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CONVERGENCE AND FREE-WILL CRISTI STOICA Abstract. If our mind is just an algorithm running on a flesh hardware, then it seems that there is no place for the free-will. An algorithm decides everything based on deterministic computations, or on random inputs, but neither inevitability nor pure hazard is free choice. Hopefully, some day, Science will be able to understand, monitor and simulate all the mind processes. Even then, it will still be a possibility for the free-will to exist, based on the convergence of the initial data. I propose a crucial experiment to test this hypothesis. Contents 1. Is there a ghost in the machine? 1 2. Minds in a physical world 2 3. The problem of free-will 3 3.1. What do we think we have, and a machine cannot have? 3 3.2. The problem of free-will 4 3.3. Is the free-will allowed by Quantum Mechanics? 4 3.4. Is there enough room for the free-will in the brain processes? 5 4. The free-will test 6 4.1. Preconditions for the test 6 4.2. The \intention beyond matter" hypothesis 7 4.3. The free-will test 8 References 9 1. Is there a ghost in the machine? The mind-body problem is of a fundamental importance for the human beings. We all want, or need, to know more about ourselves. The mind and matter are very real things, and cannot be dismissed that easily. It is no wonder that, at the beginning, many philosophers considered that they both exist, and cannot be reduced one to the other. In the same time, some thinkers, mostly in orient, proposed that there is only the mind, and the material world is an illusion. Yet, Science evolved in such a manner that provided a physical basis for more and more phenomena, which initially were though to be irreducible to matter. This progress led today to such a wide mapping of the phenomena related to mind, consciousness, thinking, feelings, that it seems that there is only one percent remained unexplained, and it is only a matter of time that we will soon Email: [email protected]. 1 provide an explanation of all the mind phenomena. Thus, everything will be reduced to materialist explanations. But, it would not be the first time scientists have the illusion that little remained to be explained. For example, at the end of the XIX-th century, it was believed that Physics is almost closed, then, in only several years, the Theory of Relativity and Quantum Mechanics opened new realms, much wider than the classical Physics. Well, for some scientists may be clear that the missing \percent" in our explanations about mind will be explained soon, as usual, by reducing it to physical phenomena. Others may think that what remained unexplained is really important and irreducible. For example, it is difficult to conceive how it will be provided an explanation of the acute feeling we all have, that we really experience our lives, and we are not just a software running on an organic hardware. And it is again difficult to admit that our bodies just follow the laws of Physics, when we are so aware that in fact we are driving them, obviously with a purpose. This is why I think that we cannot draw yet a definitive conclusion in the mind- body problem. I will not add many arguments for one viewpoint or another. Instead, I will propose a localization of the problem, such that we can formulate it in a way that emphasizes better a key aspect. Then, starting from this key problem, I will propose a crucial experiment that may provide an objective resolution of the mind-body problem. 2. Minds in a physical world The body related part of the problem involves inevitably the laws of Physics. We don't know yet everything about the physical universe in which we live. Our best theories, General Relativity and The Standard Model of Particle Physics, can explain a large part of the physical world, but still remains something unexplained. For example, we just don't know yet how to combine these two theories, despites of the progresses made in String Theory and Quantum Gravity (which are very different than the theories they try to unify). Even if we believe that only 1% remains unexplained, we can at most hope that it will be dissolved in what we know so far. In fact, there are unexplained things in Quantum Mechanics and Relativity too. Even when we will have a Theory of Everything in Physics, corroborating what we know so far, there will always exist the possibility to be contradicted by future experiments. Although we don't know which theory will win, and how our final explanation will look like, we can make some general assumptions, which are respected by probably all the theories proposed so far in Physics. As I described in [1], in most our theories and attempts, the spacetime can be represented mathematically as a topological space (including the discrete cases). The laws of Physics can be interpreted as imposing constrains on the fields allowed on the spacetime. We can therefore identify the laws with sections of a topological bundle over the spacetime. There are, of course, more than one field, but can we always combine them with ease in a single field, by operations with bundles. In order to distinguish the local laws of Physics from the global laws, we can consider instead of the global sections of the bundle, a sheaf over the spacetime, with the requirement that the solutions will always be global sections of that sheaf. I will not 2 repeat here the details, they can be found in the cited article. I will only mention that, even if we want to model theories that cannot, in principle, be represented as sheaves over topological spaces, we can consider the spacetime to be a category, and the law sheaf a contravariant functor on it. This is based on the fact that any topological space can be viewed as a category. The mathematical structure constructed in this way is named World. The analysis presented there can make us an idea of what we can expect from our theories, indepen- dent of which of them will be accepted as the description of our world. Even more, we can see that the World Theory allows an inclusion of the emergent phenomena, as extra conditions that simply refine the law sheaf. Metaphorically, some emergent phenomena can be thought as software, running on the hardware formed by the matter fields. But can we identify the mental processes with a software, implementable in terms of laws of Physics? I don't know. What I can say is that a lot of progresses are made, in understanding the mind in terms of neurons and brain. Will, in time, the (more or less) tiny part remained unexplained, be explained in terms of matter? I showed in [2] that the Turing test [3] can easily be passed by an algorithm, but this may not be that significant. The main challenge is to understand how is made that software/hardware combination. And now we come to the main problem. Let's be optimistic and suppose that, some day in the future, we will be able to monitor the brain activity, and to point precisely how is constructed the mind, and how it works, as a software. The question many of us have, is this: will that software really be a mind?. Our instincts may say that there is no way that we are just such a software. Our experience, which accustomed us with software able to do unimaginable task, saids that it may be. But is it? Our smart, or genius, cell phone that we will use at that time, will cry to charge its batteries, but will this mean that it really feels hunger? 3. The problem of free-will 3.1. What do we think we have, and a machine cannot have? Although it is very possible to simulate a human mind in such a way that we can't distinguish the simulation from an original mind, will this mean that really there is no difference? An operationalist view will say that, because we can't find any objective difference, there is no one. Some differences are suspected to exist. I believe that the more important that were raised are the following ones: Problem 1. Real human minds can have a strong feeling of free will. Problem 2. I, as a human, have a very clear feeling that I exist, that I am a subject experiencing the processes of my mind. Somebody may object that I let aside the important issue of feelings, love, generosity etc. This may be a point, but I will not discuss them here. I only want to say that a 3 large range of feelings has been showed to be accompanied by brain processes that can be monitored, and we can use these processes to make predictions about the feelings. It is easy to believe that this part of the mind activity will be describable by a mind software. What is more subtle is the feeling that we really are something having those feelings, hence the problem 2. If we monitor a brain in all details, and see the processes corresponding to a given feeling, is this a guarantee that there is somebody \in there" really having the feelings? I believe that the two problems are strongly related, but I will focus in this article on the free-will problem.
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