Proof of God: The Cosmological Proof (2)

Hume’s Trip to the Pole

This line of thought brings up another objection, one that was first noted by David Hume.

Hume, who lived from 1711 to 1776, was one of the first philosophers to examine proofs of god with a sceptical eye. As my future self will mention, my thoughts on miracles will be little more than his thoughts with a light dusting of cheese and vinegar. He also examined the Design proof, and weighed in on Cosmological as well. While he gives several objections to the last one, I’d like to focus on this one:

… The WHOLE, you say, wants a cause. I answer, that the uniting of these parts into a whole, like the uniting of several distinct counties into one kingdom, or several distinct members into one body, is performed merely by an arbitrary act of mind, and has no influence on the nature of things. Did I show you the particular cause of each individual in a collection of twenty particles of matter, I should think it very unreasonable, should you afterwards ask me, what was the cause of the whole twenty. This is sufficiently explained in explaining the cause of the parts.

(Dialogues Concerning Natural Religion, Part 9)

As I’ve mentioned before, at the core of Cosmological’s argument is a hierarchy. I can turn this into a visual metaphor by drawing a series of ever-branching pipes:

[diagram of a tree of pipes]

As we follow the flow down these pipes, we jump from cause to effect, or from mover to moved, or from creator to created, or along whatever relation was used to construct this version of Cosmological.

[diagram of an arrow flowing down these pipes]

Since these pipes have a finite length, we can attach a rope to one point, then swim around the pipes until we run out of pipe but still have some rope in hand. We can just as easily picture the rope attached to the top of this pipe hierarchy, and then pull ourselves along it until we reach the very source of all the flow.

[diagram of a rope feeding through these pipes, acting like a measure of time]

Thanks to the rope trick, it’s easy to ignore the branches and just think of it as one pipe with a well-defined beginning. Note that we don’t care about an ending; so long as there’s a beginning, we can always pull ourselves towards it. In contrast, consider a long pipe with no beginning or ending at all.

[diagram of an infinite but straight pipe]

If we attach the rope and explore, we’ll run out of rope no matter how much swimming we do. Likewise, if we pull ourselves along an attached rope, we’ll still have plenty of places to explore once we’ve reached the end of it.

Cosmological compares these two layouts, and rejects the second one. It claims an infinite pipe or chain of relations is an absurd idea, and faced with no other alternative claims the hierarchical version is the only way to go.

But are those two the only possible choices? Consider instead a loop of pipe, like so:

[diagram of a pipe bent into a donut shape]

We have a finite length of pipe, which satisfies Cosmological’s rejection of the infinite, and yet at the same time there’s no beginning or end to this pipe! If we pull ourselves along a rope we find drifting in the current, we’ll again be faced with a void that we’re free to explore. We can use this rope as a measure of how far we are from the “beginning.” If we just float and let the rope spool out, we note that we get further and further away. If instead we pull ourselves up, our rope gets shorter and shorter until we run out of rope. From this point, everything is after the beginning, since we need to let out some rope to move away from this point. This will come in handy later.

[diagram of a donut pipe with a rope attached to one point]

But for now, we’ve found a third way, one that avoids infinite spaces while also avoiding the need to stop at a First Mover. This derails Cosmological, since it was counting on finite space implying a First Mover, and again renders the proof useless.

No doubt you’re sceptical of my metaphor. We know our universe had a definite beginning, because we’ve found the evidence in and between the stars. Real life is not a one-dimensional loop, but a four-dimensional expanse of space and time. How can the two be similar?

Very easily, in fact, so long as you think four-dimensionally.

Back in 1905, Albert Einstein published his theory of Special Relativity. In this landmark paper, he proposed that space and time are actually the same thing, differing only in what direction you look, and that both of these are warped by gravity. It sounds crazy, but one hundred years of observation have backed up Einstein’s claim, and Special Relativity 2.0 (better known as General Relativity) has become one of the most successful theories ever proposed. [A]

The standard metaphor for General Relativity, handed from generation to generation, is the rubber sheet. Plunk a heavy round object, like a bowling ball, on one that’s been suspended in air, and it’ll sink down and pull the sheet with it. Take a smaller round object, say a marble, and roll it across the sheet towards the big one. It’ll go in a straight line until it reaches a bent part of the sheet, where it’ll veer towards the heavy object. Do this well enough, and you can get the marble to orbit the big ball before friction ruins the fun.

If we’re allowed to warp the sheet, however, what’s stopping us from warping it around until it touches itself? We’ve just reached the other standard cosmology metaphor: the rubber balloon. This is usually used to explain the Big Bang, by showing how space stretches and makes everything look like it’s rushing away from you. But we could also think of it as a potential model for how the universe is shaped. It has a finite area, even if you continue to inflate it, but at the same time you could walk around this shape without ever reaching an edge. This is exactly like the ring of pipes I outlined above, only in two dimensions.

A three dimensional version is too big for me to visualize, unfortunately. That one-dimensional version is actually in three dimensions; I needed to twist the pipe around so that it would meet itself, and the only way to visualize that from the outside is to invoke another dimension, and I also implied the dimension of time indirectly by having our metaphorical swimmer swim. This diver within the pipe has no way of accessing the second spacial dimension, let along proving it exists, so I haven’t spoiled the metaphor. Likewise, to explain the two-dimensional version I really used four dimensions to get the point across. I need one more dimension to describe a three-dimensional extension, but my poor brain was only designed to work in four dimensions and fails miserably when dealing with five.

And yet that hasn’t stopped similar brains from thinking about higher dimensions. Einstein was able to cope with a four-dimensional space-time by using math as a crutch, and other scientists have used the same trick to think about our world in eleven or more dimensions. To name an example, Stephen Hawking has proposed a theory that would visualize time as a sphere like the Earth, with the “North Pole” label replaced with “Big Bang.”

I was never built to be comfortable with higher dimensions, but that doesn’t rule out their existence. We humans were convinced the world was flat for a very long time, until a few of us realized we actually lived on a very, very, very, very big sphere. It only looked flat from our limited perspective. Cosmological makes the mistake of assuming its narrow perspective is the only one, that there must only be two ways to organize the world.

All this talk of spheres brings up another good rebuttal, though. Let’s return to my pipe metaphor again, with the rope attached to the head of Cosmological’s hierarchy. The proof asks us to pull ourselves hand-over-hand up the rope, until we run out of space and rope. It then asks what would happen if you tried to take up one more length of rope. It points out this would take you outside the pipe, and that the only thing which could survive out there is a god. Ergo, god exists.

But does that make sense? In our metaphor, we are constrained to follow the pipes, and to always have a length of rope greater than or equal to zero. We have no way to get outside out of either limit, and yet Cosmological is asking us to think about what’s on the outside. That doesn’t fit into our metaphor at all! David Hume indirectly realized this; since you can’t reach outside of the pipe, once you’ve swam around and reached every point within the pipe, you don’t have any place left to go. If you understand everything within the pipe, you understand everything.

[diagram of person banging on pipe, from the inside]

Let’s now extend the metaphor back to the proof. Note that “cause” and “effect” are exclusive; one object cannot be the cause of, and the effect of, another object. The same applies to creation, movement, and any other system used by variations of Cosmological to organize the hierarchy. This not only creates Cosmological’s hierarchy, it also defines a direction; if we just let things play out naturally then creators create, movers move, and so on. Having established all this, the proof asks us to go against the natural flow and walk back up the hierarchy to the top, being careful never to backtrack. Once it runs out of universe and reaches the pinnacle, it tries to take one more step. The universe defines where we can and cannot go, however, so this is the same as asking us to step outside the universe. The result is nonsense, even though every step before then seems perfectly reasonable.

This assumes a hierarchy, of course, which has a definite start. If our universe is more like a circular pipe or spherical balloon, our choice of start is arbitrary. Fix our metaphorical rope to whatever place you wish to call the start, and then take a stroll. Sometimes the rope will lengthen, sometimes it’ll shorten, but in no direction will you be forced to go beyond the “start.” Even if you make a beeline straight for it, the rope will merely shrink down to nothing then immediately lengthen again, without forcing you to backtrack.

This fits perfectly with our modern view of the universe. Relativity makes time and space interchangeable, so any physical metaphor works equally well with time. While asking “what happened before the universe” seems to be a valid question at first, it’s actually the same as asking “what’s beyond the end of the rope,” “what happened before time existed,” or “what’s North of the North Pole,” all of which are absolute nonsense.

And yet the Cosmological proof requires us to ask those questions, and requires us to think of them as perfectly valid, otherwise it has no place to insert a god. We’ve found another flaw in the proof, only this time there’s no escape hatch.

[A] Whoops, past me screwed this one up. As Rob Grigjanis points out, the Special Relativity papers of 1905 ignored gravity. I also misunderstood spacetime a bit. While space and time are integrated, there’s a difference between purely spatial paths and purely temporal paths through this space. I think one of Brian Cox’s book covers this well for a lay audience.