My guess was that very possibly you would avoid playing those numbers, if for no other reason, just to prove this arrogant scientist wrong!
The point of this thought experiment was to show that, at the level that our actual decisions are being taken, we are the sole masters in the house, and, crucially, that discussions about our “free will” and about all what science can, or cannot, claim in regards to it are a bit confused.
The question here is a question about the universal applicability of scientific pre-suppositions.
Let’s take things from the beginning.
Science works by formulating theories. Scientists posit hypotheses based on the theories; then they conduct experiments to check those hypotheses; and finally they confirm, refute, or amend the theories as needed based on the results of the experiments.
The guiding principle in all this is that the object of study of any scientific field is not “lawless”. (It would be futile to try to formulate theories if you did not accept that there are at least some laws in effect, and that these laws can be known.)
So, for example, physics can study nature, and formulate theories about nature, because we accept that nature is adhering to certain laws, which we call “natural”. We did not know all these laws from the beginning. We started discovering them as soon as we started studying nature. But first we accepted that nature operates according to natural laws –such as the law of causality. This we did not check. We accepted it as an axiom, so to speak.
Now, different scientific disciplines have different fields of study, and the concept of law can vary rather radically. For example, “causality” as a concept has a very different meaning in classical physics than it has in quantum mechanics or, say, in geology, or psychology. The same applies to any law or laws based on causality. These laws can have a very different meaning depending on the scientific field of study.
In classical physics, for example, it is conceivable that if you know in every possible detail the specific state of a system, you can predict the future and infer the past. You don’t need anything else. This, famously, was the argument of Laplace against the existence of God. “I have no need of that hypothesis” he answered to Napoleon when asked what was the place he (Laplace) gave to God is in his theories.
It’s not the same with quantum physics. According to our present understanding, you are not even able to know the details of a specific state of a quantum system in full. Heisenberg’s uncertainty principle states that the better you know the velocity of a particle, the less you can know its position –and vice versa. Quantum systems appear to be inherently unpredictable.
Or in cosmology: No scientist would claim that the law of causality is relevant when we study singularities such as the moment Zero of the Big Bang or the “inside” of a black hole.
Similarly, in psychology, the “laws” that govern human behaviour, if we accept that such laws exist, seem to be radically different to the laws of physics, and any question of predictability seems to be a bit out of place. No psychological theory of human behaviour can (or, dares to) claim that it can predict the future. At most it can hope to be able to explain the past.
What then about this whole talk about free will?
Well, this is what I meant earlier when I said that it is confused.
The neuroscientists who study the brain processes of humans and animals are falling in the trap of the so-called “genetic fallacy”. They believe that the observed lawfulness of the processes they study also can be observed –or should be able to be observed– in the actual behaviour of the human or animal under scrutiny. The conceptual error is that human or animal behaviour is taken to be the result of “nothing but” lawful brain processes.
This is an oversimplification, and my thought experiment with the lottery was aiming to show exactly that.
It might be that my decision to play this or that number is corresponding to observable and lawful brain processes, but by your telling me this (i.e. by interacting with me) my brain processes change, and I decide to play different numbers or not play at the lottery at all.
Just before I finish, let me add here Kant’s definition of free will.
Free will, he writes in the Groundwork of the Metaphysics of Morals, “is a rational causality which is effective without being determined by any alien cause”.
Here Kant anticipates the neuroscientists of more than 200 years later and points out that it is not relevant to the question of free will whether there is causality in the brain processes or not. In fact he accepts there is a causality. But he points out that my will is free to the extend that it is not determined by an alien (i.e. extraneous) cause.
In other words, it's not the causality in my brain processes which might render my will un-free but the extraneous causes that might affect it, for example if I am forced to act in a certain way (because, say, I am in prison).
If scientists would read a bit of philosophy before making big claims…