What Casti means by the title 'One True Platonic Heaven' is polyvalent - in the first place, it is frequent reference to the IAS, the Institute for Advanced Study at Princeton University, a think-tank founded for the advancement of pure science. So adamant are some that it remain 'pure' rather than 'applied', that when one of their number proposes to bring a computing device in, there is controversy among the members, that this would end up being an 'application', and implicit slippery slopes abound.
Of course, the timing of this novel (and it is a novel) is the early twentieth century - the prologue begins with snapshots of various points prior to World War II, key moments in the development of mathematics and scientific epistemology. The core of the book takes place just after the war, in Princeton, as the earliest computing machines (ENIAC, anyone?) have been developed by the military, and are now being further developed for both civilian and military applications.
The cast of characters Casti draws is impressive - the core group includes Einstein, Godel, von Neumann, Oppenheimer, and Strauss; other 'also starring' roles go to T.S. Eliot (Oppenheimer was a poet on the side, and the idea of the limits of knowledge is a multi-disciplinary task), Goldstein, Weyl, Pauli, Bohm and others. Casti draws these people together in informal and formal settings, preferring the former to the later - walking to campus and having discussions, gatherings at tea-time, etc. Casti injects the human element into the mix (we are told of Godel's eccentricity such that he starved himself to death no fewer than three times, for example) - his descriptions help the narrative flow of the novel, but can be distracting for those who wish to get directly to the heart of the arguments.
The book is rather thin - 160 pages of text, small-format pages at that - and while the subject matter is rather high end intellectual thinking, in fact the substance of the book probably only consists of about a third of those pages; the rest is psychological tid-bits about the characters (enlightening from an historical standpoint, and pointing the way in some respects as to why people thought the ways they did) or narrative linkages, so it can be read fairly quickly (unlike a mathematics textbook, which would more likely take a longer time). There are no equations here - Casti is assuming some knowledge of mathematics in general theory; Casti also assumes a grounding in physics and in philosophy. Without some background in at least one of these disciplines, the reader is likely to be lost at several points.
It is fascinating to realise that the limitations on knowledge discussed in this hypothetical construct by such exalted twentieth-century thinkers contain elements still on the table for discussion today. This is where another meaning of the 'one true Platonic heaven' comes into play - it is a theoretical construct, akin to the Forms, without direct substance, yet reflected in important ways in 'the real world'.
A bit more philosophy might not go astray here - elements such as Husserl, Whitehead, Ayer and others who have examined the crisis of science and scientific knowledge might have been drawn into the conversation (it would have required a bit more fictional stretching, but cold have proved worthwhile). However, it is remains a fascinating and fairly accessible means for exploring some of the key underlying ideas in modern scientific, mathematical, and epistemological thinking.