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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 19th 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.

 

7 comments to String theories, illusions, and mathematics

  • happyseaurchin

    i have been exploring this for a few years
    in isolation mostly

    i tried to offer a thought-experiment to the stack exchange
    http://meta.math.stackexchange.com/questions/3208/is-anyone-familiar-with-thought-experiments-in-mathematics
    but i got banned
    i eventually worked out the site is designed for factual exchange and not explorative experiment…
    the thought-experiments were flagged as philosophy
    something i am not interested in exploring
    it is precisely the non-verbal nature of maths which interests me

    i produced a video a while ago
    http://www.youtube.com/watch?v=Lkl69cqKPAo
    be sure to press pause to actually conduct the experiment 🙂

  • Joselle

    I do not know of anyone exploring this directly. But I think it is implied in other work being done and pointing to those things is one of the reasons for this blog. I will try to continue to give shape to it myself. And, no, I don’t believe I have come across any mathematical thought-experiments. Can you give me an example of ones you’ve suggested to online math groups?

  • happyseaurchin

    great!
    you have said something that i have had hints of!
    are you thinking this alone
    or are you aware of any school or theoretician who is exploring this?

    i have used thought-experiments
    which i have suggested in maths groups on line
    and they think they are related to eg einstein’s thought-experiments
    though his are related to physics
    and the idea of a mathematical thought-experiment is not well established
    have you come across any?

  • Yes, I think something like that can be done with mathematics. And I think you’re right about Lackoff and Nunez. The impediment, as I see it, is our habit of thinking of mathematics as a completely conscious effort to build a thinking tool rather than as a perceiving mechanism whose source we do not fully understand. I think mathematics has the potential to inform us about things like perception or awareness or even to bring our attention to creative drives that are as fundamental or as instinctive as the one we call survival.

  • happyseaurchin

    :(there’s no way to subscribe to a post
    so i can be notified if/when you respond)

    “engaging” definitely deserves more inspection
    precisely

    i like the parallel of
    senses are mental processes organising what’s out there
    mathematics are mental processes organising what’s out there

    and in the same way we can examine the physiology of senses “externally”
    as physical objects such as retina in the eye or cochlea of the ear
    we may also examine sense object “internally”
    as feeling, where it is sourced, how it arises in the mind, what our response is

    can the same be done with mathematics?

    lackoff and nunes have gone some way in answering this
    but perhaps not far enough…

  • Joselle

    Yes, but I think “the engaging” warrants a bit more discussion. Don’t you? We could also say that our eyes don’t show us physical reality but actually just contribute to mental processes engaging with physical reality. And many philosophers have seen it exactly that way. But we don’t usually think of the senses that way. The senses efficiently organize what’s out there for the organism, for its existence. While it’s not meeting the immediate needs of the organism the way the senses do, I still think mathematics can be viewed in much the same light.

  • happyseaurchin

    slightly simpler answer:
    the maths is less about physical reality
    and more about our mental processes “engaging” with physical reality