John Keats called it “negative capability”. Henry James referred to it as “hanging fire.” This “it” is a tolerance for, or indeed an embrace of, ambiguity, uncertainty and paradox as part of a renewed emphasis on creativity and openness to experience. Keats and James emphasized its artistic and literary aspects, but this book makes a case for the importance of accepting uncertainty and ambiguity in science (and mathematics). The author does not mention Keats or James, but although he concentrates on science and mathematics, he appears to be heading in a very similar direction.
Throughout this book the author seems to be warning us that too narrow a conception of objective truth in science and mathematics is harmful, and indeed that uncertainty and ambiguity are far more common that we would care to admit. While readers may be sympathetic to that view, they may have considerable difficulty unraveling the author’s exposition in support of that position. Indeed, it starts with the book’s title.
Just what is the “blind spot”? Actually, it’s rather hard to tell. Consider the following two passages from the first chapter:
… in the deepest and most profound sense, the things that make up the world cannot be defined, nor can they be understood or pinned down in any definitive way. This is the gap that has emerged in the order of things, a gap and a challenge that has the most profound implications for how we conceptualize the entire scientific enterprise. I’ll refer to this gap by speaking of the ungraspable.
… the danger is that one thinks of the ungraspable as something divorced from reality. The “blind spot” I am talking about is an inevitable consequence of our rational consciousness. We are aware of it as a lack, but when we turn our conscious mind to it, it inevitably disappears. Yet we can infer the existence of this domain by making a small shift in the way we look at things. The development of science in the last century contains many instances of the discovery and the rediscovery of this phenomenon under a plethora of different disguises — ambiguities, paradoxes, incompleteness, complementarity, randomness, and so on. Are they not all, in one way or another, blind spots?
Or, skipping ahead to the concluding chapter and hoping for a clarifying summary:
Wonder is just another word for the blind spot — that which is beyond any system.
It just doesn’t get much clearer than that. In the second chapter, “The Blind Spot Revealed”, we get references to the Chaitin number Ω (“the existence of a limit to total knowledge”), the loss of certainty in mathematics (Cantor’s infinities, incompleteness and undecidability), quantum mechanics and a little bit of Wittgenstein. This, except possibly for the Wittgenstein, is something we’ve all seen before, but it does not shed light on the blind spot. We get another hint in the chapter called “Certainty or Wonder?” that admiringly discusses Einstein’s “cosmic religious feeling”. At the same time, the author seems to regard much of organized religion as part of those inappropriately held certainties.
Later chapters pursue questions of ambiguity, paradox, and self reference at greater length, but nothing there is very illuminating. Take, for instance, this remark below from a chapter called “The Still Point”:
… I shall consider the possibility that fundamentally things are ambiguous and that the unambiguous is merely one particular point of view that arises out of a more basic ambiguity.
This is out of context, I suppose, but the context is even less enlightening.
All in all, it is a very frustrating book. One has the sense that there is something substantial behind all this, but the author gives us a largely incoherent jumble of ideas with fragments of a lot of different things, too much repetition, and very little clarity.
Bill Satzer (firstname.lastname@example.org) is a senior intellectual property scientist at 3M Company, having previously been a lab manager at 3M for composites and electromagnetic materials. His training is in dynamical systems and particularly celestial mechanics; his current interests are broadly in applied mathematics and the teaching of mathematics.