Reading Week 2: Excerpts from Johannes Kepler (1611/ 2010) On the Six-pointed Snowflake: A New Year's Gift.

23-01-20

Weekly Reflection 2

Summary:

In this fascinating essay, the author asks a captivating question about why snowflakes always have six corners and radii tufted like feathers. To unravel this mystery in the 16th century, Kepler delves into various aspects of nature, exploring the geometric patterns in beehives, the shapes of pomegranate seeds, and the spiral structure of snail shells. The author also touches on the formative power of nature itself. Kepler's inquiry extends to the purpose behind hexagonal bee cells, comparing them to regular solids and exploring the tightest possible arrangements of spheres. The author also examines the shape of pomegranate seeds, attributing their rhombic form to material necessity and the growth principle. The discussion extends to hexagonal bee cells' purpose, contemplating whether they align with natural philosophers' views on efficient spatial filling. Throughout the essay, there's a blend of scientific curiosity and philosophical reflections on the intricate patterns observed in the natural world.

Stops:

1. If you should ask the geometers on what plan the cells of bees are built, they will reply, on a hexagonal plan. The answer is clear from a simple look at the openings or entrances, and the sides that form the cells. Each cell is surrounded by six others and Is divided from the next by a shared side. But if you observe the bottom of each cell, you will notice that it slopes into an obtuse angle formed by three planes. This bottom (which you might call the "keel") is joined to the six sides of the cell by six other angles, three higher ones that are trilateral, just like the bottom angle of the keel, and three lower ones, in between, that are quadrilateral.  

I vividly recall a fascinating personal experience that aligns with Kepler's exploration of the geometric intricacies within beehives. During a biology class in school, our teacher brought in a beehive model for us to examine closely. As we observed the hexagonal cells, the instructor emphasized the significance of their shape in terms of efficiency and resource optimization. Looking at the openings and sides, it became apparent how each cell neatly fit with six others, forming a harmonious pattern. Reading the text and looking at the amazing internal structure of the bottom of each cell was particularly intriguing for me, with its obtuse angle and the intricate arrangement of trilateral and quadrilateral angles connecting it to the sides.

My question is how do other living organisms, besides bees, utilize mathematical principles in their behaviors and structures? Whether it's the symmetry of flower petals, the repetition of the angles in the spider web, the spiral patterns in shells, or the way animals navigate, what other examples exist in nature where math seems to play a role? how might these mathematical patterns contribute to the survival and harmony of ecosystems?

2. Having made this observation, one may go on to inquire about purposes: not the one that the bee pursues as it goes about its business, but rather the one that God himself, as the creator of the bee, had in mind when He prescribed upon it the laws of its architecture.

This thoughtful quote made me think about the deep connections between nature and divine design. It led to questions about the higher intentions shaping the precision and order found in the natural world.

Another question is how can the inherent mathematical patterns in nature inspire new approaches or solutions in human endeavors, whether it be in technology, design, or problem-solving?