3 simple points to end the discussion with any atheist

[Angrboda]

Fibonacci Flim-Flam

Fossil molluscs. None of these are Golden spirals. © 2008 by John Holden

Fibonacci Foolishness.

A search of the internet, or your local library, will convince you that the Fibonacci series has attracted a lunatic fringe of Fibonacci fanatics who look for mysticism in numbers and in nature. You will find fantastic claims:

• The "golden rectangle" is the "most beautiful" rectangle, and was deliberately used by artists in arranging picture elements within their paintings. (You'd think that they'd always use golden rectangle frames, but they didn't.)
  
• The patterns based on the Fibonacci numbers, the golden ratio and the golden rectangle are those most pleasing to human perception.
  
• Mozart used φ in composing music. (He liked number games, but there's no good evidence that he ever deliberately used φ in a musical composition.)
  
• The Fibonacci sequence is seen in nature, in the arrangement of leaves on a stem of plants, in the pattern of sunflower seeds, spirals of snail's shells, in the number of petals of flowers, in the periods of planets of the solar system, and even in stock market cycles. So pervasive is the sequence in nature (according to these folks) that one begins to suspect that the series has the remarkable ability to be "fit" to most anything!
  
• Nature's processes are "governed" by the golden ratio. Some sources even say that nature's processes are "explained" by this ratio.
  

Of course much of this is patently nonsense. Mathematics doesn't "explain" anything in nature, but mathematical models are very powerful for describing patterns and laws found in nature. I think it's safe to say that the Fibonacci sequence, golden mean, and golden rectangle have never, not even once, directly led to the discovery of a fundamental law of nature. When we see a neat numeric or geometric pattern in nature, we realize we must dig deeper to find the underlying reason why these patterns arise.

Golden Spiral Hype.

The "golden spiral" is a fascinating curve. But it is just one member of a larger family of curves/spirals collectively known as "logarithmic spirals", and there are still other spirals found in nature, such as the "Archimedian spiral." Each spiral is the result of physical processes that are worthy of study, and there's nothing mystical about them.

It's also not difficult to find one of these curves that happens to fit a particular pattern found in nature, even if that pattern is only in the eye of the beholder. But the dirty little secret of all of this is that when such a fit is found, it is seldom exact. The examples from nature that you find in books often have considerable variations from the "golden ideal". Sometimes curves claimed to fit the golden spiral actually are better fit by some other spiral. The mere fact that a curve "fits" physical data gives no clue to the underlying physical processes that produce such a curve in nature. We must dig deeper to find those processes.

Many books about Fibonacci numbers feature dust jackets with pictures of spirals from nature. This helps sell the books, because people like pretty pictures.

Order in the eye of the beholder.

Sometimes the authors who write "gee-whiz" science books for the layman engage in "Fibonacci fakery". We cite a few examples.

Nautilus shells. Consider the commonly seen assertion that shells of the Chambered Nautilus conform to the golden spiral. The photo on the right shows one that has been sawed carefully to show the inner chambers. For comparison, the actual golden spiral is shown on the left. Clearly this creature hadn't read the books! If these two were superimposed they wouldn't match no matter how they were scaled or aligned.