@Lustig Andrei,
Andy, Very good questions.
I said we
may find that the operation of the neural networks in our brains is subject to chaos (and therefore unpredictable in any computer simulation no matter how capable or fast the computer). In fact we aren't anywhere near being able to model our brain activity, though great progress is being made in understanding both what various parts of the brain do and in clinical understanting of some of the results. Unfortunately all of our data so far involves measurable statistical differences, as opposed to individual behaviors, which resist even association, much less reliable prediction.
However, it is noteworthy that what we do know about neural networks and the way the brain develops in response to stimulus suggests that it is very likely to be subject to the same chaos as that which continues to befuddle meteorologists, fluid mechanics, the future movements of ocean currents, astronomers working to predict the movement of asteroids and a host of other real physical problems.
With respect to the second question of free will, it is interesting to note that Calvin reasoned that since god created and knows everything, we can not possibly have free will and are therefore not responsible for what we do (Calvin had some trouble with that necessary conclusion, but he pressed on anyway). My belief is that the concept of free will is necessarily subjective, and doesn't require that no being of any conceivable kind cannot possibly know what we wiull (or likely will) do in any circumstance. It is sufficient (in my mind at least) that we may be able to act against our reasonable best interests or even contrary to patterns we have followed before, and be conscious of these acts.
Another interesting feature of chaotic systems (both physical and mathematical) is that, though their medium and long term behavior remains in detail entirely unpredictable, their average or gross behavior is usually steady or periodic and reliably predictable. El Ninho keeps coming back at intervals of 11 to 21 years, century after century. Almanacs have been pretty good at forecasting the average weather for centuries. Aerodymanicists have been able to design reliable high speed aircraft and predict their drag relaibly, despite the turbulence (chaotic flow) near the surface. Chaos and observable trends can coexist. I have long believed there is a greater truth in all this.