Can Physics, Biology, and Art Be Unified Under One Mathematical Constant?
The golden ratio, extracted from the infamous Fibonacci sequence, has been theorized to be a "cosmic constant," or a mathematical constant that unites all of nature. Although the number has been of interest to scientists for over two thousand years, the data regarding this theory has been inconclusive. But now, South African researchers claim in a new study that the number is "related not only to aspects of mathematics but also to physics, chemistry, biology and the topology of space-time."
The golden ratio (approximately 1.618), discovered by Ancient Greek mathematicians and symbolized with the Greek letter phi (φ), applies when the ratio between two quantities is equal to the ratio of the sum of those numbers to the larger of the numbers. The spiral, which occurs quite often in nature, is the most often cited geometric shape that follows the golden ratio. Scientists have been hypothesizing for decades that this ratio, popularized by Dan Brown's The Da Vinci Code, explains everything from the formation of geological structures to weather phenomena to human DNA to animal skeleton dimensions to the aesthetically pleasing quality of certain works of art. Some of these claims, particularly regarding animal skeleton ratios, have since been discredited, but the number is still of enormous interest to scientists and mathematicians.
Geological structure in the Sahara:
Van Gogh's Starry Night:
"A convincing case for assuming a cosmic character of the golden ratio can be made based on the ubiquity of logarithmic spirals," the researchers wrote in their paper. "Spectacular examples include the Whirlpool Galaxy (M51), ammonites, the shape of Nautilus shells, Hurricane Katrina and the distribution of planets, moons, asteroids and rings in the solar system."
Cloud twist in Chile:
For this new study, co-author Professor Francis Thackeray performed a statistical analysis of many invertebrate species, both extinct and extant, and found that there is evidence for the golden ratio serving as some sort of species constant: "Zoologists and paleontologists 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 mollusks. In addition, they identify the same value for spiral growth structures of fossil ammonites more than 65 million years old."
Multiple spiral arrangement of plant Aeonium tabuliforme:
[Credit: Max Ronnersjö]
[Credit: Marsha Heiken]
There has also been an increasing trend towards using the golden ratio to explain very fundamental aspects of physics. A 2010 study, for example, found that the golden ratio could be found in the quantum spin of cobalt atoms. The other leg of the study that there is not only further proof for the golden ratio playing a role in biology and chemistry, but in the basic rules of the universe. Jan Boeyens, a former Wits University Professor, found that there was a consistent recurrence of the ratio in quantum mechanics, relativity, and spacetime, supporting the notion that spacetime itself may actually follow this ratio, and that the constant could help to unify these disparate theories.
The researchers claim 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."