Nature: As Translated By Mathematics
Undeniably, nature is inseparable from its physical properties — its appearance, aroma, sounds, texture, and (albeit seldom compared to those aforementioned) flavors are the methods by which humanity has come to perceive it. Though these have been the primary means to witness nature, nature is understood and explained through an approach quite contrary to its link to the physical form: mathematics. Mathematics is “a language” by which humankind has come to understand the various structures, be it of aesthetics or of efficiency, and come to predict the dynamics within nature.
Beauty As Understood Through Mathematics
Throughout history, there exists a link between nature and what is found to be aesthetic. In various art, nature has been a muse of multiple painters: “Sunflowers” by Van Gogh, “Tiger in a Tropical Storm” by Rousseau, “Water Lilies” by Monet, and numerous others. Yet, in as much as nature is considered to be beautiful, beauty is subjective, it is unquantifiable. However, the inability to measure the physical appearance of an object does not equate to the inability to find the cause for said appearance. One such case in mathematics is the Fibonacci spiral — a logarithmic spiral, as explained by Vila, C. (2010), whose growth follows the sequence of the same name, and thus, approaches a resemblance to the golden spiral (another spiral with a growth factor of ~1.618, where a ratio of ~1.618:1 or phi is said to be balanced as viewed by people). The Fibonacci spiral, as mentioned by Surridge, C. (2003), is often found in the arrangement of leaves in succulents or seeds in the case of a sunflower, and in the shells of some animals, for example, those of nautili (Vila C., 2010).
Efficiency As Explained Through Mathematics
Beyond aesthetics, mathematics allows for the understanding of structures found in nature in light of their efficiency. Regarding the aforementioned sunflower seeds, Aufmann, R. et al. (2018) notes in “Mathematics in the Modern World”, “[the] Beyond aesthetics, mathematics allows for the understanding of structures found in nature in light of their efficiency. Regarding the aforementioned sunflower seeds, Aufmann, R. et al. (2018) notes in “Mathematics in the Modern World”, “[the] definite pattern of...arcs or spirals...allows the sunflower seeds to occupy the flower head in a way that maximizes their access to light and necessary nutrients” (p.9). Meanwhile, Ball, P. (2016) articulates the preference of nature towards hexagonal forms, be it in honeycombs where the shape is packable and presents a lower perimeter-to-area ratio as compared to those of squares and triangles (therefore less wax would be needed to form said combs), or in bubble rafts where the shape has less surface tension given the three-fold angles formed by the shape when tessellated.
The Future Through Math
Although the previous discussions delve into mathematics as a means to understand those currently present in nature, numbers can be further used to see those which have yet to be present in nature — in another sense, the future. In the field of meteorology, Devlin, K. (1998) provides an example of calculus as used to forecast weather. Meanwhile in biology, Arney, K. (2014) narrates the work of Alan Turning, who in 1952, developed equations which predicted the manner in which stripes on an angelfish developed, or more accurately, moved as it grew (a phenomenon proven 40 years later). Both cases fall under a field of mathematics recognized as mathematical modeling — where, as explained by Simon Fraser University (n.d.), mathematics is used alongside the observation of a phenomenon to create models which could approximate the observed phenomena given other variables. From chemistry to astrophysics, models could be created for the various fields of science to predict the atomically small, the unfathomably large, and all those in between.
Mathematics and Nature
May it be the appeal of the curve within a nautilus shell, the genius architecture behind honeycombs, and even the ability to foretell future instances of natural phenomena through models — mathematics, though unproven to be the actual language nature works in, is the language said mechanisms of nature have been translated into so humankind may understand the world around it.
Bibliography
Arney, K. (2014, August 26). How the zebra got its stripes, with Alan Turing. Retrieved from
https://ideas.ted.com/how-the-zebra-got-its-stripes-with-alan- turing/
Aufmann, R., Lockwood, J., Nation, R., Clegg, D., Epp, S., & Abad, E., Jr., (2018). Mathematics in
the modern world. Manila: Rex Book Store
Ball, P. (2016, April 6) Why nature prefers hexagons. Retrieved from
http://nautil.us/issue/35/boundaries/why-nature-prefers-hexagons
Devlin, K. (1998). The language of mathematics: making the invisible visible. New York, NY: W.
H. Freeman and Company
Simon Fraser University. (n.d.) What is mathematical modeling?. Retrieved from
https://www.sfu.ca/~vdabbagh/Chap1-modeling.pdf
Vila, C. (2010, March). Nature by numbers. Retrieved from https://etereaestudios.
com/works/nature-by-numbers/