Friday, August 13, 2010

The Greatest Dispute in Science, Part 2: The Fibonacci Sequence

In Part 1 of this series, we talked about the ancient mathematician's obsession with finding perfection in the form of a circle.

As it turns out, Pi is not the only important ratio ancient humans discovered.  There is another called Phi.  This number is approximated at 1:1.618, and much like its cousin Pi, its an irrational number with an infinite number of decimal points.  One of the important take aways from the history if Pi is that nature doesn't really provide us any evidence of a perfect circle.

This is why Phi is a much spookier number:  Nature does show us this ratio, and not just in one place, but in many places...large and small.  You find this ratio in the sunflower pictured above.  You can find it any tree near your house.  We can find in the limbs and lungs of our bodies.  We can also find it in spiral galaxies.  In fact, this one single ratio, this one number, appears to be everywhere almost as a cosmic signpost.

The Phi ratio is slightly harder to understand than Pi.  The following movie should get up you speed quickly with what Phi means.  Once you understand the ratio, we can talk about its implications more.

Now, no matter what you may think of the mystery apparent here, there is no doubt the ratio is real.  Its occurrences in nature are real as well.  It was here long before humans were; we didn't invent it, we discovered it.

Lets look at this a little closer from our  Chaos vs. Order standpoint.  It has been often said that the fibonacci number connects everything in the universe.  Unfortunately, when you really look at it closely, this is not really true.  The astute eye will notice a commonality in every instance of this number in nature.  Can you spot it?  Its natural growth.  Exponential natural growth to be exact.  We find this ratio only in instances where there has been evidence of some kind of natural growth.

Even so, while it is misleading to say this number exists everywhere and in everything in the Universe, the fact that is seen is just about all natural growth is astounding.  A galaxy 100's of millions of light years away grows at this rate.  The ratio of your forearm to overall arm?  There it is again.  The ratio between a tree's trunk and branch section?  There it is again.  Its also in your DNA.

The next video might point out the "Dan Brown" reality of the fibonacci number a bit better:

Where else might it exist?  There is a new branch of economics called "Elliot Wave" which tends to show strong past stock market correlation with the fibonnaci:

So what does it all mean?  Science really doesn't have an answer as to why this one ratio seems to govern all natural growth, aside from the fact that it tends to be the most efficient form of growth.  In this respect it appears nature tends to favor efficiency over chaos and randomness.

We'll rack one up for order.  Chaos 1 - Order 1

As an added bonus, even a well known rock band wrote a song all around the fibonacci sequence.  Once you understand it, it becomes quite a feat of composition:

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