We were supposed to write about three "How to..." blog posts. I have some ideas, but they remain nebulous now: I could write a "How to..." post on "How to Be Good at Math at Any Level," or "How to Cope with Bipolar Disorder," or "How to Read a Person Like a Book." Of these three, the reading a person like a book will be the hardest for me. Indeed, such a post will likely be full of irony, since I read books better than people. So, without further ado, I present

How to Be Good at Math at Any Level

Introduction

Mathematics is a discipline; indeed, it is the discipline, since the word mathematics comes from the Greek mathein, or "to discipline." So, in order to be good at math, one needs to be a good disciple. We need to be able to listen or otherwise receive teaching, whether it be from a teacher or from nature itself. Humility is very important in mathematics, because we are bound to make mistakes. This is in contrast to the popular perception of math, in which everything has to be precise and, dare we say it, correct. Nothing can be further from the truth, for mathematics rests on nothing.

We begin with the empty set { }. Is the set something, or is it not? We assume that it contains nothing, so if there's nothing to talk about, then we are done. However, if the empty set is something, then we can construct another set containing it: {{}}, and from there another set with different elements, {{},{{}}}, and so forth. It is possible this way to construct the entire set of natural numbers N={0,1,2,3...}, and from the set of natural (counting) numbers N to construct the set of real numbers R. Obviously, the latter approach has more describing power than the former, but there is no way to truly distinguish between the two approaches, because we could just as easily say that nothing can contain nothing, and say that something is nothing.

Personally, I don't like such a nihilistic approach to mathematics, so I prefer to make distinctions between something and nothing, or make a distinction between a bag and its contents.

How do we become good at math? We need make as few assumptions as possible, so that we can maximize the number of propositions. This is every bit as true in the field of math as it is in real life. Preconceived notions more often than not hold us back.

What I Believe

It has been said that knowledge can improve the quality of life for both individuals and communities. I have few beliefs in politics or mankind, but I subscribe to the philosophy that knowledge is power, and that using the power of knowledge has more benefits than drawbacks. For example, the misapplication of science has brought about unparalleled suffering – nuclear weapons and genetic engineering for warfare. However, proper use of scientific knowledge applied to medicine and sanitation has benefited mankind far more than scientific warfare has harmed us over the last 100 years.

My personal quest for knowledge began in elementary school, when I decided to first become a scientist. I quickly realized that I had gifts regarding mathematics, languages, and visual arts. In kindergarten, I could count to one thousand, and I could read at a fifth grade level, even though I did not speak at all until I was seven years old. By the time I reached middle school, I had managed to overcome my fear of algebra. Today, I am a mathematics major.

If knowledge truly is power, then I must find a way to continue to learn and apply that knowledge to real world situations. For example, I would like to improve the political system of this nation by becoming a political consultant or a constitutional scholar. I might one day apply my mathematics skills to the creation of a new electoral system for Congress and the state legislatures; for the most important feature of any constitution is the way it represents the people.

Language is the power that makes us truly human – the ability to make meaningful, advanced contact compared to the other animals. For me as an autistic, this is a hard thing to develop well: so much of language is actually non-verbal, with tones, inflections, stresses et cetera that change the meaning of the words actually said. I prefer to think in pictures, much as Temple Grandin does, but it is very hard to communicate casually with icons; words, though easier to use, are inferior symbolically.

For me, art and technology are the same; indeed technë is the Greek word for art. Semiotics, the study of signs and symbols, is also so thoroughly intertwined with art as to be a single organism. What is art, then, should it lack meaning to the viewer, whether it be pleasure or disgust? Art, to me, is meaningful and powerful, and not to be taken lightly. Just as words have meaning, symbols and signs have even more.

Knowledge is power. Use it, but use it wisely.