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I will talk all about my trip to NYC in due time folks. All in due time. Krystal, Saab and I were talking about math, and specifically people's impressions of it. When I tell people that I have a degree in math, I get some rather extreme reactions. Women often make up their faces like they are having some sort of fit. Really, I'm not kidding. Some immediately seem to regress to being 14 years old again (I can almost see their tits shrinking. I'm kidding.). Their eyes glaze over, they become timid and sad, very sad. Sad because they feel so stupid compared to, me, I guess. They are back in Grade 9 with a frustrating teacher that is growing impatient with their lack of progress. Others start shaking their heads rather quickly, like they are trying to shake the memory of math out of their heads. In almost every case, they say, "Wow. I can't do math." Men react differently. The men either did okay in math, or they didn't care then, and still don't. Sometimes it seems that they are saying, "Math...Cool." but are thinking, "All right there, egghead! I hope he doesn't start trying to prove shit or anything." It's a real shame that people have this negative impression of math. It's just a subject like every other one. Anthropology. Biology. Math. They're just subjects. I only have a degree in math because it's the only one I could get without doing any term work. But math is a beautiful thing. It's artistic. It's ordered. It's chaotic. It's everything. But it's nothing. And as far as I am concerned, existence of math => existence of God, but that's another entry, or debate. Many people believe that math geeks are rigid, unimaginative and uninspired. When we see clouds, they're only clouds. Being the mathematician that I am, I am going to prove that this isn't true. **DISCLAIMER** The following will be a long-winded, but rather simple mathematical and philosophical discussion. If you don't think you can hack it, try another entry, or another diary. Number systems have developed over thousands of years, but intuitively we know what most of these systems are, and what they mean. When we started counting things, we discovered the counting numbers, 1, 2, 3, etc. Immediately after, we discovered the addition operator. 1+2=3, we found. And when you can add things, you can take them away. 3-2=1. But what if you took everything away? 3-3=? We needed a new term, and that term is zero (0). A new number system was born. Eventually we discovered a meaning for 5-6, and negative numbers were found. All the numbers we had at this point came to be known as the integers. Then through division we got the fractions, or rationals. Finally we found special numbers that aren't expressible in terms of ratios of integers, but are still "visible" interspersed among the rest of the rational numbers, namely the irrationals. Some of these you know. Pi is such a number. The square root of 2 is another. All of the rationals and all of the irrationals together form the real numbers, the set of which is easily thought of as a line. All the numbers you know and easily conceptualize fall on the real number line. In fact, much of our collective (physical) reality pretty much falls on this line. Ever notice that you can't multiply a number by itself once to get anything less than zero? That is, for any real number x, x*x=x2 is always greater than or equal to zero. That means that you can't take the square root of anything less than zero. If the square root of -1 did exist, then it certainly doesn't lie on the real number line. It's not part of reality, not on this plane (I'm not using that word mathematically here) of existence. Let's say that the square root of -1 did exist, just for shits and giggles. Let's call this imaginary number i. That means that i2=-1. Without getting into the details, we have just extended the real number line and entered the complex plane. In other words, we have created a whole new number system that uses its own rules and theorems as well as some of the ones you know. We have transcended reality and have entered another dimension. We know the number 5. Its purely imaginary counterpart, 5i, is like a ghost or an otherworldly shadow to us. We can't see it or touch it, but we can prove that it exists. Think it sounds fishy? Besides making certain mathematical calculations much simpler, or possible, complex numbers are already well-known and applied in the field of electrical engineering. Ren� "I think, therefore I am" Descartes, among others, had the imagination and the faith to imagine a world that does not conform to the physical realities imposed on us by the real numbers. We know that much of art and music is mathematical. Can you imagine what kind of music you could listen to in the complex plane? A world where the order of numbers, and therefore notes, has a very different meaning? (There are an infinite number of complex numbers of size 1, but only two real numbers that size, 1 and -1. That WILL screw up the way you put numbers in any order.) Mathematicians imagine these things all the time. They, we, are just like everyone else. We dream. And so ends my "proof". I know it isn't as rigorous as some would like, but I hope you get my point. We do good and worthwhile things. Perhaps I should get back to a classroom, or at least brush up on my complex analysis. 0 scrawls at the end of this hallThe look: The feel: The taste: ________________________ |
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