Patterns in life: rats whiskers (Introduction)
by David Turell 
, Sunday, March 15, 2020, 15:39 (1712 days ago)
We all know sea shells follow mathematical patterns. Gould's Ph.D. was on certain shells:
https://theconversation.com/how-we-found-a-special-maths-equation-hidden-in-rat-whisker...
"Rat whiskers can vary hugely. In our recent research, my colleagues and I analysed 523 whiskers from 15 rats and found that each whisker had a different length and shape. We wanted to investigate more about the shape of these hairs as a first step in understanding what rats feel through their whiskers.
"We found that rat whiskers can be accurately described by a simple mathematical equation known as the Euler spiral. It’s an example of how special spiral patterns are found throughout the natural world. And spotting them can help us not only understand nature better, but also improve our own engineering.
"The Euler spiral – also called the Cornu spiral, Spiros or Clothoid – is a shape whose curvature changes linearly with its length. It looks quite like an s-shape, where the tips of the “s” carry on curving in to spirals that get rapidly tighter. As a result, aspects of the curve can fit a wide variety of shapes including those that are straight or s-shaped, those that increase in curvature and those that decrease in curvature.
"This is why the Euler spiral can be used to describe all types of rat whisker, even though they come in many different shapes. Some are s-shaped, some get more curly towards the tip and some get less curly towards the tip.
"Most natural structures don’t display all of these three shapes. But there are many spirals in nature that get more curved along their length. Many sea shells, sheep and antelope horns, sea horse and lizard tails and even the cochlear in our own ears have all been shown to have a linear radius of curvature along their length, making them into a shape called a logarithmic spiral.
***
"Nature is full of mathematical patterns. Given how rat whiskers follow the Euler spiral, and that spirals are so common in nature, we think there’s a good chance the whiskers of other mammals probably follow similar rules and may also be described by Euler spirals. In this way, maths can give us a special insight into how biological structures and systems work."
Comment: It looks as if God is a mathematician, especially as life follows precise patterns which we find when studied..
Patterns in life: math is God's thoughts
by David Turell , Tuesday, March 17, 2020, 15:07 (1710 days ago) @ David Turell
God planned our reality with mathematics:
https://www.firstthings.com/article/2020/04/keep-it-simple
"Mathematics appears to describe a realm of entities with quasi-divine attributes. The series of natural numbers is infinite. That one and one equal two and two and two equal four could not have been otherwise. Such mathematical truths never begin being true or cease being true; they hold eternally and immutably. The lines, planes, and figures studied by the geometer have a kind of perfection that the objects of our experience lack. Mathematical objects seem immaterial and known by pure reason rather than through the senses. Given the centrality of mathematics to scientific explanation, it seems in some way to be a cause of the natural world and its order.
"How can the mathematical realm be so apparently godlike? The traditional answer, originating in Neoplatonic philosophy and Augustinian theology, is that our knowledge of the mathematical realm is precisely knowledge, albeit inchoate, of the divine mind. Mathematical truths exhibit infinity, necessity, eternity, immutability, perfection, and immateriality because they are God’s thoughts, and they have such explanatory power in scientific theorizing because they are part of the blueprint implemented by God in creating the world. For some thinkers in this tradition, mathematics thus provides the starting point for an argument for the existence of God qua supreme intellect.
"There is also a very different answer, in which the mathematical realm is a rival to God rather than a path to him. According to this view, mathematical objects such as numbers and geometrical figures exist not only independently of the material world, but also independently of any mind, including the divine mind. They occupy a “third realm” of their own, the realm famously described in Plato’s Theory of Forms. God used this third realm as a blueprint when creating the physical world, but he did not create the realm itself and it exists outside of him. This position is usually called Platonism since it is commonly thought to have been Plato’s own view, as distinct from that of his Neoplatonic followers who relocated mathematical objects and other Forms into the divine mind."
Author: Edward Feser is a professor of philosophy at Pasadena City College. I will add that he is a follower of St. Thomas theology. As a book review a long discussion follows the text above