In their recent article "Complexity and the nervous system," Christof Koch and G. Laurent attempt to quantify complexity, specifically the complexity of the human brain, and speculate on its significance. They make the following points:

1) The brain has a function -- to protect the individual (or its kin) in its particular ecosystem and to ensure the propagation of its genome -- and that possession of a function is "the most relevant difference from other large physical systems such as galaxies and their tens to hundreds of billions of stars."

2) The authors propose that "everything biological must be considered within an evolutionary framework." The brains that exist today are the result of 0.6 to 1.2 billion years of metazoan evolution, and this vast span of time has allowed for a very large number of adaptive steps between our stem ancestors and today's animal cohort. These iterative elaborations can perhaps be related to certain ideas of "logical depth" in complexity theory.

3) Brain complexity is reflected in the complexity of its structural makeup. At the most elementary level, *voltage- and neurotransmitter-gated ionic channels of all types are found throughout the animal kingdom. The genome of the worm Caenorhabditis elegans contains sequences for 80 different types of potassium-selective ion channels, 90 ligand-gated receptors, and approximately 1000 G protein-linked receptors. "The combinatorial possibilities are staggering for a nervous system with only 302 neurons."

4) The authors suggest that it is important to recognize the differences between brains and computers. Individual transistors are homogeneous and nonadaptive. The interconnectivity of transistor gates is very low: in the central processing unit of any microprocessor, one gate is connected, on average, to two or three others. This pales in comparison to interneuronal convergence and divergence ratios, often in the tens of thousands.

5) The authors conclude: "A positive correlation between complexity, as measured across large neuronal ensembles over a fraction of a second or longer, and consciousness is not implausible. Alternatively, it is at this time equally plausible that consciousness arises out of a novel feature of certain types of brains, some cellular or circuit property with a unique molecular, anatomical, or physiological signature. Only time will tell if and how the mind arises out of 'complex' brains."

C. Koch and G. Laurent: Complexity and the nervous system. Science 284 (2 Apr 99): 96.

Contact: Christof Koch <koch@klab.caltech.edu>