One might think this means that imaginary numbers are just a mathematical game having nothing to do with the real world. From the viewpoint of positivist philosophy, however, one cannot determine what is real. All one can do is find which mathematical models describe the universe we live in. It turns out that a mathematical model involving imaginary time predicts not only effects we have already observed but also effects we have not been able to measure yet nevertheless believe in for other reasons. So what is real and what is imaginary? Is the distinction just in our minds?

Thus it seems that even God is bound by the uncertainty principle, and can not know both the position, and the speed, of a particle. So God does play dice with the universe. All the evidence points to him being an inveterate gambler, who throws the dice on every possible occasion.

I don't believe that the ultimate theory will come by steady work along existing lines. We need something new. We can't predict what that will be or when we will find it because if we knew that, we would have found it already! It could come in the next 20 years, but we might never find it.

These lectures have shown very clearly the difference between Roger and me. He's a Platonist and I'm a positivist. He's worried that Schrödinger's cat is in a quantum state, where it is half alive and half dead. He feels that can't correspond to reality. But that doesn't bother me. I don't demand that a theory correspond to reality because I don't know what it is. Reality is not a quality you can test with litmus paper. All I'm concerned with is that the theory should predict the results of measurements. Quantum theory does this very successfully. It predicts that the result of an observation is either that the cat is alive or that it is dead. It is like you can't be slightly pregnant: you either are or you aren't.

Einstein is the only figure in the physical sciences with a stature that can be compared with Newton. Newton is reported to have said "If I have seen further than other men, it is because I stood on the shoulders of giants." This remark is even more true of Einstein who stood on the shoulders of Newton. Both Newton and Einstein put forward a theory of mechanics and a theory of gravity but Einstein was able to base General Relativity on the mathematical theory of curved spaces that had been constructed by Riemann while Newton had to develop his own mathematical machinery. It is therefore appropriate to acclaim Newton as the greatest figure in mathematical physics and the Principia is his greatest achievement.

Many people would claim that the boundary conditions are not part of physics but belong to metaphysics or religion. They would claim that nature had complete freedom to start the universe off any way it wanted. That may be so, but it could also have made it evolve in a completely arbitrary and random manner. Yet all the evidence is that it evolves in a regular way according to certain laws. It would therefore seem reasonable to suppose that there are also laws governing the boundary conditions.

I regard [the many worlds interpretation] as self-evidently correct. [T.F.: Yet some don't find it evident to themselves.] Yeah, well, there are some people who spend an awful lot of time talking about the interpretation of quantum mechanics. My attitude — I would paraphrase Goering—is that when I hear of Schrödinger's cat, I reach for my gun.

The subject of this book is the structure of space-time on length-scales from 10<sup>-13</sup>cm, the radius of an elementary particle, up to 10<sup>28</sup>cm, the radius of the universe. ...we base our treatment on Einstein's General Theory of Relativity. This theory leads to two remarkable predictions about the universe: first, that the final fate of massive stars is to collapse behind an event horizon to form a 'black hole' which will contain a singularity; and secondly, that there is a singularity in our past which constitutes, in some sense, a beginning to the universe.