Tweaking the math to explain the universe

At the start of 2011, I posted a series of articles dealing with the nature of reality — more accurately, the nature of our descriptions of reality.

The series was later edited into a longer essay titled “Is Reality Unreal?” In that essay, I concluded that “there is ‘reality,’  as far as we can know it, and there is ‘truth,’ as far as we can perceive it.”

This practical position acknowledged that our understanding of the universe and of the forces and things within it, including ourselves, is constrained by the limits of our perception and the scope of our reason.

Viewing the universe from within, with limited perceptual and conceptual tools, we may well never be able to understand its entirety. The restrictions of Flatland are relevant here.

If there are dimensions and energies and particles that lie forever beyond our ability to find or to understand them, there’s no material way out. And immaterial, supernatural routes to knowledge lead only to an interior feedback loop of gratuitous assumption and self-serving assertion.

So we are left relying on something like the “model-dependent reality” that Hawking and Mlodinow described in The Grand Design. In this view, theories of the nature of the universe rise or fall on the extent to which they correspond to the evidence. The best theory is the one that best fits and least contradicts the available data.

It’s in this sense that Hawking and his Cambridge team of mathematicians and theoretical physicists have published their latest work, “Accelerated Expansion from Negative Λ.”

The core problem Hawking et al. address is that the mathematics of string theory does not describe the world that we observe. The failure of string theory to match our observations of the universe has fueled a modest revival of minority claims that string theory is wrong.

Hawking and friends are not among the string theory skeptics. Their work is designed to find the mathematical framework necessary to “fit” string theory to the observation that the universe appears to be both flat and endlessly expanding. Current string theory models don’t describe how either a flat or expanding universe could come to be.

The mathematics of string theory describes a universe that is a kind of “hyperbolic space,” a geometry that is not flat but, in the words of a pay-walled article from New Scientist,  rather “resembles a twisting, wiggly landscape of saddle-like hills.” The New Scientist article compares our perceptions of a flat universe to the two-dimensional representations of three-dimensional space created by Max Escher, in which those bats dwindling away at the edge of the circle are really the same size as all the others.

String theory, in the meantime, offers a beautifully complete picture of the universe’s history and connects gravity to quantum mechanics – but is most comfortable in a universe with a negatively curved, Escher-like geometry and with a negative cosmological constant.

The problem can be summarized most simply as “a universe that works but lacks a complete theory … [and] a complete theory that doesn’t describe the actual universe.”

It appears that switching a + to a – might solve the problem. Or something like that. At this point, my limited exposure to mathematics catches up to me, and I lack the competence to describe any better than that what Hawking and team are up to.

But that’s ok, as my interest and attention are drawn to a different kind of abstraction associated with the quest for an accurate model of the universe. It’s not the math or the physics but the “meta-physics” that intrigues me.

I often describe myself as a realist, a materialist, and a naturalist. I have no patience for magical, supernatural stories of the origin or nature of all things. But while reading the report on Hawking’s work I was struck by how much theoretical physics and higher mathematics appear to resemble more traditional metaphysics.

Is this resemblance merely a superficial similarity, or is there a deeper connection between typical spirituality and advanced theoretical science? Are the theologians right, is science “just another religion”?

In one way, the similarity between the spiritual and the theoretical appears strong. Both approaches to describing the origins and nature of reality claim that there is the world that we perceive (the world as we perceive it), and there is the world as it really is.

We don’t see God, and we don’t see elementary particles. The physical realities in which we live are not the only reality, in some views not even real at all.

There is a spiritual dimension that underlies our reality, theists say, and in its invisible but fundamental realm all of our apparent realities are created and controlled. There is a quantum dimension (if string theory is right, lots of dimensions) that underlies our reality, theorists say, and in that invisible but fundamental realm all of our apparent realities are created and controlled.

At this level of description, there’s not much difference. But there is a difference, and it’s crucial to a defense of realism against the claim that it is just metaphysics with another name.

That difference is, of course, the insistence by theists that their explanation of the universe does not depend on evidence, that the spiritual realm is “other” by definition. To accept the spiritual view, you rely on faith and feeling, not on evidence.

Theorists, on the other hand, insist that their descriptions of the universe match up as much as possible with experimental and observational evidence. To accept the theoretical view, you rely on data and mathematics, not on wishful thinking.

Thus, while the models that theorists provide may not be complete descriptions, and while they may describe things that are hard to observe (or that so far may be unobservable), they are directed at a description of what is, not by a faith in what one wishes would be.

So realism may be no more complete than theism, but it has its focus on this world, which we know exists, not on another world, which some hope exists.

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