To what extent is nature governed by mathematics? Take note of the above shape, known as a “logarithmic spiral.” A logarithmic spiral is a curved line that increases in distance from the origin in a fixed geometric progression. A geometric progression is a sequence of numbers that is achieved in a simple way: you start with one number, then multiply that number by a fixed number known as the ratio. You then multiply the product by the ratio and then the product of that by the ratio as well, and so on and so forth. The most famous sequence of geometric progression is known as the Fibonacci sequence. Shorthand for achieving the sequence is as follows: start with 1. Add 1, and you have 2. Add 1 and 2, and you have 3; 2 and 3 and you have. You can proceed to add each number to the sum of the numbers before it for all of eternity.
The Fibonacci sequence is an important aspect in the design of nature. The Fibonacci sequence is very much related to something known as the golden ratio, a type of logarithmic spiral. The golden ratio appears naturally in nature as a proportion to which living and non-living things appear. For instance, the spiral of many sea shells can be calculated using the golden ratio, and though it does not follow the golden ratio, the shore of Half Moon Bay in California follows a geometric progression and forms a logarithmic spiral.
Though they don’t follow the golden ratio, the Pinwheel Galaxy and Typhoon Rammasun (both pictured above) are examples of naturally occurring logarithmic spirals. As strange as the lands may be in other galaxies, we know at least that the laws and patterns of mathematics are common throughout the universe. These laws of nature, as they are called, are astonishing and abundant proof that our reality is not chaotic, but in fact very predictable.
(Photo via APOD)
