The Emperor

“The Emperor’s New Mind – Concerning Computers, Minds, and The Laws of Physics”
by Roger Penrose.
Oxford University Press, 1989. Rs. 425.00

Roger Penrose’s present volume is required reading for every thinker. For quite some time philosophers have ceased to take an interest in the reality surrounding us, and the mantle of Philosophy has fallen on those who make it their business to do so, namely, Physicists. Though the objectivity of Penrose’s arguments does not make it apparent, the book is a documentation of Penrose’s personal convictions. On a level deeper than what is plainly visible, it is also a philosopher’s quest for his self. Penrose’s search for his own identity takes him to the foundations of logic, the geometry of space-time and the quantum laws governing the very small.

Most of the book is a very illuminating explanation of physics and mathematics for the layman, though Penrose includes more mathematics into his discussions than many others. This book, however, does not come within the category of “Science explaining books”, such as the classics by Gamow and the more recent books by Weinberg and Hawking. It goes beyond explanation when it attempts to define the implications that these sciences have on conventional ideas about the nature of human thought and the behavior of the brain. And what sets it apart is the vision that Penrose presents to the reader about future developments in physics. Not only does he brilliantly explain past and current physics, but also the physics that is to come.

Penrose rejects the idea advanced by some researchers in the field of Artificial Intelligence that it will be possible for computers in the near future to duplicate the human mind. Not only to duplicate the reasoning that the brain does, but also to duplicate the feelings and emotions of the observer who is doing the reasoning. That is, it would become possible for computers, not just to appear human, but to be human; like you, me and indeed like Roger Penrose himself. This idea is called ‘Strong AI’, and Penrose bases his attack on it by an analysis of the laws of physics and computation to show that computers can only do what is computable, and that the phenomena occurring in the world around us, including the phenomenon of being human, may not be computable.

Penrose starts by introducing the reader to the world of computers and computation. In order to be convincingly human, a computer should be able to fool a person sitting in front of a terminal into thinking that he is dealing with another person sitting in front of another terminal somewhere else. That is, it should pass the Turing Test, now considered to be the standard for judging the “humanness” of computers. But if a computer did pass this test and was awarded the “Certificate of Humanness”, would it have the rights and privileges of a human? For example, would it be eligible to vote?

Could this computer, which is merely executing a program, be said to possess a free will? Even though a person and a computer may do a certain task in the same way, the person would (presumably!) be doing it out of a sense of purpose; could this teleological aspect of human behavior be captured by a program? What is free will anyway? Such awkward questions are kept in abeyance until the end of the book.

It will be difficult to wade through the chapter on Turing Machines without suppressing quite a few yawns. But the patient reader, as happens always, is suitably rewarded when the link between Mathematics and Turing Machines becomes clear. The Turing Machine was devised in an attempt to answer Hilbert’s question – Is it possible to solve mathematical problems mechanically? By constructing a machine which would churn out a stream of true propositions one would ultimately be able to prove all that is provable. But the reader is convinced of the futility of this method when the text gives an example of a true proposition which has no proof in any formal mathematical system; that is, it is a proposition which is undecidable. The proposition can be written as

P(a) = “There is no proof for P(a) in X”

where X is the mathematical system in which the proposition has been formulated. If there is a proof for P(a) in X then what P(a) asserts must be true – that is, there really is no proof for P(a) in X. A mathematical system should not contain proofs of things which cannot be proved! Hence a formal proof of P(a) in the system X does not exist. What this means is that we have concluded that P(a) is true without the help of any mathematical proof for it. Thus the formal system X Is incapable of deciding whether P(a) is true or not. Hence no Turing (or any other computing) Machine would be able to stumble onto this or other similarly true but undecidable propositions. It is this which serves to convince the reader that “Strong Al” may not be so strong after all.

In his examination of Classical Physics and Relativity, Penrose exposes the limitations of the concept of Determinism on which it fundamentally rests. Most scientists would agree that, in principle, the behavior of non-quantum systems is predictable in the deterministic sense. That is, if we know at some instant of time the positions and motions of the objects that make up a system and if we know how to find out the forces which act on them, it is possible to predict its behavior at all later times. This, however, may not be the case for all systems, because if the required computation takes an infinite time to complete then the idea that the system obeys deterministic laws has no meaning. Hence classical systems may not be deterministic if they possess an infinite number of degrees of freedom. But whether this kind of non-determinism can be useful in describing the behavior of our brains is not elaborated. Another aspect of classical systems is that some of them are very sensitive to small variations in initial conditions. This means that if the initial conditions are not known accurately enough the computed prediction of the later state of the system can be widely off the mark. This is the field of study known as Deterministic Chaos.

In discussing Relativity the emphasis is on how the observer sees the world. Instead of describing the theory through the usual reference frame technique, Penrose utilizes the geometrical approach of space-time diagrams. This serves to directly illustrate the contradictions inherent in the viewpoints of two independent observers moving relative to each other. Is there an objective “reality’ when the same event is in the past for one observer and in the future for another?

A field of which Penrose is a master is Quantum Theory. Instead of arguing whether Quantum Theory is or isn’t a complete description of reality, Penrose states his belief without mincing words. Whether we like it or not, there is a “reality” out there which is very successfully described by Quantum Theory, and that the wave-function must have an objective meaning as the description of a quantum system, because the Schrodinger Equation gives a complete and deterministic time history of the system’s evolution once the wave-function is specified initially.

There is, however, one missing link in the theory : the intrusion of an observer into a quantum system. There is no formulation which gives a description of the interaction of a classical system with a quantum state – this is the famous “measurement problem”. The Schrodinger Equation does not incorporate measurements. Because, once a measurement is performed on the system, it serves to throw it into one of several possible states, and in advance one can only calculate the probability of the manifestation of the various states.

This behavior is non-deterministic, and Penrose does not speculate much about this, except to use it as a prelude to the well known Cat and EPR Paradoxes. There is a suitably protected scientist inside the box, observing the doomed cat, as well as another scientist outside it, with no communication between the two. The one outside would claim that the wave-function of the cat would be a superposition of two orthogonal state-vectors, the “dead cat” and the “live cat”, whereas the observer inside would claim that the cat is in only one of the two states. The question to ask is not “Which description is more complete?”, but “What is it that really happens when quantum effects are magnified many times to the classical level?”

Similarly, when a measurement is performed on one quantum system, it affects another correlated system far away by throwing it into some particular eigenstate. The discussion on Relativity has convinced the reader that signals cannot travel faster than the speed of light, and the EPR paradox convinces the reader that quantum systems have no respect for Relativity. How can one resolve these differences? Along the way, Penrose removes many commonly held misconceptions. Quantum Theory is not, as is widely misunderstood, applicable only to systems which are very small compared to human length scales. Many macroscopic phenomena require the Quantum Theory for their explanation. Does it mean that a Quantum world is necessary for thinking beings to exist? This is speculation at its intellectual best.

Penrose’s penchant for asking incisive questions is exemplified by his treatment of entropy. We all know the Second Law of Thermodynamics – The entropy of an isolated system always increases. Hence the entropy of the Universe is continually increasing. But increasing from what? Why, from a low value to high value, of course. Now comes the big one: Why did the Universe have such an amazingly low value of entropy in the past? This is one of physic’s unsolved puzzles, and attempts to answer this leads to space-time singularities like Black (and White) Holes, the Big Bang, and the Big Crunch.

But the best is yet to come. The first half of the book is just a prelude to the torrent of speculation that engulfs the reader in the second half. The purpose is to find answers to the questions raised earlier. Penrose’s formulation of a theory of Quantum Gravity gives the perceptive reader a peep into the workings of a scientist’s mind, apart from the insight that he gets regarding the theory itself. The basic idea behind his hypothetical theory is that all the information regarding the various states in which a quantum system can exist is present within the wave function describing the system. When the system evolves, it will naturally interact with its surroundings and these states will become more and more different until the difference in mass-energy between one of the possibilities and the others exceeds the ‘one graviton” limit. At this stage the system collapses into that particular state. When will this limit be crossed? The speculation is that such a catastrophically large difference will occur only when the quantum system interacts with a classical system. That is, when a “measurement” takes place. Here may lie the confluence of the quantum and the classical world.

What does all this have to do with our brains? In what way is the working of the brain similar to the working of computers, and in what way is it not? The examination of the mechanism of the brain shows that our thoughts and actions lie on several levels. the uppermost one of which we call “consciousness”. It is here that the working of the brain cannot be described by an algorithm, and where the non-computable aspect is dominant. In so far as mathematical insight is concerned, it must be non-algorithmic. Because if it were not, then the process by which a mathematician perceives the truth of the undecidable proposition P(a) above could be replaced by a suitable algorithm – lets call it the “Insight Algorithm” or IA. Since mathematical truths are communicable (at least within the community of mathematicians!) it must be true that all mathematicians use equivalent, though personalized, versions of IA. Hence we could, in principle, construct a Universal IA which would be able to perceive the truth of P(a). Since IA is equivalent to a formal system, one could also construct a proposition within it which would be true, but which the IA would not be able to perceive as true, but which would be perceived as true by a mathematicians insight. Hence this kind of insight cannot be represented by an algorithm. That is, the IA cannot be attained by AI.

And where does the mind come into the picture? Penrose’s attempts to apply physics to the mind is far removed from the patchwork of philosophy and pseudo-science that is generally found in popular articles. The reader will have to go through the book to appreciate the fact that the new mind of “Strong AI” is not yet a mind at all and, if Penrose is correct, not capable of being one.