The Mind of Newton
24 January 2012

The minds of great scientists have always fascinated me. How could they think the remarkable things they thought? After years spent reading his papers and poring over his notebooks and letters, if I know any of these minds at all, I know Einstein's mind best. There is something comforting and familiar in it. I cannot know ahead, where he will go or what he will do. But when it happens, it seems right and good and reasonable and sensible.

That this should be so may say rather little about my accomplishments. Perhaps it is just telling me that I live in the age of Einstein and that in my era Einstein's ways have become the obvious, the natural and the proper way to proceed.

Hundreds of years before Einstein, in quite another age, the great Isaac Newton saw further. It is enthralling to retread the sure path he struck that takes us from the phenomena of the heavenly motions to the wonder of universal gravitation. Yet as I follow in his footsteps, I see that his mind is alien to mine. For how else can I explain his General Scholium to Book III of his magisterial work, Principia Mathematica?

It begins with a triumphant disposal of Descartes' fluid vortex theory of planetary motions. It is "pressed with many difficulties," he notes with innocence. He had just created the modern theory of fluid flow in Book II to create those very difficulties. The discussion flows on to god and then to a minute dissection of the words used to name him. One sees the precise and exact mind of Newton at work in the dissection. But what is it doing among the theorems and ellipses of planetary motion? This mind sees connections and significances that elude me and carry a slight whiff of madness.

There are scholars who have devoted a lifetime to studying this greatest of great minds. Mary Domski, presently visiting in the Center, is one of them. Today she will tell us about Newton. I rarely admit my expectations for such talks. I've no doubt of the excellence of the material. But I've also no doubt that the speaker will immerse me so rapidly in Newton minutiae that I will drown in the first few minutes.

Mary's presentation was different. We were not thrown instantly to drown in the arcane depths. We would get there, but she knew enough of her audience to carry us there slowly. She set the stage with the sort of thing that grasps any philosopher: she defined a simple and compelling problem. After that, she kept the connection and, aside from one or two dunkings, my head stayed above water all the way through.

Newton's great Principia was founded on the idea of Absolute Space. He needed to distinguish, he said, "absolute and relative, true and apparent, mathematical and common"; and to this end he declared, “Absolute space, in its own nature, without relation to anything external, remains always similar and immovable.”

It is a statement of breathtaking boldness. How, Mary asked us, can he justify this flight to the metaphysical heights. How can he be so confident of the applicability of mathematics to space? This Absolute Space is not the space that any of us experiences. That is mere "Relative Space."

Mary assures us that Newton does indeed have the philosophical resources to justify this flight. To show it to us, she will take us to a an earlier document of Newton's and to a commentary by Proclus on the first book of Euclid's Elements.

Our first trip was to "De Grav." More completely, it is De Gravitatione et aequipondio fluidorum et solidorum, a document written by Newton a decade or more before Principia. There Newton pondered the nature of space. He told us what it is not: neither substance, accident nor nothing at all.  Space could not be a substance, he averred, because it is an emanative effect of god.

This reasoning, however, was alien to me. My late 20th century mind was stalled so long trying to grasp that first argument that I missed the flood of further arguments and only dimly glimpsed the six properties positively attributed to space. The fourth read mysteriously "Space is an affection of a being just as a being."

I was quite at sea. But now Mary held out hope of rescue. In amongst his commentary from around 450 CE, Proclus had included a neo-Platonic account of the order of being and the order of knowing. To know, we ascend up the order of being from sensible things, learned from experience, through objects of mathematics, known through understanding, to the highest level of objects of the intellect.

Newton, Mary assured us, must have been aware of the commentary, since it was in the lectures he attended of his teacher Isaac Barrow. Most importantly, Proclus' order of knowing provided a philosophical grounding for Newton's introduction of his mathematical Absolute Space. I had planned to relate the details of how Mary's narrative deftly mapped Proclus' neo-Platonic scheme onto Newton's analysis. However I fear trying to condense Mary's careful exposition into a few words.

So I will just report the little insight that enthralled me. I had not thought much of Newton's contrast of "absolute, true and MATHEMATICAL" with "relative, true and common." I'd always sense that I was missing something. Newton's choice of words in these most central passages was not hasty. His writing was like a lawyer eager to give precisely the correct wording to the contract. Clarity of exposition matters. But what matters more is that wording should be utterly unequivocal when brought before a court of law, or in Newton's case, when brought before the court of his critics.

The "mathematical" here was not merely a loose synonym for the limp "theoretical" of my late 20th century mind. It designated a quite specific level of immaterial object in a Platonic order of knowing to which Newton was tacitly subscribing. It was an assertion as clear and strong as the ascription "Absolute."

All this now seemed so clear and simple that it was hard to imagine any dissent. This happy reverie was broken towards the end of the talk. Mary was wrapping up some lesser point and finishing her sentence, "...last two claims are not controversial."

A quiet growl came from Peter Machamer, sitting near the front,  "...Oh yes they are."

He hadn't been resting his eyes, I realized. He was listening.

The course of question time was now determined. Peter had the first question; he insisted on it. He rattled off a series of points, beginning with an impressive but (to me) obscure sermon on emanation. Then there was weight and equilibrium and balances and the mixed quantities of mechanics and more.

Peter's display was quite forceful and Mary listened with her chin cradled in her hands. I could not read in her face what she was thinking. The sense was of a speaker being called to account for her errors.

But that was just the sense I was reading into the energy of Peter's eruptions. Then Mary moved to speak. "Nothing you are saying contradicts what I said," she reported. Here, I mused, was the immovable object to match Peter's irresistible force. She had, it turned out, a spare transparency prepared for just this occasion. And then there was another; and she thanked Peter for the opportunity to show it.

John D. Norton