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P (An ) = P (A) More specifically, if A1 . . An is a set of n mutually exclusive events that is complete - so that exactly 1 of those events is certain to occur - then probability theory requires that P (A1 ) + . . + P (An ) = 1 Given the obvious nature of these requirements, it is surprising to find that people violate them reliably and systematically. However, experimental studies have shown that people do violate these requirements, and in a characteristic way. Results show that, for mutually exclusive events A1 .

2 Probabilities for Noisy Reasoners Designing systems to minimise noise is costly, both in computational time and computational power. A better approach may be to design probabilistic reasoning systems to include an expectation of random error. To do this we can use the equations described previously, but with corrective estimates of the amount of random variation to which the reasoner is suceptible. Suppose the reasoner is suceptible to a known rate of noise d: that is, the reasoner knows that in the long run every X bits read from memory will contain dX bits whose read value is incorrect.

Springer-Verlag Berlin Heidelberg 2012 42 D. Deca Growth of neuroscience over the years 250000 200000 150000 No of neuroscience publications per year 100000 50000 0 1979 1985 1988 1990 1995 1998 2002 2011 Fig. 1. The growth of the number of neuroscientific publications per year. The data were obtained by indexing the medical database2,3. A fundamental issue for neuroscience and for reverse engineering the brain is the connection between structure and function. The current methods only allow us to make some potential correlations at different levels in time and space.