This doesn't tackle the issue head on. The problem that emerged in the 20th Century was a lay perspective on science that looked at the old theory of Newtonian Mechanics and compared it to the new theories of Quantum Mechanics and Relativity and saw the differences but not the similarities.

Science consists of both theory and experiment. The old theory does a reasonable job of explaining the old data that came from the old experiments. Along come new experiments producing new data that the old theory cannot explain.

To understand science you must contrast it with folk-wisdom. Folk-wisdom comes up with a three part explanation of the new data. It is conservative in that it keeps the old theory, as its explanation of the old data. It comes up with a new theory that explains the new data, but not the old data. Thirdly it offers an ad hoc guidance as to which theory applies.

Science is also conservative, but with a different vision of what this means. Scientific conservatism lies in the high esteem granted to the old experiments. The new theory cannot merely explain the new data, it must do pretty well on the old data. Experimental error is important and we must at first cut the new theory some slack as experimenters are prone to optimism about the accuracy of their experiments especially when they agree with established theory. But not for very long. Old experiments can be redone with greater accuracy, and the new theory is expected to win both on the new experiments and on the most accurate versions of the old experiments.

Notice my gradual build up to the central dilemma. A good theory has a degree of inevitability about it. Newton's Law of Gravity is an inverse square law. Distance raised to the power of 2. Perhaps we can get a better fit to the orbit of Mercury with 2.00036, but that would be silly. Inevitability implies brittleness. If new data contradicts the theory there may be no way to adjust the theory.

If the old theory is a good one, but new experiments contradict it, folk wisdom can accommodate this straight forwardly by keeping the good old theory as the folk account of the old experiments. Scientists however have a serious problem. The good old theory breaks when they try to bend it to fit the new data, and the new theory has to agree with the old data, even though the old data appear to force one to believe in the old theory as the unique good fit.

Scientists are caught in a trap. Their conservatism with respect to old experiments forces them to be radical with respect to new theory. The new theory cannot just beat the old theory on the new data, it has to beat the old theory on the old data, the very data that gave rise to the old theory! This requires radical new ideas. As [Lampedusa says](http://en.wikipedia.org/wiki/The_Leopard) "If we want things to stay as they are, things will have to change."

Hence the 20th century phenomenon of lay people reading popular accounts of Quantum Mechanics and of Relativity and coming away with the impression that scientific truth is prone to dramatic changes. Is there any antidote? I recommend A Quantum Mechanics Primer, by D.T. Gillespie. This slim, clear book reaches Ehrenfest's equations on page 111, allowing the interested layman to see how Quantum Mechanics leads to F=ma and beats Newtonian dynamics on its home ground. But the book requires single variable calculus and a good enough grasp of three dimensional vector spaces to realise that nothing goes too horribly wrong when we add more dimensions. Is it really accessible to a layman?

Ehrenfest's equations symbolism a new paradigm of total backwards compatibility through radical change. Asimov ably covers the data side of this, but wimps out of trying to explain the implications for theory.