A CERTAIN AMBIGUITY | Gaurav Suri and Hartosh Singh Bal
Mathematical beauty and truth have fascinated humans, ancients and moderns alike. The rub is that both are hard to get to. Unlike a painting or a piece of music created by someone else, one needs to “do” math to appreciate its beauty. This is something that is not possible for a large, if not huge, number of people. Mathematical truth, and its mirror image, certainty, represent more serious challenges.
A certain ambiguity: Penguin/Viking, 281 pages, Rs450
Woven around these themes, A Certain Ambiguity is an attempt to get these ideas across to a bigger audience, one with little mathematical training.
Authors Gaurav Suri and Hartosh Singh Bal, trained in math, believe this can be done in a storytelling format. Complex ideas usually cannot be reduced to simple terms; otherwise there would be no need for abstraction. This novel manages to communicate without diluting the flavour that accompanies these ideas.
Moving back and forth between modern-day Stanford and Morisette in New Jersey, a fictional town in early 20th century America, the book explores two fronts simultaneously. It is about a boy’s discovery of his grandfather’s life—and facing the same questions in his own life. Both seek answers through math, a common language.
The grandfather, mathematician Vijay Sahni, a contemporary and an acquaintance of Srinivasa Ramanujan Iyengar, is arrested for blasphemy. He is booked under an obscure anti-blasphemy law. The case arouses strong passions between those who want religious values upheld and those who believe in freedom of expression. The governor of the state chooses a judge to make recommendations on whether to proceed with the trial or not.
That sets the stage for a long dialogue between the judge and the mathematician, in prison. Each is certain about his beliefs; the judge, about the existence of god, and Sahni, about the ability of math to analyse all manner of situations. The judge cannot understand why his belief in god should not be acceptable to the prisoner, while the latter demands strict proof for everything.
The authors attempt to explain how geometrical themes are pervasive in everyday life
By the end of their argument, both are uncertain about their beliefs. “Mathematics has come up short” for Sahni. The judge has existential doubts over his beliefs. Both come to appreciate each other’s position better.
To some, this might represent a comfortable and convenient meeting point, suited to the requirements of a novel. It is familiar to Indians with their innate sense of a middle path. The grandson, Ravi, too traverses such a path of uncertainty, but in a much more forgiving and conducive academic environment. He finally chooses to follow his grandfather’s footsteps to become a professional mathematician.
Mathematics as a subject has traversed a similar path. From absolute belief in the certainty of mathematical theorems to a realization in mid-20th century that certainty is an illusion. This, in spite of the greatly sophisticated branches of the subject: Unlike the time of Henri Poincare in Paris around 1900—when one mathematician could range across the subject—today there are sub-area specialists who probably cannot fathom other branches of the discipline.
This lack of a firm foundation accompanied by great specialization now engulfs many subjects that make use of math. Economists, for example, are prone (indeed happy) to combine risk and uncertainty. Barring few notable exceptions, this has been the trend. Why? Because any “measure” of uncertainty would be meaningless beyond a point, while risk allows useful quantification. That, of course, has not been helpful. Astute observers such as Nassim Taleb, the trader-turned-writer (Fooled by Randomness, The Black Swan), are aware of this. But, as in math, to no avail. The subject marches on, insouciantly.
This does not prevent one from appreciating the beauty that is at the core of mathematical ideas. Symmetry, recurring patterns, infinity and geometry, among other themes, are pervasive in our lives. Yet, the awareness of connections between these and everyday life is something difficult for many, if not most people. In the last 25 years, popular writing on the subject has tried to bridge this, with varying success. Names such as Martin Gardner and Douglas Hofstadter now sound familiar even if the content they tried to put across still doesn’t appeal to popular imagination.
A Certain Ambiguity goes some distance in connecting the two, by telling a story and weaving in math. It does not require a great deal of math to wade through the book; interested reading will ensure that. Whether it can suffuse a sense of mathematical beauty in the reader is a difficult question to answer.