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It is often claimed, in popular media, that the golden ratio (Fibonacci series) in for example some face measurements is aesthetically (and hence reproductively) attractive with respect to the humans. I wonder if this is particular for today's (maybe since 10,000's of years or so) human anatomy and aesthetics. As in an after-the-fact acquired taste which was culturally psychologically emerged from the actual human ratios of anatomy as it has happened to evolve for whatever practical reasons, way out of intuitive comprehension for human consciousness. Or if it is deeply biological and evolutionary across all lifeforms.

Is the golden ratio as verifiable (if at all) also for the primates who came before us? Some examples are easy to find, but how statistically significant is the golden ratio as an advantage for sexual evolution for non-humans?

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  • $\begingroup$ Interesting question. However, I'd consider removing the subjective sections in your second paragraph, as the question is not really about what you individually find attractive but what the pool of reproductively capable peers find desirable in a mate. $\endgroup$ – blep Jun 4 '15 at 17:00
  • $\begingroup$ This question seems fairly opinion-based $\endgroup$ – C_Z_ Jun 4 '15 at 17:07
  • $\begingroup$ Perhaps Cognitive Sciences is more receptive to this kind of flavor of questions. $\endgroup$ – AliceD♦ Jun 5 '15 at 10:13
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    $\begingroup$ @AliceD I'm actually interested in the anatomy of animals here. If anatomies in general somehow follow the golden ratio, it would indicate that animal minds do too. $\endgroup$ – LocalFluff Jun 6 '15 at 1:37
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I have some insight into this from an engineering perspective. Years ago, I worked on some computational and search algorithms which used a growth factor to determine how far to widen a search space, or how much more memory to allocate. For some of these algorithms, I ran a series of random trials to search for an optimal growth factor and found that for some, that optimal factor approached 1.618. Completely outside the realm of biology, this golden mean popped up as the most efficient growth factor for some of my algorithms.

Over the years since then, I have recognized that this is an optimal factor for various engineering problems (although in practice I often find it more trouble than it's worth to explain to colleagues why they want to use it). So, I have gradually come to believe that this is why we see this ratio all over nature, in the way seashells grow, the proportions of various body parts, the arrangement of seed structures, etc. It appears that natural processes have ultimately led various lifeforms all over our world to tend toward this ratio to optimize their own functions.

The fact that we find this ratio "beautiful" is a far more fascinating study of what appears to be a meta-adaptation. Consider all of the various ways that the recognition of this ratio is important beyond just sexual reproduction. When we select our food, choosing vegetable or meat specimens which exhibit this ratio most perfectly is more likely to lead us to the healthiest food. Choosing to take shelter under the more "beautiful" tree may also be a good bet that it is the more stable, healthy tree. Making tools, clothing, or structures with this ratio may serendipitously lead us to better formed products. We don't have to find this ratio more beautiful to look at, but because we do, it leads us to better choices in a variety of odd ways. So, those of us whose brains appreciate these things thrive a little more.

Your question was not about underlying causes, but about statistical prevalence. I don't know the answer to that. And I think it would be very difficult to obtain those numbers accurately for another loosely related reason. The human brain is very attuned to finding patterns, and the human brain likes to find this ratio. Taken together, this presents a huge bias for any researcher trying to objectively measure the frequency of this ratio in nature.

However, once we understand that this ratio is the solution to a variety of engineering problems, it becomes clear that it is an indicator of optimization, or proximity to perfection. And even if we cannot say how many species are able to recognize, appreciate, and seek after this ratio, we can say that those who do will most likely find it a beneficial adaptation.

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    $\begingroup$ Are those who don't "find this pattern" really less successful? Our brains do like to find this particular ratio pattern (imagination maybe). Me, I do care. But I wonder if my dog cares about it. If my dog's loved one, which it has only sniffed and never seen, has a Fibonacci nose length to leg length or something. Maybe I'll subject my best friend to some experiments... However I know that it would cheat, just like I would. Could the Golden Ratio be a human cultural construction without relevance to common natural structures? $\endgroup$ – LocalFluff Jun 4 '15 at 22:30
  • $\begingroup$ @LocalFluff Relevance to common natural structures is precisely what I'm trying to demonstrate here. If this number turns up as an optimal growth factor in a context in which the ratio itself is not the target at all, per se, then it certainly carries meaning independent of the observer. The algorithms preferred it. In most contexts, our own preferences muddy the observation, but in this case, I would consider it an objective finding. And if it is objectively useful, then the ability to recognize it must be beneficial (provided said ability does not cost the organism more than it's worth). $\endgroup$ – Mark Bailey Jun 5 '15 at 15:48

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