[T]here's a version of this a version of this idea which John Wheeler has promoted, which is that in each of these cycles, since nobody really knows … - Roger Penrose

How is it that mathematical ideas can be communicated in this way? I imagine that whenever the mind perceives a mathematical idea, it makes contact with Plato's world of mathematical concepts. ... When one 'sees' a mathematical truth, one's consciousness breaks through into this world of ideas, and makes direct contact with it ('accessible via the intellect'). I have described this 'seeing' in relation to Gödel's theorem, but it is the essence of mathematical understanding. When mathematicians communicate, this is made possible by each one having a direct route to truth, the consciousness of each being in a position to perceive mathematical truths directly, through this process of 'seeing'. (Indeed, often this act of perception is accompanied by words like 'Oh, I see'!) Since each can make contact with Plato's world directly, they can more readily communicate with each other than one might have expected. The mental images that each one has, when making this Platonic contact, might be rather different in each case, but communication is possible because each is directly in contact with the same externally existing Platonic world!

Some years ago, I wrote a book called The Emperor's New Mind and that book was describing a point of view I had about consciousness and why it was not something that comes about from complicated calculations. So we are not exactly computers. There's something else going on and the question of what this something else was would depend on some detailed physics and so I needed chapters in that book, which describes the physics as it is understood today. Well anyway, this book was written and various people commented to me and they said perhaps I could use this book for a course Physics for Poets or whatever it is if it didn't have all that contentious stuff about the mind in that. So I thought, well, that doesn't sound too hard, all I'll do is get out the scissor out and snip out all the bits, which have something to do with the mind. The trouble is that if I did that — and I actually didn't do it — the whole book fell to pieces really because the whole driving force behind the book was this quest to find out what could it be that constitutes consciousness in the physical world as we know it or as we hope to know it in future

The idea of having an ambient space-time of some specific dimension seems to play less of a role of string theory than in conventional physics, and certainly less than the kind of role that I would myself feel comfortable with. It is particularly difficult to assess the functional freedom that is involved in a physical theory unless one has a clear idea of its actual space-time dimensionality.