That’s how relativity works. Spacetime has coordinates (points) that are oriented in a particular way, but no objective frame of reference. In fact, spacetime can be stretched and squished, and the relative position of the coordinates won’t change. This implies that there is some truth about the relationship between these points that is even more fundamental than their positions and their distances from each other. If we take the square and squish it into a different shape, the lines and corners have all moved, but B is still between A and D.

In mathematical terms, the shape’s geometry has changed, but its topology is the same. Topology does not involve a particular metric, so we can’t talk about lengths or distances, but we can still define a kind of order.

 

Similarly, relativity says that there is something even more fundamental to time than its duration, and that is the logic of causality. There are all sorts of things in general relativity that are observer-dependent and relative, but this is the one thing that stays constant (I’ve even heard it said that the speed of light should more accurately be thought of as the speed of causality). In other words, time is more fundamentally about causal structure and the relative orientation of events than it is about how long events take.

 

This brings us to the concept of topological time. My perspective is that, rather than trying to describe God with the simple binary of God being either “timeless” or “in time”, we need to understand the fundamentally topological nature of time. In my view, God is outside of our universe’s physical metric time, but he has eternally experienced a dynamic, active life of logical and relational flow, which we can call topological time².

 

 

What is topological time?

 

Topological time is like metric time in that it has order and direction, but it doesn't have a quantitative structure - no duration, no measurable intervals, and no metric divisions. Without a metric, you are left with a set of events that can still have a kind of flow of relational structures³, but without any sense of duration through countable moments⁴.  I guess you could say that a day would be like a thousand years, and a thousand years would be like a day.

While it’s hard to imagine events without definite durations, unlike timelessness, the ordering and directional flow of topological time allow for things to actually happen. In fact, there are all sorts of mind-bogglingly beautiful things that can happen in topological time. The concept of topological time is tricky to imagine, so I'll start with some imprecise analogies to try and build some intuition. Just bear in mind that these analogies are all wrong or incomplete in some capacity:

 

Topological time is like a river that can flow and has direction, even if it can't be divided up into individual countable sections - there are no “chunks” or “slices” of a river. Topological time is like a large rubber sheet that can stretch and squish, but can't be cut into pieces and rearranged. Topological time is like the logic that underlies a geometric shape - a triangle is the same kind of shape no matter how big it is or what units we use to measure the sides or the angles (and a shape is best defined as a relationship between points, not as a structure built out of a bunch of lines or points stacked together). Topological time is like the logical relationship between grandparents and grandchildren - grandparents are temporally prior to grandchildren, but the existence of a grandchild logically implies the existence of a grandparent in a bidirectional way - the two ideas are fundamentally connected. Topological time is how the Father begets the Son and the Son is begotten of the Father in a way that is eternally true, independent of any temporal causation. Topological time is like a rotating circle (it can turn forever in one direction without fundamentally changing its state), whereas metric time is like lines that grow out of that circle in specific increments (there’s a definite beginning to the line because it has its origin at the circle). I believe much of our confusion about God and time stems from our failure to grasp the fundamental topological nature of time.

 

Questions without answers

 

I’m going to return to some spatial examples to illustrate how our limited understanding of a concept might lead us to ask questions or make assumptions that don’t actually make sense. As with the relative orientation of geometric shapes we talked about earlier (it doesn’t make sense to ask “Which corner of the square is really objectively on the left?”), there are several time-related questions that don’t make sense if time is topological. Let’s imagine a hypothetical conversation between someone who is confused about math and a mathematician who attempts to explain.

 

Q: When I add two numbers (e.g. 2+2=4), which number is added and which one is what is added to?

A: The old convention is that the first symbol written is what you already have (the augend), and the second is what is added (the addend), but that’s arbitrary and is only relevant if you’re telling a story about a transaction happening in time (e.g., you have some apples and then get more). The underlying math of addition is more fundamental because the order you add things is arbitrary and doesn’t change the total.

Q: But I want to know which 2 is actually the one added. Which is the real addend?

A: Addition is commutative and associative, so your question doesn’t make sense.

 

Q: Do equal angles cause equal sides, or do equal sides cause equal angles? Also, do parallel lines cause right angles, or do right angles cause parallel lines?

A: There is an intrinsic connection between those properties such that they logically depend on each other.

Q: But which one is the real cause? Which one is the ultimate or primary cause?

A: Given the nature of geometry, your question doesn’t make sense.

 

Q: In this figure, which path leads from A to D?

A: Both path ABD and path ACD.

 

Q: But I want to know the real path? Which is the correct, actual path?

A: That question doesn’t make sense. Both paths exist and are equally valid. This is a fundamental fact of geometry.

 

 

My point is this: there are some relationships that are more fundamentally logical than they are temporal, and there are some realities that are logically bidirectional or circular, in that they entail each other. Some questions we might think are logical because of our beliefs about the world might just be reflections of our ignorance. A mathematician isn’t limited in his knowledge because he can’t define one geometric path as objectively actual. In fact, he would be in error if he suggested there was such a path when the geometric or topological reality is that there is no such fact as the “actual path”.

 

If time is more fundamentally topological than it is physical, I think many of the historical questions we ask about God and time don’t actually make much sense. If God has given you a range of possible options and you can freely choose from them, it doesn’t make sense to ask which future choice is the “real” one. They are both valid paths, and God knows both paths. This is not an example of his ignorance or a limitation of his power; it is the nature of the reality he has created.

 

If time is most fundamentally topological, then God perfectly knows its topology, or “shape”. If the future vibrates in a superposition of states, God’s knowledge of the superposition is more accurate than our ignorant idea that there is one and only one path. If God, by his foreknowledge, knows what you will freely choose, then your choice and his knowledge are logically and topologically connected. But to try to conclude that his knowledge unilaterally causes your “free” choice is a logical contradiction, as is the idea that you could choose to do something that an omniscient God doesn’t know about. God sees the whole shape of physical time all at once from a vantage point “outside” of it, but that idea would only imply determinism if time were a single, solitary line. If time is more like a topological surface, the question of which future is “actual” is a question that simply doesn’t make sense. It’s like asking which path leads from one point to another point in space.

In the example of the landscape in the image above, it’s not just that there are two paths that lead from the top of the hill to the house. There is actually a whole surface with many possible paths that lead to the house; it’s just that some are more likely than others.

And some paths are only possible hypothetically rather than in practice; you could theoretically fly through the air or tunnel under the ground, but humans aren’t generally well-equipped for personal flight or long-distance digging. Generally, we are constrained to paths along the surface of our physical spaces.

 

In the same way, humans are constrained by the nature of the universe to follow certain trajectories within a finite range. We follow the geometry of spacetime and are bounded/limited by its shape. This shape is determined both by God’s unilateral decisions to shape some parts in specific, predetermined ways (pro-orizo = pre-establish the boundaries) and by our free choices to navigate through that field of possibilities. God or other creatures could plausibly navigate differently in spacetime (in the same way that birds can fly through the air and moles can tunnel), but humans traverse the topology of spacetime along paths that, from our perspective, look like lines on a surface.

 

Are there really a bunch of possible timelines?

 

If you think of topological time like adding up a bunch of parallel timelines where there are practically infinite possibilities that all stack together into one spread out space - that feels pretty convoluted. But I don’t believe that's the best way to think about it.

 

A 2D geometric shape is not actually built out of lines or paths between points that get all stacked together. It doesn’t make sense to imagine that zero-dimensional points (i.e., points of zero length) can be added up infinitely into a line or that one-dimensional line segments (i.e., segments of zero width) can be stacked together infinitely into a plane. Zero plus zero equals zero, no matter how many times you try to add another zero. Even if you do it infinitely, it would still be zero. Instead, lines, shapes, and topological spaces are best defined by their boundaries.  

 

 

It seems likely to me that God has defined the shape of our universe’s spacetime by establishing certain limits and constraints on it, but that he has also left a broad space of possibilities within it open. This shape that God has defined would constrain humans traveling through spacetime the way the surface of the Earth constrains where we (typically) move (i.e., across its surface), and the way the boundaries of a shape constrain what paths fall inside of it and what paths are outside. God doesn’t need to meticulously define every possible timeline; the boundary is enough to define the shape.

 

This is actually the most intuitive and relational way humans exercise our will in the world. I have children, and I give them a lot of freedom to do a variety of things from a whole range of options. But I certainly don’t do this by laying out in meticulous detail all the possible things they can do at every possible moment. Imagine if I tried this: “You can play Yahtzee or Monopoly, or dominos, or …[list of all games we own] or you can read a book like…[list of all books we own], or you can ride your bike…[list of all allowable positions, speeds, and angles of acceptable bike riding trajectories], and you can decide whether you want to do that at 10:03 or 10:04 or 10:05 or…[list of all allowed times] or you can do…[list of all remaining permitted activities done in all possible orders and in every conceivable way].” Even if I were God, this would be a very silly way to parent.

 

Instead, I give my children simple boundaries (e.g., “stay where I can see you”), general guidelines (“be kind to your brother”), and occasionally some specific instructions (“go play outside”). The difference between my boundary setting and God’s is that I don’t have the capacity to hold all the possible options in my mind or to see the reality of all the possible permutations simultaneously, the way I believe God does. God can do this by virtue of his power, wisdom, and his divine perspective on our physical geometric time. He doesn’t need to predict anything (as on Open Theism), and his knowledge doesn’t mean he determines everything (as on Calvinism). He can know everything perfectly simply by knowing the geometry of space and the topology of time.

 

Some objections to God eternally experiencing topological time

 

William Lane Craig has argued that, while God now experiences time along with the created universe, without the physical universe, God was timeless. From what I understand, the main thrust of his argument against God’s eternal temporality is that, if God were eternally temporal, he would need to experience an infinite sequence of moments. Craig has made a strong case that the existence of infinite past moments is impossible because they would be impossible to traverse (even for God). He has also argued persuasively for the impossibility of actual infinities.

 

I generally agree with Dr. Craig’s reasoning, but I think there are some reasonable ways to defend God’s eternal temporal existence while avoiding the objections he raises. Firstly, I think topological time is not best defined as an infinite sequence of moments. My height is not made out of feet, and time is not made out of moments. Similarly, a square is best defined by describing the spatial relationships of its vertices and sides, not by adding up an infinite number of one-dimensional line segments or zero-dimensional points. Even standard set theory describes sets of infinite numbers with definitions that do not require actually counting to infinity.  

 

Secondly, in just the last fifty years, mathematicians have discovered new, sophisticated ways to model infinitely recursive systems that do not require an infinite succession of finite additions. Craig first published his conclusions about divine timelessness in 1979, long before Peter Aczel explained hyperset theory (1988), showing that there is a perfectly coherent way to model infinite and recursive systems (this seems especially appropriate for describing the Trinitarian idea of perichorisis or mutual indwelling). Jean-Yves Girard proposed linear logic in 1989 and later developed the Geometry of Interaction, which describes infinities as ongoing, self-sustaining patterns of interaction based on the structure and rules of a system rather than from the completion of an infinite sequence. (I have briefly outlined one way of mathematically describing the Trinity using these tools in this post and have made a lot of art about it.)

 

Mandelbrot did not publish a single image of the famous recursive set that bears his name until 1980. The Mandelbrot set has a logical, self-contained recursive definition that is quite short and simple, but it describes an infinitely complex mathematical fractal. Today, we can watch the beauty that emerges from this infinite recursive structure for free on YouTube⁵.

 

The underlying point here is that processes do not necessarily need to be built out of successive additions; they can have logical definitions that are fundamentally structural and recursive, just like topological time. The Father glorifies the Son, who glorifies the Father, who glorifies the Son, who glorifies the Father in an infinite dynamic loop that happens both between them and in them through the Spirit, who is also both from them and in them (see for example, John 10:28, John 14:10-11, John 17, I Corinthians 2:10-11, 2 Corinthians 3:17). The loop has direction and infinite activity without being bound to physical time or being defined by measurable incremental moments. And it is full of beautiful, dynamic, glorious complexity that is as far above the beauty of a Mandelbrot visualization as our universe is more beautiful than the timelines, trees, or vibrating strings we use in our diagrams of it.

 

Doesn’t the Bible say God is timeless?

 

No, the Bible describes God with expressions like “eternal”, “from everlasting to everlasting”, “Ancient of Days”, the “Alpha and Omega”, He “who was and is and is to come”, and “reigning forever and ever”, all of which are perfectly consistent with God eternally experiencing topological time. The bible also describes God’s wisdom, knowledge, and perspective as being fundamentally different than that of humans: He is “the High and Lofty one who inhabits eternity”, He, “declares the end from the beginning”, the “number of his days are unsearchable”, and to him “one day is like a thousand years and a thousand years are like a day.” If anything, these passages seem more consistent with the idea that God experiences a special kind of time, rather than claiming anything about him being completely timeless.

 

More importantly, the Bible describes God as eternally relational, which seems at the very least difficult, if not impossible, to imagine in timeless terms. God is love, meaning he must be able to love necessarily and independently of any universe. Can love really be love with no temporal expression of loving acts? The Father loved the Son “before the foundations of the world” - how could he love him “before” the creation of the universe if that was the beginning of any kind of time? The Son is “the radiance of the glory of God” - what could “radience” mean other than some kind of temporal procession or dynamic process involving a source and that which projects from it (radience with no flow or direction seems contradictory)? How does the Spirit “search everything, even the depths of God” if their relationship is one of purely mental and static fact-knowing?

 

I’m not sure about this

 

When early Christian theologians imagined God as outside of time or wrestled with the degree to which he could be considered temporal or timeless, they did not have access to the language of metrics, spacetime geometry, or topology, and they didn’t have the mathematical tools of general relativity. When the scholastic reformers were coming to their conclusions about God’s sovereignty and human decisions in terms of primary and secondary causes (or what later came to be called synchronic contingency), they didn’t have the language of superposition or the mathematical tools of quantum mechanics. And when William Lane Craig was concluding that God must be timeless sans creation because otherwise there would have to be an infinite succession of events, he did not have the language of hypersets and fixed point coalgebras or the mathematical tools of AFA Set theory, Geometry of Interaction, and Linear Logic. Craig could not have been aware of these mathematical descriptions of infinite dynamical systems, because they simply hadn’t been developed yet.

 

The things I’ve described make a kind of sense to me, but it can be overwhelming to think of all the things I don’t yet understand, not to mention all the true things about the world which no one has yet discovered. Whenever we reflect on deep theological mysteries, there is always a sense in which we are seeing things “as in a mirror dimly.” We need to acknowledge our limited mental capacity, the constraints of our language, our ignorance of scientific and mathematical realities, our failures of logic, and our selfish and arrogant desires to be right in our arguments. It’s very possible that everything I’ve written is utter nonsense and that I’ve wasted a lot of time without realizing some glaring hole in my reasoning. I confess I still have many questions, and that I am stretching my brain to its limits to grasp the tiniest fringes of these ideas. For example, I’m still not sure about the metaphysical interpretation of the topology and superposition ideas. Are all the paths along the modal topology really actual paths that exist out there in parallel worldlines, or is there some kind of global objective collapse that defines a single history? Physicists are wildly divided on their interpretations of what is really going on in quantum mechanics (though they agree on the math).

 

All that to say, I would welcome correction and direction from some other minds to help me evaluate these ideas and point out where I’ve gone wrong. I would love to hear whatever questions, objections, confirmations, or incoherent ramblings you would like to share with me! This is an open invitation to come and explore with me the many glorious paths of ultimate reality.