| As my background is mainly in the brain sciences, I was most interested in what Penrose had to say about consciousness and the brain in this book, so I'll concentrate mostly on the chapter that had to do with that. This is not to say I didn't enjoy the other chapters, just that I'm not as qualified to critique those as I am the one on the brain. There has been a lot of speculation in recent years about such things as computability and the brain, quantum consciousness, and so on, and I was interested to find out what Penrose might have to say about that. One of Penrose's major ideas in this chapter is his demonstration that consciousness, although perhaps mathematical, isn't computable, in the sense that you could program a computer to simulate it. Penrose uses the example of geometric tilings or polyominos that are deterministic in their coverage of the Euclidean plane, but that aren't computable, to show this. Since, as Penrose points out, there are plenty of mathematical concepts that aren't computable and that can't be done on a computer, but that the human mind can understand, Penrose concludes that there is something beyond computability in both pure mathematics and the human brain. This is interesting, and Penrose might be right about that. However, I must point out that while consciousness itself may not be computable (and I'm not really prepared to conclude this for sure at this point, because of what I'm about to say), nevertheless, many aspects of the brain's functioning have been shown to be computable, so I'd like to discuss that briefly. For example, sensory neurophysiology has been shown to be both quite mathematical and computational as a result of the work of a pioneering mathematician by the name of David Marr 25 years ago, whose ideas revolutionized neurobiology almost overnight, after which the field was never the same. Marr examined a number of different fundamental sensory mechanisms, and showed, for the first time, that the way in which the visual system was processing light information was consistent with the operation of certain sophisticated spatial-frequency filtering transforms that are well-known in many engineering applications. To mention just a few of his important ideas, Marr's demonstrations that retinal receptive-field geometry could be derived by Fourier transformation of spatial-frequency sensitivity data, that edges and contours could be detected by finding zero crossings in the light gradient by taking the Laplacian or second directional derivative, that excitatory and inhibitory receptive fields could be constructed from "DOG" functions (the difference of two Gaussians), and that the visual system used a two-dimensional convolution integral with a Gaussian prefilter as an operator for bandwidth optimization on the retinal light distribution, were more powerful than anything that had been seen up to that time. It was as if vision research suddenly acquired its own Newtonian Principia Mathematica, or perhaps General Relativity Theory, in terms of the new explanatory power Marr's theories provided. Basically, in one fell swoop sensory neurobiology also became an area of theoretical physics rather than purely biology, giving the area a rigor and elegance never before seen--an amazing achievement for a young man who died so prematurely from leukemia at the age of 36. The main point of all this is that all of these mechanisms are both mathematical and computable, although the way in which they're done in the brain is probably more like how a computer would use numerical analysis to solve a differential equation, rather than using the original equations in a purely analytical way themselves. Since Marr's time, there has been further progress in this area, such as the great Bela Julesz's demonstrations that the visual system can extract and compute binocular disparity cues point-by-point for depth information from abstract, non-representational pictures or textures such as random-dot stereograms, the extension of Marr's ideas about monochromatic edge detection into color edge detection, the mathematical bases of non-linear visual field distortions present in optical illusions, and many other areas. Furthermore, in the last few years, the nature of consciousness itself has been shown to be composed of many different separate mechanisms in the brain that are being coordinated in time in order for consciousness to occur. It simply isn't one process or central program that runs in the brain, nor is there a "master" brain center that one can point to where it can be said that consciousness resides. I'm sure the progress of this research will also have implications for ideas about the nature and computability of consciousness. So overall, a fascinating and enjoyable discussion about the brain and consciousness by Penrose, even if I don't completely accept one of his major ideas about it for the reasons that I discuss above. |
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