If Infinity Is The Devil, What Is God?

If the universe harbors an endless sea of bubbles like ours, in every conceivable variation, then there can be no meaning to it all. Infinity won't allow it.
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"If there is a God, He is infinitely incomprehensible since, having neither parts nor limits, He has no rapport with us. We are therefore capable of knowing neither what He is nor if He is."
-- Blaise Pascal (Pensees, 233)

Ever since Galileo hoisted his telescope to the skies and shattered the myth of celestial perfection, science has relentlessly hammered away at the edifice of religion. Where once science served to explain the ways of God to man, it now explains away the need for God altogether.

Though zoologist Richard Dawkins may perhaps be the most famous atheist among scientists, no branch of science produces more exponents of atheism than physics. Steven Weinberg, Lee Smolin, Victor Stenger, Lawrence Krauss, and Stephen Hawking are notable examples of physicists who trumpet their view that science has not only falsified many religious claims about the world, but has demonstrated that when it comes to creation, no Creator need apply.

I entirely agree with the first part of their critique. Religious narratives about the past, present, and future of the world are indeed unreliable guides to the world, except perhaps as metaphorical inspiration. But has science ruled out rational belief in a Creator? I'm not so sure.

A brilliant essay by Paul Steinhardt appears in the current issue of Scientific Amercan. Every theologian in America should read it. I must hasten to add that Steinhardt writes not one word about God. Rather, he explains why he has come to have serious doubts about cosmological inflationary theory. Yet, I say again, every theologian should read it, as should everyone who is interested in the rational pursuit of knowledge.

Why? Steinhardt helps us grasp a fundamental truth: Infinity is the devil. Not literally Satan, of course, but a destroyer of rational comprehension. This is as important to religion as it is to science, and more than that, it may provide a bridge between the two. That is, it may help us to a more rational, less extreme conception of a plausible creator.

Infinity makes trouble in many arenas of physics. In classical theory, it pops up in the description of a particle, such as an electron, as a point. When physicists write out the equations, they find that a point particle has infinite inertia -- an absurd result. Infinity nearly wrecked the most beautifully precise theory ever devised: Quantum Electrodynamics, or QED. In certain QED self-interactions it looks as if the energies go all infinite, meaning they have no mathematical meaning.

Only a technique called "renormalization" could save the theory from itself. Renormalization is, as best I can judge, a highly sophisticated kind of cheating. The practitioner peeks at the answer nature gives and then crafts a mathematical patch over the infinity to closely approximate nature's answer. The Standard Model, used by everyone working in high energy particle physics, is chock-a-block with renormalization.

But let's push on to the case of inflation. This is widely regarded as the scientific best explanation we have for how the Universe got its present-day characteristics. Cosmologists puzzle over why it is so smooth. A God's eye view of our Universe in two dimensions would reveal a surface like a smooth wooden table top with an even dusting of galaxies and barely visible lines of grain. Inflation theory explains that within the first fraction of a second after the Big Bang, inflation pumped up the Universe from a nothinglike point to macro-ball of fury that continues to expand, albeit not as madly.

Inflation is textbook stuff these days. But Steinhardt says, not so fast, bubba. His beef is not with the data (they match up "exquisitely" with theory, he admits), but with the quantum dimension of the theory. The problem there is that old devil, infinity. If any inflation is possible, he notes, then infinitely repeating inflation must happen -- because those impish quantum variations that pop up randomly here and there cannot be constrained. "Eternality," Steinhardt laments, "is a natural consequence of inflation plus quantum physics."

When we speak of spacetime bubbles popping out of the "nothing" of quantum foam, "eternal" is equivalent to "infinite." And that's where the trouble arises. Inflation purports to be a scientific theory that makes testable predictions, and moreover, one whose predictions agree with observation. Beautiful, right? But then along comes infinity and puts the kibosh on a rational basis for those calculations.

"What does it mean to say that inflation makes certain predictions -- that, for example, the universe is uniform ... -- if anything that can happen will happen an infinite number of times?" Steinhardt asks.

The problem may be hard to grasp, because infinity has such a quixotic nature. Steinhardt explicates it beautifully, but rather than steal his thunder I will give you the simple example that blew my mind when I first started grappling with the infinite decades ago.

Suppose you have a number line. You are standing at zero. In front of you are all the positive integers -- 1, 2, 3, 4, and so on stretching to infinity. Now, I'm standing next to you, on a parallel number line identical to yours -- until I push a button and zap all the odd numbers in mine out of existence. Every even number in my line moves back a space, so that it now goes: 2, 4, 6, 8, and so on. Here's the weird thing. My line is still exactly as long as yours. I could push another button and reduce my line to just powers of ten -- 10, 100, 1000, etc. -- and it would still be just as long as yours.

Makes no sense, right? In short, whenever it pops up in equations, infinity produces weird, arbitrary, or incomprehensible answers. Steinhardt regards this as fatal to inflation theory. "[T]he oft-cited claim that cosmological data have verified the central predictions of inflation theory is misleading, at best. ... The truth is that quantum physics rules inflation, and anything that can happen will happen."

That last idea, mordantly known as the Totalitarian Principle of physics, has important implications for theology. If true, it implies that no rational theory can embrace all of existence. Mathematically, such a theory would come to grief on the shoals of infinity. Theologically (or indeed philosophically), such a worldview would be as empty of meaning as a screen of text in which every pixel is white.

Now, it ain't necessarily so. There may be a true version of cosmology that describes a rational universe -- perhaps one with so-called bounded infinity. Or, it may be the the universe has an undiscoverable rational structure. (For example, it may be something like a computer program that simulates infinitude but is in reality finite.)

But, it may also be that at root the universe really is absurd. Call it the Sartrean Principle.I would certainly call a universe dominated by the Totalitarian Principle absurd, but there are many other absurd possibilities -- perhaps infinitely many. In any event, a failure of the scientific project to rationally explain the universe would not imply "God did it." In fact, it would be bad news for believers everywhere.

If the universe harbors an endless sea of bubbles like ours, in every conceivable variation, then there can be no meaning to it all. Infinity won't allow it. We may be tempted to say that everything would cancel out -- that every "good" action would be offset precisely by its opposite "bad" action, and so forth. But we can't even have the slender, existential satisfaction of that knowledge, for, as implied, above infinity minus infinity does not yield a meaningful answer.

In short, then, Pascal may have had it right. God, if infinite, is unknowable. We can't even know if he's there. Yet, through the continued pursuit of science, we may yet come to a more humble, rational understanding of our existence, one that may even include a loving if limited, perhaps even long-gone, Creator.

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