Mathematics for Teaching Mathematical patterns in nature

## Mathematical patterns in nature

I believe that not to know mathematics is to miss one lens through which God viewed His creation and pronounced them very good. This amazing video by Cristobal Villa shows us what we can see wearing the mathematical lens  as Mr. Villa did. Enjoy the video.

More videos:
The Story of Math

## 3 thoughts on “Mathematical patterns in nature”

1. Your reference to Mr. Villa’s wonderful video is well taken !!! However, to describe mathematics as “one lens through which God viewed His creation” is very incomplete. Sadly, many books on patterns in Nature limit themselves to describing a shape in “reductionist” terms.

While a mathematical formula describing a pattern in Nature can be useful it can also be very misleading. A pattern in Nature is not an object. It is a complex system within a larger complex system. Complexity science has shown that mathematics cannot adequately describe complex systems because the state of a system at any given time is dependent upon its initial condition — an unknown state. Mathematics is a predictive science and one cannot predict system states. Instead of (or in addition to) an exclusively mathematical approach, one needs to communicate the organizing principles behind a pattern in Nature. Typically, these principles are categorized as self-organization, self-similarity, and scaling. All of these ideas use mathematics — but in an algorithmic sense where computer simulations are employed to demonstrate organizing principles. The only instance where pure mathematics shines out is to demonstrate unity amongst organizing principles in patterns in Nature. The mathematical power law model has been used to portray the same value for the exponent when describing many seemingly different interrelationships in Nature (Google: “Geoffrey West”). The most well known model is Kleiber’s Law (see Wikipedia) where the most recent work shows the constant power law exponent describing many relationships to be a multiple of 1/4. Some of us believe that this constant power law relationship that characterizes underlying organizing principles may be a unifying principle in Nature.