The Impossibility of Predicting the Universe, in All Possible Universes

Determinism, when taken to its ultimate conclusion, is beset by a paradox for which I am unaware of a widely accepted term. For now, I won’t try to make a creative name for it, I will simply refer to it as what it is: a deterministic infinite recursion loop.

It is a kind of undecidability problem. If you’re familiar with programming, you may be familiar with the most famous undecidability problem, the “halting problem”, coined by Alan Turing. Our problem here is not the same as the halting problem, but it is in the same camp of chaos theory undecidability.

Determinism suggests that the future can be calculated with the same precision as the past. This is based on the premise that events follow a causal chain that can be traced in either direction, given that the state of every particle in the universe is accounted for.

But as I will explain, this is actually impossible, not just technologically, not just practically, but philosophically impossible. Not just in this universe, but in all possible universes. What we will encounter here is a true metaphysical impossibility.

We will watch the universe adapt to itself.

Will You Make Coffee?

Suppose you build a supercomputer that can calculate the future state of the universe 5 minutes from now, and display that output on a screen.

So, the simulation is run, and the computer display informs us that in five short minutes, we will be brewing coffee. The logic is undeniable. Every particle of the cosmos has been taken into stock, every movement considered, and it has arrived at the perfect conclusion that our next logical course of action must be to make coffee.

But there was one variable it missed.

It was something always completely inaccessible to the program, something that was never considered:

Its own output.

Are we now bound by law to make coffee? No, the screen before us, and our reaction to that screen, was never accounted for in the initial prediction.

You may avoid making coffee out of sheer spite, or raw curiosity. I mean, just consider how uncool you would be if some computer demanded that you make coffee and you simply abided by it. How could you live with yourself? You would most likely tell the computer to shove it where the Sun doesn’t shine.

And you would be perfectly capable of doing this. The fact of the matter is that this is a new event, new information that neither you or the computer were privy to until this moment. Now, the entirety of the universe must readjust, rendering the prediction useless.

Why? Why couldn’t it calculate your reaction to its own output? If it can’t do that, can it even predict the future at all?

This is precisely the paradox.

It would have to calculate the future, before it calculated the future. How else would it retrieve its prediction and account for it? There’s a causality problem here.

How do you calculate the consequence of predicting the future, prior to actually making the prediction?

If that’s still a mindbender, consider the number of times the program would have to cycle through:

It runs a simulation, calculates your response to its first result, then runs a second simulation taking into account your reaction to its second result, then a third simulation taking into account your reaction to its third result, and so on, ad infinitum. It's a never-ending cycle of simulation, calculation, and prediction.

It’s an infinite recursion loop, and therefore impossible.

It’s not just impossible in this universe, but every possible universe. There is no possible universe where you can solve an equation that has an infinite number of infinitely-changing variables.

What we are seeing here is a logical impossibility, one of the hard limits on information systems, which there may be many. It would always be an impossibility to calculate things that are in fact impossible to calculate. To throw out the baby with the bathwater on this point might be foolish.

Salvaging Determinism With a Loophole

What this suggests is that there is an inherent limit to causal prediction - a threshold where our predictions must ultimately breakdown. That threshold depends on the degree to which our prediction itself influences the future.

Is determinism beaten then? No, not necessarily. Determinism as a concept can still be relied upon to predict a tremendous number of simple events and even many complex events. However, the grander our prediction becomes, the more likely we will run into this undecidability problem.

To reiterate, the accuracy of any prediction depends upon the degree to which the prediction influences the system. If we are attempting to predict the entire system, that probability is 100%.

However, what about subsystems within the system? Is there perhaps a loophole here?

Let’s try this again with a similar thought experiment, but add some constraints:

Suppose there is a room, and inside this room sits a person and a coffee machine. This room is completely isolated from the outside world.

Outside of the room somewhere, there is a supercomputer that has mapped the state of every particle in that room. The computer has no direct correlation or influence to that room; let’s suppose it’s 3000 miles away. Every precaution has been taken to ensure that the room is so isolated that any outside event will have no statistically significant effect on the inner contents of that room.

A team of researchers is observing the computer, but they have taken an extra precaution as to not be shown the result of the simulation until after 5 minutes into the future, when the predicted event has already passed. They can watch a video of the test subject after the fact to determine if the event in question was correct.

The computer calculates that in 5 minutes, the person inside the room will make coffee. Does that person make coffee?

Yes.

In this instance, we can be sure. By all rules of logic, it should be a guarantee that this person will make coffee, and we should be able to make consistently accurate, slightly-useful predictions.

However, once the computer is placed into that room, or if there is an unexpected vulnerability in our isolation of that room, all bets are off. You will once again watch reality adapt to your prediction.

It is also extremely difficult to know if there are any vulnerabilities in your information system, so one might find extreme rates of error when applied to environments without such strict controls.

There is also another loophole, one that was masterfully portrayed in the show Devs. If you’ve ever watched the show, the one-second projection scene is most-likely forever etched into your mind. It is truly an unparalleled sense of existential terror. Masterful.

I will not go into detail here as to avoid spoilers, but I do suggest watching the show. Basically, it might be possible to predict the future on a timeframe where the universe doesn’t have enough time to adapt to it, but this prediction will still break down when extended to longer timeframes.

The Game of Life

I want to give you one more tool to think about this problem. There is a semi-famous game developed by a mathematician called Conway’s Game of Life. The problem we’re experiencing here is not exactly the same problem encountered in the game, but what is similar is the concept of perfectly logical unpredictability.

There is nothing we’ve stated thus far that defies logic. Everything is still very-much airtight. The reason nothing can predict the future is very logical.

This is the same way Conway’s Game of Life works. It’s a computer program, perfectly logical, and yet, totally unpredictable. You actually don’t play the game, you set the initial seed value and watch the game unfold. The catch is, nothing can predict the future state of that game until after it’s already been played. Nothing.

The undecidability problem of this game is in fact the halting problem that we mentioned earlier.

If you play that game, you are watching the universe adapt to itself.

Not Just a Hypothetical

We are able to calculate simple systems with extreme accuracy, but we already encounter this prediction threshold all the time in more complex systems.

Any stock trader that "solves the market" i.e. finds a consistently profitable trading strategy, finds that their strategy eventually sends them towards bankruptcy, as the market inevitably adapts to the strategy.

When the strategy is divulged, the market adapts to it very quickly. Even when the strategy is not explicitly divulged, that trading behavior has an effect on the market that will eventually alter its behavior, rendering the equation useless.

This is an example of the same infinite recursion phenomenon in real, everyday life, where reality is adapting to predictions of the future. The only way to truly “solve the market” would be to also calculate the market’s every reaction to your prediction.

Free Will?

I suppose it would be a disservice to lay out this world-changing idea and then not even address the idea of free will. Do we have it?

If by free will, you mean we can magically avoid our deterministic, causal existence? That our decisions are completely authoritarian - a top-down decision making process? That our actions and reactions transcend the logical nature of existence? No, I don’t think so.

If by free will you mean, the future is not certain, that the future doesn’t even exist until it happens, and that it is possible for the universe to react and adapt to your actions, then yes.

It depends on what you mean.

Update: I have found an obscure term to describe this: “the paradox of predictability”, which comes from Michael Scriven in his paper An Essential Unpredictability in Human Behaviour.

He describes a vaguely similar idea, but I don’t think it’s exactly the same idea. His idea, by my understanding, is that in a deterministic systems, small changes in initial conditions can have a magnified effect on predictions over time. The paper is very hard to follow and then he tries to mathematize the concept making it completely unreadable.

However, this paper is far more readable and I believe comes closest to describing the concept I have described here. He also tries to mathematize it but I had an easier time understanding this one.

“…even in a deterministic universe, there are fundamental, non-epistemic limitations on the ability of one subsystem embedded in the universe to predict the future behaviour of other subsystems embedded in the same universe.”