The deeper an explanation is, the more remote from immediate experience are the entities to which it must refer.

It is like saying that the purpose of a spaceship is to burn fuel.

To say that prediction is the purpose of a scientific theory is to confuse means with ends.

This view is called instrumentalism (because it says that a theory is no more than an ‘instrument’ for making predictions).

To them, the basic purpose of a scientific theory is not to explain anything, but to predict the outcomes of experiments: its entire content lies in its predictive formulae.

But not all languages are equal. Languages are theories. In their vocabulary and grammar, they embody substantial assertions about the world.

What makes the general theory of relativity so important is not that it can predict planetary motions a shade more accurately than Newton’s theory can, but that it reveals and explains previously unsuspected aspects of reality,

The difference between the real trajectory and the predicted trajectory, calculated from slightly inaccurate data, tends to grow exponentially and irregularly (‘chaotically’) with time, so that after a while the original, slightly imperfectly known state is no guide at all to what the system is doing.

As mathematical reasoning became more sophisticated, it inevitably moved ever further away from everyday intuition, and this had two important, opposing effects. First, mathematicians became more meticulous about proofs, which were subjected to ever increasing standards of rigour before they were accepted. But second, more powerful methods of proof