So far as I can tell your post is actually "casually wrong". The sunflower seed example given by Chomsky seems to be mathematically well supported as a representation of Phi/Fibonacci sequences [1][2]. There's no mystification going on here, Chomsky is simply saying we don't fully understand the morphogenetic systems that produce these results. You offered some speculation as to why this might be, but so far no formalized results. Rene Thom did some excellent early work in this area, and demonstrated that chaotic dynamics can help to model some of these issues, but the topic is far from fully explored [3].
Whoops, you must have written your response and submitted as I was typing mine. Thank you for saying this far more succinctly and intelligently than I could have (or tried to).
Nautilus shells and sunflower petals are consistently logarithmic spirals, not golden spirals, and deviate from the golden ratio. See e.g. Sharp 2002.[0]
"Starting with the observation that shell spirals are logarithmic spirals, many people automatically assume that, because the golden ratio can be used to draw a logarithmic spiral, all shell spirals are related to the golden ratio, when, in fact, they are not.
Sharp's own measurements of nautilus shells also confirmed that the golden ratio rectangular spiral and the nautilus spiral 'simply do not match.'
Nonetheless, many accounts still insist that a cross section of nautilus shell shows a growth pattern of chambers governed by the golden ratio.
'One of the amazing things about such misconceptions is that it is so widespread, even by mathematicians who should know better,' Sharp observes. 'It is a prime example of why geometry needs to be taught more widely and not only geometry, but the visual appreciation of shape and proportion.'"
There is of course a mystification going on, which is exactly what Chomsky is trying to invoke. I am pointing out that these phenomena are far better understood than "oh, we don't know why there are spirals with a particular magic ratio all over the natural world."
See e.g. Devlin 2007:
"Part of the process of becoming a mathematics writer is, it appears, learning that you cannot refer to the golden ratio without following the first mention by a phrase that goes something like 'which the ancient Greeks and others believed to have divine and mystical properties.' Almost as compulsive is the urge to add a second factoid along the lines of 'Leonardo Da Vinci believed that the human form displays the golden ratio.'
There is not a shred of evidence to back up either claim, and every reason to assume they are both false. Yet both claims, along with various others in a similar vein, live on."[1]
There's only one leap I'm making here, but it's the only logical hypothesis I've heard: that the self-similarity of logarithmic spirals is the reason for their apparent prevalence.
Comments
So far as I can tell your post is actually "casually wrong". The sunflower seed example given by Chomsky seems to be mathematically well supported as a representation of Phi/Fibonacci sequences [1][2]. There's no mystification going on here, Chomsky is simply saying we don't fully understand the morphogenetic systems that produce these results. You offered some speculation as to why this might be, but so far no formalized results. Rene Thom did some excellent early work in this area, and demonstrated that chaotic dynamics can help to model some of these issues, but the topic is far from fully explored [3].
[1]: http://www.popmath.org.uk/rpamaths/rpampages/sunflower.html
[2]: http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci...
[3]: http://www.amazon.com/Structural-Stability-Morphogenesis-Adv...
Whoops, you must have written your response and submitted as I was typing mine. Thank you for saying this far more succinctly and intelligently than I could have (or tried to).
Fairly certain of the following:
Nautilus shells and sunflower petals are consistently logarithmic spirals, not golden spirals, and deviate from the golden ratio. See e.g. Sharp 2002.[0]
Sharp's own measurements of nautilus shells also confirmed that the golden ratio rectangular spiral and the nautilus spiral 'simply do not match.'
Nonetheless, many accounts still insist that a cross section of nautilus shell shows a growth pattern of chambers governed by the golden ratio.
'One of the amazing things about such misconceptions is that it is so widespread, even by mathematicians who should know better,' Sharp observes. 'It is a prime example of why geometry needs to be taught more widely and not only geometry, but the visual appreciation of shape and proportion.'"
There is of course a mystification going on, which is exactly what Chomsky is trying to invoke. I am pointing out that these phenomena are far better understood than "oh, we don't know why there are spirals with a particular magic ratio all over the natural world."
See e.g. Devlin 2007:
"Part of the process of becoming a mathematics writer is, it appears, learning that you cannot refer to the golden ratio without following the first mention by a phrase that goes something like 'which the ancient Greeks and others believed to have divine and mystical properties.' Almost as compulsive is the urge to add a second factoid along the lines of 'Leonardo Da Vinci believed that the human form displays the golden ratio.'
There is not a shred of evidence to back up either claim, and every reason to assume they are both false. Yet both claims, along with various others in a similar vein, live on."[1]
There's only one leap I'm making here, but it's the only logical hypothesis I've heard: that the self-similarity of logarithmic spirals is the reason for their apparent prevalence.
[0]https://www.sciencenews.org/article/sea-shell-spirals
[1]http://www.maa.org/external_archive/devlin/devlin_05_07.html