Roger Penrose

· Professor of Mathematics at Oxford University, U.K., & also a physicist.

· Collaborated with Stephen Hawking transforming our understanding of the universe.

· Believes the next great challenge is that of understanding the human mind

· Doesn’t support the strong AI (materialist) viewpoint

What are his views?

First need to be clear on a few concepts & ideas:

· Algorithms are systematic procedures to be followed to achieve a particular type of outcome. Can also be described as mathematical devices for problem solving.

· Turing tried to create a general definition of an algorithm to solve all problems in the 1930s. Very imaginative.

· Came up with the concept of a Turing Machine – this is a machine made of anything that is able to compute any algorithm, he believed the mind was a Turing Machine (& he followed this with the idea of the Turing test). He was considering the question of whether there was a method in principle to solve all mathematical questions.

· It can be shown that a Turing machine can be constructed to carry out all basic mathematical operations or any mechanical operations.

· Other mathematicians worked on this and the viewpoint became known as the Church-Turing thesis. I.e. the Turing machine defines what, mathematically, we mean by an algorithmic procedure.

· After the war this idealised machine was realised, in the form of a real computer.

Penrose’s arguments

· Strong AI says that doing algorithms is all there is to thinking, but others disagree.

· Penrose uses mathematics to argue against strong AI, which is a different approach to that taken by others e.g. Searle.

· In the video he discusses how humans understand intuitively, e.g. the idea that for any pair of numbers a x b = b x a, tiling an infinite plane

· Cites Godel’s Incompleteness Theorem (1931) – syas that ‘any precise mathematical system […] must contain some statements that are neither provable nor disprovable by the means allowed within the system’.

· (This disproved the earlier work of Hilbert (1900) - whether there was a general algorithmic procedure for resolving all mathematical questions.)

· This points to ideas we see in Plato’s ideal world.

· Penrose believes we see this in the relationship between Physics (physical) and Maths (ideal)

· Says that Einstein’s theory of relativity is also Platonic – we see the evidence as we observe more

· Moves on to discuss quantum theory – where we deal with the ‘very small’ – physics at atomic and sub-atomic levels.

· It’s possible to find ways to compute ideas at the classical level and at the quantum level, but there is a gap in this framework that is un-explained and this is where Penrose believes the answer to consciousness lies.

· Quantum theory says that all things that might happen at the quantum level do happen, describes using Schrodinger’s cat – thought experiment.

· At the classical level we see something in one state or another, never in two or more at the same time. At quantum level we do, and something happens in the transition from quantum level to classical level (i.e. when we scale up) that results in these different observations.

· Looking at our brains, we are able to understand about how the neurons work etc.

· at a lower level though, the neurons are made up by the cytoskeleton, which contains micro-tubules, and these are operating at the quantum level – but they cause effects at the classical level,

· and it is in the transition (or scaling up) from the quantum level activity in the brain to the classical level, that Penrose believes we will find non-computability, and hence the key to consciousness. (& strong AI is therefore only addressing the idea of intelligence at the classical level.)