The last line of the Conclusion chapter (which was actually written first) reads: "For, with evident rhyme but illusive reason, the Universe is what it is!", but what does this mean? It means that the world around us clearly exhibits a pattern susceptible to mathematical description, but seeking a rationale — a how, or why — is quite different, and likely a futile subjective aspiration.
When Albert Einstein developed his theory of special relativity, he showed that space and time could be treated in a mathematically orthogonal fashion, and that this resulted in the laws of physics — crucially including Maxwell's equations of electromagnetism — being the same for all inertial observers. Hermann Minkowski reformulated his equations using a coordinate system involving an imaginary time (following an idea previously considered by Henri Poincaré) and showed that the equations of relativity and electromagnetism both took on a much simpler and symmetrical form in this space-time continuum.
The block universe is a view of reality in which space and time are equally real and unchanging. The idea can be traced back to the Greek philosopher Parmenides of Elas, from around the early fifth century BCE. Special relativity, and particularly in its Minkowski space-time form, is often considered a model for a block universe, and yet Einstein used it to describe the kinematics of objects and observers in relative motion. This is a problem because there can be no motion, nor change of any kind, without a flowing time, and yet by treating time as a space-like dimension then he had already removed that notion. It is easy to draw a world-line on a space-time diagram and claim that it represents a series of linked events charting a particle's progress through space-time, but there is no inherent succession, no progression, nor any specific direction.
In 1926, Einstein met renowned French philosopher Henri-Louis Bergson, and the pair began a heated debate over the nature of time. Bergson was a great believer in the importance of experience, and criticised relativity for it having distanced itself from experience and for it leading to counter-intuitive consequences. Relativity made sound sense, mathematically, but Einstein didn't try to explain the connection between experience and his mathematics.
In 1927, English philosopher John M. E. McTaggart introduced the concepts of A-series and B-series times, which roughly correspond, respectively, to the subjective and objective times defined in this book. McTaggart's terms are not used in order to avoid the accidental implication of propositions that might be conflicting. McTaggart argued that A-series time was contradictory, and yet necessary for any description of change. He tried to define a C-series time that retained some connection to the sequencing that we experience, rather than adopting the less palatable B-series, but the notion of some ordered sequencing of discrete events or mental states was ill-founded. Not only is there no true simultaneity in special relativity, but there is no cosmic equivalent of 'now'.
The more perdurant approach taken in the book is essentially to posit that we exist in a true block universe, and that this explains the appropriacy of mathematical description. In other words, the fact that all change is relative means that the smooth and finite differences we observe across time can be modelled by mathematics. But mathematics cannot fully capture any aspect of our experience, including the passage of time, dynamical change, causality, consciousness, etc. It is then necessary to deconstruct these aspects in order to see how they can emerge within the block universe.
A notable casualty of the premise is quantum theory: the prevailing probabilistic interpretation is invalid in a block universe, and must be substituted with a more deterministic interpretation. The one put forward actually gives a clearer picture of why wave-function collapse (the so-called 'measurement problem') is deemed to be at odds with a wave-function description, and demonstrates that the problem goes away in a block universe.
The book concludes that all of experience can be reconciled with the block universe, in addition to quantum mechanics and the second law of thermodynamics, but it has repercussions for the scope of mathematics and the pursuit of knowledge in general.