Book Review: Everything and More – A Compact History of Infinity by David Foster Wallace

American novelist and essayist David Foster Wallace’s  book Everything and More: A Compact History of Infinity, a self-proclaimed exercise in “pop technical writing” – technical writing for layman, or, individuals without advanced degrees in mathematics. 

Everything and More specifically tackles the esoteric topic of the mathematical, historical, and metaphysical concept of infinity, as well as a narration of “infinite set-theory”, i.e., the foundational equations positing infinity in a style of prose, that as Wallace claims, attempts to make “the math beautiful” or at least presents it in a way “to get the reader to see how someone might find it so.”  

Wallace’s conquest of translating infinity into natural language has been criticized by some mathematicians; most critics highlight what they consider oversimplifications of some aspects of the hard math in Wallace’s narrative.  

However, these criticisms are unfounded and ignore the chief purpose and scope of Wallace’s pop technical manual.  

W. W. Norton publishing hired Wallace to write Everything and More as an installment of the series “Great Discoveries” and indented on contracting great literary minds with working knowledge of topics in technical fields to write technical manuals on the most complex, but popular ideas floating in our collective consciousness, in a way that retains literary and artistic value.

This technique is embodied in the famous analogy Wallace uses to illustrate the sketchy nature of the faith we put into abstract mathematical reasoning as it corresponds to the concrete world through the paradox of the “inductive principle.”  

In Wallace’s analogy the brightest chicken in a coop becomes convinced through induction that at a certain time (T) every morning when the farmer (F) appears at the coop with a burlap sack (S) in hand that means feeding time (Feed).  So when the chicken hears the farmers footsteps he starts pecking at the ground in anticipation.  This chicken has discovered the inductive principle as: T (F+S) = Feed.  One morning the chicken hears the footsteps of the farmer and starts pecking at the ground but when the farmer arrives outside he grabs the chicken and swiftly rings his neck.

Wallace’s analogy illustrates not only the arbitrary relationship between abstract form and real world dynamics, but also begs the question what can we really Know to be True about reality through math?  There is Wallace asserts, “Something about the fact that Mr. Chicken not only didn’t suspect a thing but appears to have been wholly justified in not suspecting a thing… [which is] creepy and upsetting” and where this level of uncertainty exists in the very ordinary case of the chicken what does that tell us about what we can know about the extraordinary concept of infinity?

Still, Wallace’s ability to make concrete and philosophically disconcerting formal math, to portray the kind of abstract thinking and faith in logic which allows a conception of infinity and the infinitesimal is the chief strength of Everything and More, one of many reasons to give the challenging pop technical manual a chance.

– Matthew Ramirez

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