11 ratio really a solution to our pursuit of beauty? Much to our surprise, this might just be our wishful thinking. It may be overthinking that has led us to identify its seemingly overwhelming presence in nature. The human brain loves seeking patterns, so much that perhaps it “favors” the emergence of φ in many of these instances, even when there is no concrete evidence to support the notion [1]. The most compelling case of this myth is the look of nautilus shells. Naut i l us i s a sea creatu re f rom the same animal class, Cephalopoda, as squids and octopi. Unlike other cephalopods, its home is a beautiful, chambered shel l with a spi ral. These spi rals are known as logarithmic spirals or growth spirals – spirals that keep growing further apart from the innermost curves as illustrated in Figure 3. Nautilus shells are said to be the prime example of the appearance of φ in the natural world, with their logarithmic spirals s u g g e s t e d t o h a v e a n aspect rat io equivalent to the golden ratio – a deeply held belief that is so popular in no small part due to literature such as Dan Brown’s Da Vinci Code, renowned sci ent i s t s and academic institutions like the Smithsonian (footnote 2) perpetuating this “fact” [2]. Yet , i f you w e r e t o e v e r inspect a nautilus shell for yourself in real life, you may find the aspect ratio actually closer to 4:3 (1.333) than φ (1.618). When this myth of every nautilus shell having the golden ratio is thought about more deeply, isn’t it kind of odd to think that every single nautilus shell in existence would have the same ratio? It would be more believable if this ratio is varied, even by a few decimal numbers, in different specimens, right? That’s precisely the same thought a cer tain researcher by the name of Christopher Bartlett had. He went so far as to surmise that even the 4:3 ratio is not an accurate aspect ratio for most nautilus shells. When 80 shells were examined from the Smithsonian collections, the average ratio came out to be 1.310. All shells had varying ratios with slightly different number; making it absolutely wrong to state that all these spirals somehow have the same measurement, say, 1.6 – a value much closer to the actual value of φ than 1.310 [2]. Why did so many scientists and educators believe this myth then? Well, as covered in this article before, the way humans survive and interpret the world is through seeking out patterns. Sometimes we do this subconsciously against our better judgement, which leads to flawed speculations such as the fantasy of the golden ratio being all around us; however, another great thing about humanity is our insatiable curiosity, which helps us not only create these myths but debunk them just as well. Figure 3 Logarithmic spiral of nautilus. 1 The golden angle: Imagine that we want to divide a circle into two sectors in the golden ratio. After setting up a quadratic equation with the smaller and larger central angles as x degrees and (360 – x) degrees respectively, you will be able to get the golden angle x, which is approximately 137.5 degrees. 2 The Smithsonian Institution: A large museum, education and research complex in Washington, D.C. in the US. 流言終結者：黃金比例真是無處不在嗎？ Ratio Around Us
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