The Brainwash

For the past week there wasn't much challenge in CSC165. Almost everything was straightforward. Even though I couldn't attend few of my classes last week due to busy exam schedule, I still managed to catch on fairly quickly. Not to mention the tutorial exercises, they are a great way for me to keep up to date in the course since I don't review much until a week before the exam (which is going to be in February 8th). I am hoping that the professor will upload onto the course website some past tests, which if I get my hands on I will most likely dissect it and study it to its bare bones, so I can achieve a high score like for all my other courses.

If there was one thing that was really a pest for me this week, it was the "if and only if" statement. In English, you would normally use it to link a declaration with a condition, such that the declaration can only be made if the condition is right. For example:

I will eat apples if, and only if, it is already cut and peeled.

Most people will probably understand from this sentence that there exists a certain someone who is so lazy that he will not eat a fruit unless it is cut and peeled. Now, consider a scenario where "I" is in a room with nothing else but a table with a plate of cut apple sitting on the top. Will "I" eat the apple? According to CSC165, "I" will eat the apple. The reason being that in logic, the statement "I will eat apples if, and only if, it is already cut and peeled." is equivalent to saying something like "I will eat cut and peeled apples no matter what!". This is the same thing as saying that "if there exists cut and peeled apples, I must have eaten it". This sentence also suggests that  no other person could have eaten the cut and peeled apple except of "I".

This has bugged me for the past several days now because to my knowledge "if, and only if" is used synonymously as "only if" in English. If you replaced the sentence above with "only if", then I believe that the sentence is trying to get across the same meaning. The other problem is that nothing in the sentence suggested that it is mandatory for "I" to eat the cut and peeled apple, and no other person can eat the cut and peeled apple. If they wanted to express that idea, then they could have said something like "I is the only possible person who will eat cut and peeled apple and no other apple." instead of using something confusing as "if, and only if".

At this point, the only way that I will be convinced that "if, and only if" is different from "only if" is if someone can give me a English grammar textbook and point out that they are actually different statements. Likewise, I cannot be bent to believe that "if, and only if" have a two-way implication function unless someone shows me that it can be used in such a way in real-life, not just in logic. Until then, unfortunate as it may be, I will have to brainwash myself into believing it for the assignment and next week's test. I would appreciate it if someone can post under comment section a link that "if, and only if" is just one of those grammatical thing rather than something logical.

Its time for the rebellion......

Have you ever gotten involved in a situation where your teacher proposed one answer for a math problem while you proposed another, and started a relentless argument over which answer is correct? I had a few of that during my life time and I had never won any of them, mostly because I was actually wrong with my answer. In rare occasions, my teacher would convince me his/her answer was right even though that was not the case. When others students were involved in this sort of situation, I have seen them give up and go with the flow, which is truly saddening in an academic institution. I believe that one of the most important reasons for people to attend school is to question authoritative facts. This is important because it keeps people thinking about what they are learning and prevents them from falling into the trap of blindly memorizing facts to get good grades. I am one of those people who believes that higher education and society's work forces will benefit more from having people who can think critically and creatively.

Regarding the scenario that I just described, I nearly fell into the trap this past week in my tutorial class for the computer science course that I am currently taking. The problem that we were doing was simple. This is the link to the problem:

http://www.cdf.toronto.edu/~heap/165/W13/Tutorials/T1/t1.pdf

The question that I will talk about is 2d, but you have to read question 1d to do 2d (I highly recommend you to read it, because you won't know what I am talking about unless you fully understand what was going on in the problem). No one had trouble drawing the venn diagram for the "True" scenario. However, the trouble came when we had to fill the venn diagram based on the "False" scenario. Most commonly, students falsified the statement into "None of the three python programs fails all three tests". This is a correct "False" statement, and most students saw that if all three python programs passed all three tests then it would easily satisfy this statement.

When it was time to take up this question during that tutorial class, there were several different answers proposed by the students (this was the only question in the entire tutorial where different answers were proposed). Some students proposed to X mark Q, O mark for the intersection, and ? mark for everything else, which is the answer you would get if you solely consider the scenario that all three python programs passes all tests. Then where did the other answers come from? The other proposed solution, where everything on the venn diagram is ? mark, came up because a scenario where all three python tests only partially pass the three tests can also satisfy the "False" statement. Think about it. As long as you don't have a program that fails all three tests, then what's stopping you from only passing only one or two tests? If we solely consider this scenario, then on the venn diagram Q would have an O mark, intersection would be X marked, and everything else is ? marked. However if we consider this scenario and the scenario where all three python programs pass all the tests together, then both Q and the intersection can either be X marked or O marked, which would lead to the conclusion that they should both be ? marked. This actually turned out to be the correct answer, but it was only after a few days that the correct answer was public announced.

I am proud to say now, that I was one of the people who considered both scenarios, but during that tutorial, because the teaching assistant of the tutorial advocated the "all three pass all three" answer, I started having doubts about my own answer. The partner who I worked on the problem with also got the same answer as the TA, which didn't help my case. My TA and I then started an argument of which answer was correct, but in the end I succumbed. You can be asking "how did you lose your argument even though your answer was right?" Well, the course of the argument had less to do with logically arguing our cases but had more to do with which of our "aura" was stronger. The TA, being the TA, looked superior to me in terms of subject expertise. Everything the TA said to me forced me to re-evaluate my argument because there was always the possibility that I missed something in crucial in solving the problem. But the opposite is not true, because being a student, it was likely impossible that I knew something that the TA did not.

Don't get me wrong though, I am not saying that I have a bad TA. Everybody can make mistakes, and my TA just happened to make one during that tutorial. What I am saying is that when it comes to education, there is no such thing as "teacher and student"; status doesn't matter. Although you should respect your teachers for passing down their knowledge to you, you shouldn't stop questioning them for its validity. The next time you encounter a situation similar to mine, don't be afraid. Talk to your teacher, and don't hesitate to point out any flaws in their reasoning. Even if you lose your argument and make yourself look like a dork, the act of courageously questioning the authority and validating what you are learning will make the experience of education totally worth it.

Introduction

Recently I noticed that everywhere I go on the internet, there are blogs everywhere. I met a few people of my age who made their own blogs, and I've seen some blogs on the internet that I actually enjoyed reading. I think it recently became pretty popular because more people started having access to internet around the world, so if bloggers post some stuff up online, other people can see it and discuss ideas about worldly topics. I recently got a school assignment asking me to write a blog about the class/course where the assignment came from, so when this opportunity came up I was pretty eager to start it up right away.

That being said, the posts that I am going to make will discuss a fairly obscure subject, because the course where my "blogging assignment" came from is about "how to think logically". You might ask, "why is this n00b taking a course about something that every non-handicapped human being on earth should be able to do? Am I reading the blog of a retard?". Well let me say this, in my high school I was a straight A student (I might have done better if I wasn't so lazy and addicted to games and anime), and I am the guy who always got above 90 on all my Math and Computer Science courses. But this course has surprised me in two things. First thing that I was surprised at was the mountain load of work that we have to do in this course. I definitely didn't sign up for this aspect, considering how I heard this is one of the easiest courses in my university. The second thing that I was surprised at was how brutally difficult thinking logically can be when you are reading a programming code. For those who are familiar with python programming, here are the programs that I had to analyze: http://www.cdf.toronto.edu/~heap/165/W13/Lectures/W1/q.py. Although each definition only consisted of four lines, for some reason I had the hardest time figuring out what each of them did. Just the other day, the professor made every student in the lecture hall write down on a piece of paper the function of one of the four definitions that I just mentioned, and then the students had to pass down the paper that they wrote their functions on to another person in the lecture hall so that person can match which definition the function came from. I don't know about you, but I believe matching is probably the easiest type of question that can come up on any sort of tests. The professor tallied the number of pieces of papers that correctly matched the function with its definition, and it turned out more than half of the class matched them incorrectly. This could be due to two reasons. It could either be that students were still groggy after coming back from winter break, or that we truly were a bunch of "retards" who couldn't do something so simple as matching functions to definitions. Just to let you know, this is a course from University of Toronto, which is known for having one of the most brilliant group of undergraduate students in Canada. When the professor first asked us to do this exercise, I expected at least 80% of the class to match them correctly.

What conclusion this leads me to? For one, I should probably do the homework to get more familiar with the way that the questions make me think. The other is that I am glad that I am taking this course. It has already piqued my interest with its lectures and challenging problems, which is a good sign for the start of any course (I took so many courses that the professors just info-dumped students, so much so that I came to hate classes where you just memorize things). Challenging problems are always good for learning. It makes you think critically and feel engaged in the course (but I wouldn't want those kinds of problems on a test). It also means you are learning something new (if nothing in a class challenges you, then you should probably skip to the next level of the subject or just not attend the classes).

That basically ends my post for this week. One thing I got to mention is that I am not particularly good at writing (my high school English mark was in the range of 80 even though I spent more effort than those kids who got like 90s and stuff), so feel free to point out any grammatical errors I might have made or any methods or ideas that can make my posts easier to read in the comments section.