> Free will is equivalent to randomness with many (asymptotically infinite) degrees of freedom.
I don't think this is obviously true. I can make a random number generating device with as many degrees of freedom as you like by producing a bunch of vertically polarised photons and measuring their horizontal polarisation. I don't think anyone would describe this system as having "free will".
Conversely humans with "free will" don't usually behave very randomly. They often have reasoning (good or bad) and are able to explain why they took whatever actions they took.
Free will seems to be qualitatively different to randomness.
I think that's true, I think free will is more reason (of the general kind that's not only logical but takes into account your mind), than more randomness. Rather, the more your actions are aligned with your own good, brought by understanding yourself and reality, the more free I think you are. (to give an example: is an addicted person free, even if he is in principle doing "what he wants?", or is he trapped by his own desires?) In this sense some people would say I'm a 'compatibilist', because I think there's no great tension between determinism and free will.
One step back please, the "free will" was an ill-conceived start. The core claim is about how random is human will. Throwing in the word "free" adds confusion.
The will of an addict is a bit less random, okay. Is there anything quantitative going on here besides "some stuff can increase randomness" and "some other stuff can decrease randomness"?
My claim is that randomness is a dead end. It's irrelevant. But I do think free will can be a useful concept (with little relationship to randomness), although it's too complicated for a short comment I think (a complex quantification of how you can realize good things for yourself and the world).
That said, I think this is a nice experiment exactly for surfacing this kind of questioning.
Following reason is as deterministic as following your addiction.
Sure determinism and free will are compatible as long as you believe that free will is your emotional reaction to discovering what your mind has determined.
I don't agree that reason correlates with free will. Many people act irrationally. Behavioral economics was developed because "rational actor" predictions applied to large groups of people turned out to be consistently incorrect.
One can willfully be irrational.
I do agree with you though, that free will doesn't necessarily mean "doing what I want" (which is a libertarian principle from the French Revolution), but instead, is freedom from desires. That's true freedom, but is rarely found and achieved only after years of ascetic practice.
Don't confuse "having reasons" with "being rational". Free will is a freedom to act according to your internal reasons, with that process of deliberation over your reasons being responsive to various types of feedback. Those reasons don't have to be rational.
Interestingly, this book is from 1971, whereas a famous duck went through a similar plot already in 1952 [1]. Now, how to decide if I should add this to the Wikipedia entry of "The Dice Man"?
> I can make a random number generating device with as many degrees of freedom as you like by producing a bunch of vertically polarised photons and measuring their horizontal polarisation.
Unless I misunderstand you, this is simply not true. Your device will be exceedingly easy to model, it's just a simple sum of i.i.d. random variables and subject to central limit theorems. (While humans definitely aren't.)
While the sum of many i.i.d. random variables may be easy to model, that doesn't mean that everything involving i.i.d. random variables is easy to model.
> Free will seems to be qualitatively different to randomness.
There is no such thing as free will, so any attempt to define it will fail.
If we naively define it as something that isn't just pure randomness, but also something that isn't pure causality, then what is it?
Either things are causal, in which case, you can replay everything and arrive at the same point. That doens't fit an intuitive definition of free will.
Or there is randomness, play the same sequence of events again and some inherent randomness will cause a different outcome. That also doesn't fit any intuitive sense of free will.
So, since we can't even define it, it is meaningless to assume there is free will in the first place. We can talk in terms of causality or randomness.
> If we naively define it as something that isn't just pure randomness, but also something that isn't pure causality, then what is it?
Read up on Compatibilism. Free will can be defined in a way that's compatible with determinism. A deliberation over values resulting in a justification for a choice, aka "reasons" or "will". When you are "free" to act in accordance with those reasons, ie. you haven't been coerced into acting against your own reasons, then you've made a choice of your own free will. Simple and totally compatible with determinism.
> Either things are causal, in which case, you can replay everything and arrive at the same point. That doens't fit an intuitive definition of free will.
I think this is somewhat inaccurate. I'm not sure if I personally agree with it, but at the very least compatibilism is a serious philosophical viewpoint and shouldn't just be dismissed like this.
In any case I think the concept of "free will" is pretty much independent of randomness. If you provide me with some source of randomness (e.g. some quantum random number generator) I don't think I get more free because of it.
There's an incongruity between a "mechanistic" model of causality and how we actually live, and actually should live.
Your explanation is a good response to the posted experiment, but I don't think it's a good response to common sense, especially when we consider important (largely pragmatic) concepts like agency and responsibility.
Not sure if the experiment tests this. (Pressing a different key or closing the browser tab are also variables in this probability distribution.)