Truth and proof in science.

  Experiments sometimes produce results which cannot be explained with existing theories. In this case it is the job of scientists to produce new theories which replace the old ones. The new theories should explain all the observations and experiments the old theory did and, in addition, the new set of facts which lead to their development. One can say that new theories devour and assimilate old ones (see Fig, 1.2). Scientists continually test existing theories in order to probe how far can they be applied.

  

Figure 1.2: Saturn devouring his sons (by F. Goya). A paradigm of how new theories encompass old ones.

When an old theory cannot explain new observations it will be (eventually) replaced by a new theory. This does not mean that the old ones are ``wrong'' or ``untrue'', it only means that the old theory had a limited applicability and could not explain all current data. The only certain thing about currently accepted theories is that they explain all available data, which, if course, does not imply that they will explains all future experiments!

In some cases new theories provide not only extensions of old ones, but a completely new insight into the workings of nature. Thus when going from Newton's theory of gravitation to Einstein's our understanding of the nature of space and time was revolutionized. Nonetheless, no matter how beautiful and simple a new theory might be, it must explain the same phenomena the old one did. Even the most beautiful theory can be annihilated by a single ugly fact.

Scientific theories have various degrees of reliability and one can think of them as being on a scale of certainty. Up near the top end we have our theory of gravitation based on a staggering amount of evidence; down at the bottom we have the theory that the Earth is flat. In the middle we have our theory of the origin of the moons of Uranus. Some scientific theories are nearer the top than others, but none of them ever actually reach it.

An extraordinary claim is one that contradicts a fact that is close to the top of the certainty scale and will give rise to a lot of skepticism. So if you are trying to contradict such a fact, you had better have facts available that are even higher up the certainty scale: ``extraordinary evidence is needed for an extraordinary claim''.