The Free Will Loophole

In a recent blogpost called “How to live without free will” [5] Sabine Hossenfelder, a well-known theoretical physicist, is making a categorical argument: acording to physics, humans have no free will. It’s a millenia-old debate that keeps hunting humas: are we really deciding anything, in the sense of “selecting one of possible futures”, or is the future, in principle, already decided event though we cannot practically predict it?

As the author makes the case, modern science seems to sugest the second option due to a feature of our universe called determinism. In our deterministic universe, be it classical or quantum, the “party pooper” for having something like free will is causal closure: everything that happens happens either for a physical cause or is completely random (has no cause at all). Hence, if you agree with the view that our minds are essentially physical computing devices (this is called the Chuch-Turing thesis), then all we do is exclusively caused by some movement of the matter at a physical level. Due to the enormous complexity of both our brains and the universe, that does not mean that one can practically compute what you or another person will do, but just that all you do is ultimately derivable from what happens at particle physics level.

It might seem that, if you don’t accept the idea that minds are physical computing objects (hence, deny the Church-Turing thesis) — for example by believing in the idea of an immaterial soul — the free will problem disappears. However, in this case the burden of proof and of an explanatory theory is with you. No one has, to my knowledge, come up with such a theory, at least not one to be taken seriously. Many “no-go” attempts have been made — most famously the brilliant physicist Sir Roger Penrose is a proponent of a non-computational nature of the mind [6], but its arguments are speculative and unconvincing to most of the scientific community.

Going back to S. Hossenfelder’s blog post, her arguments are drawing heavily from some of her previous texts in which she explains her position much more detailed. Crucially, it is based on a scientific concept called strong emergence. I encourage you to read [1] for details, it is written clearly and in an accesible manner. The short version: strong emergence means observing some physical phenomenon that is not explainable, or reducible, not even in principle, to smaller-scale physical theories — a concept called reductionism, or weak emergence, that has worked well for most physical theories. Because we never observe strong emergence, so the author, we do not have free will.

My post is an attempt to point to a “loophole” in this argument, along the lines of what the Dr. Hossenfelder herself mentions in [1].

EDIT: It has been pointed out to me that the answer I’ve wrote as a direct response is not intelligible outside the context of [1], so I will try to briefly sketch more of that context for the impatient reader.

Goes like this: there would be a chance to have “true” free will if we observed the strong emergence I’ve mentioned above, in other words: if we could point to the existence of a strongly emergent physical theory. But what does that exactly mean ? To understand, we need to define a few more things— don’t worry, they’re easy to follow.

First of all, what is a physical theory — as opposed to a mathematical one? Simply put, a physical theory is a bunch of mathematical stuff out of which some (but not necessarily all) stuff can be identified with observable, or measurable, phenomena in nature. Like, for example, Newton’s second law of motion states that when we push objects around by applying forces this happens acording to a mathematical equation: F = ma.

Secondly, because we currently don’t know how describe nature using a single physical theory (that’s what a “theory of everything” would be), we have a bunch of them describing different phenomena at different scales: subatomic particles, atoms, molecules, living cells and so on. According to [1], all physical theories are falling into one of two main classes:

• either a theory can be entirely derived — at least in principle — from another theory (or perhapse several other) at a lower scale, in which case it is said to be weakly emergent from that theory
• or the theory cannot be entirely derived from other theories, in which case it is said to be fundamental

For example, particle physics is fundamental, while chemistry is weakly emergent, because it can be, in principle, derived entirely from particle physics — the fact that doing so is extremely impractical is (arguably) irelelvant for this discussion.

Thirdly, here comes the thing we’re interested: according to S. Hossenfelder “a physical theory is strongly emergent if it is fundamental, but there exists at least one other fundamental theory at higher resolution” [1] — higher resolution means at a lower scale (particle physics is at a lower resolution than chemistry, for example)

It is precisely these three criteria which I am adressing in my response below with respect to the theory of computation:

1. it is a physical theory (it uses abstract math to say something nature)
2. it is fundamental, not being weakly emergent of any other theory
3. there is another fundamental theory at a smaller scale: particle physics

Therefore, the theory of computation is strongly emergent. Faith in free will restored.

Here’s my original answer:

“I enjoyed both this text and the one you quoted in the comments [1]. Looks that you yourself are in a superposition of both denying and accepting free will, as per your final statement in [1]: ‘I herewith grant you permission to believe in free will again’.

I took the time to read and understand your position in [1] wrt. hopefully much of the things that have generated misunderstandings in the discussion of your blog post: causal exclusion, strong vs weak emergence, reductionism and free will. Very much liked your honest search for a loophole in your own argument.

As a software engineer myself, I’d like to make a suggestion as a candidate for strong emergence: the theory of computation.

1. Unlike popular (mis)understanding, the theory of computation is a physical theory, not a mathematical one, because whatever can or cannot be computed, as well as what can be efficiently computed, depends on the laws of physics (for example, D. Deutsch makes this quite clear in his book and in [2]). It sure seems to fit your definition of a physical theory as “mathematically consistent axioms combined with an identification of some of the theory’s mathematical structures with observables”: indeed, (small) stuff in the physical universe can be arranged in systems that perform computations. More specifically as realizations of (deterministic) Turing machines, be it silicon based, biological, etc. or as “the use of a physical system to predict the outcome of an abstract evolution” as defined in [3]. For the sake of simplicity, I’m abusing the name Turing machine here: the systems we’re discussing are finite memory rather than Turing complete. However, “naturally computing” systems could, in principle, solve their “out of memory” issues by simply incorporating more stuff into their computations — like atoms and molecules, which are plenty (but not infinite). For example, when a fertilized egg is executing the DNA code instructions to create a living organism out of stuff around it, this can be seen as the Turing tape being extended into the environment.

2. Computation theory is not weakly emergent from any known theory. Some computation might be reducible to laws of physics at higher resolutions, but precisely because computations can be arbitrarily complex I fail to see how computational theory concepts like, say, complexity theory or the P=NP question can be reducible to any other known physical theory. I also don’t see how EFT can help. Hence, I must conclude that computation is fundamental. This part of my argument would probably benefit of more precise formal treatment, but time and space are scarce.

3. There is at least one other fundamental theory at a higher resolution. This one should be rather obvious: particle physics, that’s where the dicussion started.

Given the three properties above, it would seem therefore that computation theory is a strongly emergent one.

I (partially) agree with your statement that Gödel is not relevant to most laws of physics. But once small stuff groups into larger systems that can perform computation, it seems that Gödel, Turing and friends creep in. Indeed, once sufficiently complex, such systems are capable of tricks like self-replication, self-reference (the “strange loops” as called by D. Hofstadter), arithmetics and, arguably, consciousness — although we do not know yet how and must appeal to the Church-Turing thesis. In this light, there is most likely not by chance that the 2 examples of strong emergence you quote in [1], one of them being the spectral gap, are essentially related to computations. In [4], the following argument is made: ‘the undecidability ‘at infinity’ means that even if the spectral gap is known for a certain finite-size lattice, it could change abruptly’ which is inline with the idea that computation theory has strong emergent features without requiring infinite systems”.

[1] https://fqxi.org/community/forum/topic/3065.
[2] https://www.cs.indiana.edu/~dgerman/hector/deutsch.pdf
[3] https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4123767/
[4] https://www.nature.com/news/paradox-at-the-heart-of-mathematics-makes-physics-problem-unanswerable-1.18983
[5] https://backreaction.blogspot.com/2019/05/how-to-live-without-free-will.html

[6] Roger Penrose, “ The Emperor’s New Mind: Concerning Computers, Minds and The Laws of Physics”