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Science Tribune - Commentary - February 1999


Professor Penrose's mind

or Why Penrose is popular with the public

Max Hammerton

Newcastle University, UK.
E-mail : Max.Hammerton@newcastle.ac.uk

It caused me a great deal of surprise when The Emperor's New Mind by Professor Roger Penrose appeared in paperback (1). Not because I thought it unworthy; on the contrary, I found it fascinating; but the old publishers' dictum is that each line of algebra halves the sales; and there are many such lines in The Emperor's New Mind. So what was the compensating attraction?

The answer dawned on me when an aquaintance in the media told me how glad he was that Penrose had proved that the human mind had to be non-material! Since Penrose quite explicitly rejects this conclusion, I conclude that the Great Innumerate Public had simply supposed that he had told them what they would like to hear and responded accordingly.

Curiously, Penrose's popularity with the G.I.P. is not matched by a comparable popularity amongst those professionally concerned with trying to understand the mind. Both Crick (2) and Pinker (3) dismiss his views out of hand -- almost with contempt -- and Dennett (4), though far more courteous, is equally convinced that he is in error. So what is the position which the public likes, with or without understanding, and the professionals do not?

Penrose's standpoint

What Penrose is claiming (1) (5) is that the human mind can never, in principle, be completely represented by a computer, however advanced in structure or programming. In other words, the research programme espoused by Pinker and others, and by the 'Strong A.I.' (artificial intelligence) school is foredoomed to failure. This is a very strong, and, if true, vastly important claim.

Note, of course, the word completely. I do not suppose that Penrose would object to the notion that the brain processes involved in, say, catching a cricket ball might be faithfully rendered by a computational process. He does claim, however, that there are some processes, particularly, though not necessarily only, in mathematical thinking, which can never be so treated.

His argument, stripped to its essentials is as follows.

1) It can be shown that, for any computational device (technically, a Turing Machine), however advanced and programmed howsoever you will, there must exist at least one question which the device will be unable to decide.

2) A competent human mathematician will, nevertheless, be able to intuit what the decision must be, correctly.

Therefore, the human mind cannot be completely represented by any computational process.


It will be at once evident to the reader (read: it occurred to me after a long time) that the two premises are different in kind.
The first is a matter of mathematical logic and is, as far as I am aware, watertight.
The second is part social observation and part act of faith.

No one will deny that good mathematicians can display an astonishing power of insight. They are not, however, infallible. There is a well-known mistake in statistical reasoning known as d'Alembert's fallacy, after a first class mathematician who perpertrated it; and we all know that Fermat believed that he had a proof of his famous theorem, although he almost certainly did not (6). Further, each individual mathematician will have a brain slightly different from the others' and will have had different training and experiences: In other words, each one has unique hardware and unique programming.

If we go along with the 'computer brain' hypothesis we have to accept that any mathematician may bump into a problem which he cannot decide. We may yet suppose that the others may be able to intuit the answer and, perhaps, put him right; which might be called adjusting his programs.

I thus tentatively conclude that we need not give up yet.

What next?

This is not to say that there are not some very serious problems in understanding the evolution of human brains. I expect that they will be solved since there is every reason to believe that the neo-Darwinian position is correct.
One is: What was the survival value in paleolithic conditions of the most powerful kinds of intelligence?
Another (which puzzles me a lot) is: Why is human intellectual ability so enormously variable? Galileo once remarked that the differences between human beings in intelligence seemed greater than that between humans and other animals.

But life would be very dull if there were nothing left to understand.


1. Penrose R. The emperor's new mind, Oxford University Press, Oxford, 1989 (Vintage paperback 1991).

2. Crick F. The astonishing hypothesis: The scientific search for the soul , Simon & Shuster, US, 1994.

3. Pinker S. How the mind works, WW Norton (US), Allen Lane (UK), 1997 (Penguin paperback 1999).

4. Dennett D. Darwin's dangerous idea, Simon & Shuster (US), Allen Lane (UK), 1995 (Penguin paperback 1998).

5. Penrose R. Setting the scene. In: Broadbent D. (ed) The simulation of human intelligence, Blackwell, London, 1993.

6. Singh S. Fermat's enigma: The quest to solve the world's greatest mathematical problem, Walker & Co, 1997 (Bantam paperback 1998).