secret Manual About General Methods To Earn Marks You Have No Bloody Right To, send S$29.95 (special time-limited offer) with a self-addressed and stamped envelope to me. Thanks.

Maybe there are people out there who will not employ such tricks due to their personal ethics, but one must consider - what do exams really determine? Well, first and foremost they determine who does well in exams. There was this Taiwanese variety show during the CNY period that had two professional basketballers demonstrate their three-point skills on stage. Both made seven of ten three-pointers. Then they were introduced to this teenaged girl who was a dab hand at some arcade hoops machine, where the objective is to score as many baskets in a moving basketball hoop a metre or two away.

Well, she simply annihilated the first proballer with a wickedly consistent backspin release motion, outscoring him by a factor of three or so. Then the second proballer had to suffer the ignomity of losing to her by a factor of two - when she competed blindfolded. To even things up a little, she could only manage an airball from the three-point line, but this just goes to show that being an expert in one domain doesn't necessarily mean much even in a very closely related domain.

I have a sneaking suspicion that when most jobs don't entail being fired if one fails to solve a problem or write a complete proposal in exactly two hours, and bosses don't withhold reference material from their employees to "test their knowledge". Oh, there probably is a correlation between exam scores and competency levels, i.e. given two untried candidates, one who excelled in school for some reason and another, while the other did not, who should an employer pick ceteris paribus? Indisputably the former. But sometimes, I wonder at the point of it all.

That's why I enjoy the occasional opportunity to burrow down in the Central Library and pick up some Philo books, though many of them are far too dense for my taste. Take Nietzsche's famous Thus Spoke Zarathustra. I got all the way to where Zarathustra carried the dead rope-dancer out of town ("Verily, a fine catch of fish hath Zarathustra made to-day! It is not a man he hath caught, but a corpse."), then got no further. Not that I thought I could have gained anything at this stage in my philosophical education by going any further.

Quote of that library visit:

"It is said that the spirits of the night are alarmed when they catch sight of the executioner's sword: How then must they be alarmed when they are confronted by Kant's Critique of Pure Reason! This book is the sword with which deism was put to death in Germany. Frankly, in comparism with us Germans, you French are tame and moderate. You have at most been able to kill a king... Immanuel Kant has stormed... heaven, he has put the whole crew to the sword, the Supreme Lord of the world swims unproven in his own blood." - Heinrich Heine

(from Nietzsche's Critiques - The Kantian Foundations of his Thought, R Kevin Hill)

Fundamental problem of philosophy:

"Is there any knowledge in the world which is so certain that no reasonable man could doubt it?"

(from The Problem of Philosophy, Bertrand Russell)

It seems that we just cannot run away from the scourge of "reasonableness" - in the end, one has to assign some sort of "reason" to others, for himself to "make sense". Ah, as Dave Berry said in Dave Barry on the Value of a College Education, "(Philosophy basically) involves sitting in a room and deciding there is no such thing as reality and then going to lunch. You should major in philosophy if you plan to take a lot of drugs."

Berry's one clever customer. Here's another great observation:

"Basically, you learn two kinds of things in college:

(A) Things you will need to know in later life (two hours). These include how to make collect telephone calls and get beer and crepe-paper stains out of your pajamas.

(B)Things you will not need to know in later life (1,998 hours). These are the things you learn in classes whose names end in -ology, - - -osophy, -istry, -ics, and so on. The idea is, you memorize these things, then write them down in little exam books, then forget them. If you fail to forget them, you become a professor and have to stay in college for the rest of your life."

 Finally, presenting TPKant: a bit of code I wrote last sem when discussing Langton's Ant with tpk. Wanted to add programmability into it, but what the heck. Warning: May slow down your computer. Manually forward it 10 or 100 steps at a time for best results.




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