TO READ OR NOT TO READ

A Mathematical Novel

Book Review on A Certain Ambiguity

Would you read a Math book? How about a Math novel? A MATHEMATICAL NOVEL? NOVEL? Seriously, who would do such thing? Who would murder art and literature? Gaurvan Suri and Hartosh Singh Bal did with their A Certain Ambiguity, A MATHEMATICAL NOVEL.

The book is intertwined with two stories. First is about Ravi Kapoor narrating his learning from a class on Infinity at Stanford. Second is the life Vijay Sahni, Ravi’s grandpa, who gets imprisoned for a brief period in his life.

The story begins with a regretful flashback experienced by Ravi Kapoor to the time when his grandfather gave him a problem to try on a calculator. The problem was given with gentleness and warmth that suggests the grandfather's relationship with Ravi and the magical effect of the solution might have on him. The grandfather died the next day. The memory of Ravi’s grandfather played an important role in his life. In the absence of his grandfather's guidance Ravi grows uninterested to math.

Flash forward. Ravi was accepted to Stanford. He was leaning towards economics. He took a course, "Thinking about Infinity", and befriended the course professor Nico. Nico specialized in the field of Ravi's grandfather. The narrative proceeds in two dependent threads. On one hand, Nico's lectures presented math topics where infinity plays a major role. On the other, Ravi's research into his grandfather's imprisonment produces transcripts of philosophical discussions on the nature of truth, certainty, and mathematics that the grandfather conducted in jail with a judge assigned to investigate his case. The grandfather had landed in jail under a blasphemy law. Here is a snippet from one of the conversations between Vijay Sahni and the Judge,

“This freedom has me in awe. It is unbounded, and every single one of us possesses it. We are free to believe or not to believe; we may create mathematics or build homes or write poetry or do nothing at all; we can marry and raise a family or stay in bachelorhood; we can quest for new adventure or find comfort in the familiar; we can seek meaning or we can doubt that it is possible to find meaning. Every path is there to be taken or ignored, and none is ordained. We are given no certainties, yet we are given the capacity to feel certainty. There is no absolute meaning to latch onto, yet transcendence is within our grasp. We are free to chart our course, free to pursue our passions, and free to create the axioms of our lives. And it is in this glorious freedom that I find grace. This freedom, then, is my proof of His existence.”

The math topics discussed in the novel was from Zeno's paradoxes and infinitude of primes through Godel's Incompleteness, and Paul Cohen's Consistency theorems.  Gaurvan Suri and Hartosh Singh Bal had master's degrees in mathematics. They wrote confidently and competently. Do Euclid's axioms truthfully express the geometrical structure of the world or are they just articles of faith laid down more two thousand years ago. If the former is the case, how can one explain existence of non-Euclidean geometries? Here is the 5 postulates of Euclid based on which the entire “ELEMENTS” is built.

1. It is possible to draw a straight line from any point to any point
2. It is possible to produce a finite straight line continuously in a straight line
3. It is possible to describe any circle with center and radius
4. All right angles equal one another
5. If a straight line falling on two straight lines makes the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which are the angles less than the two right angles. (The fifth postulate controversial nature lead to the development of Non-Euclidean Geometry)

Why not to adjoin an axiom natural to many? Everything has been created by somebody? First is the viewpoint of Ravi's grandfather, the other is of the judge. Both have been deeply affected by the 1919 confirmation of Einstein's General Relativity by Sir Arthur Eddington's experiments.

Authors present additional view points. That is adopted by the present day mathematical community. There is so much in this book. The authors have managed to present mathematics as a human endeavor by many timely excerpts from the diaries and letters of great and remarkable mathematicians and scientists. The rest of the book are mostly fiction, but succeed in giving mathematics a human face.

This is a novel with a captivating plot. It is a book about mathematics, philosophy, beauty, and about its relevance to the human understanding of the world. Mathematics is woven into the story line itself. There is no page where mathematics isn’t mentioned. I can say that the plot evolves with the mathematical precision. The book is a delightful and informative read. This is a mathematical novel.

References:

·        Danny Calegari, Princeton University Press, 2008, Book Review of A Certain Ambiguity

·        Safeis Risky, A Certain Ambiguity : Book Summary