We can understand the universe, but why? Nobel Prize-winning physicist and mathematician Eugene Wigner said in 1960, “The enormous usefulness of mathematics in the natural science is something bordering on the mysterious and there is no rational explanation for it.” Albert Einstein expressed a similar thought: “The most incomprehensible thing about the world is that it is comprehensible.”

What some Christian apologists claim

Many Christians have seized on this, claiming that an understandable universe points to God, both because God would want us to understand it and because only a theistic approach can explain such a universe. Christian apologist William Lane Craig gave this religious interpretation:

It was very evident to me that [naturalists are not] able to provide any sort of an explanation of mathematics’ applicability to the physical world, and this was self-confessed. . . . Theism [enjoys] a considerable advantage in [being able to answer this question].

Philosopher Nicholas Maxwell added:

Why should the physical universe, utterly foreign to the human mind, nevertheless be comprehensible to the human mind? We have here, it seems, an utterly inexplicable link between the physical universe and the human world. . . . Of course if God exists, the comprehensibility of the universe is entirely understandable.

This needs some pushback. These interpretations make a huge, unstated assumption that a godless universe could not look like our universe, but what supports this? Do they think that the dependability of physics is only due to God? Do they think that a godless universe would be unstable, with constants, exponents, and relationships continuously changing? Perhaps in this universe, e = mc² would be valid one moment but then e = mc^2.1 the next and e = 17mc^3.5 the next?

And why imagine that the physical facts of the universe must baffle us? Some aspects are counter-intuitive, of course, but evolution adapted us to be in tune with physics—at least the physics of our not-too-big and not-too-small world. For example, the inverse-square law says that radiation intensity falls off as the inverse of the square of the distance. Stand in front of a campfire and you soon get an intuitive understanding of this law.

That our physics wouldn’t look like it does without God is a very bold claim, for which I see no evidence. Furthermore, “God did it” is unfalsifiable, which is a fatal trait for any theory, let alone one that claims to explain all of science’s most perplexing problems.  (I give a more thorough analysis here.)

But hold on—is the universe understandable?

Let’s reconsider the initial claim, that the universe is understandable. Sure, we can find simple relationships between aspects of reality with scientific laws such as the Ideal Gas Law, Ohm’s Law, and Newton’s Law of Gravity, and so on, but things become more complicated. Corrections for relativity must be added to Newton’s Law of Gravity (F = Gm₁m₂/r²). Ohm’s Law (V = IR) ignores capacitance and inductance, which make calculations of time-varying voltage or current much more complicated. And the Ideal Gas Law (PV = nRT) makes assumptions about gases that limit its applicability.

Nature often isn’t particularly reliable, at least at first glance. The speed of light in a vacuum is constant, but that speed varies depending on what medium it’s going through. The boiling point of water varies around the world (only at one precise pressure does it boil at 100 °C). Weather and natural disasters are hard to forecast. Chaotic systems are deterministic but not predictable. And so on.

It might make sense after we get used to it, but beforehand, it can seem to be a random jumble. For example, what’s the simple law that tells us which isotopes are radioactive and what their half-lives are? Things outside our familiar middle world may never be intuitive. As Richard Feynman noted, “If you think you understand quantum mechanics, you don’t understand quantum mechanics.”

If the comprehensibility of the universe points to God, what does its incomprehensibility point to?

It’s not that the universe is understandable. Rather, what we understand about the universe is understandable, which isn’t much help in anticipating how science will continue to progress as we push the frontiers. How much about the universe will we eventually understand?

What we know vs. what we don’t

Knowledge about the universe can be divided into four categories, as illustrated by the Venn diagram above.

1. What we know. This has expanded dramatically since the modern period of scientific discovery beginning around 1800, which includes scientists such as Maxwell, Mendeleev, and Tesla, and even more so since the Enlightenment period, which might include Galileo, Newton, and Pascal. Imagine how small the “What we know” ellipse was 500 years ago.
2. What we will know. No one knows if we’ll continue learning about the universe at the current rate, but it seems a safe bet that we’ll know much more a thousand years in the future (assuming human society stays safe).
3. What we’re capable of knowing. What more could we understand if we only asked the right questions or if super-smart aliens taught it to us? Theoretical physics, like science fiction, can only take us to places that its practitioners can dream up.
   Another limit is our finite ability to create technology. Scientists and engineers have built the Large Hadron Collider, the Laser Interferometry Gravity Observatory, and the Hubble Space Telescope, and they’re planning next generation versions. But what if we eventually need versions that were a thousand times bigger or more expensive? Or a billion times? Human society, even far into the future, might have limits. Without these monster machines, unimaginable truths might remain unimagined.
4. All foundational knowledge of reality. The final ellipse is everything—not trivial specifics like the atmospheric composition of Alpha Centauri’s fourth planet but every concept, law, and theory needed to describe life, the universe, and everything.
   Our imperfect brains have limits. Imagine an alien species that is smarter than we are to the same extent that we are smarter than chimpanzees. While we share a common ancestor with chimps from just six million years ago, we can find in chimps only the rudiments of higher-order intelligence such as humor, problem solving, and morality. Chimpanzees are our closest living animal relative, but human children surpass their intelligence at perhaps four years of age. These aliens would intellectually be to us what we are to chimps. If chimps can never understand algebra or geometry, let alone calculus or quantum physics, what would these aliens be able to understand that we could never hope to learn? And if chimps will never understand all the science behind reality, why do we think we will?
   Now take it a step further and make the aliens’ cognitive gap the same as between us and lizards. Our understanding the new science these aliens could teach us might be as unlikely as a lizard understanding a joke.

A pessimistic look at our understanding of reality

The figure above gives one version of what we know (and will know) compared to what we won’t, but that’s just an optimistic guess. Imagine if the four ellipses actually look like this:

With this interpretation, we will still make a lot of progress from what we now know to what we will eventually know, but this more pessimistic version imagines the overwhelming majority of science out of our reach, either because imagination or lack of data let us down (third ellipse) or because it is beyond our cognitive reach (fourth ellipse). Will humans eventually understand 99 percent of the science behind reality? Or 0.1 percent?

Most frustrating, we can never know how big the third and fourth ellipses are! We can never understand the size of our ignorance. We will always perceive only ellipse #1, never sure if we’ve learned most of the science or a tiny fraction, never sure if we will learn much more or if we’re near our inherent limit.

Let’s return to our marvelously understandable universe. The universe is indeed understandable . . . but only to the extent that we can understand it. And how far is that? No one will ever know. “The universe is understandable” is an empty statement.

Here’s an interesting connection between Nature’s counter-intuitive laws and the growth of religion.

The cause of religious belief in human beings is intimately related to the desire on the part of individuals to have an explanation for various phenomena, and in fact, if nature possessed easy, simply-discoverable laws, it is doubtful that religion would have ever developed. As it happens, however, natural law is by no means simple, and thus it undoubtedly appeared to the primitive mind that the forces of nature were chaotic and unpredictable. From this point of view, however, it was but a short step to attributing an anthropomorphic character to nature: Unpredictability became whimsicalness; the raging storm became the work of an angry god who, like an angry man, will become calm again in time; the personal calamity became the punishment of evil-doers; the occurrence of an unusual event became a sign that the deity was engaged in something special that would affect his minions; and so on.

If Christians want to find proof of God in there somewhere, they must imagine a God who tantalizes us with some bits that are understandable, makes us work very hard to understand more, and refuses to tell us just how much of this mess we will ever understand. Doesn’t sound like a proof of anything to me.

See also:

• The Argument from Mathematics Doesn’t Add Up to God
• Stupid argument #36: Nature is intelligible.

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(This is an update of a post that originally appeared 8/19/16.)

Image from Olga Reznik (license CC BY 2.0)

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