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Response to Quora Question: Are there any popular science books on information theory?

There are a small handful that may meet your requirements:

Information, Entropy, Life and the Universe: What We Know and What We Do Not Know by Arieh Ben-Naim
http://www.amazon.com/gp/product/9814651672/ref=as_li_tl?ie=UTF8&camp=1789&creative=390957&creativeASIN=9814651672&linkCode=as2&tag=itbio-20&linkId=A67ICW76GUS5PBJ5

An Introduction to Information Theory: Symbols, Signals and Noise by John R. Pierce
http://www.amazon.com/gp/product/0486240614/ref=as_li_tl?ie=UTF8&camp=1789&creative=390957&creativeASIN=0486240614&linkCode=as2&tag=itbio-20&linkId=FXIGZDG722UWRA3D

The Information: A History, A Theory, A Flood by James Gleick
http://www.amazon.com/gp/product/1400096235/ref=as_li_tl?ie=UTF8&camp=1789&creative=390957&creativeASIN=1400096235&linkCode=as2&tag=itbio-20&linkId=SH3QLZDFQKUFAILF

Decoding the Universe: How the New Science of Information Is Explaining Everything in the Cosmos, from Our Brains to Black Holes by Charles Seife
http://www.amazon.com/gp/product/0143038397/ref=as_li_tl?ie=UTF8&camp=1789&creative=390957&creativeASIN=0143038397&linkCode=as2&tag=itbio-20&linkId=KAC3KXORX7PKWLP7

Complexity: A Guided Tour by Melanie Mitchell
http://www.amazon.com/gp/product/0199798109/ref=as_li_tl?ie=UTF8&camp=1789&creative=390957&creativeASIN=0199798109&linkCode=as2&tag=itbio-20&linkId=QPXNSL7NK4SQWKNM

Programming the Universe: A Quantum Computer Scientist Takes on the Cosmos by Seth Lloyd
http://www.amazon.com/gp/product/B000GCFBP6/ref=as_li_tl?ie=UTF8&camp=1789&creative=390957&creativeASIN=B000GCFBP6&linkCode=as2&tag=itbio-20&linkId=SAUTIICZBWUIROVD

The Mathematical Theory of Communication by Claude E. Shannon and Warren Weaver
http://www.amazon.com/gp/product/0252725484/ref=as_li_tl?ie=UTF8&camp=1789&creative=390957&creativeASIN=0252725484&linkCode=as2&tag=itbio-20&linkId=KR7IE3CY2GDWRVH3

The Ben-Naim book is coming out at the end of May, and is probably the best popular science book on the topic that you're likely to find (I've read most of an early draft). Following that it's still very hard to beat Pierce's presentation all these years later. Seife wasn't too bad while Gleick comes at things from the most broad viewpoint and covers more history than anything else. Lloyd's book mentions it tangentially. Mitchell's book is excellent, and though it only has one chapter on information theory, some of the other areas it covers are tangential to the subject and very interesting in their own right.

Finally, after Ben-Naim and Robinson, I'd really recommend the UofI Press edition of Shannon/Weaver. Though you can get a copy of Shannon's paper for free online, the introduction by Warren Weaver is really excellent (and similar to Robinson's presentation) and then one can delve into a bit of Shannon's actual math, which isn't too difficult and should be able to be followed by most reasonable high school students. Shannon's text is the only one I've listed that has any mathematical equations, but the Weaver half of the book is certainly a popular science presentation without any math.

 

[1503.02776] The Emergence of Life as a First Order Phase Transition

We demonstrate a phase transition from non-life to life, defined as non-replicating and replicating systems respectively, and characterize some of its dynamical properties. The transition is first order and demonstrates many characteristics one might expect from a newly emergent biosphere. During the phase transition the system experiences an explosive growth in diversity, with restructuring of both the extant replicator population and the environment. The observed dynamics have a natural information-theoretic interpretation, where the probability for the transition to occur depends on the mutual information shared between replicators and environment. Through the transition, the system undergoes a series of symmetry breaking transitions whereby the information content of replicators becomes increasingly distinct from that of their environment. Thus, the replicators that nucleate the transition in the non-life phase are often not those which are ultimately selected in the life phase. We discuss the implications of these results for understanding the emergence of life, and natural selection more broadly.
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Interestingly, Erwin Schrödinger's seminal paper "What is Life?" came out in 1944, almost contemporaneously with the creation of information theory in 1948. Unbeknownst to most Claude Shannon's (the researcher who created the field of information theory and whose Masters thesis literally launched the digital revolution) Ph.D. thesis (1940) was entitled: "An Algebra for Theoretical Genetics," so he could certainly be said to be the god-father of the entire area.

Since then, certainly dozens of researchers have looked at the potential of using information theory to create a better hard core definition of what life really is (certainly the place where any self-respecting Platonist would begin.)

One of the best definitions and frameworks I've seen thus far has to be that of Christoph Adami. To start, and depending on your level of sophistication, take a look at his recent arXiv paper (Information-theoretic considerations concerning the origin of life - http://arxiv.org/abs/1409.0590) and then take a crack at this popular press article about it in Medium (https://medium.com/the-physics-arxiv-blog/information-theory-and-the-origin-of-life-4cf6b93d156c). If it's something that blows your skirt up, then you can certainly begin to delve more deeply into some of his journal articles over the past decade or so.

For further references, I maintain a nice list of resources at Information Theory and Biology Resources (http://boffosocko.com/itbio/), as well as a "journal club" of sorts at Mendeley: ITBio: Information Theory, Microbiology, Evolution, and Complexity (https://www.mendeley.com/groups/2545131/itbio-information-theory-microbiology-evolution-and-complexity/).

If you really want to blow the top off of your definitions, you might also consider taking a much broader look at the universe (a distant reading, so-to-speak) and read through David Christian's conceptualization (Maps of Time: An Introduction to Big History: David Christian, William H. McNeill http://www.amazon.com/gp/product/0520271440/ref=as_li_tl?ie=UTF8&camp=1789&creative=390957&creativeASIN=0520271440&linkCode=as2&tag=itbio-20&linkId=R3CFNWGXPDTSA5GG) of the relatively new area known as "Big History" (see http://www.bighistoryproject.org) . There, he posits the universe, the stars, and other structures as living things. Admittedly their structures are much simpler than what we might "traditionally" think of as life, but which when considered deeply, certainly are living by the broadest definition - they have less "complexity" but are far longer lived than human beings.