The article reviewed here is a brief one by Mariano Sigman colourfully titled ‘Bridging Psychology and Mathematics: Can the Brain Understand the Brain?’ and freely available here. Sigman describes his move from physics into biology and draws parallels with the work of Galileo in the need to bridge the ‘gap’ between observation and theory. He chooses a concept introduced by mathematician Kolmogorov about concepts themselves. He showed mathematically that categories (conceived of as being analagous to concepts in a paper discussed here) can be described by an optimal statement and the length of this statement indicates the complexity of the category (or concept). Sigman then discusses a paper in which people were found to be able to recall concepts with a difficulty that was proportionate the complexity of the concept and that they could do so implicitly suggesting perhaps that Kolmogorov’s mathematical idea had a neurobiological useful equivalent. He then suggests that mathematics is a function of the biology of the brain and in a similar vein to Godel, the brain may never understand itself.
Indeed it seems entirely reasonable that the brain would never understand itself. This is the equivalent of saying that a neuron may understand itself, since for every additional neuron that is added to the neuron, the complexity of the system increases. Can we understand the brain? Again we can also say that this is semantics. What does it mean to understand the brain? The best that we ourselves can probably do, is to understand trends, principles, some properties. We may never fully understand the brain, nor perhaps will artificial intelligence systems – the reason being that the brain is a complex physical structure, for which we will only ever have a limited amount of information on. Let us consider a thought experiment. Suppose we could record activity from the brain. We could record surface activity in neurons, and that would provide us with some valuable information, but we would still be unable to make the most accurate predictions, because for this we would need information on other neurons that are influencing the surface neurons. However, in order to measure these, we need to interact with them in some way. On measuring the activity of the deeper neurons in this imagined brain, the measuring apparatus will impact in some way on the neurons in the structure and the recorded activity will be ‘artificial’. In other words, not a true representation of the activity that is occuring in the ‘natural’ state. Maybe the best that we can ever hope for is a more precise definition of what understanding is and once defined a determination of the boundaries of our understanding.
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