(I now see this answered in the first few comments on the link eliezer posted.)
Purely armchair neurology:
To answer the question of why cow brains would need to be bigger than rat brains, I asked what would go wrong if we put a rat brain into a cow. (Ignoring organ rejection and cheese crazed, wall-eating cows)
We would need to connect the rat brain to the cow body, but there would not be a 1 to 1 correspondence of connections. I suspect that a cow has many more nerve endings throughout it’s body. At least some of the brain/body correlation must be related to servicing the body nerves. (both sensory and motor)
The cow needs more receptors, and more activators. However, this would lead one to expect the relationship of brain size to body size to follow a power-law with an exponent of 2⁄3 (for receptors, which are primarily on the skin); or of 1 (for activators, which might be in number proportional to volume). The actual exponent is 3⁄4. Scientists are still arguing over why.
West and Brown has done some work on this which seemed pretty solid to me when I read it a few months ago. The basic idea is that biological systems are designed in a fractal way which messes up the dimensional analysis.
We have proposed a set of principles based on the observation that almost all life is sustained by hierarchical branching networks, which we assume have invariant terminal units, are space-filling and are optimised by the process of natural selection. We show how these general constraints explain quarter power scaling and lead to a quantitative, predictive theory that captures many of the essential features of diverse biological systems. Examples considered include animal circulatory systems, plant vascular systems, growth, mitochondrial densities, and the concept of a universal molecular clock. Temperature considerations, dimensionality and the role of invariants are discussed. Criticisms and controversies associated with this approach are also addressed.
Edit:
A recent Nature article showing that there is systematic deviations from the power law, somewhat explainable with a modified version of the model of West and Brown:
A recent Nature article showing that there is systematic deviations from the power law, somewhat explainable with a modified version of the model of West and Brown:
(I now see this answered in the first few comments on the link eliezer posted.)
Purely armchair neurology: To answer the question of why cow brains would need to be bigger than rat brains, I asked what would go wrong if we put a rat brain into a cow. (Ignoring organ rejection and cheese crazed, wall-eating cows)
We would need to connect the rat brain to the cow body, but there would not be a 1 to 1 correspondence of connections. I suspect that a cow has many more nerve endings throughout it’s body. At least some of the brain/body correlation must be related to servicing the body nerves. (both sensory and motor)
The cow needs more receptors, and more activators. However, this would lead one to expect the relationship of brain size to body size to follow a power-law with an exponent of 2⁄3 (for receptors, which are primarily on the skin); or of 1 (for activators, which might be in number proportional to volume). The actual exponent is 3⁄4. Scientists are still arguing over why.
West and Brown has done some work on this which seemed pretty solid to me when I read it a few months ago. The basic idea is that biological systems are designed in a fractal way which messes up the dimensional analysis.
From the abstract of http://jeb.biologists.org/cgi/content/abstract/208/9/1575:
A Science article of theirs containing similar ideas: http://www.sciencemag.org/cgi/content/abstract/sci;284/5420/1677
Edit: A recent Nature article showing that there is systematic deviations from the power law, somewhat explainable with a modified version of the model of West and Brown:
http://www.nature.com/nature/journal/v464/n7289/abs/nature08920.html
A recent Nature article showing that there is systematic deviations from the power law, somewhat explainable with a modified version of the model of West and Brown:
http://www.nature.com/nature/journal/v464/n7289/abs/nature08920.html
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Can something be mathematical and yet not strict?
Overly-simple mathematical models don’t always work in the real world.
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