Arthur and free will

In recent days and weeks I read an interesting but rather heavy book about
Arthur Schopenhauer, his philosophy and his times. And I think this was the main reason I did not
find the will in me to write something on this blog. I still don't have too much
to offer, except the following silly story...


This story is about a very smart physicist and her simpleton friend. Among other things
the smart physicist entertained herself by predicting his behavior. This was possible because
they lived in a Dennett-Newtonian universe, where all thoughts and all behavior was
a function of the configuration of molecules constituting a brain and the movement of these
molecules was deterministic, following Newtonian laws. The bouncing of molecules was not so difficult to predict with all forces well known.

The physicist had several machines in her laboratory to determine the configuration
of huge numbers of molecules to arbitrary precision and a supercomputer (also made of Newtonian particles of course)
to calculate the future configuration of molecules ahead of time.
Since her friend was made of a large but finite number of molecules, all she had to do was e.g. to
use her machines to measure the configuration of molecules at 9am (he did not even notice it), feed the result
into her supercomputer and read out the calculation which predicted his behavior at 10am. And when she determined that
he would say "I am bored, let's go for a walk" this was exactly what happened, like clockwork.
Easy as pie and quite funny.

Unfortunately, she made a mistake. She wanted to show him how smart she was and wrote down her prediction
so he could see it and for some reason all of a sudden it failed to work.

Of course, on one hand it was immediately clear what happened. As soon as he read that at 10am he would "go to the window
and open it" he decided to open it earlier and at 10am already closed it.
There was nothing mysterious about it, actually it was a completely deterministic process, with Newtonian
photons carrying the prediction to his Dennett-Newtonian brain, which was not very complex, but smart enough to do simply
the opposite of what she wrote on the paper. He did it just to prove a point. And of course it was quite irritating.

On the other hand, she did not understand this at all. Her machines could measure the configuration of all
molecules in the room (including herself) and the supercomputer calculated this forward to arbitrary precision. So the calculation 'knew' that a prediction was
written on a piece of paper and the Newtonian photons carrying the message and his simpleton brain receiving it and doing the opposite of what was written etc.

So how could this prediction go wrong? Everything was deterministic! And still, no matter how many times she tried,
her simpleton friend with his simpleton stubbornness did the opposite of what she wrote down. Every time. Was Newton wrong after all? Or Dennett?

She found a solution, of course, it was easy enough. Get another friend. But still...


If you have a good explanation of what caused this 'failure' of determinism then please post a comment. The first to solve this silly puzzle will win a Golden Llama award for major contributions to the blogosphere of physics, which includes a free subscription to this blog.

Of course, if you just want to debate the whole thing feel free to post a comment too, or if you want to let me know just how silly this silly story really is.

added: And the winner of the Golden Llama Award is Chris, who pointed out that the problem is with the supercomputer (trying to) predict its prediction. (See the comments for more details).



Ponder Stibbons said...

Seems to me that if her program was genuinely accurate this would not happen. It would calculate that the physicist would show her friend the prediction at a certain time, and the friend would react the way she did...

wolfgang said...

On the one hand this is what one would expect in a Newtonian universe.

On the other hand, the brain of her friend is 'wired' such that it will do the opposite of what is predicted, or at least something different.
I dont see how one can make the case that a Dennett-Newtonian world necessarily rules out such stubbornness.

Chris said...

Ponder, you missed the point: as soon as the machine predicts some one of "free will" will act in a certain way, that person can consciously act in opposition to the prediction.

If we assume the computer is outside the lab and the lab is closed in some appropriate sense, then the paradox seems to go away. Each prediction does not include the prediction itself in the system of lab+friend, so the friend never sees the prediction. If you added that the prediction was to be included, so the computer was now calculating the evolution of lab+friend+prediction then a new prediction will be generated.

So it seems the paradox only arises once the computer is in the room. The problem is the computer predicting its own prediction, no?

wolfgang said...


Yes, exactly.

If the computer is made of N molecules it will not be able to predict its own future, because it would need more than N molecules to store and update its own state plus the configuration of the physicist and the stubborn friend.

PS: And if the computer would try an iterative approach (calculate a prediction p0 without assuming the simpleton knows it, then use p0 to calculate prediction p1 which assumes the simpleton knows p0 etc.) it is easy to see why the iteration will not converge with a stubborn simpleton present.

Peter said...

Hi, Wolfgang!

I think you were right to give the llama to Chris. However, lurking in there I see an interesting possible theory about free will. Maybe the special problems which attend the prediction of our own behaviour explain why we seem to ourselves to have free will, though believing in determinism for other people doesn't seem a problem...

wolfgang said...


>> the special problems which attend the prediction of our own behaviour

yes indeed. But if I cannot determine my own microstate it also means that I cannot predict the microstate of anything or anybody interacting with me.

Therefore, 'believing in determinism for other people' may not be a problem (and in this story it was explicitly stated that we consider a Newtonian universe!), but there IS a problem if one actually wants to do something with this believe, like making predictions.

Bryan said...

>> If the computer is made of N molecules it will not be able to predict its own future, because it would need more than N molecules to store and update its own state plus the configuration of the physicist and the stubborn friend.

Only given a non-trivial assumption about what a computer can and can't do, e.g., the Church-Turing Thesis. But if the CTT is false, then the "spoiler" (the physicist's friend) might still turn out to be the impossible part of the story, as Ponder suggests.

wolfgang said...

>> But if the CTT is false

Well, assuming that the computer is an omniscient oracle, then perhaps the only way out would be for the 'spolier' to behave e.g. in an oscillating way. Perhaps he would e.g. go to the window, then walk away from it, then go to the window again, etc.
and if the frequency increases then perhaps the prediction would come true although he tries to make it false.

But honestly, I think one would run into real contradictions if one assumes that the computer is a real omniscient oracle (e.g. the 'spoiler' would remain inactive whenever the computer predicts activity and do some activity whenever inactivity is predicted).

So perhaps one can turn this little story into a proof of the CTT ?!