On Infinity and Eternity
As may be evident from my numerous past articles on the subject, I have an avid interest in the philosophy of Time. The nature of time is one of the oldest questions in philosophy, and one which has enormous repercussions on the physical sciences. Since the middle of the 20th Century, the evidence from cosmology has become stronger and stronger for the idea that our universe has a finite starting point, in the past. Many theistic philosophers– especially proponents of the Cosmological family of arguments— have jumped on these reports, claiming vindication for their belief that the universe was therefore created. When I disagree with this claim, I often find that the people with whom I am conversing becoming extremely confused. They ask me if I think the universe is eternal, and I reply that I do. Then, they ask me if I think that cosmologists like Alexander Vilenkin are wrong when they assert that the universe had a finite starting point. I reply that I actually agree with Dr. Vilenkin, and that I believe the universe has a finite past. This is where the confusion abounds: how can something be both finite and eternal?
The concept of Eternity has been defined in numerous different ways by numerous different philosophers, as this article from the Stanford Encyclopedia of Philosophy will attest. For the purposes of this article, I intend to use “eternity” in the sense of “timelessness.” That is to say, something which is eternal is not, itself, subject to time, change, or dynamism of any sort. It is, instead, a completely static entity. I contend that time is a part of the physical cosmos and therefore, the cosmos as a whole must be eternal. Time is a measurement of the universe’s properties; it does not govern the universe.
Since modern cosmologists utilize geometric models to understand the nature of space-time, I’m going to switch tack from pure philosophy to mathematics, now. You see, a part of the problem is that most people have a very limited understanding of geometry. Even the majority of college educated students with experience in calculus have only briefly (if ever) been introduced to any method of performing geometry outside of the Cartesian plane. To illustrate the issue, let’s imagine space-time as two-dimensional, for a moment, having one dimension of space and one dimension of time. Actual cosmological models of space-time are generally four-dimensional (3 space, 1 time), but that becomes incredibly difficult to visualize. Two-dimensional objects are much easier to picture. Our simple space-time, then, might look something like this:
On a model such as this, time and space are bidirectionally infinite. This is where the confusion arises. A person might reason that if cosmology tells us that the universe began at some time, say , then one could show that when , the universe did not exist. The problem, here, is that our friend is conflating a subset of the universe for the universe. The truth is, if modern cosmology tells us that there is a finite initial point in time, then the graph in Figure 1 cannot be used to model the cosmos. This graph has no finite initial point in time. Time is infinite in both directions, on such a model. Therefore, since this model doesn’t match our understanding of the cosmos, it is useless for drawing conclusions about the cosmos.
One way around this might be to simply utilize a Cartesian plane which is finitely bounded. Figure 2 illustrates a variation on our previous graph in which time is unidirectionally infinite. The bold line on the left marks a boundary, , previous to which no time exists. This is a more coherent description of a past-finite space-time, but it is visually unintuitive. The bold line appears like a wall, and in human conceptual experience, a wall is meant to separate something on one side from something on the other. Even though the question is completely lacking in cogency, people who see such a wall on a graph will naturally begin to ask, “What is on the other side?”
If the usual Cartesian plane makes for an inadequate or confusing model of space-time, might there be a better model available to us? Let’s look at another type of two-dimensional graph, one which is somewhat less familiar. Now, I’ll fully admit that this is certainly not a perfect model for modern cosmological understandings of space-time, but it does provide a coherent example of a system in which time has some initial point. This is a two-dimensional Polar Graph. The displacement, , from the center point of the graph– that is, the pole– represents our dimension of time; while the angular rotation, , about the pole represents our dimension of space. It does not matter in what direction, , we are headed; any displacement, , away from the pole is positive in value.
On this model, our pole would represent the time , the initial point of time, and it is very clear from the nature of the graph that there is no such thing as . This model offers a completely coherent picture in which time is past-finite. It is bounded in one direction, infinite in the other, and yet offers no “other side of the wall” to confuse us. A model like this makes it immediately apparent that a question like “what came before time?” is completely nonsensical.
At first, the polar graph might seem like a completely alien thing, to you. Many people have a very difficult time relating to polar graphs, while Cartesian graphs seem fairly natural and intuitive. However, I’ll bet you’ve actually been exposed to a sort of polar graph, before, without even realizing it. Think about any time you’ve seen a map of the globe. Now, generally, such maps are displayed in a sort of Cartesian, rectangular way; but you know that the Earth is (more or less) spherical, and that a rectangle can’t really do its surface justice.
Looking at the first map, a child might be forgiven for asking, “What is beyond the northern border of the map?” We again see a sort of conceptual wall, in that map, which the human brain wants to believe has another side. However, the second map shows why such a question is nonsensical. If you leave the North Pole, any direction you head will take you to the south. It doesn’t even make sense to ask, “What is north of the North Pole?” Even the statement, “There is nothing north of the North Pole” is not quite right, as it implies that there exists some place north of the North Pole in which nothing resides. The statement, “There was nothing before time,” is nonsensical in exactly the same manner.
This is what I mean when I say that the universe is both past-finite and eternal. The dimension of cosmic measure which we call “time” has a temporal pole, in the past; but the universe, as a whole, is a static entity which is not subject to any transcendental dynamism. Even though there may be a finite, initial point in time, there was never a point at which time did not exist.