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ChristianKl comments on Welcome to Less Wrong! (7th thread, December 2014) - Less Wrong
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Thanks for the encouragement!
I will try my best to work through the sequences. I have just finished map and territory and mysterious answers to mysterious questions. I noticed that many articles in the sequences confuse me at times because I can think of multiple interpretations of a particular paragraph but have no idea which was intended. Also, many actions/thoughts of Harry in HPMOR confuse me. I might have interpretations of the events but I don't think those interpretations are likely to be correct. Is this normal?
I have edited the post though, I think that saying that I am on track to receive First Class Honours in both is too optimistic. I can say with quite a high degree of certainty that I am on track to receive at least Second Upper in both. But then again, I tend to be too pessimistic when it comes to grades and honours.
I just really don't get why I don't do well in math, which I assume would be the best measure of one's fluid intelligence. Things such as why dividing by zero doesn't work confuses me and I often wonder at things such as the Fundamental Theorem of Calculus. It seems that my mind lights up with too many questions when I learn math, many of which are difficult to answer. (My professor does not have much time to meet students for consultations and I don't think I want to waste his time). It seems that I need to undergo suspension of disbelief just to do math, which doesn't seem right given that a lot of it has been rigorously proven by loads of people much smarter than me. (But yes, I understand there is the Gödel's theorem as well). Is this normal too?
The thing is, I can't find any convincing evidence (maybe a study or something) that fluid intelligence cannot be fully described by mathematical ability (if effort exists).
Thanks again for your encouragement!
A very easy way to improve your writing would be to separate your text into paragraphs. It doesn't take any intelligence but just awareness of norms.
Math.stackexchange exists for that purpose.
Not everybody is good at math. That's okay. Scott Alexander who's an influential person in this community writes on his blog:
Math is about abstract thinking. That means "common sense" often doesn't work. One has to let go of naive assumptions and accept answers that don't seem obvious.
In many cases the ability to trust that established mathematical finding are correct even if you can't follow the proof that establishes them is an useful ability. It makes life easier.
In addition to what CCC wrote http://math.stackexchange.com/questions/26445/division-by-0 is a good explanation of the case.
I hope you don't mind that I have now separated my comment into paragraphs. It's such an obvious problem in hindsight.
Thank you for your reply! It encouraged me a lot!
Accepting feedback and directly applying it is great :)
While yes, that can make life easier, it also means that if the reason why you can't follow the proof is because you're misunderstanding the finding in question, then you're not applying any error checking and anything that you do that depends on that misunderstanding is going to potentially be incorrect. So, if you're going into any field where mathematics is important, it can also make life significantly harder.
It's hard to put in words what I mean. There a certain ability to think in abstract concepts that you need in math. Wanting things to feel like you "understand" can be the wrong mode of engaging complex math.
That doesn't mean that understanding math isn't useful but it's abstract understanding and trying to seek a feeling of common sense can hold people back.
I... think I learnt math in a very different way to you. If I didn't feel that I understood something, I went back until I felt that I did.
I do not understand the difference between an "abstract understanding" and a "feeling of common sense". Is a feeling of common sense not a subtype of an abstract understanding (in the same way that a "square" is a subtype of a "rectangle")?
On the contrary, failing to feel common sense is usually a sign that you don't really understand what's going on. Your understanding of an abstract concept is only as good as that of your best example. The abstract method in mathematics is just a way of taking features common to several examples and formulating a theory that can be applied in many cases. With that said, it is a useful skill in math to be able to play the game and proceed formally.
There's an anecdote about a famous math professor who had to teach a class. The first time, the students didn't understand. A year later, he taught it again. Learning from experience, he made it simpler. The students still didn't understand. When he taught it a third time, he made it simple enough that even he finally understood it.
I will concede that in practice it can be expedient to trust the experts with the complications and use ready-made formulas.
This doesn't seem to be true for anything that's normally analyzed statistically: the stock market, for example, or large-scale meteorology.