Today's entry is about the following thought experiment, which suddenly came to me as I was day dreaming about a Futurama episode I saw recently.
Imagine that I reveal to you that half of the Human population are completely deterministic robots, that their behavior is always predictible and computatble from their internal state (which is partially determined by the sum of their experiences so far) and the current context. For instance, you cannot rule out somebody being a robot from the observation that they answered differently when the same question was asked to them twice. Indeed, the second time the internal state wasn't the same as the first time since they accumulated data between the first time the question was asked and the second time it was. This said, the determinism is reflected by the fact that if you knew the complete internal state at the moment the second question was asked, you would have been able to predict the answer (and same for the first time actually). Also note that you cannot control those robots, to do so you would need to have the complete specification of their programs (programs that are not necessarily the same from one robot to the other) as well as completely controlling their experiences (which you cannot do because there are other entities than you in their environment).
The question now is: you do not know whether you are one of them or not. What could you do to determine whether you are deterministic or not ?
And then, a more interesting question: what did you learn about free will by trying to answer the above question ?