1. The World Within the World (TWWTW)
2. Theories of Everything (TOE)
Of the two TWWTW was more enjoyable, thought provoking and revealing than I had anticipated. It spanned philosophy, science, physics, cosmology and religion and from the Greeks to the present (circa 1990).
It revealed that physicists such as Maxwell, Einstein, and Newton were more religious than I had thought. (Of course, Einstein was already known by his remark to Bohr that he did not believed that God played dice.) It was thought provoking in that it asked questions that I never really thought much about:
Why are the Laws of Nature mathematical? Are there Laws of Nature? Does mathematics (differential equations) describe the laws of nature because the laws are mathematical or is nature inherently mathematical? What is accuracy and error?
One might think that the answer ... is increased accuracy of observation. The more accurate our present knowledge of the world, so the more reliable will be our future predictions. Unfortunately, increased accuracy does not really help us, because the uncertainty about the future grows so fast that it very easily overcomes our paltry attempts to improve our specification of the present (pg. 276)
To the scientist the term [error] means two other things. The first is straightforward: the limiting accuracy to which a quantity can be measured. A simple example is experimental error ... [which] is not terribly interesting, but it is obviously one of the goals ... to make it as small as possible. ... We have already seen that the Heisenberg Uncertainty Principle ... ensures that there are inevitable errors associated with the measurement of all quantities even if the measuring instruments are perfect ... This strange limitation arises becase the very process of observation is inseparable from the state being measured. Perfect knowledge of the Universe is impossible because the act of knowng influences the Universe in an unknowable way. It is as if, by the time we record its state, it has changed slightly.
... The second form of error ... [is] more serious in its consequences because one can never be certain that it has even been identified, let alone minimized or eradicated. This species of error we call a 'selection effect' or 'systematic error'.... Experimental arrangements and observational procedures have built-in propensities to gather certain types o facts more readily than others. In order to be sure that you are observing what you think you are observing, it is always necessary to have some theoretical understanding of the wider spectrum of phenomena that could be biasing your observations. [e.g. only stars of a certain brightness can be measured]
TOE was less satisfatory - it seemed more of a rehash of TWWTW and combined it with chaos theory and sensitivity of things to initial conditions and hence read more as a critique then a description that more entertaining in TWWTW.
Both books are sprinkled with delightful quotes, some of which I extract here:
If everything on Earth were rational, nothing would happen. FYODOR DOSTOYEVSKY
As far as the laws of mathematics refer to reality they are not certain; as far as they are certain, they do not refer to reality. ALBERT EINSTEIN
Physics is mathematical not because we know so much about the physical world, but because we know so little: it is only its mathematical properties that we can discover. BERTRAND RUSSELL