The Rigor of Angels is about the unknowable nature of reality and how our "metaphysical prejudice" of continuous spacetime leads us into antimonies and paradoxes. It approaches these abstract subjects through the work of three men who demonstrated the irreconcilable difference between reality and our experience of it: Immanuel Kant, Werner Heisenberg, and Jorge Luis Borges. (So, an alternative title in the style of Douglas Hofstadter, would be Heisenberg, Borges, Kant.)
In his Critique of Pure Reason, Kant showed that our concepts of space and time do not derive from experience but rather are necessary assumptions that our understanding projects onto reality. With his uncertainty principle, Heisenberg proved (in the mathematical sense) that spacetime is not continuous, that subatomic particles flicker in and out of existence. In his stories, Borges reflects on the limits of our understanding in the infinitude of the universe.
Egginton sets himself the ambitious and difficult task in this book. He essentially argues that we humans cannot conceptualize the nature of reality, because our understanding critically depends on assumptions (about space and time and causality) that fail us at their limits. He believes that his three protagonists managed to abjure those assumptions and accept, even celebrate, our limitations.
Egginton makes mind-expanding connections between quantum mechanics, ancient Greek philosophy, Kantian epistemology, and modern literature. He addresses Zeno's paradox, the question of free will, the origin of the cosmos, the riddles of quantum mechanics and special relativity, and more. However, I'm not sure his explanations would be clear (or astonishing) to a reader who is not already familiar with the thinkers and ideas involved.
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