After reading a post earlier regarding song lyrics and their breakdown, as well as the hidden genius referred to within the lyrics of Mr. Bob Dylan, it got me thinking back to an incredible combination of lyricism and mathematics written by my favourite band, TOOL, on their last album, Lateralus. The genius therein lies with the title track.
First, a little background on the Fibonacci sequence. A mathematician named Leonardo De Pisa (also known as Leonardo Fibonacci) used rabbits to devise his theory. He set a pair of rabbits, male and female, in a controlled environment and studied their breeding patterns. He found that after the first month, the rabbits had mated to create one new pair. After the second month, there was another pair plus the first pair, meaning there were now two pairs. I'm not going to describe the whole process, suffice it to say the numbers came out like this: 0,1,1,2,3,5,8,13,21,34,55,89,etc. If we give the new number created the value of 'n' and the previous number the value of 'y' and the number two before the new one the value of 'x', the equation is a simple one: each new number is created by adding the previous two (n = y+x). This sequence is infinite, and creates what is known in mathematics as 'The Golden Spiral' (if you plot this sequence on a graph using the above equation, it forms a perfect spiral.) For further information and a good watch, check out the Darren Aronofsky film 'PI'.

On to the connection with the song 'Lateralus.' Notice the spelling of the name....LATERAL-US. That's just the beginning of Tool's unbounding cleverness. Now, the opening lyrics in the song are as follows, sung in the syllable structure I've depicted:

Black (1)
Then (1)
White are (2)
All I see (3)
In my in-fan-cy (5)
Red and yell-ow then came to be (8)
Reachin' out to me (5)
Let's me see (3)

I'm not going to write out the whole song, the above verse makes the point. Throughout the song, the majority of lines end in Fibonacci numbers (usually 5 or 8 syllables, but they're EVERYWHERE in the song!)

Pretty sweet eh....but here's the best part! Remember, the Fibonacci sequence forms the 'Golden Spiral.'

Lyrics found later on in the song:

Swing on the spiral (5 syllables!!!)....swing on the spiral of....our divinity and....still be a human (5 syllables!!!)....

If we were able to remove the of and the and from the above lines we'd also have....our di-vin-i-ty (5 syllables!!)

Also, in an amazing sequence of lyrics, they throw in:

With my feet upon the ground
I lose myself between the sounds (8 syllables!!)
And open wide to suck it in (8 syllables!!)
I feel it move across my skin (8 syllables!!)
I'm reachin up and reachin out (8 syllables!!)
Reachin for the random or
Whatever will bewilder me (8 syllables!!)
Whatever will bewilder me (see above!!)
And following our will and when (8 syllables!!)
We may just go where no-ones been (8 syllables!!)
We'll ride the SPIRAL to the end (8 syllables!!)
We may just go where no-ones been (see above!!)
SPIRAL out (3 syllables!!), keep going (3 syllables!!)
SPIRAL out, keep going (see above!!)

Pretty clever huh? But....it's not done there!

During the part where he's singing about weeping like a widow which leads to 'swing on a spiral of our divinity' as depicted above, we hear Adam Jones' guitar playing....1 note...1 note...2 notes...3 notes....5 notes...in FIBONACCI time!! Then he varies with his picking, but they are always Fibonacci numbers!! I'm not even going to get into the connection to PHI and the golden ratios, or what THAT may mean. But, PHI is connected to Fibonacci numbers and their ratios, and found everywhere in nature.....coincidence?? Not with Tool writing the songs.

Go ahead, folks, read up on the Fibonacci sequence and then listen to the song. Count the syllables in each line. The majority of them come out to be Fibonacci numbers, and often they are in the proper mathematical sequence. Just wanted to share this with you folks as TOOL are amazing musicians as well as amazing mind-magicians, and they are releasing a BRAND NEW album (so I'm told) for the first time since Lateralus (circa 2001) on May 2nd of this year!! Pearl Jam is also releasing a new album the same day!! Buy them both....perhaps Tool has embedded some other incredible mathematical gems within this new effort. I certainly hope so, as this made me love and respect the band that much more. Incredible.

By the way, Danny Carey (Tool) is the greatest drummer alive today (respect to Jon Bonham, may he rest in peace...)

For further (and a MUCH better) explanation of Fibonacci numbers and PHI, go to http://en.wikipedia.org/wiki/Fibonacci_number

Sir Smittius