The 'Effective Theory' of Free Will

I was reading an article by Stephen Hawkings, 'Is Everything Determined' and it was certainly an excellent piece of writings, revealing the author's brilliant insight. One of the ideas that really struck me was his concept of an 'effective theory of free will'. As a Physicist he believes that there exists a 'Theory of Everything', a set of fundamental mathematical equations that would describe everything in this universe, theoretcally. The questions arises, will such a fundamental theory be able to predict human behaviour, because theoretically human behaviour would also be determined by this theory of everything?

The answer is No. Even though human behaviour would be determined by these equations, the human brain is too large a structure for the equations to be applied. Even the very simple Newton's theory of Gravitation can be solved exactly for 2 particles, but when the number of particles increases more than 2, the equations become too complex to the solved, and one has to resort to approximations. And consider human brain with 10^ [raise to power] 26 particles. This is such an enormous number than the fundamental equations would become too complex to the solved.

Secondly, even if such a prediction is made, the very fact of making this prediction would alter the system and therefore lead to a different result. [For example, it is predicted that you'd have a Big Mac for lunch, you might just change your mind on hearing this, and instead eat a Pizza.]

In physics whenever we are dealing with Macroscopic systems, the number of particles is too large to use fundamental equations. So instead we use 'effective theories', which use approximations. An example is Fluid Dynamics. Although a stream of fluid is made of millions of particles, we ignore this fact, and consider the liquid to be a continuous medium, characterised just by velocity, density and temperature. And this theory works in practice, even though it is not true in reality.

Similarly, Hawkings suggests that the concept of free will is an effective theory. Cause we are unable to predict human behaviour, we adopt the effective theory that humans have free will and are responsible for their actions. Now even though this is not true in reality, but it works in practice, and therefore we use it. And it seems that a society that believes in free will and responsibility has much more 'survival advantage' than a society that doesn't.