The Shape of Things to Come: Cylinder vs. Tree

In the previous article, I presented the difference between indeterminism and determinism by whether or not duplicated things become different from one another. If the universe is indeterminiate, then this is to say there are things that, if duplicated, can diverge from their originals.

This is about as good as we can get from a practical standpoint. We don’t need to duplicate the entire universe, we just need to duplicate some things in it. Of course, it is impossible to verify that something is a perfect duplicate. There is always closer to look at an object, and we may find a discrepency where none showed itself before. Moreover, at the quantum level, measuring that something is a perfect duplicate might be impossible. Thus there are reasons to doubt that anything is a perfect duplicate.

But we know many things with good evidence while having reasons to doubt. If you hold up your hand and observe it, you have good evidence that you have a hand right there. Even if we are living in a simmulation. And even if the hand just became a hologram due to a glitch in the simmulation. Raising a hand and looking at it is still as good of evidence for hands as it gets. In the same way, there can be good evidence that something is a duplicate, even if we can never be certain that it is a duplicate. And from multiple duplicate things observed multiple times, we can build up evidence that supports indeterminism or determinism. If we duplicate things as far as we can tell, and we get repeated divergent results, then that’s strong evidence for indeterminism.

The practicality is clear. But a part of the theory is unclear. When I say that there are some things that, if duplicated, can become different from their originals, what do I mean? To start, I am not talking about mere logical possibility. Lots of things are possible logically speaking just because they are non-contradictory. I rather mean “can” in a forces, abilities, or physical sense. If I can jump to Jupiter, it’s because I have the ability. If I cannot, it is because I lack the ability. In this physical sense, indeterminate things can diverge from their originals. And what if some indeterminate things don’t diverge? Room is left for this case, because we say that they can diverge—they don’t have to. It just happens that no divergence happened. The duplicates do not diverge, but it’s still possible that indeterminism is at play regardless. But what does this mean?

The shape of the future explains how indeterminism can still be in play when things don’t diverge. In a deterministic future, the object has one possible path forward in time. The shape of a deterministic universe may be likened to a cylinder. To illustrate this, let’s say we take the present universe and flatten it into a circle (don’t wreck things, just reposition them). From this, take the universe of next future interval and flatten it into a circle in the same way as well, and lay it on top of the present universe. Keep stacking the subsequent intervals after this, one on top of the other. The resulting shape is a cylinder extending as far as the intervals we’ve added.

The cylindrical picture makes a deterministic assumption. For the next interval, there is just one possible universe that can occur. But if there is not just one possible universe, but rather many possible paths forward as in indeterminism, then the shape is not a cylinder, but is rather like a tree. In an indeterministic future, there are many possible paths forward. The present is the trunk, and any branches are the possible ways that it can have things within them diverge or stay the same. The branches can themselves have further branches according to what is possible next. If we flatten the universes and lay them on top of one another as we did before, there are different universes to lay down on different branches of the tree for the same interval according to what can happen next.

The sense of “can” in saying that duplicate things can diverge from their originals is then that there are these diverging future possibilities. If something can become different from its original but did not, then there were diverging future possibilities for something that included becoming different, and also staying the same. The future possibility of staying the same is just the pathway that occured. The possibilities were there and no longer are, since one path has been claimed.

Some may wonder if we can drop this talk of the future and its shape as theoretical nonsense. But it makes perfect sense. There is “the future,” which is what can happen later. And either determinism or indeterminism is true. That is, either there’s one or more than one future possibility. And these futures can be differentiated by different shapes, either by that of a cylinder or that of a tree.

Which is the correct shape? By practical evidence, many human actions and quantum events present us with branches of a tree-shaped future. This estimation might be wrong. But so can anything else with strong evidence. I have perhaps not explained how strong the evidence is in order to help us make a determination here. We’ll leave explaining this further as a branching future possibility.