><i>"Or, take the mathematical series called the 'Fibonacci series'. It shows up all over the place in nature; nobody knows exactly why. If you take a sunflower and you look at the flower, it has spirals that go in different directions. The number of parts that appear in adjacent spirals are related to one another as successive terms in the Fibonacci series. You find that kind of thing all over nature; it is not well understood why. There is something about the physical world that forces certain kinds of structures to emerge under particular conditions."</i><p>So this is why I find Chomsky's conclusions to be suspect when he speaks about topics of which I have no understanding: he's often casually incorrect about topics in other fields. We understand why the Golden Ratio shows up all over the place, especially in biology: it doesn't.<p>In reality, it's the logarithmic spiral that's common, and it's a due to logarithmic spirals being a necessary characteristic of certain structures that exhibit self-similarity.<p>This quality was well known to Renaissance and Enlightenment era mathematicians and physicists, as well as to the ancients as the "spira mirabilis", or "marvelous spiral." But it seems to have lost favor in the modern era to a mythos surrounding the Golden Ratio Phi and the Fibonacci sequence.<p>For example, Jacob Bernoulli, the famed mathematician and no stranger to the Golden Spiral and the Spira Mirabilis, requested the latter be placed above his headstone, with the inscription "Eadem mutata resurgo," meaning "Although changed, I shall arise again," a reference to the then well-understood ability of logarithmic spirals to change scale while preserving shape.<p>Living organisms likely exploit this property of self-similarity for easy scaling. It's likely helpful to sunflowers to maximize the area of solar exposure, and snails to maximize living space. Once an organism evolves a roughly spiral structure, logarithmic spiral patterns are easy local maxima for the evolutionary algorithm to find, because it gives organisms the ability to scale aspects of their biology without major structural changes. Non-living systems exhibiting logarithmic spirals, such as certain galaxies, are a result of various (different) physical forcing functions that cause self-similarity to arise.<p>One way to debunk the pseudo-mystical notions surrounding Phi is to very carefully measure the spirals themselves. What you'll actually find is not a series of systems all approximating the same Golden Spiral, but rather very different systems all exhibiting different logarithmic spirals, with the shared characteristic of self-similarity.