Infinity is both understandable and incomprehensible.
Infinity, then, is a most fitting attribute of God, making Him known to us by reminding us of His absolute incomprehensibility.
Theology traditionally has affirmed that there are at least three ways of knowing God: by His effects, by things implied by His nature, and by His revelation in Sacred Scripture. For example: creation is an effect of the Creator, omnipresence and omniscience are things implied by a divine nature that is uncreated and therefore unbounded, and the Trinity is revealed to us. (My chief sources for this are St. Thomas Aquinas and St. John of Damascene, see below for more.)
But there is a fourth category of knowledge: what we know about God in His essence. St. Thomas Aquinas said such knowledge is incomplete and imperfect. For example, we do know that God is good but His goodness is so great that it cannot be fully grasped by our intellect. St. John Damascene went a step further than this: we know God’s substance by knowing ‘what He is not.’ This is the way of apophatic theology. (The above paragraph incorporated two terms that illustrate this method—‘uncreated’ and ‘unbounded.’)
It follows that our highest form of knowledge about God in His essence occurs when we recognize we don’t know Him.
One way to do this is by contemplating His infinity.
- extending indefinitely: endless
- immeasurably or inconceivably great or extensive: inexhaustible
- subject to no limitation or external determination
- extending beyond, lying beyond, or being greater than any preassigned finite value however large
We often think of infinity as things that are unmeasurable — like all the sands on the earth, the water molecules in the sea, or the stars in the sky. Of course, all these things are actually finite, if only we had the technology to count them. In fact, there are few real instances of infinity in creation. The universe isn’t infinite, which means that space isn’t either. Time also is finite, at least with respect to the past. Numbers are infinite, but only in a theoretical sense.
But let’s assume that the universe was infinite — that it extended outwards endlessly. This in no way would infringe upon the infinity of God, which is not expressed in material terms, as Aquinas explained. Augustine likewise draws a distinction between between the infinities of the material world and the infinity of God. This is one way of knowing God by knowing what He is not:
For it is no small part of knowledge, when we emerge from these depths to breathe in that sublime atmosphere, if before we can know what God is, we are at least able to know what he is not. He is certainly not the earth, nor the heavens, nor like earth and heavens, nor any such thing as we see in the heavens, nor any such thing as we do not see in the heavens and yet may perhaps he there all the same. Nor if you increase the light of the sun in your imagination as much as you can, whether to make it greater or brighter a thousand times even or to infinity, not even that is God (De Trinitate, 8.3).
We can talk about the infinity of God in nonmaterial terms: He is infinitely good, infinitely loving, infinitely just, and infinitelymerciful, as the Catholic Encyclopedia notes. But this is to further distance our ability to know God from the knowledge of God. We can, if we strain a bit, imagine infinite space, or an infinitely bright star, or an infinitely dark black hole. But infinite goodness or infinite justice, for example, are beyond the capacity of our imagination.
How can we break through the barrier of the unknown to reach a higher contemplation of God?
In the 15th century, Nicholas of Cusa pointed a possible way forward. Nicholas of Cusa was a true Renaissance man. The Encyclopedia Britannica describes him as a ‘cardinal, mathematician, scholar, experimental scientist, and influential philosopher.’ In fact, this leaves out a few titles and roles: he also deserves to be called a theologian and, in the Church, he was not just a cardinal, but he rose to become what in today’s terms would be something akin to deputy pope.
Among the many things Nicholas of Cusa studied was mathematics, which gave him a special appreciation for what infinity was. Nicholas of Cusa realized that this was the key to ‘knowing’ God. We cannot know the infinite, either materially or spiritually. Because God is infinite we cannot know Him in His essence. Therefore, the path to God lies through ignorance, or what Nicholas of Cusa famously called ‘learned ignorance.’ As he puts it in The Vision of God,
O God, you are infinity, and no one can approach you except one whose intellect abides in ignorance, that is, one whose intellect knows that it is ignorant of you….The intellect knows that it is ignorant and that you cannot be grasped because you are infinity. For to understand infinity is to comprehend the incomprehensible. The intellect knows that it is ignorant of you because it knows that you can be known only if the unknowable could be known, and the invisible seen, and the inaccessible reached.
Through math, he further described how we can contemplate God. And he did so in a way that combines our deepest yearning for the beyond with the reality that we are mortal beings bound to fleshly bodies. In other words, Nicholas of Cusa was very Incarnational in the way he approached the reality of God.
His approach can best be summarized here as a sort of thought experiment.
Imagine a circle. This is something finite: we can calculate its area, measure its circumference, and pinpoint its center. But let’s say we stretch out this circle. From our vantage point, it would look less and less like a circle. Keep stretching it. Eventually, that finite circle will look like—or, as Nicholas of Cusa believed, actually would become—a line that stretches on indefinitely.
We actually don’t have to work too hard to imagine this. We experience something like it as part of our everyday existence: we call it the horizon.
Here, then, we have what Nicholas of Cusa called the ‘coincidence of opposites,’ where the finite touches the infinite. But this is not where God is found. According to Nicholas of Cusa, God is to be sought beyond the coincidence of the finite and the infinite.
God’s infinity is such that He is beyond any conception of the finite or infinite that we have. Even if we push the finite to the infinite (like the circle stretched to the line), or find a way to bottle the infinite in the finite (by reverse engineering Nicholas of Cusa’s thought experiment) we still have not comprehended the infinity of God.
As one of Nicholas of Cusa’s contemporary biographers, Erich Meuthen, explains it, “[God’s] infinity is more than the greatest; it is maximum and minimum at the same time. This is the highest possible form of knowing that we can attain, namely the analogous recognition of knowing that we do not know, and this lifts us beyond the boundary of the conceivable.”
Contemplating the infinity of God, then, is one way to practice apophatic theology — that is, knowing God by knowing what He is not. Just as terms like uncreated, unbounded, and incorporeal express knowledge about God in terms of what He is not, so also does the term infinity. Infinity in its most literal sense means not finite—endless, unbounded, unmeasurable.
We come to better ‘understand’ God’s infinity using the same method: we define it by what it is not. It is not the infinity of an infinitely vast universe or an infinitely bright star, assuming there were such things. Nicholas of Cusa pushes the boundaries of such thinking even further, showing us how contemplating God as absolute infinity—beyond any infinity in creation, real or theoretical—enables us to step out beyond the threshold of the knowable.
A Note on Sources: My sources on the types of knowledge we have about God are as follows. In the Summa Theologica, Question 12, Article 12, in the answer, Aquinas discusses how a First Cause can be known from His effects. It is St. John of Damascus who discusses the idea that we can know things about God that follow from his nature. This occurs in Book 1, Chapter 9 of The Exposition of the Orthodox Faith. Aquinas addresses the knowledge afforded by divine revelation in Question 12, Article 13, in the reply to the first objection. For the debate over what can be known about the divine substance see Question 13, Article 2 of the Summa and compare Book 1, Chapter 9 in John of Damascus.