Can mathematics and physics be unraveled? What is mathematics making?

As I talked about in a recent post, string theories, and the multiverse models they imply, have been widely criticized for their lack of testability.  Some physicists argue that the problem is that the theory is more mathematics than it is physics.  Is the distinction becoming fuzzier?  And why isn’t that discussed?  Why not bring the role mathematics plays in this and other ideas into the foreground?  Does mathematics make things?  The following statements are from a transcription of Alan Boyle’s interview with Brian Greene from Cosmic Log on msnbc.com.

While Greene consistently acknowledges that mathematics is leading the way, the debate never seems to include questions about why or how the mathematics may be leading the way.  Here’s an excerpt:

Brian Greene: Well, when we are doing mathematical investigations in physics, we as theorists allow the math to take us where it will go. We have seen, time and again, that math is a very potent guide to revealing the true nature of reality. That’s what the past couple of hundred years have established. So all we’re doing is following the same kinds of procedures that we always have. And as we follow the procedures, as we push the mathematics forward, the math is clearly suggesting that there may be other universes out there.

 

Q: You make the point that it’s very difficult to have any sort of direct contact with other universes. The differences are just so great. The only way to conceptualize other universes, I suppose, is through mathematics and the bits of evidence that can be gleaned from particle collisions or the cosmic microwave background radiation. Is there any possible avenue to get substantive information about the bigger picture, or are we pretty much stuck in our own little corner of the multiverse?

 

A: I think we’re certainly stuck physically. But I would not underestimate the power of mathematics to provide the kinds of insights you are referring to. We are definitely at a rudimentary state in our understanding of these multiverse proposals. But if we can refine that understanding, we could produce detailed “universe demographics.” We could gain a very detailed understanding of the percentage of universes that would have this or that quality.

Perhaps it’s a good thing that, despite the fact that mathematics plays so significant a role in driving physics theories, the theories are described in a non-mathematical way, or without any reference to the mathematics.  This could mean that, in physics, mathematics is never fully distinguished from the actions that define observation itself.  In other words, the brain (or the body) builds what we perceive from fairly disparate pieces of sensory data and now we accept that mathematics extends this nervous system action to the things the senses cannot access directly.  We don’t talk about our eyes when we talk about seeing something.

But this warrants some discussion itself, since most people do not think about mathematics in this way.  Even for many readers of popular science books, mathematics isn’t seen as building the reality that physicists encounter, but more, as something that provides a technical description of it.  This misunderstanding is evident in another interview with Brian Greene on NPR’s Fresh Air when Terry Gross:

GROSS: Now, you said something that really baffles me. You said: When we study those universes in mathematical detail – what do you mean by that? I mean, we don’t even know those universes exist. So when you say when we study them in mathematical detail, what are you talking about?

GREENE: Well, that is a confusing idea, I think, for people who don’t actually engage in the kind of research that I’m talking about because what we do is we sit down with equations, equations that describe space and time, equations that describe how matter can move through space and time.  And using those mathematical equations, we can get a sense of what it would be like to be in one of those other universes, even if we can’t actually visit or see or interact with that universe in any real sense. That’s the power of mathematics.

And I have to say, underlying everything that we’re talking about, in fact underlying everything I do with my entire life, pretty much, is a firm belief that mathematics is a sure-footed guide to how reality works. If that’s wrong, then all bets are off.

I should note here that one of the criticisms of the kind of research in which Brian Greene is engaged is that it is too completely characterized by mathematics.  But researchers find the strength of this work in exactly this – how it puts both quantum mechanics and general relativity into a mathematically consistent framework, when nothing else that we’ve imagined can.  Lawrence Krauss once said that string theories were, mathematically, the most intoxicating ideas around.

I plan to discuss the string theory debate again in another post.  But I want to end this one with a transcription from a talk given by David Deutsch at a TED conference in 2006.  The punch line of his talk was actually about what he considers to be the only productive response to the problem of global warming.  But on his way to that thought, he painted this wonderful image of human understanding as a kind of construction, beautifully re-connecting us (and our mathematics) to the universe itself.  I should clarify that referring to humanity as chemical scum points back to a description of our existence from Stephen Hawking.

Deutsch is describing the energy (that was pressed out by magnetic fields around a galaxy collapsing into a black hole) that shot out in jets (producing a quasar).  His observation is that this happened:

in precisely such a way that billions of years later, on the other side of the universe, some bit of chemical scum could accurately describe and model and predict and explain what was happening there, in reality.  The one physical system, the brain, contains an accurate working model of the other not just a superficial image of it (though it contains that as well) but an explanatory model embodying the same mathematical relationships and the same causal structure.  Now that is knowledge.  The faithfulness with which the one structure resembles the other is increasing with time.  This chemical scum has universality.  Its structure contains, with ever-increasing precision, the structure of everything.  This place is a hub which contains within itself the structural and causal essence of the whole of the rest of physical reality.  The fact that the laws of physics allow this or even mandate that this can happen is one of the most important things about the physical world.