Above:  Partial view of the Mandelbrot set.  Created by Wolfgang Beyer with the program Ultra Fractal 3. [For copyright information see https://en.wikipedia.org/wiki/File:Mandel_zoom_11_satellite_double_spiral.jpg]

Some of the most common objections to belief in God are based on a way of thinking about God that differs radically from that of Christian tradition, although one finds it even among some Christians.  It imagines God to be just one more thing or actor in the world, alongside of natural ones and essentially on a par with them, though having certain qualities to a much higher degree, for example being supremely powerful, wise, and good.  This way of imagining God is understandable, for our imaginations are tied to what we can experience, and our experience is tied to what we can sense. This limitation affects all of our thinking, not only about God, but also in philosophy, mathematics, and natural science.  To take a simple example from mathematics, we are unable to picture  spaces of four or more dimensions in our minds — even though we can understand and prove many things about them —- because the world of our experience is three-dimensional.

Of course, as this example shows, our intellects can reach far beyond what we can experience or imagine.  We can do this through careful reasoning and the use of analogies that relate things that we cannot experience or imagine to things that we can.  This is especially important when we think about God.  Since all of our experience is of created things, the only way we can speak about God or understand anything at all about Him is through analogies to created things, as Catholic tradition strongly emphasizes.  Such analogical thinking can take us quite far in understanding, but it always carries with it the risk that we forget the infinite disproportion and differences between God and the created things to which we make analogy and thereby fall back into conceiving of God as if He were on the same level as the natural world.

One common mistake that comes from putting God and Nature on the same level is thinking that they are in competition with each other as causes, i.e. that every event or effect must either be caused by Nature or be caused by God, not both.  If that were the case, then the more we can account for by natural explanations, the less there would be for God to do.  This is a view held both by atheists and by “God-of the-gaps” believers.

A second mistake that comes from lowering God to the natural level is that God’s act of creating the universe is conceived of as though it were a natural and even a physical process.  For example, the late Stephen Hawking famously wrote that when physics eventually explains how the universe began, no one will any longer think that it happened by God using “blue touch paper” (i.e. a match) to set off the Big Bang.  Even some believers fall into this way of thinking.

A third mistake that arises from the same source is to think that any evidence for the existence of God must be of the same kind as the evidence for the existence of physical objects.  This lies behind the common claim that there is “no evidence” for God.  For example, the zoologist and well-known atheist Richard Dawkins has written that there is no more evidence for God than there is for “flying spaghetti monsters,” because no one has actually seen either.  Dawkins thus put himself in the company of such deep thinkers as Soviet Premier Nikita Khrushchev, who is said to have declared triumphantly that Yuri Gagarin, the first cosmonaut to return from outer space, had not seen God out there.

The question, then, is how we should think about God if we are to avoid such mistakes.  How do we go beyond what we are able to experience or imagine?  What analogies are helpful in this?  And how can we avoid being misled by our analogies?  Before getting into that, let us look at how natural science handles these questions when thinking about the things that it studies.  Modern science, especially modern physics, has been very successful in going beyond the level of the imaginable, and perhaps we can draw some lessons from it.

Transcending the limits of imagination in natural science

The limits of human imagination are felt in many branches of natural science.  Consider, for example, the difficulties we face in trying to understand the minds of other animals.  Some animals have senses that we lack.  Humans can only see light that is in a certain narrow range of wavelengths, which we refer to as “visible light,” and light of different wavelengths within that range register in our perception as different colors.  Bees, however, can see into the ultraviolet part of the electromagnetic spectrum.  What color sensations they might have is impossible for us to imagine.  Even more remote from our experience is the ability of bats to “see” using sound.  The philosopher Thomas Nagel, in making a point about consciousness, famously asked, “what is it like to be a bat?”  Obviously, we can’t imagine.  Nor can we imagine what it is like to be able to sense objects electrically, as sharks can, or magnetically, as animals of many types can.

A more subtle problem is the tendency to project onto the minds of animals aspects of our own minds.  Even when dogs use the same senses that we use, are they really perceiving the world around them as we do?  A dog can see the mailman coming, but the dog does not see him as a mailman as we do.  If we were to try to understand how a dog experiences the world, we would have to leave aside or “think away” aspects of our own minds that have no counterpart in the minds of dogs.  That is, if we use our own minds as an analogy for dogs’ minds, we would have to try to compensate for the distortions that analogy can introduce by attending explicitly to where it breaks down.

The limitations of our imaginations are also sharply felt in theoretical physics.  Consider, for example, various ideas about space and time.  As already noted, we cannot visualize spaces of higher than three dimensions; and that is a considerable handicap when working on theories with “extra” space dimensions, such as Kaluza-Klein theories, supergravity theories, and superstring theory.  But we also have difficulty in thinking about even the ordinary three-dimensional space we move around in, because, as Einstein’s theory of gravity (called “General Relativity”) tells us, this space is curved (as is also four-dimensional “space-time”). We can see what a curved one-dimensional line is like, because we can draw one on a piece of paper; and we can see what a curved two-dimensional surface is like, because we can look at the surface of a balloon or ball.  But we cannot picture in our minds a curved three-dimensional volume.  Therefore, when explaining to physics students the spatial curvature of the universe, professors typically say, “imagine the space of our universe to be like the surface of a balloon, except that it has three dimensions rather than two.”  But the analogy of the balloon tends to mislead.  For, while the balloon itself is a two-dimensional surface, it exists within a three-dimensional world. Balloons therefore have an inside, filled with air, or helium, or something else, and an outside.  And indeed, our experiences of “curvature” are always of lines or surfaces curving around within a higher-dimensional space in which they are embedded.  So students naturally ask, “if the curved three-dimensional space of our universe is analogous to the curved surface of a balloon, shouldn’t there be something corresponding to the inside and the outside of the balloon, i.e. an “inside” that our universe encloses, and also an “outside,” both of which would be four-dimensional? To which their professors must reply, “No. Try to imagine only the balloon itself, without imagining it to have an inside or an outside.”  In other words, the student must learn to “think away” those things in the analogy that have no counterpart in the reality he is trying to grasp by it.

There are many other examples having to do with space and with space-time where our imaginations can only take us so far, and then we must use analogies and careful reasoning to get further.

The most famous example coming from modern physics of the limits of human imagination is quantum mechanics.  We talk about particles, but our everyday experience of macroscopic particles is that they travel along definite paths or trajectories, and that at any moment of time a particle has some definite position on its path and is moving along it at some definite rate.  We therefore cannot imagine a particle acting in any other way.  But this is “classical physics” thinking.  According to quantum mechanics, particles do not behave in this way.  They do not move along definite paths from one point to another.  Similarly, we cannot imagine — and therefore cannot have any solid intuitive grasp of — how a thing can be both a wave and a particle.  Here too, analogies from everyday experience tend to lead us astray, unless we constantly remind ourselves to “think away” the misleading aspects of them.

Modern science, especially physics, has increasingly had to learn to think about humanly unimaginable realities.

Thinking about the humanly unimaginable in theology: How God and Nature are related

As already mentioned, when we think of God causing things or events in the world — or causing the world itself by “Creation” — we have to use analogies, because God Himself and divine causation lie beyond our experience and therefore beyond our imaginations.  Some analogies are more misleading than others, however.  As already noted, some analogies make God seem to be just one more thing or actor in the world alongside of other, natural ones, and thereby make Him appear like a competitor to natural causes.  When one of my daughters was small, having heard in the Nicene Creed recited at Mass that God is “the creator of all things, visible and invisible,” she asked at dinner whether God had created our house.  Hadn’t some people built it?  Not only little children are confused in this way.  Noted atheists with advanced degrees consider it foolish to pray for health when it is doctors, medicines, and proper nutrition and hygiene that produce health.  Imagining God as a supernatural construction worker or doctor obviously can lead to confusion.  Are there better analogies?

Instead of thinking about construction workers building houses, let us think about an author writing a novel.  And to be concrete, let us think about J.R.R. Tolkien as author of the novel The Hobbit.  In that novel there is a dragon named Smaug and a character named Bard the Bowman who shoots an arrow at Smaug and kills him.  Consider the following question: What caused the dragon to die in The Hobbit?  Did he die because Bard the Bowman shot him with an arrow?  Or because J.R.R. Tolkien wrote the story that way?

Of course, it is ridiculous to have to choose between those two explanations, because they are both 100% correct.  Bard the Bowman is the cause within the plot of the novel of the dragon’s death, whereas J.R.R. Tolkien is the cause of the novel itself and of all that happens in it.  Tolkien is the reason there is a novel, that it contains the characters and events that it does, and that there are all the various relationships among those characters and events, including their causal relationships within the plot.  There is simply no competition between Bard the Bowman and Tolkien.  They are causes in completely different ways on different levels.  One could say that Bard the Bowman acts horizontally, within the novel’s plot, while Tolkien acts vertically to invent the plot.

In Catholic theology, God as “author” of the universe is called the “primary cause,” whereas the causes within the plot of the universe are called “secondary causes.”  There is no competition between them.  This distinction helps us understand why there is no contradiction between Evolution and Creation.  Did this hippopotamus arise by a sequence of natural causes within the plot of the universe — such as Evolution and sexual reproduction — or because God wrote the plot of the universe that way?  Both.  Did workmen build our family’s house, or did God write the story of the universe with the building of that house by those workmen being part of its plot?  Again, both.

The analogy of God as “author” of the universe is very ancient and traditional.  Many of the early Church Fathers said that God is the author of two books, the Book of Scripture and the Book of Nature (or “book of the universe”).  This analogy helps us understand many things, including the traditional doctrine of Creation.  For example, it makes clear the distinction between the Creation of the universe and the beginning of the universe.  Consider The Hobbit again.  If someone were to ask what the beginning of The Hobbit is, the correct answer would be this set of words:

“When Mr. Bilbo Baggins of Bag End announced that he would shortly be celebrating his eleventy-first birthday with a party of special magnificence, there was much talk and excitement in Hobbiton, … .”

But if someone were to ask what the cause of The Hobbit is, i.e. why there is such a novel, it would be utterly foolish to point to those words.  The cause of the novel, its creator, is J.R.R. Tolkien.  By analogy, if someone were to ask what the cause of the universe is, i.e. why there is universe at all, it would be just as silly to point to the beginning of the universe in the sense of the first part of its plot.  That is why investigating the physical events and processes that occurred near the Big Bang and the natural causes that were involved in them cannot yield an explanation that in any way competes with God as Creator.  Physics deals only with the horizontal or “secondary” causes “within the plot” of the universe, whereas God is not a part of the universe and its plot.  (Though, in the Incarnation, the divine Author made himself a part of the plot.)

In the same way, the author-novel analogy makes clear that the Creation of the universe is not some event that happened billions of years ago.  God is equally the Creator of every part of the universe, every event and thing in it, just as Tolkien is equally the author of every word of The Hobbit, not just its beginning words.

The author-novel analogy helps us understand even more. Tolkien’s writing The Hobbit did not happen in Hobbiton or anywhere else in Middle Earth, nor in the time of Middle Earth.  It would be utterly meaningless to ask whether Tolkien decided to write The Hobbit or published it before or after Bilbo Baggins’s eleventy-first birthday, or before or after Smaug was killed.  Tolkien is completely beyond the space and time of the world he created.  His activities are not a part of that world, including his activity of writing The Hobbit.  This corresponds to the traditional understanding that God is completely outside the universe He created and its matter, space, and time.  God is not “eternal” in the sense that He lives for an infinitely long time, but rather in the sense that He is atemporal, i.e. the categories of space and time and matter, which are features of the physical world, do not apply to Him at all.

At this point we can see that, as helpful as it is, there is an important respect in which the author-novel analogy is misleading.  While Tolkien was outside the space and time of his creation, Middle Earth, he nevertheless did exist in another kind of space and time, namely that of the real world.  And his writing of The Hobbit involved processes that unfolded in time — not the time of Middle Earth but the time of the real world.  Moreover, those processes involved physical activity on the part of Tolkien — arranging pieces of paper, typing on the keys of his typewriter, and so on.  Nothing about God as author of the “book of the universe” corresponds to these aspects of the analogy.  God is not only beyond the space and time of the world He creates, but of any space and time.  He does not inhabit a “divine world” with its own space and time and with divine objects that He manipulates to produce effects.  So we must “think away” those aspects of the author-novel analogy, which have no counterpart in God.

One way to purify the author-novel analogy of some misleading elements is not to focus on Tolkien’s physical activities of typing and so on — “think them away” — but focus rather on his creative mental activity.  This brings us a bit closer to a sound way of thinking about God, for the idea that God (in his divine nature) has a body is contrary to Christian doctrine, whereas it is completely traditional to ascribe to him a mind.  But even here there is a danger, since our only experience of minds is of our own minds, which think piecemeal and discursively, going from one thought to another, understanding one thing at one time, then turning attention to something else.  So we must somehow also “think away” those features of our own minds and conceive of God’s mind as eternal, knowing all that it knows, willing all that it wills, understanding all that it understands, in one infinite and timeless act.

That is literally unimaginable to us, of course, but there are some human mental phenomena that may give us a very weak analogy to it.  For example, it can happen that when a person has been struggling for some time to understand a complicated and abstruse matter he or she is rewarded with a sudden, seemingly instantaneous, flash of insight that makes it all clear.  The most famous instance of this in history is the great mathematician Archimedes leaping naked from the public baths with the cry “Eureka!” (“I have found it!”) on his lips.  Archimedes had a moment of illumination in which his mind grasped the whole matter at once.  The famous mathematician Roger Penrose tells of a similar experience he once had, where the proof of a difficult theorem suddenly came to him as he stepped off the curb when a traffic light changed.  The timelessness of the divine intellect may also have a faint image in those moments of joy or bliss or exaltation when time seems to stop.

Another way that the author-novel analogy can mislead us is on the question of free will.  If God “wrote” the entire plot of the universe, then wouldn’t all the thoughts and deeds of all the characters in it be scripted and determined and therefore any freedom we might attribute to them be merely an illusion?  If God were exactly like a human author of a novel, then the answer would be yes.  For a human author does not really create a world, he merely creates a description of a world.  His characters are described as living, feeling, thinking, loving, willing, suffering, experiencing joy, and so forth; but those descriptions are no more than words on a page.  The divine Author does something that no human author could do.  He “writes” reality.  He “writes” characters who really live, feel, think, love, will, suffer, and experience joy.  But this aspect of God’s creative power has no counterpart in our experience.

Finally, let us return to a mistaken claim that we mentioned earlier, namely that there is “no evidence” for the existence of God.  Here again the author-novel analogy can be of help.  The way we know of the existence of things that are parts of the world is either (a) by sensing them, or (b) by inferring that they exist as the natural causes of things that we can sense.  (For example, even though humans, unlike some animals, cannot sense magnetic fields, we infer that these fields exist as the natural cause of such things as compass needles being deflected, iron filings lining up, or the paths of charged particles bending.)  But God cannot be known in either of these ways.  Not being a part of the physical universe, God cannot be sensed.  Nor is He a “natural cause” within the universe, like a magnetic field or Hawking’s “blue touch paper.”  Thus, indeed, we do not have the kinds of evidence for God that we have for magnetic fields, or rocks and trees, or subatomic particles — or would have for Dawkins’s “flying spaghetti monsters,” if such things existed.  But we do have evidence for God of a different kind.

A novel gives evidence of the existence of its author, even though the author is not part of the novel and does not appear as a character within its plot.  The very fact that the novel called The Hobbit exists tells us very eloquently that there is an author and even something about the author.  The novel’s very existence, its elaborate structure, its beauty, and the meaning that can be found in it, all bespeak a mind that conceived of it.  Of course, the characters in the novel (if they were really alive) would not have the same kind of evidence for its author that they have for each other.  Frodo, Bilbo, and Gandalf will not run into J.R.R. Tolkien walking along some byway of Middle Earth.  To expect to physically see God somewhere in this world, as Dawkins and Khrushchev imagined would be possible if God existed, is simpleminded, not to say childish.  Nevertheless, as with the novel of the analogy, the very existence of the universe, its elaborate structure, its beauty, and the meaning that can be found within it all bespeak a Mind that conceived of it and brought it into being.

Conclusions

Religion speaks of invisible realities that are fraught with paradox and mystery.  For many, this makes it less credible than natural science, which is about the kinds of things we can see and touch, and which therefore seems much more solid, down-to-earth, and commonsensical.

But this picture of science was always an illusion.  It had some plausibility when science was at an earlier stage of development and was dealing with phenomena that lie closer to everyday experience.  In the last century, however, science (especially physics) has penetrated far beyond the world of everyday experience and consequently far beyond the reach of human imagination.  As it has done so, it has encountered its own paradoxes and mysteries.  Its insights require for their precise expression highly abstruse technical concepts that can only make contact with our intuition through analogies, which if taken too literally lead to confusion and error.

Theology encountered such issues long before science did, for it deals with the deepest realities of existence and ultimately with God Himself, who infinitely exceeds human comprehension.  But even though natural science deals with realities of a lower order, it should not be surprising that, as it has explored further and further upon what Newton called the “great ocean of truth” and has been led into deeper and deeper waters, it should have come to feel more keenly the limitations of human imagination.