You are probably convinced that all the laws of physics are symmetrical under any kind of change whatsoever, so now I will give a few that do not work. The first one is change of scale. It is not true that if you build an apparatus, and then build another one, with every part made exactly the same, of the same kind of stuff, but twice as big, that it will work in exactly the same way. You who are familiar with atoms are aware of this fact, because if I made the apparatus ten billon times smaller I would only have five atoms in it, and I cannot make, for instance, a machine tool out of only five atoms.

It is perfectly obvious if we go that far that we cannot change the scale, but even before the complete awareness of the atomic picture was developed it became apparent that this law is not right. You have probably seen in newspapers from time to time that somebody has made a cathedral with matchsticks - several floors, and everything more Gothic than any Gothic cathedral has ever been, and more delicate. Why do we never build big cathedrals like that, with great logs, with the same degree of 'ginger cake', the same enormous degree of detail?

The answer is that if we did build one it would be so high and so heavy that it would collapse. Ah! But you forgot that when you are comparing two things you must change everything that is in the system. The little cathedral made with matchsticks is attracted to the earth, so to make a comparison the big cathedral should be attracted to an even bigger earth. Too bad. A bigger earth would attract it even more, and the sticks would break even more surely!

The fact that the laws of physics were not unchanged under change of scale was first discovered by Galileo. In discussing the strength of rods and bones, he argued that if you need a bone for a bigger animal - say an animal twice as high, wide and thick - you will have eight times the weight, so you need a bone that can hold the strength eight times. But what a bone can hold depends on its cross-section, and if you made the bone twice as big it would only have four times the cross-section and would only be able to support four times the weight.

In his book Dialogue on Two New Sciences, you will see pictures of imaginary bones of enormous dogs, way out of proportion. I suppose Galileo felt that the discovery of the fact that the laws of nature are not unchanged under change of scale was as important as his laws of motion, because they are both put together in the tome on Two New Sciences.