I think that sometimes philosophy is important and this may be true for neuroscience right now. I don't mean ivory tower, "what is life?" type philosophy (although that is important too) but trying to pin down what it would mean to say "we understand the brain." When would we know that the game is won? I think this is important for neuroscience now to help to guide research. What should we be doing?

So what does it mean to understand something? I would say there are two aspects. One is predictive power, which would mean that we would be able to know what drugs or therapies would be useful to cure a brain disorder. The second aspect is more difficult to pin down but would basically mean incorporating something seamlessly into your worldview. The simplest example I can give is a mathematical theorem. Predictive understanding would correspond to the ability to follow all the steps of the proof of the theorem and use the theorem to prove new theorems. Incorporative understanding would be the ability to summarize the proof in a way that relates it in a highly compressed form to things you already know. For example, we can understand bifurcations of complicated dynamical systems by reducing them to the behavior of solutions of simple polynomial equations.

Sometimes the two views can clash. Consider the proof of the Kepler Conjecture for sphere packing by my friend and former colleague Tom Hales. The theorem is difficult because there are an infinite number of ways to pack spheres in 3 dimensions. Hales made this manageable by showing that this could be reduced to solving a finite (albeit large) optimization problem. He then proceeded to solve the finite problem computationally. To some people, the proof is a done deal. The trick was to reduce it to a finite problem, after that it is just details. Even if you don't believe Hales's computation you could always repeat it. Others would say, it is not done until you have a complete pen and pencil proof. To me, I think the proof is understandable because Hales was able to reduce it to an algorithm. However this is not a view that everyone shares.

Now we come back to the brain. What would you consider understanding to entail? I'm not sure that we, namely people working in the field today, will ever have that satisfying incorporating understanding of the brain because we don't have anything in our current worldview that could encapsulate that understanding. We will never be able to say, "Oh right, I understand, the brain is like X." In that sense, it is like quantum mechanics (QM). This is a theory that is highly successful in the predictive sense. As a predictive theory, it is quite simple. There are just a few rules to apply and much of our modern technology like lasers and electronics rely on it. However, no one who has ever thought about it would claim any understanding of QM in the incorporation sense. The Copenhagen interpretation is basically a "Don't ask, don't tell" policy for the theory.

In this sense, trying to understand any complex system, no matter how unrelated it is to the brain, could help in the long run to provide a foundation for an incorporating understanding of the brain. That is not to say that I believe there are laws of complex system similar to classical and quantum mechanics. My own view is that there are no laws in complex systems such as the global climate, economics or the brain; there are just effective theories that sort of work in limited circumstances. However, it is by slowly creating effective theories and models that we will form a new worldview of what it means to understand complex systems like the brain. In the meantime, we should continue to try to build a predictive understanding so that we can cure diseases and treat disorders.

## Sunday, August 31, 2008

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