Sunday, January 3, 2010

Thoughts on the New Years Growth with Fibonacci

Fibonacci was a 13th century mathematician.   His family name was Bonacci, and somehow Family Bonacci became known at Fibonacci.  He was famous in his day, and still is.  Let me start at the end:


He came up with a series of numbers, that by sequential adding, created a ratio that quickly converged on a certain number .618.   People call this magic number "phi".   See the table below, it's pretty neat, I did it with my own spreadsheet. By dividing the fib numbers the reverse way, you converge quickly to Phi=1.618 which has its own interesting relations to phi.

Some interesting relations 1-phi = phi Squared = 1/(Phi Squared) = 38.1%
Some Math Head came up with phi = (SQRT (5)-1)/2, Exactly

Since it's Sunday AM, my slow moving brain concludes that no other Base 10 number can possibly have these same properties.  I wonder about other numbering bases.  After all, we have 12 moons in a year, 12 hours in a half day, 12 eggs in a dozen, 12 fingers....oh wait.  Base 12 is hard to work with and you can't count on your fingers.....

The Elliot claim is that the Fibonacci Series also described precisely many growth patterns of shells, plants, vein systems.  However, full  disclosure...there are many growth patterns that are spirals that DO NOT use the Fibo phi or Phi as a base, but many do.

Riddle me this---The Fib Sequence is based upon a numbering system called Base 10.   There are an infinite number of counting systems, Base 2, Base 3, Base 23, Base 77, whatever.

What would a Fibonacci Series look like in different numbering systems?   Why is Base 10, somehow a "magic" system to create a Fib Series that then describes so many natural phenomenon?

Did we as humans migrate to the Base 10 just because it somehow fit with our basic nature and effects upon the physics of the world in the way that natural items become ordered?  This seems rather extreme.

The base 10 appears to be an Indian invention, Centuries before the Family Bonacci.
Or are we forcing things into patterns?  And the Base 10 Fib just happens to get lucky based on "things change a certain amount" while bouncing around in cycles.  The human brain is great at finding patterns, it simplifies the massive information that comes at us.  For the most part I think this is a valuable thing, but the potential for misleading information should not be ignored.

Anyone have any input on this line of thinking?

The following is the Fibonacci Series, created with a 5 minute spreadsheet.

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Insightful and Useful Comment!