We see Fibonacci series in the way the flowers are made in, the spiral galaxies are formed by, or even so many parts of organ of creatures are biologically evolved over time ( say hard shell of snell etc). Even of late, we have observed notion of golden ratio to be present in quantum mechanics.
Dear Samit,
certainly, Fibonacci numbers cannot explain everything in nature (btw "42" is not a Fibonacci number...). However, they play an important role in nature. One possible reason for that is that the golden ratio is known as the "most irrational number". This has important consequences e.g. for the stability of dynamical systems as reflected by the KAM theorem which states that the movement of a classical three-body system is most robust against perturbations if its frequency ratio is the golden ratio.
Samit,
Q1: It is not a terribly special series.
Q2: No.
There are many numerical series hat, if you look for them, will emerge in phenomena of the real world. We don't get excited by spotting power laws at work in earthquake discharges or in flood events - but perhaps we should.
Just because phenomena may display similar numerical properties does *not* imply that there is a causal or factual link.
The convection cells in a pan of boiling soup may arrange in a hexagonally-packed manner. Does this mean that honeycombs in bee hives are related to boiling soup? Or snowflakes?
No.
What you are seeing, in terms of geometric similarities is the consequence of finite small-number dimensions and evolution's 'desire' to make fitter organisms with fewer failures and less material.
I concur with Peter that there are some numerical series that *are* more prevalent as they exhibit particularly 'robust' properties. But they are not answers to life, the universe, and everything.
-What's so special about Fibonacci Series? - The idea behind it is simple and ordinary people could easily grasp that idea. That's why it is special. Power law is not that easy to explain. Also the name Fibonacci is catchy. This is what authors of fiction need. Then, this series becomes very popular with the masses. Thus, the fuss about it.
- Can it explain how everything evolved in nature? - No!
I concur with the guys above.
To me Fibonacci series is a specific example of the more general Farey series that allow to approximate irrational number by rationals (continued fractions). All irrational can be approximated by a continued fraction but the convergence speed varies. The golden ratio, corresponding to the Fibonacci series, is the hardest to approximate (slowest convergence). This mathematical property has a physical consequence: dynamical systems exhibit resonances which can have a dramatic impact on stability. There are known examples (KAM theory, Arnold tongues) where the stability of a system depends whether its naturall frequency is close to a rational number. The more distant the natural frequency is from a rational number, the more robust it is. In such systems, the more robust natural frequency is therefore the one corresponding to the golden ratio.
As already mentioned by others before, I also consider the fact that Fibonacci series can be related to the golden ratio, self-similarity, power laws, quasicrystals, and fractals quite appealing. I think it is a nice way to connect a simple series of integer number to some of the most complex phenomena observed in nature.
@James Garry: Actually, what interests me is the the possible connection between mathematical laws and rules and the very real-world phenomena. I wonder if life can be explained in plain mathematical stuffs, the way it has evolved. BTW, living-body is nothing but made of atoms, molecules and all the mechanisms in it can be very much mathematical. Fibonacci series has been observed in the structures of flowers, epidermis of snails, distribution of galactic masses in spiral galaxies. So , I feel there could have been some sort of reasons of explanations.
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