This is just a short post that aims to show that determinism and free will are totally compatible with one another.

Preamble

If you have never seen this debate, you way understand what’s it all about by reading this short section right here.

My definition of determinism:

Determinism is the idea that there exist a function/formula that accepts the current state of the universe, as an argument and that outputs the state of the universe at some later or earlier time.

This principle seems true (at least in the smaller-scale), but the main reason it gets so much attention is that all of science is based on it (after all, science is all about verification which is predicting the outcome of some experiments and natural phenomena).

Now, why do some people think that this principle is incompatible with free will? To understand that, we have to look at the personification of this idea — a theoretical creature known as “Laplace’s Demon”. I talked about it in my post about universal knowledge - it is a creature who somehow acquired this function and also the state of the universe at one time and is smart enough to compute all states of the universe, therefore it knows everything.

We may regard the present state of the universe as the effect of its past and the cause of its future. An intellect which at a certain moment would know all forces that set nature in motion, and all positions of all items of which nature is composed, if this intellect were also vast enough to submit these data to analysis, it would embrace in a single formula the movements of the greatest bodies of the universe and those of the tiniest atom; for such an intellect nothing would be uncertain and the future just like the past would be present before its eyes. — Pierre Simon Laplace, A Philosophical Essay on Probabilities

And if you consider this view for scales that are larger than individual atoms (but yet smaller than stars and planets), it follows that Laplace’s Demon can also predict the behavior of people i.e. it knows what are you going to do yesterday and the day after, it even knows what the contents of your brain would be, and for this reason you don’t have free will.

This is the gist of the argument, there are a bunch of YouTube videos that describe it as well.

There are a whole bunch of physical considerations regarding the existence of Laplace’s Demon, the most serious of which is that quantum physics is not deterministic, but I won’t go into these, as there is a simpler way to call out the paradoxes that its existence would lead to.

A proof that Laplace’s Demon cannot exist in this universe

Here I aim to prove that even if the principle of determinism is/was true, Laplace’s demon cannot reside in this universe. I’d say that the fundamental reason for this is that the fact that the universe has certain limits/constraints/boundaries, which any Laplace’s Demon Candidate will inevitably run into. I will submit two versions of the proof, based on two such constraints - time and space.

Space-based proof

The first version of the proof is the following:

Suppose that Laplace’s Demon exists. Then, its mind must contain, within itself, a representation of the whole universe e.g. if it is a regular brain, it has to have, let’s say, at least one neuron per each particle of the universe, if it is a computer, it must have a memory cell per each particle etc. But, Laplace’s Demon is itself part of this universe, therefore it must contain a representation of itself in itself, which leads to infinite regress — the representation of the Demon has to contain a representation of the universe which must contain a representation of the Demon and so on. Therefore Laplace’s Demon cannot reside in this universe.

Further, assume that Laplace’s demon is still able to do its thing in some parallel universe, but that I am able to get a hold of its computations. If so, I can find the part where he says what I will do next and do something else (I can do that because the computation deterministic i.e. fixed). Therefore even if Laplace’s Demon does exist in some other universe, we cannot ever have access to its predictions.

Time-based proof

Another proof of this sort can be carried out, based on limits in time rather than space:

Suppose that Laplace’s Demon exists. In order to predict something that would happen in say 10 years time, they would have to compute everything that will happen in this 10 years in less than 10 years. However, this is impossible, since some processes in the universe move at the speed of light, and predictinghow they would end up would involve modeling them in a way that is faster than the speed with which they are actually carried. Therefore it will require the computation to happen faster than the speed of light, which is impossible.

Moreover, in order to predict everything, Laplace’s Demon has to obtain the state of the whole universe at a given time e.g. he has to know when a given star that is in the other part of the galaxy would disappear. However, this is impossible, since, again, information cannot travel faster than the speed of light.

What does this proof mean

So, while we didn’t prove that Laplace’s Demon cannot exist at all, but we proved that it can only exist if it:

1. Lives outside this universe.
2. Nobody from this universe has access to its readings.
3. Is not subject to basic physical limits that we have, as the speed of light.

That, in my opinion, makes Laplace’s Demon Not Very Interesting, when discussing free will. This is so, because it shows that Laplace’s Demon cannot be an agent in the universe, the behavior of which it is predicting. If it exists, Laplace’s Demon would just constitute another universe - computing the state of the world one second from now would amount to one second passing in our universe.

Conclusion

If Laplace’s demon exists and is reading this text (and if it exist it has to be reading it, if you think about it), I would give it the following piece of advice:

Dear Laplace’s Demon,

Seems that you are so powerful and that you have a whole universe at your disposal, I don’t see you are bothering with computing all the future states of the universe manually. Instead, just arrange a couple of trillion atoms in your universe in the same way as they are arranged in ours and watch the magic unfold. I mean, why would you create a representation of our universe, with all its overheat, when you can just create a copy of it?

You get my idea: if Laplace’s Demon follows this advice , its universe would just be some kind of copy of our universe with no particular criteria making one of them more real than the other. And even if Laplaces Demon doesn’t follow my advice, the situation would not be so different, e.g. beings that reside in it’s brain would be just as sentient as the ones who reside in the “real” world.

So, if there may exist another (simulated?) universe that is an exact copy of our universe, where there is another version of me who is doing exactly what I am doing, does that mean that I don’t have free will? For me, the answer is “No” — I am freely making all of my decisions, it is just that the decisions that I am making happen (quite unsurprisingly) to be the same as the ones that the “other me” is making. But that does not mean my (our) decisions are not free.

Our futureh is not determined, it might be determinable, if all that will happened has happened before, but that is a different thing.

PS Iegor Reznikof proved a similar result in a similar manner in 2012.

Addendum: Quantum mechanical ramblings

Here I want summarize the argument that David Deutch makes in “The fabric of reality” about quantum mechanics, non-determinism and life. He explains how DNA (which we can view as the embodiment of “free will”) has a special place in the universe because it copies itself in a way in a manner that is deterministic despite the fact that the world in general isn’t deterministic.