Shadows Of The Mind: A Search For The Missing Science Of Consciousness by Roger Penrose

Author:Roger Penrose [Penrose, Roger]
Language: fra
Format: epub
Tags: 978-0198539780, Non Fiction, Mathematics, Physics, Neurology, Artificial Intelligence, Philosophy
ISBN: 9780198539780
Published: 2013-07-18T00:36:40+00:00

Does mind have a place in classical physics?

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computationally. Nevertheless, within the possibilities that these laws allow us, we must try to find an opening for a hidden non-computational action that the functioning of our brains must somehow be taking advantage of. I shall defer, for the moment, a discussion of the possible nature of this noncomputability. There are reasons for believing that it must be of a particularly subtle and elusive kind, and I do not wish to get embroiled, at this stage, with the issues that will have to be involved. I shall return to the matter later ( §7 .9,

§7. 10). Suffice it to say that we require something essentially different from the pictures that we have been presented with in our physical theories so far, either classical or quantum.

In classical physics, one can, at any one particular time, specify all the data needed for defining a physical system, and the future evolution of that system is not only completely determined by this data but it can also be computed from it, by the effective methods of Turing computation. At least such computation can in principle be performed, subject to two (interrelated) provisos. The first proviso is that it be possible for the initial data to be adequately digitized, so that the continuous parameters of the theory can be replaced, to a sufficient degree of approximation, by discrete parameters. (This is in fact what is normally done in computer simulations of classical systems.) The second proviso concerns the fact that many physical systems are chaotic-in the sense that a completely unreasonable accuracy is needed for the data, if the future behaviour is to be calculated to any tolerable degree of precision. As was already amply discussed earlier (see §1 .7, in particular; also §3. 10, §3.22) chaotic behaviour in a discretely operating system does not provide the type of

'non-computability' that is needed here. A chaotic (discrete) system, though difficult to compute accurately, is still a computable system-as is borne witness by the fact that such systems are norltlally investigated, in practice, by means of electronic computers! The first proviso is related to the second, because the issue of whether or not we consider that the degree of precision of our discrete approximation to the continuous parameters of the theory is

'adequate' depends, in a chaotic system, upon whether we are concerned with computing its actual behaviour-or whether a typical behaviour of such a system will do. If it is just the latter-and as I have argued in Part I, this appears to be all that we need for the purposes of artificial intelligence-then we do not need to worry that our discrete approximations are not perfect, and that small errors in the initial data may lead to very large errors in the subsequent behaviour of the system. If this is all that we need, then the above provisos do not seem to allow us room for any serious possibility of a noncomputability of the type required, in accordance with the discussions of Part I, in any purely classical physical system.

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