The golden ratio is known as the divine proportion because it is found so often in nature. It has fascinated mathematicians since Euclid. A golden ratio is when the ratio of two numbers is the same as the ratio of their sum to the larger of the two quantities.


Credit: Wikipedia

Represented by the Greek letter phi (φ), its value is 1.61803399.

Now a team of scholars are suggesting that the Golden Ratio also relates to the topology of space-time, and to a biological species constant (T), a “cosmic constant” found in the curvature of elephant tusks, the shape of a kudu’s horn, the destructive beauty of Hurricane Katrina, and in the astronomical grandeur of how planets, moons, asteroids and rings are distributed in the solar system. 

And they manage to do all that in two pages.

These claims have been made in the past, based on bizarre fits to data (or just made up, as in Dan Brown's The DaVinci Code) and the new paper is on shaky ground because  it is based on statistical analysis of measurements obtained from animals of the same species. They seek to convince that 1.61 is present in biology as an approximation of the absolute mean value of a hypothesised species constant (T) – associated not only with living species of mammals, birds, reptiles, insects and beetles, but also with extinct species (Australopithecus, Paranthropus and early Homo). 

“Zoologists and palaeontologists recognize the number 1.618 in the logarithmic spiral in the growth of mammalian ear structures (the cochlea), whether in modern humans or in australopithecines about 2 million years old. They recognize the same number in the growth structures of the spiral shells of certain molluscs. In addition, they identify the same value for spiral growth structures of fossil ammonites more than 65 million years old,” says Professor Francis Thackeray, a palaeontologist at Wits University.

Jan Boeyens, from the Centre for Advancement of Scholarship at the University of Pretoria,  believes 1.618 can be found in the context of chemistry, physics, space-time, relativity and quantum mechanics. He says Meteorologists recognize the number 1.618 in the spiral structure of hurricanes, while astronomers claim that the structure of certain spiral galaxies can also be identified with Phi. He also claims that concepts associated with relativity and quantum mechanics can be integrated, through the number 1.618.  

The researchers say that the “time has come to recognize that relativity and quantum theories can be integrated, and linked numerically to the value of a mathematical constant – whether in the context of space-time or biology”.

Citation: Boeyens JCA, Thackeray JF. Number theory and the unity of science, S Afr J
Sci. 2014;110(11/12), Art. #a0084, 2 pages. http://dx.doi.org/10.1590/sajs.2014/a0084