Sir Roger Penrose, Rouse Ball professor of mathematics at the University of Oxford, spoke on the relationship between science and the mind to a standing-room-only crowd of over 150 in the Math/Physics Building yesterday.
Penrose presented a mathematical argument that no computer could completely imitate a human mind, because the human mind possesses understanding in a way that computers cannot. "The claim is that no knowable computational procedures can encapsulate human understanding and insight," he said.
To set up his argument, Penrose spoke of the existence of three worlds: the physical, mental and Platonic realms. The Platonic realm encompasses abstract ideals such as mathematics.
Each world, he explained, arises from one of the others: the Platonic from the mental, the mental from the physical and the physical from the Platonic.
"Each one seems to come from a small part of another," Penrose said. "The more that we understand about the way the physical world operates..., the more and more we are driven to mathematics."
Penrose claimed that the portion of the physical world that gives rise to the mental realm-which includes the human brain-cannot be completely described by computational mathematics-a subdivision of the Platonic world. To support this claim, Penrose argued that an abstract computer known as a Turing machine could not imitate the intelligence of a human mind.
"If it can be shown that understanding is beyond computation," he said, "then intelligence is not a matter of computation."
Using a theorem of 20th century mathematician Kurt Gödel, Penrose proved no Turing machine could understand mathematics in the way humans do.
"Gödel tells us that no system of computational rules can characterize the properties of the natural numbers," he said, "yet a child can grasp the idea of the actual natural numbers after being given only very simple descriptions."
Penrose proposed that the limits of a Turing machine rest on the fact that the operation of the brain is based on both classical physics and quantum physics. Since the theory currently used to describe the interaction between quantum and classical physics does not follow computational rules, Turing machines cannot imitate this interaction.
Penrose suggested that a new "objective reduction" theory of the interaction between classical and quantum physics is necessary to explain the workings of the brain.
He will give two more lectures this week in the Math/Physics Building. His series of lectures is sponsored by the Mathematics Department in memory of former department chair John Gergen.
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