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" "What right do we have to claim, as some might, that human beings are the only inhabitants of our planet blessed with an actual ability to be "aware"? … The impression of a "conscious presence" is indeed very strong with me when I look at a dog or a cat or, especially, when an ape or monkey at the zoo looks at me. I do not ask that they are "self-aware" in any strong sense (though I would guess that an element of self-awareness can be present). All I ask is that they sometimes simply feel!
Sir Roger Penrose (born 8 August 1931) is an English mathematical physicist and Professor of Mathematics at the Mathematical Institute, University of Oxford, famous for his work in mathematical physics, cosmology, general relativity, and his musings on the nature of consciousness.
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In its simplest form, the 2nd law of thermodynamics... You imagine... a glass of wine sitting on a table... it falls off and wine splashes out onto the carpet...[etc.] If you just think of this as a Newtonian situation, as the system evolves the thing proceeds according to Newtonian laws, but Newtonian laws are reversible in time... What's not so agreeable [about the reverse] is that it violates the 2nd law...
[T]he randomness is measured... by... entropy, and it's telling us that this entropy is increasing with time. ...[I]t can be given a clearer definition ...the idea due to Boltzmann ...we imagine... a ... a space... of a very large number of dimensions, where each point in the space represents a state of the system at one moment. In fact it contains both the positions of all the particles and the momenta (or velocities) of all the particles. So if you know where the point is in this large dimensional space at any moment that describes a particular thing... then the dynamics will tell you where that point moves. So that there will be a unique path through that point, wiggling around somewhere through this phase space.
Gödel's theorem shows that this point of view is not really a tenable one in a fundamental philosophy of mathematics. The notion of mathematical truth goes beyond the whole concept of formalism. There is something absolute and 'God-given' about mathematical truth. This is what , as discussed at the end of the last chapter, is about. Any particular formal system has a provisional and 'man-made' quality about it. Such systems indeed have very valuable roles to play in mathematical discussions, but they can supply only a partial (or approximate) guide to truth. Real mathematical truth goes beyond mere man-made constructions.