By coincidence, both have Entropy at their core.
Roger Penrose develops Conformal Cyclic Cosmology (CCC), primarily from an analysis of the exceptionally low entropy at the the time of the Big Bang, and his argument that the theory of "inflation" in the early universe does not sync up with Entropy calculations.
Gleich, on the other hand, studies the rise of information, and while the whole book is interesting, I found the sections on Claude Shannon and the development of Information Theory to be the most interesting. While I have used the outcome of Shannon's theory in some of my digital signal processing projects (years ago!), I did not know that his original insight was around Information Entropy. That's pretty cool.
So, I am reading Gleick when I get stuck. Amazingly, the high level descriptions of Entropy in The Information is giving me some insights into what Penrose is describing. Lucky coincidence :-)
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