String theories, illusions, and mathematics

Back in July, David Castelvechhi blogged about a conversation between John Horgan and George Musser. I missed it when it was new, but I’m glad I didn’t miss it completely.   Most of their discussion focuses on the value or viability of what has come to be known as string theory. It was a thoughtful debate that addressed the subtleties of considering the meaningfulness and testability of the theory.

One of the major difficulties with string theories is that there is no clear way to test them.  High energy physics experiments have been enormously successful at finding the reasoning, and the equipment, that can make a view of the early universe possible.  Particle physicists have identified, measured and recorded the fundamental constituents of matter. They are able to describe and predict the matter and energy states of physical systems very precisely.  Various string theories have been proposed to unify the forces described in these quantum mechanical systems with those of general relativity.  But it is striking that, within the experimental possibilities of particle physics, there is no way to see, or to detect, the fundamental constituents of nature that various string theories propose.

The particle detectors of physics experiments are like giant elaborations on the senses.  They detect the presence of something when that thing hits the detector and interacts with it, the way visual components of the world are produced when light hits our eyes or, more generally, the way various aspects of the world hit sensory mechanisms of the entire body.  If the elements of string theories are outside the range of even the sensory mechanisms of particle detectors, then the question arises, can a theory like this contribute to science?  John Horgan is of the mind that it cannot.  But George Musser defends the possibility that indirect evidence can, over time, develop into the pictures that string theories predict.

The elements of string theories have been considered to precede space and time, matter and energy.  And so Horgan understandably asks,

What is a string then? If it’s not something that can be situated in space and time and if it’s not constituted of matter or energy, what the hell is it? Is it some kind of pure mathematical form?

Except for this one moment, mathematics doesn’t really come up, despite the fact that string theory is largely a mathematical idea. Musser described how space and time or energy and matter have been described as emergent properties of the elements of these theories.  Talking about something that precedes space and time,” as Horgan says, seems to not make sense and we might even think that this is modern physics leading itself astray.  But this is not just a modern idea.  As Frank Wilczek says in The Lightness of Being,

Philosophical realists claim that matter is primary, brains (minds) are made from matter, and concepts emerge from brains.  Idealists claim that concepts are primary, minds are conceptual machines and conceptual machines create matter.

Plato was an idealist, but so was Leibniz.  For Leibniz the world was not made of material.  Anything that took up space, or had extension, was by definition complex, meaning that it could be divided.  The truly fundamental elements of the universe would not be divisible and so were necessarily immaterial.  The idea that the physical world emerges from immaterial elements is outside the range of most contemporary science-minded individuals (but not all).

I would like to suggest that what is being left out of this discussion is the lingering problem, identified by physicists themselves – the problem of objectivity or that there really is none.   It is the way we perceive that builds the worlds we see.  It could be said that some of the profound developments of 19^th century mathematics were prodded along by insights into the illusion, produced by the senses, that the space we see around us is an objective space that contains us.  And that Euclidean geometry describes it.  But space is an organizing principle, not a thing.  It shows up often, in things like the circular display of time, or the portrayal of color on a wheel.  We talk about the years ahead of us or behind us, or the ups and downs of the market.  Riemann’s insights into the foundation of geometry were inspired, in part, by insights into visual processes. And in his work are the seeds of the kind of topological thinking that is the groundwork for string theories.

The senses function largely as organizing processes and I have come to see that mathematics often reflects that.  What’s missing from these discussions about the true nature of reality, or how far science can reach, are questions about how the mathematics we discover brings novel possibilities into our imagination and otherwise hidden aspects of nature into our awareness.  If we find a universe in our mathematics that we can’t see yet, that doesn’t mean it isn’t there.  Perhaps we just haven’t grasped our relationship to it yet, which we likely have, since it emerged from the symbolic systems that define physics ideas.  Trying to see how it happens, how it is that mathematics can extend the range of our awareness is a difficult path to navigate.  But there is no question that it is worth exploring.