Equations are just the boring part of mathematics. I attempt to see things in terms of geometry.
Stephen HawkingIt is tribute to how far we have come in theoretical physics that it now takes enormous machines and a great deal of money to perform experiments whose results we can not predict.
Stephen HawkingIf the total energy of the universe must always remain zero, and it costs energy to create a body, how can a whole universe be created from nothing?
Stephen HawkingOne 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?
Stephen Hawking