Mathematics and philosophy have come together and separated countless times in Western civilization. It seems to me that they diverged in one of the strongest ways just over 100 years ago when Einstein published his great works on special relativity, the photoelectric effect and quantum mechanics. Suddenly science and mathematics seemed to encompass such an important and large part of the imagination that philosophy was relegated to dealing primarily with human suffering and existential dread. Both of these are important, but they are limited to human consciousness, while physics was not just reaching towards far away galaxies, but also inwards. It was analyzing time in new ways and exploring the invisible, but real worlds of atoms and molecules. This was the unofficial debut of the theoretical scientist as the stars of logic. The idea of theory to an artist and philosopher is one of ideas. To a scientists theory is mathematics. Theoretical physicists use mathematics to model the universe. To extrapolate our experience beyond our vision.
Recently my wife Marine was explaining Montessori education to me, and the systems that are used for teaching mathematics. Though I am now deeply interested in this, I still don’t know much at all. The main point was that children will learn numbers as a physical reality in small quantities. They can then extrapolate the concept for larger values. Only after this do they learn the symbols, which are written numbers. Though this is a digression from my point, it is what got me thinking about abstraction and science for this blog.
A scientist derives, proves and calculates in order to represent reality in a precise way. What the artist and theoretical scientist have in common in this regard is that both pursuits exist only with a strong ability to abstract. Physics which is the study of nature is not explored by the theoretician in a manner of direct observation, but by manipulation of matrices and formulae.
Abstraction may be a unique human ability which makes the creation of technologies, sculptures, space ships and books possible. It is also likely connected to our desire to distance ourselves from real nature by abstracting it further and further into our models. Goethe, the great poet, famous for words, which are abstractions en par with numbers, pushed back from Newtonian reductionism in favor of a more observation based science of Optics. In most ways Goethe’s scientific ideas were wrong. Newton describes nature in a much more accurate way; the question which remains however is who saw it (as opposed to describe it) more accurately? I believe what the Physicist Richard Feynman said to an artist friend who complained to Feynman that scientists take away the beauty of a yellow flower by reducing it to its scientific components. Feynman said that because he understands why a flower is yellow he appreciates it more. Feynman was unique in his ability to see nature on a deeper level esthetically and realistically while representing it with numbers and diagrams. This is the human intellectual evolution where we can congregate to abstract, but not without first observing. A child may not be able to calculate 1,000,000, but because she understands how to get from 1 to 10, from both observing and abstracting, she can comprehend the concept of 1,000,000. This is what Marine explained to me. As scientists we need perhaps to intuitively understand those things we can see, create numerical abstractions, then extrapolate. With that the theoretician, artist and philosopher can meet on common ground.