Resonant Constellation

Today I was bored beyond all belief-my optics teacher decided that today would be a great day to repeat everything he’s been saying for the last few weeks. I had been listening to the album Lateralus by Tool and I remembered that the title track features a chorus wherein the syllables of each line form the first few numbers of the Fibonacci sequence. Observe:

Black, (1)
Then, (1)
White are, (2)
All I see, (3)
In my infancy, (5)
Red and yellow then came to be, (8)
Reaching out to me, (5)
Lets me see. (3)
There is, (2)
So, (1)
Much, (1)
More and, (2)
Beckons me, (3)
To look through to these, (5)
Infinite possibilities, (8)
As below so above and beyond I imagine, (13)
Drawn outside the lines of reason, (8)
Push the envelope, (5)
Watch it bend, (3)

Pretty neat, huh? There’s lots of interesting mathematical things in that song, but the Fibonacci sequence thing is the coolest. So in my bored state I decided to set out to compute the Fibonacci sequence as far as I could go. It begins easily enough, but with the addition of each new digit the computations become a bit harder. I got to the 113th term before I stopped (this lasted well beyond the end of class, extending into the astrophysics colloquium I always attend). Now, I’m sure there’s mistakes in there somewhere, by the end I was adding 24 digit numbers, and you can’t do that too long without introducing error. Still, I’m relatively proud of it and I was vastly intrigued by the patterns that emerge. The first few numbers appear all over the place (as soon as you get two 1s in a row, you’re pretty much bound to get the sequence). Perhaps I shall continue in a more structured way later. Aside from that, it was a wonderfully diverting way to pass the time and I quite enjoyed doing the math, even though it was simple.