Newton’s Alchemical manuscript. Click to enlarge.Newton’s Laws applied to physical situations describe a Universe that is totally deterministic. For scientist-modelers, the canonical methodology for predicting future events is based on Newton’s process: stuff the initial conditions of a system into the appropriate "laws", and let time increase in the resulting equations of motion. Here’s your prediction as a time series extending as far out into the future as you need. Next problem!
Chaos theory does not violate this Newtonian modeling process. Instead, chaos demonstrates that the equations of motion are so non-linear that small inaccuracies in the initial conditions lead to wildly varying future predictions - the so-called sensitive dependence on initial conditions that is the foundation of the butterfly effect. In effect prediction becomes limited in many situations, with weather one of the chief systems where predictability is desperately needed, but often leaves all of us wondering where the TV weather people ever got their degrees…So prediction is diminished, even though determinism is as strong as ever.
I was thinking about Newton’s legacy of determinism as I read a piece on Newton written several years ago by James Gleick for Slate, titled Isaac Newton’s Gravity. Gleick, the author of the text that brought Chaos to the masses (Chaos - The making of a new Science) is also the author of a well-received 2003 bio of Sir Isaac.
Gleick argues convincingly for the need to display Newton’s achievements in the context of his rather bizarre life (of which the pathological aloneness in the title of this post is one of Gleick’s signature descriptions). In this his approach reminds me very much of the recent biographies of Einstein.
Was Newton as methodical as the way physics is now presented seems to suggest? Were his life, beliefs, etc., a product of immutable beliefs and processes?
It may be that superstitions were more apt. With his "obsession with alchemy and theological heresies" Gleick writes that "we misunderstand Newton if we imagine him as a paragon of rationality and public science in the modern style."
This contradiction between the clockwork universe of laws, initial conditions, and deterministic futures, and the swirling passions of Newton’s studies suggests that there is some truth to the often-found "madness & genius" mix.
For me, reading about Newton and trying to imagine what physics would be like without him is simply impossible. Would our ideas of determinism be as strongly fixed if calculus and differential equations had not arrived until much later? (assuming the Leibniz did not produce the physics breakthroughs with his flavor of calculus.) Would Chaos Theory be as significant? Would we even need it? Maybe not - perhaps some of the linearizations that appeared along the way as Newton’s Laws were applied to certain intractable non-linear situations would not have occurred. Maybe we would learn non-linear equations on an equal footing with linear equations.
All of this is an interesting thought-experiment. But Newton did live,and create magic with his laws and mathematics - even though he may not have been ready for the universe he himself created. Gleick recounts a remarkable view of Newton by John Maynard Keynes:
"Newton was not the first of the age of reason," Keynes said. "He was the last of the magicians, the last of the Babylonians and Sumerians, the last great mind which looked out on the visible and intellectual world with the same eyes as those who began to build our intellectual inheritance rather less than 10,000 years ago." Newton opened a door to our world, sure. But he belonged to the world we have left behind."
Again, there are similarities to Einstein, only he just had the 200-plus years of Newtonian physics to overthrow. With his quixotic attempts to argue against the probabilistic realty described by quantum mechanics, his fundamental belief in determinism and causality, he too belonged to the older world - of Newton.