(My own copy)
Penrose certainly has a generous idea of his readers' mathematical ability. It's a kind of running joke among Penrose-fans: he always starts his books by saying you'll find it tough going if you haven't got a 12th Year (in Portugal)/GCSE (in the UK) in math, but that he'll explain it as he goes if you haven't. Twenty pages later you're on Gödel and conformable geometry. He doesn't do it deliberately; he really does believe his books are popular science. How can you not love him? I purchased an on-line kindle edition of this book back last year via Amazon and it was more about bringing myself up to date (I read it for the first time in 1991 when the book came out), although such things are never truly current due to Theories being debated and tested for very many years within Scientific Realms. Roger Penrose's books are as stated often inclusive of more mathematical devises than many books aimed at more laymen realms, so I often regard them as perhaps Bridging that gap between Solid Science Headaches and Laymen 'I read an article and am a common law know-all expert'. What to say about this re-read? What I liked within this particular tomb over multiple other works and writers from his genre was that Penrose took the opportunity to use more analogy & metaphor in his descriptions of the function of the ideas. So, you read the math and then you might see an image or descriptive wording of the comparisons. Overall as I have stated above, this is potentially overwhelming for your Mr/s-Average-Layman and Not-Hard-Core-Enough-for-Scientists. Though for anyone looking for a kind of Half-Way-House bridging zone, this book may well serve and be fit for the purpose.
Anyone read Raymond Kurzweil's "The Singularity is Near"? It discusses this exact same stuff in more detail. Personally, I think it's a little more optimistic about strong AI than reality warrants. Penrose has interesting ideas about quantum consciousness, but I don't see humanity making any major gains on "the hard problem of consciousness" any time soon. It's like the holy grail of several disciplines. In reading about an electromagnetic theory of consciousness, a good point was brought up - if the brain develops its own field, then contemporary traditional computer engineering will never achieve the goal of true AI, simply because now actively creating shielding against short-circuits won't allow any field to develop. The closest I've seen to understanding consciousness seems to be the promising ideas about quantum theories of consciousness. We have yet to develop computers that can grow their own neural connections, much less create consciousness. It's been proven that memory doesn't reside in any one neuron - you can't create a lesion which excises a given memory, for instance. There's got to be some kind of unknown field. Until we understand the toughest riddle of all - consciousness - we will never develop true AI. Nor, I might add, will we be able to do what Kurzweil suggests - "uploading the mind". Bullshit. The day we can achieve either of those things we will also be able to create the ability to travel at the speed of light, but transmitting our consciousness, with perhaps genetic meta-data to reconstruct the body nanoscopically at the other end. It's the stuff of SF, to be sure.
(Bought in 1991)
One only has to refer to Alan Turing's famous "Can Machine's Think?" to understand the singularity is total nonsense. Machines, hardware are nothing w/o a program to function it, which is nothing more than a theory. When one compares the structure of our ability to speak (our language) with that of programming, it's not even close to being in the same field of discussion. Programming languages follow a somewhat commonsensical pattern, because we're the ones manipulating it. When one looks at the core structure of our language, it's so remote from common sense notions that it is not for the ear, but more soothing for the mind. It's striking the deeper we look into out cognitive faculties, the more it diverts from our presumptions. Man's fascination with machines and their impact began to fully realize itself with Galileo and Descartes, only to get smothered rather abruptly forever (apparently not) by Newton not too long after. We should pay much more attention to history, most certainly politically but scientifically as well.
NB: It's worth pointing out that towards the end of his life Hawking gained an interest in what is known as model dependent reality...which actually totally negates any notion of a "theory of everything". So, Hawking's book "The Grand Design" actually contradicts the very idea that a theory of everything is even possible. Hawking also worked with Professor Paul Davies on ideas about reverse causality....a very fringe and not widely accepted area of speculation. All of which shows he was open to new ideas.