I hope to get such a post up soon, when I have the patience to produce such a diagram.
For the meantime, I will just write a little about a part of myself that I only became truly aware of in the process of thinking about mathematical plotting of religion. The crux of the matter is this: I am simultaneously both fascinated by, and quite bored by mathematics. This apparent contradiction has been of a slight concern to me, but I mostly put it out of my head. I am concerned no longer, because I believe I have worked out how to differentiate what interests me and what puts me to sleep.
The essential difference is between concepts and process, For example, it's really cool to know that a function can be differentiated or integrated, and doing so will yield interesting results, and have great utility in real world (differential equations appear everywhere). That said, why on earth do I need to know how to find the integral of some particular complex function. I'm happy just knowing that it can be done.
Mathematical concepts are awesome.
Imaginary numbers are incredible.
The the concept of 4,5,6 or even 92-dimensional space is amazing.
The concept of prime numbers is ingenious.
The relationship between Mersenne Primes and Perfect Numbers is mind-blowing (especially when you find it yourself).
Exploring arithmetic in base 8 or 23 (or if really experimental, negative bases) is what I call a fun filled afternoon.
The point is that I am transfixed by mathematical concepts, however too much of what I am actually studying in maths at the moment is "Here is an expression. Go through this process, Arrive at the right end-product." This is where the mind-numbing dullness arrives, and I think "What is the point? I understood and was suitably intrigued by the concept the start of the chapter, anything beyond this is just overkill." I am not going to become an engineer where process and calculations becomes important when the results go on to be part of some physical process. Why can't I just leave maths at comprehending the amazingly beautiful concepts?
In this respect, Linear Algebra (what I'm studying this semester) is considerably better than Calculus 2 (last semester) where the one concept is differentiation and integration and the whole subject is about different processes where you use calculus. It is considerably better but still there's a whole lot of process.
Anyway, if anyone's made it to the end of my nerdy maths rant I congratulate you.
Hullo John Rice-Whetton. I suspect they teach maths in this turgid way because a majority of people are far to stupid to ever comprehend the concepts in themselves. They can only achieve a kind of pseudo-understanding which comes through the constant repetition of the process involving the concept. This understanding is limited and uncreative and absolutely useless to the progressive and active mathematician, it does, however, suit the aspiring accountant. Here you must suffer stoically for the masses. Not a noble act unfortunately, rather an ugly, perfunctory and one that should be made with as little notice as possible so as to decrease your pain. Try to project interesting things into your mind's eye when subjected to this gross crime against education and intellect. Yours singularly, Matthew Gregory Schmalkuche.
ReplyDeleteGreetings Gregory! I was considerably surprised, pleasantly of course, to find that you had located this 'blog' of mine, since twitter is the only way I would know to get here, and you haven't tweeted for well over a year. I suppose you still visit that site occasionally then?
ReplyDeleteAs for the content of your comment, I can only say that I agree whole-heartedly!
I hope you are well, and I hope to catch up soon.
Yours Philously, John