It means that we have been aiming at a false ideal of a complete description of the world. There has not yet been time to make serious search for a new epistemology adapted to these conditions. It has become doubtful whether it will ever be possible to construct a physical world solely out of the knowable—the guiding principle in our macroscopic theories. If it is possible, it involves a great upheaval of the present foundations. It seems more likely that we must be content to admit a mixture of the knowable and unknowable. This means a denial of determinism, because the data required for a prediction of the future will include the unknowable elements of the past. I think it was Heisenberg who said, “The question whether from a complete knowledge of the past we can predict the future, does not arise because a complete knowledge of the past involves a [Pg 229] self-contradiction.” It is only through a quantum action that the outside world can interact with ourselves and knowledge of it can reach our minds. A quantum action may be the means of revealing to us some fact about Nature, but simultaneously a fresh unknown is implanted in the womb of Time. An addition to knowledge is won at the expense of an addition to ignorance. It is hard to empty the well of Truth with a leaky bucket. [33] The evidence is much stronger now than when the lectures were delivered. [34] The energy is required because on cooling down the matter must regain a more normal density and this involves a great expansion of volume of the star. In the expansion work has to be done against the force of gravity. [35] Each orbit or state of the atom requires three (or, for later refinements, four) quantum numbers to define it. The first two quantum numbers are correctly represented in the Bohr model; but the third number which discriminates the different lines forming a doublet or multiplet spectrum is represented wrongly—a much more serious failure than if it were not represented at all. [36] The probability is often stated to be proportional to instead of , as assumed above. The whole interpretation is very obscure, but it seems to depend on whether you are considering the probability after you know what has happened or the probability for the purposes of prediction. The is obtained by introducing two symmetrical systems of -waves travelling in opposite directions in time; one of these must presumably correspond to probable inference from what is known (or is stated) to have been the condition at a later time. Probability necessarily means “probability in the light of certain given information”, so that the probability cannot possibly be represented by the same function in different classes of problems with different initial data. [Pg 230] Chapter XI WORLD BUILDING