This will be rather brief and incomplete. But gee, it’s my free will to publish it as is.

Scientists have become notoriously sceptic or pessimistic about free will. Guys like Sam Harris or Victor Stenger, for instance. Also german physicist Sabine Hossenfelder published on her blog three articles, by the names of „You probably have no free will. But don’t worry about it.“ (2013), „10 Misconceptions about Free Will“ (2014) and „Free will is dead, let’s bury it.“ (2016).

Very roughly speaking, these people hold that the laws of nature (be it the basic laws of physics or the inner working of our brains) do not leave any room for anything that could be righteously called „freedom“.

Now, being a scientist myself, I kinda felt the need to answer back. After all, free will is quite an important question, but it’s also notoriously muddy. Therefore, I chose to just focus on the 2012 arxiv-article on „The Free Will Function“ by above mentioned Sabine Hossenfelder. In her paper, Mrs Hossenfelder gives some reasoning as to why the basic laws of physics would preclude freedom from being possible in the physical world; and that is (since there is nothing but a physical world) possible at all.

Let us look, how she does it. She starts out by giving two necessairy conditions for free will:

1’) An agent in possession of free will is able to perform an action that does not inevitably follow from all in principle available information at any time preceding the action.


2) The actions of an agent in possession of free will cannot be consequences of fundamentally random processes.


And then she goes on to say that all known basic laws of physices violate either 1’) or 2), because they are either fully deterministic xor fundamentally random; therefore, free will can not exist (I shortened the argument quite a bit, but it’s main line of reasoning is hopefully preserved).

However, Mrs Hossenfelder goes on to say, that freedom might be possible, if the fundamental laws of physics would entail something she calls a „free will function“ (FWF). This FWF would be determined by the past of an agent but not deterministic about its entire future (she distinguishes between „determined“ and „deterministic“). That is, while an FWF can serve to predict the very next step of an agent (or its inner brain processes, for that matter), it does not so for all future steps/actions. She then proposes that an FWF could be thought of for instance as the digits of some transcendental number tau: From the known row of digits one can calculate the next digit but not the nth digit. If decision-making would be governed by brain processes with FWF-like causal structure, physics would in principle allow for freedom. But then she returns to her original refusal of freedom and concludes:

"Of course these examples are arbitrarily constructed and are certainly not meant to describe actual reality. Their purpose is merely to show that it is possible to have a mathematical description of reality that does allow for free will to exist and give operational sense to the act of making a decision in a world that is determined but not deterministic. This admittedly opens more questions than it answers: How can one embed such a free will function into the currently known laws of physics? (…)"


Now. While I found reading Mrs Hossenfelders Blog and paper to be enlightening and thought-provoking, I suspect the whole reasoning about there being no room for freedom of will in the known physical world to be faulty. Actually, on many different accounts, but here I’ll focus on one particular.

It all goes down to misconceptions about causation and reductionism; more precisely, I believe it to be erroneous to equate the ontology (and laws of motion) of elementary particles with the ontology (and laws of motion) of all causes there can be. Let me explain below.

Reality of the „Free Will Function“

And let us start this by inquiring about the ontic state (i.e. „reality“) of the Free Will Function (FWF). In her arxive-paper, Mrs Hossenfelder proposes to implement the FWF via a computer algorithm which computes some transcendental number tau, the digits of which could be used as a choice-function, which is neither deterministic nor random, i.e. which fullfills her free will conditions 1’) and 2). And let us also assume that the digits of tau are used to switch on or off ten pixels on a computer screen (pixel 0…9).

I do hold that this FWF is „real“ in most meaningfull senses of the word: Its is real as an arrangement of elementary particles, which make up a computer and eventually cause some electrons to emit light (or not); but it is at the same time real as a causal structure (lines of code), causing pixels on a computer screen to flicker in some pattern according to the succession of digits of tau.

And what that entails is that it is possible to construct a „real“ FWF (which is neither deterministic nor random) out of elementary particles obeying the basic laws of motion (which are only deterministic xor random). Which is to say that, contrary to what Hossenfelder states, an FWF is not just an „arbitrary construction“; it does, in fact, „describe reality“. If a tau-computing computer can be real, then so can an FWF.

But I concur that it is hard to see why and how. There is nothing „emergent“ or mystical or non-physical about a (von-Neumann)-computer, computing tau to switch on and off pixels on a screen. In fact, everything about such an arrangement is known down to the minute detail; that is to say down to the finest grained description of the world that we know off. And yet, the causal structures of both stories — the finest grained and the coarser grained — differ from one another. But here (in contrast to dubious and still largely unknown systems, like brains), we have the possibility to look for the mechanism which brings forth the possibility of a non-deterministic but also non-random causal structure from an underlying deterministic xor random structure.

I suspect, however, Hossenfelders opinion about the reality of an FWF is somewhat more fundamentalistic. For an FWF to be „real“ she wants it to be engrained already in the basic laws of physics. This is how I understand her final question in the above citation; i.e. for free will to be possible, it must be possible to „embed such a free will function into the currently known laws of physics“. — Why exactly?

And this sentence also begs the question: Which laws of physics does she pertain to? If it is the basic (quantum mechanical) laws of motion, I beg to differ. Her own idea of a computer, which is able to compute tau, renders it wrong; obviously, a FWF with real causal power is possible without the basic laws of motion leaving room for freedom in her sense. If, OTOH, the talk about the „laws of physics“ on coarser grained features of the world and in particular about the „laws of translation“ which go from a finer grained level of description to a coarser grained level of description, then I am perfectly fine with that statement. But reading the rest of the paper (and her blog), I do think that Mrs. Hossenfelder really believes for freedom to be „real“ (eg. as an FWF governing decision-processes the brain) it must be somehow present already in the most basic level of physics.

I can perfectly see how she comes to this idea. It is, as mentioned earlier, something along the lines of: (1) There is nothing but elementary particles and the fundamental laws of motion that govern their future/past*; (2) The laws of motion are only deterministic xor random; (3) The notion of „freedom“ pertains to laws of motion that are neither deterministic nor random; (4) Therefore, freedom can not exist.

*I just want to point out, that already this starting idea has met quite some scepticism, i.e. in the vein of Nancy Cartwright who is a „theoretical-law anti-realist“.

In any case, this reasoning holds only if all causes in the world could be reduced to singular quantum events and -motions. Which is not the case. Some causes require a coarse grained description over ensembles of particles to be understood/described. Like for instance, the light emission pattern of electrons located at some semiconductor-structures we call „pixels“ of the above mentioned computer screen. To understand/explain, why a particular pixel on the screen is switched on or off at a given point in time, requires to reconstruct the knowledge of the causal structure of the lines of code wich calculates tau.

Causes

In Mrs. Hossenfelders formulation of the problem of free will it matters if coarse grained descriptions of the world can righteously be seen as „real“ causes. There is actually an answer to this question: If coarse grained descriptions of the world could not be counted as real causes, then there would be nothing to argue about in the first place. The whole problem of „free will“ would be non-existent, because the talk of „brains“, „will“, „agency“ and so forth pertains to the causal power of exactly coarse grained descriptions of the world; actually, any notion of a „sub-system“ already entails some coarse graining. And without these descriptions one would, in fact, be unable to formulate the problem at all. So, yes, if we want to debate free will, then we must concede the possibility of coarse grained descriptions of the world to bear causal power in the first place.

This should not be much of a problem for physicists. There are many coarse grained descriptions of the world, to which physicists seem to have no difficulties whatsoever to attribute causal power to. For example: temperature, pressure and, perhaps most importantly, entropy. The latter being basically the number of configurations of fine-grained configurations through which a coarse-grained description can be realized. And although this number is not explicitly embedded in the basic laws of motion of the fine grained description of a sub-system, it has nontheless a real causal power and can be seen as a good example of how coarse grained causes can be „really there“ without being „embedded in the basic laws of motion“.

Also, many causal chains make use of coarse grained descriptions of the world, which are, while being in perfect agreement with a fine-grained description, neither perfectly reducible to them nor similar in their causal structure. Examples for such causes are: Genes (as a causal structure in Evolution); and presumably also thoughts, feelings and even such complicated relations between humans as hate or friendship.

(Think of Schillers „Bürgschaft“: The whole story unfolds with hate and friendship as a cause. This holds regardless of the concept of a cause you want to stick to, be it regularity, contrafactuality, operationality etc. Hate and friedship are just regular, real causes, whithout anybody being able to point at some physical subsystem of the world to say: „And these particles and their movements make up („are“) friendship“. The reason not being, that „friendship“ is just awefully complex to describe in terms of moving elementary prticles, but that „friendship“ is a relation (i.e. as much in between things as physical laws).  Which is to point out that relations (and I even suspect relations only!) can be bearers of causal power.) — And ofcourse, a computer computing tau to switch pixels on a screen is just another example of that.

Brains & Will & End

The question stands if there might be a FWF embodied in those biostructures we call brains? Many indications point to a positive answer: Yes, the brain is yet another coarse grained description of an ensemble of elementary particles which (among other things) is able to exhibit the causal structure of an FWF.

The way, the FWF is realized in brains is in all probability through self-reference/recursiveness. There is a very nice paper about this by Seth Lloyd „A Turing test for free will“, who traces this causal structure down to Alan Turing’s halting problem. He reasons that any self-referential system (i.e. a system capable of asking a self-predictive question) has the features of a Free Will Function (i.e. fullfills Mrs Hossenfelders conditions 1’) and 2)).

I am far from being a brain-expert. Nonetheless, Lloyds reasoning seems to be consistent with the current understanding of the inner workings of brains; namely with the „free energy principle“. It seems to be appropriate to describe the brain as a Bayesian inferential computer, which constantly samples the world (i.e. extracting different kinds of coarse grained descriptions, however that works), thereby constructing and updating a (coarse grained) model of the world and updating its priors such that the amount of surprise is minimized. And the „update“-part is just another way of saying that the causal structure of the brain is self-referrential (feeds back some of its output to its input) in the Lloydian sense.

After all, free will seems possible, if a computer computing tau (and having causal power) is possible, too. This was my main point here. Ofcourse, computers do not exhibit signs of having a „will“ (the often neglected, but equally important and difficult part in „free will“). Which is to say that I don’t believe a computer computing tau to possess something like a free will (nor any other computer program that I know of, which goes to object to some of the ideas put forward by Seth Lloyd in his Turingtest-paper). But I easily admit that the possibility of such a computer seems to be a necessary prerequisite for free will to be at all.