One of the small pleasures of the mind is the discovery, in an unexpected place, in another discipline, even, of support for a concept that you might have thought original, but, it turns out had been anticipated 500 years before. That was my recent pleasure in the pages of Walter Isaacson’s monumental biography of Leonardo da Vinci. Leonardo, of course, is the epitome of what we have come to call a Renaissance Man, a true generalist who excelled in whatever he set his mind to. In his world renowned paintings, in the science he developed for that work, in his keen observations of nature in all its particulars, he still challenges us to be clear and articulate. Here, in this quote from Isaacson, is his insight into physics, particularly into the question of what is real and what is perception, a standard to which all physics thinking should be held, clearly articulated 500 years ago.
Shapes without lines* (p. 268)
Leonardo’s reliance [as a painter] on shadows rather than contour lines to define the shape of most objects stemmed from a radical insight, one that he derived from both observation and mathematics: there was no such thing in nature as a precisely visible outline or border to an object. It was not just our way of perceiving objects that made their borders blurred. He realized [as a scientist] that nature itself, independent of how our eyes perceive it, does not have precise lines.
In his mathematical studies he made a distinction between numerical qualities which involve discrete and individual units and continuous quantities of the sort found in geometry which involve measurements and gradations that are infinitely divisible. Shadows are in the latter category; they come in continuous seamless gradations rather than in discrete units that can be delineated. “Between light and darkness there is infinite variation because their quantity is continuous,” he wrote.
That was not a radical proposition. But Leonardo then took it a further step. Nothing in nature he realized, has precise mathematical lines or boundaries or borders. “Lines are not part of any quantity of an objects surface nor are they part of the air which surrounds the surface,” he wrote. He realized that points and lines are mathematical constructs. They do not have a physical presence. They are infinitely small. “The line has in itself neither matter nor substance and may be rather be called an imaginary idea then a real object; and this being its nature it occupies no space.”
*Walter Isaacson, “Leonardo da Vinci,” 2017
You, faithful readers of these pages, will, I’m sure, recognize the parallels to many of my prior assertions. There is a real world out there, separate from our perceptions and frequent misinterpretations of those perceptions. We see an apparent edge and interpret it as a line. We assume, because Democritus, Lucretius, et al, said so that everything is made of particles. We invent a measurement and, suddenly, say it exists as an object. The separation between object and description disappears, and then, and then, a whole discipline grows up about this new “object.” The classic, for me, is the quantum. Can anybody tell me what a quantum is? Invented by Max Planck and popularized by Einstein, the best I can tell is that Planck needed a measurement unit to plug into his equations about black body radiation, so he invented (not “discovered!”) a unit that became a monument used to reify every mysterious phenomenon hypothesized by scientists for the next century. Other questions: What is a quantum computer? a quantum leap? a quantum theory? Calling something a “quantum” something makes it less mysterious? or just beyond questioning or explanation. What about “relativity”? A close reading of the conceptual notion of relativity reveals that neither Galileo or Einstein were describing real physical things or events. In both instances, they were describing theories of perception. I am convinced that we will find, eventually, that the world is rough and analog and that only mathematics is precise and, perhaps, digital. Who said that first? Plato, of course.
A second pleasure from Isaacson’s biography of Leonardo is the reminder of how many scientific insights he had, years, even centuries, before they were rediscovered and published. His failure was that he never published them, but there they were in his notebooks, in his drawings, and his backward script.
Enough of my ranting. Suffice it to say: We will never have a real physics, that is, a physics untainted by extraneous verbal or philosophical meanderings until we become rigorous about the separation between the real world and our mostly defective perceptions of it. “Orders of abstraction” (Korzybski) and “logical types” (Russell) need to be clear and clearly stated if we are to make it out of this jungle and make real progress.