Orchestrated Objective Reduction - The Quantum Level

The Quantum Level

If correct, the Penrose-Lucas argument creates a need to understand the physical basis of non-computational behaviour in the brain. Penrose went on to consider what it was in the human brain that might not be driven by algorithms. Most physical laws are computable, and therefore described by algorithms. However, the nature of quantum collapse is not known (and it appears to have some unusual features, such as irreversibility) making it a candidate for a non-computable process.

In quantum theory, the fundamental units, the quanta, are in some respects quite unlike objects that are encountered in the large scale world described by classical physics. When sufficiently isolated from the environment, they can be viewed as waves. However these are not the same as matter waves, such as waves in the sea. The quantum waves are essentially waves of probability, the varying probability of finding a particle at some specific position. The peak of the wave indicates the location with maximum probability of a particle being found there. The different possible positions of the particle are referred to as superpositions or quantum superpositions. When the quanta are the subject of measurements, the wave characteristic is lost, and a particle is found at a specific point. This change is commonly referred to as the collapse of the wave function.

According to most believers in collapse, when the collapse happens, the outcome is random. This is a drastic departure from classical physics. There is no cause-and-effect process or system of algorithms that can describe the choice of position for the particle deterministically.

This provided Penrose with a candidate for the physical basis of the non-computable process that he proposed as possibly existing in the brain. However, this was not the end of his problems. He had identified something in physics that was not based on algorithms, but at the same time, randomness was not a promising basis for mathematical understanding, the aspect-of-mind that Penrose particularly focused on.

According to Marvin Minsky, because people can construe false ideas to be factual, the process of thinking is not limited to formal logic. But, this is exactly Penrose's point—that human thinking and consciousness is not formal logic, not a Turing machine, as are today's computers. Another dissenter, Charles Seife, has said, "Penrose, the Oxford mathematician famous for his work on tiling the plane with various shapes, is one of a handful of scientists who believe that the ephemeral nature of consciousness suggests a quantum process."

Solomon Feferman, a professor of mathematics, logic and philosophy has made more qualified criticisms. He faults detailed points in Penrose's reasoning in his second book, Shadows of the Mind, but says that he does not think that they undermine the main thrust of his argument. As a mathematician, he argues that mathematicians do not progress by computer-like or mechanistic search through proofs, but by trial-and-error reasoning, insight and inspiration, and that machines cannot share this approach with humans. However, he thinks that Penrose goes too far in his arguments. Feferman points out that everyday mathematics, as used in science, can in practice be formalized. He also rejects Penrose's Platonism.

John Searle criticizes Penrose's appeal to Gödel as resting on the fallacy that all computational algorithms must be capable of mathematical description. As a counter-example, Searle cites the assignment of license plate numbers to specific vehicle identification numbers, in order to register a vehicle. According to Searle, no mathematical function can be used to connect a known VIN with its LPN, but the process of assignment is quite simple—namely, "first come, first served"—and can be performed entirely by a computer. However, as an algorithm is defined in the Oxford American Dictionary as a set of rules to be followed in calculations or problem-solving operations, the assignment of LPN to VINs is not a computation as such, merely a database in which every VIN has a corresponding LPN. Thus, Searle's counter-example does not describe a computational algorithm that is not mathematically describable.