After every exercise read of a Chapter, I would like to write an after-thought post on how I think. I wrote one for Chapter 2 so I will also write one for Chapter 3.
I finished Chapter 3 much faster than Chapter 2. Mainly because Chapter 3 is more mathematical than algorithmic. So I usually spent less time in implementation. Though it's interesting to see that Chapter 3 gave me more pain because some of the problems simply requires more than normal amount of creativity.
There was once I read a post by Prof. Terrence Tao, widely known as the "Mozart in Mathematics" and the youngest professor in the history of UCLA's Math. department. In the post, he encourage young researchers to think and innovate. At the same time, he also suggest when you got stuck, you should revisit old proofs, old exercises.
When I first read it, I am quite surprised. These kinds of advice are usually from Math Tutor to non Mathematical inclined students. But when you think about this, this is actually a great advice.
We usually think Math and Science as a kind of chain process - one reason is derived from another. You can visualize this by thinking the arrow of implication go from one argument to another. And progress in Math and Science is simply whether we create a new arrow. And the speed of progress depends on how fast these arrows create.
So if you thought in this mode, then what really matter is
who is working on a problem. Because if a person a
"smarter", then they can certainly solve a problem faster.
I believe this view is wrong. Why?
In real-life, people who can solve problems in a particular field (or a task) are usually people who
associate more. That is to say, if you can associate concepts to your problem, you would be more likely to resolve an issue.
That explain a lot of sayings in Math learning like "
You should learn the fundamental well".
At a certain level, a different point of view will bubble up. Like Prisig, let's call it the Romantic point of view, that is to say ideas such as
Intuition, Creativitiy become more important. I believe there is certainly degree of truth. But intuition and creativity always mean somebody has a mysterious hunch to get a problem solved. It doesn't really explain why
such hunch exists in the first place. That makes me believe the theory of association is a better view. Another advantage of it: it is something one can acquire by hardwork and it's learnable.
That is why I believe my read in Chapter 3, though a bit painful, it won't be a flop. I learned something in that process. To really quantify, I need to count how many factoids I acquired. But it is how human learn.
Similar issues will come up in Chapter 4. I hope I can use the same mind set to resolve the problems
