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Archive for September, 2007

Discovering Phibonacci

For the past six months, I’ve been listening to a lot of Maynard Keenan’s work, such as Tool, A Perfect Circle, and some of his other not-so-popular music. The symbology that he uses in his music and lyrics in pretty amazing. One particular instance is the use of Fibonacci numbers in the song “Lateralus.” The intro is as follows:

Black
And
White are
All I see
In my infancy
Red and yellow then came to be
Reaching out to me
Lets me see
There is
So
Much
More and
Beckons me
To look through to these
Infinite possibilities
As below so above and beyond I imagine
Drawn beyond the lines of reason
Push the envelope
Watch it bend

The lines portray the syllable count of 1, 1, 2, 3, 5, 8 the first six numbers of Fibonacci’s sequence, and the reverse, indicating the “spiral” that is talked about in the song. This, along with several other instances of Fibonacci numbers and calculations, interested me in the sequence and numerology in general.

While in study hall one day, I got bored, and wrote out the sequence. I thought to myself, “There must be some sort of pattern or formula to this.” So I sat there and started dividing each of the numbers by its term, then divided each of those numbers by the previous set, and found that the number, as I continued to calculate, increased by very small amounts, those decreasing each increment. Getting bored with doing each by hand, I created a program to calculate this approaching number for me, and named it “FIB.”

Surprisingly, my calculator got to the point where the numbers were so large that the calculations weren’t being executed correctly. I thought about why this would happen, and came to the conclusion that it was the terms by which I was dividing that elongated this number-finding process.

I made another program called “FI,” taking off the “B” from the last one, and took out the term divisibility section, and executed the program. I got this number, 1.618… And didn’t really know what it meant. I messed around with it a bit, trying to figure out if it was a square root of a number, or something similar, but when I squared it, I got 2.618… the remaining decimals staying there. It was pretty amazing, a number, if squared, was the same as adding one to it.

x2 = x + 1

This inspired me to start doing other calculations that don’t pertain to this topic. I did a bit of messing around, and remembered the number Phi, from Dan Brown’s books, and my previous math classes. I have no idea why it took me this long to realize it… I feel kinda ashamed about it.

But the whole concept of the Golden Ratio, Phi, is pretty amazing. I’ve read a few articles relating Phi to the human body, and other natural occurrences. Now it is one of my obsessions in the mathematics world, and an object of my boredom being turned into something productive.

Looking into the past

Because of a star’s gigantic mass, it affects the objects around it, pulling them in closer, the intensity depending on its density. Eventually, some stars will turn into a black hole, where its escape velocity is faster than the speed of light. When a light beam is flashed enough to one side of the center of the black hole (if you could locate it) to avoid being sucked in by the black hole, it would curve around the black hole, coming very close to the event horizon. This would cause it to either loop around and eventually be sucked in, or be shot out again after curving around the hole.

What if we could look to the edge of a black hole? If accurate enough, we could aim our viewpoint so it would loop around the black hole, and shine directly back towards us, showing us ourselves. And because light doesn’t travel instantaneously, the image we would be looking at would be historic.

And, if our aim was even more accurate, we could allow the light to loop the hole multiple times, then shine back to us, being even older. We could look at the earth 4.5 billion years ago, when it was still forming, or 65 million years ago, to watch the dinosaurs become extinct. We would be able to observe the past, and rightfully, prepare for the future.

Gridlock Enabled

Over this past weekend, I switched over from my Unbalanced theme that I had been working on, to Gridlock 1.4 by hyalineskies. It uses sIFR to render most of the headers, which makes them look fantastic. I added six of the “Secondary Features” to display the latest in each of the most popular categories.

I also cleaned up the categories so I now have eight stable cores, instead of the 20-some I had a week ago… I’m still trying to decide if I should make sub-categories.