## Review: The Number Sense

Oxford University Press sent me a review copy of The Number Sense: How the Mind Creates Mathematics, Revised and Updated Edition, by Stanislas Dehaene. The book is an update of the original edition, which was published in 1997.

The author writes in the preface of this new edition that the goal of the first edition of the book was

"to assemble all the available facts on how the brain does elementary arithmetic, and prove that a new and promising field of research, ripe with empirical findings, was dawning."

This new edition updates the reader on findings in the field of numerical cognition. Wikipedia has a nice introduction to the subject, including a list of questions at the heart of the field.

- How do non-human animals process numerosity?
- How do infants acquire an understanding of numbers (and how much is inborn)?
- How do humans associate linguistic symbols with numerical quantities?
- How do these capacities underlie our ability to perform complex calculations?
- What are the neural bases of these abilities, both in humans and in non-humans?
- What metaphorical capacities and processes allow us to extend our numerical understanding into complex domains such as the concept of infinity, the infinitesimal or the concept of the limit in calculus?

Like most of the popular Math books I read, I didn't read "The Number Sense" from cover to cover. When I wanted to take a break from some other task I would pick up the book and read a section or three. I wasn't concerned with whether the book flowed (as one Amazon reviewer expressed concern about) or whether it had cohesiveness to it. I wanted to be intrigued by interesting stories of number sense and I was not disappointed.

Chapter 6, Geniuses and Prodigies, was my favorite part of the book. Dehaeny tells about a severely handicapped autistic man who can instantly factor three digit numbers and who can tell, in a second, if a three-digit number is prime or not. Dehaeny compares thus autistic man to the great Ramanujan. What do the two have in common? Dehaeny argues that both men have a relationship with numbers that far transcends the ordinary. Then there's the question of whether mathematical talent is a biological gift. And there's an exploration of the role of passion in developing talent in mathematics. Finally, Dehaeny explains some techniques lightning calculators use to perform their feats. All of this is in one chapter.

No discussion of number sense would be complete without an exploration of how infants relate to numbers. And, if that's not interesting enough, then how about the question of number sense in animals? Speaking of questions, I tend to like books which ask fascinating questions, and this one does. Here are some examples.

- Do numbers have color and do they occupy space?
- At what age are children able to tell the difference between two and three?
- What does the fact that a dozen or so people in the world suffer from epileptic fits only while performing arithmetic (but not other intellectual activities) tell us about the human brain?
- How can idiot savants, with IQs of 50 or less, perform calendar arithmetic flawlessly?
- How has our understanding of number sense evolved in the 15 years since the first edition of the book was published?

I liked "The Number Sense." It's a well-written and very engaging book. It's a nice blend of psychology, brain biology, with some light Math.

StevenAugust 19th, 2011 - 19:58

I have yet to pick up this book, but I appreciate you writing a review about it as it has refreshed my interest in it (even if the review is two months old and I am just stumbling upon it now). Stanislas Dehaene appeared on an episode of Radiolab (an excellent podcast) titled “Numbers” in which he and the hosts of the show discuss how infants relate to numbers and how that relationship is connected to how natives in the Amazon–who are removed from traditional methods of teaching mathematics–use numbers. I assume that this is covered in his book, but the production of the podcast makes it a particularly enjoyable listen; they also cover other quite interesting stories in this episode (including Benford’s Law, and Paul Erdos). Moreover, I wanted to plug Radiolab in case you have not heard of it. It is a podcast that I imagine most math-and/or-science-minded people would enjoy. You can find the “Numbers” episode on their website (radiolab.org) or on iTunes for free. Other math-related podcasts include “Stochasticity,” “Walls of Jericho,” and “Limits” (not limits as in calculus).