Today is one of those remarkable days because my tutor argued with a few students during tutorial, to the point where voices were raised and tensions were quite high. A student even insinuated that he is a poor teacher when he said a good teacher would always encourage discussion in the class. In response the teacher asked the rest of the class to bear witness to the fact that he already allowed another student two chances to present his case, and that he had clearly refuted both that student's arguments in an intellectual way.
Anyway, it all started from an intellectual disagreement between the teacher and some students. A student had presented a shorter method to a question which gave the same answer as the teacher's longer's method. The teacher argued that while both methods gave the same answer, they are not the same and his method is more mathematically sound. (Was a qns on probability, and his method clearly listed out all cases; the students' version didn't, though it yielded the same answer) Some students attempted to show how their shorter method is the same as the longer method. The teacher then disputed their interpretation of his method, saying the way they presented it is not the same as the solution he presented, and thus they were making a non-argument by trying to show that students method = teacher's method. The students argued that while the first step was different, it IS still the same if the teacher would allow them to elaborate further, but the teacher said no, it cannot be the case that the method they interpretated as his is really his when the first step is wrong and modifications are added in later steps to manipulate it back to look like his method. That's where things started to get ugly.
I am more inclined towards the teacher's position in part because the way I answered the question was similar to his, but also because I think the students were not being critical enough of their own presentation. I suspect what they felt was that the teacher was picking on a small detail instead of focusing on their argument, which is that students method = teacher's method.
And though the 2 cases are somewhat different, I felt the same way during the tutorial as I do when someone goes 'tsk' when someone else asks, can you prove that I exist? or can you prove that WWII actually happened, as if the answer to those questions is so obvious as to be regarded as true and not worthy of discussion.
Both mathematics and philosophy, I think, attempt to prove certain fundamental things in life that we all take for granted. Take, for example, the probability that event E will happen and the probability event E won't happen is always equal to one, ie P(E) + P(not E) = 1. According to the tutor this hasn't been proven yet, and yet so much of our theories are based on that and it seems so intuitively correct that we may feel that it cannot be wrong. Take, for example, the historical *fact* that WWII happened. How does one go about proving this is the case? I don't think photos and eyewitnesses accounts and evidence of architecture succeeds in doing that.
Today is also a remarkable day because I had a very nice game of chess with someone. Was a relatively long game, over 1.5 hours, lost in the end but I was literally trembling with adrenalin when I made a sacrifice to mount an offensive. There was so many permutations I think I must have thought for 15 minutes on that move alone, maybe will have to run it through a computer program or something to check where I went wrong in the attack, or whether it could have been mate in the first place. I like playing chess not because it gives intellectual pleasure, or because it gives a sense of satisfaction in employing tactics and all that, but because chess to me is another expression of
creativity and individuality. Attempting to always express creativity in the usual medium (eg. literature and the arts) is in itself uncreative, and a tactical, arguably rule-based game like chess paradoxically becomes a creative game precisely because it is not usually associated with art. The individuality part is pretty self-evident when you see different sorts of players opting for different openings and going for different styles of play.
Today is also a remarkable day because on the way home I thought of a question that may potentially be the definitive question I can ask to evaluate whether someone can be my girlfriend. You know how people tend to have some list of criteria that they would like a potential suitor to have? I don't believe in such things, but if I were to compelled to come up with a filter system it would have only two aspects. The first is, she must be intelligent. I don't mean intelligent in the academic way, I don't mean intelligent in the intelligent way. I mean intelligent in the think-about-life kind of way. Elaboration maybe some other time or never. The second aspect would be her answer to the question that I thought of on a remarkable day home, and that is: are you, at the very least, an occasional litterbug?
