April 2, 2007

hood_ornament.jpgI’m not claiming to be a genius at math, but I have been around the block once or twice. My ill-fated math carreer started off in 7th grade with me getting bored in pre-algebra and finding out I could ‘skip’ classes. A couple years later I figured out I could skip unwanted teachers and so I took geometry over the summer to avoid two years of “personality incompatibility”. My efforts were in vain as I spent Trigonometry and Calculus I under the watchful gaze of Mrs. Stewart. That was when I adopted the phrase “C is for Calculus.” After that, I suffered from math brain damage/aversion for two years then tried to tackle Calculus II my sophmore year in college. Combined with the Computer Science Matrices and discrete math course and statistics I have had a wide view of the abyssal depths of math. In conclusion, I like math because it is useful and fun. Savvy?

So along the way I’ve run into a lot of really wierd things. In fact, I think there are more wierd things in math than things that follow common sense. My professor Draper, when teaching on Fourier Sampling entitled his slide “Fourier Analyspi.pngis Magic“. I think it says a lot that he had to tell us this, since it wasn’t obvious to a room full of computer scientists. Maybe our definition of magic is just skewed? What strikes me about this is that with the exception of algorithms everything in math is discovered, not created. Remember fractals? Here’s a couple examples for you with illustrations by xkcd. (Sorry for the language, I didn’t write it.)

Pi is the ratio of a circle’s circumference over it’s diameter. Apparently, it also made a pretty interesting movie. I haven’t watched it yet. If you bring the movie I’ll provide the nachos. Pi occurs entirely in nature, no human being wrote Pi, it simply exists. It’s an infinite number with no way to express it that is not some kind of algorithm (to the best of my knowledge). Because Pi is infinite it is the subject of a lot of jokes because you’re never 100% accurate, scientists hate that.

E to the Pi times i
This is the most inexplicable thing I have ever seen. E is the natural logrithm, for things like compound interest and bacterial growth. Pi is the circumference of a circle divided by its diameter. ‘i’ is used to express numbers at a right angle to “real” numbers (read reality). So what is the interest on my circle in imaginary space? It’s -1 of course.

Universal Constants
The rabbit hole continues further down as we realize that physics, the way of describing our universe, is merely an extension on math. We run into these naturally occuring, often infinite, numbers all over the place. The catch about physics is that if you mucked with these seemingly arbitrary numbers a lot of them would wipe out all life on this planet. Stephen Hawking spends a lot of time talking about this in his book Universe in a Nutshell.

Math is cruel.

Go to XKCD.com

Further Comments: Bwahahaha. If you’re in the mood to seriously hurt your brain I just found out someone has created a 5 dimensional Rubiks cube. Like we didn’t already have enough people jumping off tall buildings. The even more obscene thing is that it’s actually been solved! Check out the list of people who have been crazy enough to tackle this. MagicCube5D. Also, the 120 cell puzzle looks like it has an even higher chance of causing permanent mental breakdown. We’re messing with dangerous forces here. I wonder what the mortality rate is?


One comment

  1. E to the Pi times i is insane. It’s fascinating that two numbers that people have discovered and a third that isn’t “real” combine into something so normal.

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