Ratio and Logos

Logos most commonly refers to Reason and Order but one of it's other less well known  meanings is "proportion". For Heraclitus,  the harmonia of the world - the construction of a complex whole according to rational principles and in due proportion - was dependent on Logos. The mathematical form of representing proportional relationships that exist in the world is the ratio. The Latin for Logos is in fact Ratio. 


Kepler uses the word ratio roughly 500 times in Harmonices Mundi. Newton mentions ratio about 850 times in Philosophie Naturalis Principia Mathematica. Fast forward to the early 20th century and Bertrand Russell and Alfred Whitehead's book Principa Mathematica. Ratio only appears once in Volume 1 and three times in Volume 2.  In Einstein's paper on Relativity, ratio only gets mentioned a couple of times more. 

For the early mathematicians and physicists, mathematics was a tool for exploring the underlying relationships (ratios) of the world around us and the cosmos above us. These ratios supported the notion that God had created a divine order to the universe.   For Newton and Kepler, the fact that the planets moved in an orderly and predicable way, according to fixed ratios and laws, was proof of God's existence. The ratio aspect of mathematics has in modern times being sidelined and replaced by a more theoretical and measurement based discipline.  Newton never actually bothered to calculate the gravitational constant - he was more interested in discovering the underlying relationships of nature that underpinned the force of gravity. When the Irish philosopher, George Berkeley, wrote that numbers were useful fictions without independent reality, he was only partially correct. The ratios and proportions that have existed in nature long before humans became aware of them are real and independent of human consciousness. Without them, the world as we know it, would look completely different. 

Quantum mechanics presents a non deterministic random molecular world that is at odds with the predictable celestial mechanics of Kepler and Newton. How can random atomic forces lead to a solar system with fixed laws and ratios that applies without exception to all the planets, moons and comets in it ?   Mathematics has lost it's Logos.