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Comment by kaler on Welcome to Less Wrong! (7th thread, December 2014) · 2015-02-05T14:12:37.450Z · score: 0 (0 votes) · LW · GW

define a "complex number"

My best guess: A ball with a radius X and a rotation Y. Inflate it when multiplying with a real number. Rotate it when multiplying with an imaginary part.

//My thoughts: Rotation of objects? another type of object that interacts with ordinary numbers in multiplication and division? i is a number that can be visualised running perpendicular to a real number line. Euler formula?

//I have Y objects. I can allocate them to X sets and get X objects in each set. X is the root of Y. If I owed Y objects, then I can allocate ... Ok I don't know where to go from here.

//A complex number is a number of objects, where some or none of those objects are roots of debts.

Comment by kaler on Welcome to Less Wrong! (7th thread, December 2014) · 2015-02-05T13:44:34.994Z · score: 2 (2 votes) · LW · GW

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!

Comment by kaler on Welcome to Less Wrong! (7th thread, December 2014) · 2015-02-05T13:21:54.245Z · score: 1 (1 votes) · LW · GW

Thank you for the reminder that precision in language is very important. I learnt that in the Knowledge and Inquiry course I was enrolled in. Thank you also for taking time and effort to type out that reply. It is deeply comforting and a great encouragement to me.

Comment by kaler on Welcome to Less Wrong! (7th thread, December 2014) · 2015-02-05T13:11:42.940Z · score: 1 (1 votes) · LW · GW

Thank you so much for this, CCC. You really made my day.

I think I overcomplicate things. When I read your answer, I was thinking, (seriously no offense because I know you are really smart) I don't know for sure that this definition works for complex numbers. I was wondering how I could conceptualize it.

And then I was thinking that mathematics relies on definitions and deductive reasoning and intuition cannot give the certainty of deductive reasoning, thus it might be a fallacy to think that something simple and intuitive is an accurate model of mathematical reality... then I remembered that it was taught in kindergartens even... Sucks to have my mindset, doesn't it?

I also keep thinking that I can't be sure that I covered all possible cases with my definition - another major problem of mine.

Define "multiplication"

X*Y : I have Y sets of X objects, how many objects do I have? Works with fractions, and negative numbers (thinking in terms of debts).

"addition"

X+Y : I have X objects. I am given Y objects. How many objects do I have? Again works with fractions and negative numbers. It's easy to visualize imaginary numbers as another type of object 'x', and I am given y objects. So I have x + y imaginary objects and X + Y real objects.

"subtraction"

X-Y : I have X objects. Y objects are taken away from me. Again, same question, and works with fractions and negative numbers, and having 'x' and 'y' objects helps me deal with imaginary numbers.

What I've been wondering is why y – y1 = m(x – x1) works but m = (y - y1)/(x-x1) does not include the point when x = x1. After learning what you've taught me, it is intuitive that these two equations are very different (in terms of giving and taking apples).

But before today, it shocked me to think that we can't always manipulate algebra by dividing both sides by something, and I have to be extremely careful. Then it makes me wonder what other exceptions to manipulation there is, and what kind of deductive reasoning is in use here, if there are exceptions.

I also wonder that teachers and professors have not been telling me all the exceptions to different types of manipulations and that I don't know the limits of my mathematical knowledge, or whether even any of it is completely true. I guess it's similar to how a rotten apple makes the entire basket go bad.

Comment by kaler on Welcome to Less Wrong! (7th thread, December 2014) · 2015-02-05T12:13:30.254Z · score: 1 (1 votes) · LW · GW

Wow! Thank you so much for your time and effort in typing out that reply!

(I'm not actually sure what the difference between Second Upper and First Class Honours is - I assume that's because you're referring to the education system of a country with which I am not familiar).

Well, About 3-5 percent of the best students in a cohort can expect to get First Class Honours. It basically means 97th percentile, or 95th percentile, depending on the quality of the students. The 75th to 95th percentile can expect to get Second Class Honours.

Define "division".

I must admit that this question stunned me. I don't actually know. What first came to my mind is that it is some sort of algorithm (case 1: two integers that divide cleanly, case 2: two integers that divide to make a fraction, case 3: an unknown ...) that has useful applications (e.g. it is useful to know that you can divide 6 apples by 3 people to allocate 2 to each person). This is my shot at a definition: division is an operation that gives the ratio of number/function F and another number/function G. The ratio can be determined by seeing how many of G can be added together to comprise F. It can be a fraction/real number/complex number/function. Argh. I am stumped. This definition seems like Swiss cheese.

Comment by kaler on Welcome to Less Wrong! (7th thread, December 2014) · 2015-02-05T10:41:20.285Z · score: 3 (3 votes) · LW · GW

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!

Comment by kaler on Welcome to Less Wrong! (7th thread, December 2014) · 2015-02-05T09:28:20.574Z · score: 6 (6 votes) · LW · GW

Hi! Lesswrong first came to my attention when I read HPMOR. I took a 2-year course in Knowledge and Inquiry - which includes critical thinking and epistemology (also includes philosophy of science). I was a Christian but reading some articles on Lesswrong and reading counter-arguments to Christianity convinced me otherwise (trying to reduce confirmation bias and trying to falsify the belief of Christianity).

Pardon me for taking this opportunity to express one concern I've had for more than a year. I'm a college student and I am concerned that I am not smart enough expect a net gain in utility by aspiring to rationality (added in edit).

I don't do well in Math (about 60th percentile for multivariable calculus), but consistently do relatively well in Physics, Chemistry, Engineering and Programming modules. (consistently in top 8 percent of students in top university in Asia). I'm in a double degree in Chemical Engineering and Business and on track to receive at least Second Upper in both (First Class in one and Second Upper in the other seems to be the most likely outcome, though of course I am striving for First Class in both. I am usually too pessimistic when it comes to grades and honours).

Yet I find it difficult to multiply two 2-digit numbers in my head. I always forget what numbers I was trying to multiply and the progress of the multiplication so far. I tried Dual N-Back and had to work for half an hour to pass n=2. I can't remember numbers and always make tons of errors in my mathematics work (not switching signs for one or more terms when factoring out a negative number, for example, or just plain getting stuck).

I'm worried that my fluid intelligence just isn't enough. I'm also quite sad at the expectation that my fluid intelligence will decrease throughout my adulthood. 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). Should I aspire for rationality or am I too stupid?

Thanks!

Edit: I'm also in another predicament - I am no longer a Christian, but I still go to church every week. I treasure the friendship and companionship of my Christian friends. They are really nice and caring people. I cannot predict reliably what their reactions would be to me revealing the current status of my beliefs. I meet them only once a week in church and if I were to stop going to church, our friendship would most likely perish.

There are other benefits to going to church as well: Here, church is a marketplace for contacts and relationships. I believe going to church would help me in the future if I were to go into business.

However, my parents and all my relatives who are descended from my paternal and maternal grandparents are Christians, and most of my extended family beyond that are Christians. My parents are devoted Christians and it would break their hearts to find out that I am no longer a Christian. My relatives would judge me and proclaim me a failure. Most of our Asian community would do the same (Where I'm from, it is considered odd, or mad not to have a mainstream religious belief. We are categorized by religion as much as we are categorized by race). Even if I were to succeed financially, they would say that I am not someone to be trusted because I am somehow immoral for rejecting Christianity.

Would anyone care to offer my some advice?