The Number Sense: How the Mind Creates Mathematics
By addebook • Jun 29th, 2008 • Category: Mathematics •
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The Number Sense: How the Mind Creates Mathematics
The Number Sense: How the Mind Creates Mathematics
By Stanislas Dehaene
Publisher: Oxford University Press, USA
Number Of Pages: 288
Publication Date: 1999-10-30
ISBN-10 / ASIN: 0195132408
ISBN-13 / EAN: 9780195132403
Binding: Paperback
This may surprise those who have trouble carrying the remainder in division or figuring out a 15 percent tip on a $20 lunch bill, but according to mathematician and psychologist Stanislas Dehaene, mathematics is an inborn skill. In The Number Sense, Dehaene makes a compelling case for the human mind’s innate grasp of mathematics. Take, for example, the fact that place value systems (such as the Arabic numeral system we use) arose independently in four separate civilizations–evidence of a universal sense of number. Dehaene’s book is filled with examples to support his thesis, from young babies’ ability to “count” (i.e., to react when single objects are replaced by two or more) to examples of how brain damage affects various individuals’ number sense. Even more fascinating is his discussion of the relationship between language and numbers. Though Dehaene’s book is about mathematics, even those readers with the worst math anxiety will find The Number Sense an intriguing exploration of the world of numbers–and the human mind.
The Number Sense is an enlightening exploration of the mathematical mind. Describing experiments that show that human infants have a rudimentary number sense, Stanislas Dehaene suggests that this sense is as basic as our perception of color, and that it is wired into the brain. Dehaene shows that it was the invention of symbolic systems of numerals that started us on the climb to higher mathematics. A fascinating look at the crossroads where numbers and neurons intersect, The Number Sense offers an intriguing tour of how the structure of the brain shapes our mathematical abilities, and how our mathematics opens up a window on the human mind.
Summary: “The number sense” revealed
Rating: 5
This is a masterful account of how people, and animals, use their number sense to bring mathematics into their world. It uses recent advances in neuroscience and evolutionary theory to create a coherent account of how we evolved our mathematical abilities. For instance, he shows how and why we have a marvelous analog capability, a subitization capability for immediately recognizing the numerosity of small collections, and a natural knack for counting.
But he also explains how and why we are very bad at digital computations and ‘unconnected’ memory tasks, like remembering multiplication tables. Not much use for knowing what 7 * 8 is amongst hunter gatherers! His solution — let children use calculators! This pragmatism, and caring attitude, pervades the book relieving math anxiety like a wine French wine reduces stress.
He attacks the “Bourbaki” school for demolishing mathematical education in France (and elsewhere) by forcing axioms down children’s throats instead of gently stimulating their intuition and allowing them to use their inborn number sense. Piaget also comes under attack for not allowing that children are born with number sense, and can do ‘hard sums’ much earlier than Piagetian dogma allows for. This attack is backed up by references to dozens of research papers that make his case conclusive.
The final chapter is a tour-de-force overview of mathematical philosophy , with a devastating attack on Platonism and a harsh critique of formalism. He comes down (mostly) on the side of the intuitionist mathematics of Poincaré, but is quite harsh on the constructivist Brouwer.
All in all, a jaw-droppingly brilliant book on the philosophy and psychology of mathematics. I’ve read a few such books, and this is by far the best I’ve read. Start here if you want to begin to find out what mathematics might really be about. He also has a superb bibliography to lead you to more mathematical wonders.
Summary: Illuminating! Captivating! Pass the salt!
Rating: 5
Dehaene is a witty, gifted writer with an invisible style. He elucidates his subject matter so plainly that no one could be lost. Even a complete neophyte such as I am would have no trouble following his constructs. Or better to say if I was lost, I never knew it because the book made a lot of sense to me.
As a math teacher, I had long suspected mathematics was an unnatural act of the mind. Dehaene confirms my suspicion. The chapter on patients with severed corpora callosa put me in mind of similar split brain findings in the field of linguistics.
I’m not sure about the limits on subitizing. The handful of my students with innate math reasoning seems to be able to subitize beyond what Dehaene suggests.
The evolutionary build-up should be taken with a grain of salt. Can we just observe the increasingly complex organization of living things along a continuum without making the presumption that nature is showing up a time-lapse film?
Summary: Good book
Rating: 4
This book is a tour de force of neurology as it applies to mathematics. From anectodes and case studies of mathematical greats and autistic calculating prodigies to brain scans and theory of the evolution of our calculating ability.
The only reason I give it four stars is its obvious political correctness is parts where it fails to even consider taking group differences into account (read genes) before ascribing differences to culture. For instance, the bulk of Chinese superiority in math at grade school level is ascribed to the fact that chinese sounds for numbers is smaller than english, allowing chinese students to keep longer strings of calculations in their short-term memory. Well, this could very well be a contributive factor, but what about American second or third generation chinese who speak only english who also show heightened mathematical ability? Not a peep about that!
Of course the above is just a small complaint in the end. The book on the whole is fascinating and well worth a read.
Summary: Amazing, objective research scores an A!
Rating: 5
Fascinating. That’s the word I’ve been using to describe this book. From the information on numerical experiments with animals to the solid evidence presented for the hardwired concept of numbers from birth, the author ties together an amazing work.
The clear organization of the book, described from the onset, was my first clue that this was a bit more polished than other works. From a gradual examination of an innate “number sense” in even lower animals, through babies identifiying that 1 1 is not 1 or 3 but 2, up to the examination of innate calculatory facilities, this book covers it all. By the end, you will have been presented with practically all the evidence you need to make your own conclusion–and the case for the existance of the “number sense” is incredible. Psychology and neurology are both linked to the examination.
As a math teacher, I’ve even gleaned a few points to help in the presentation of the topic to my students. While I don’t agree with all of the authors views on education, I do think he made some very profound points (the comment that standardized education has probably stunted natural development ofthe culture–specifically language–is a good example.)
Probably my only real disappointment with the book is the author’s overemphasis on evolution throughout the text. Yes, most technical types unfortunately seem to be passionate about evolution’s role in everything nowadays; it wouldn’t have been that big a deal had the last few pages of the book not delved wholeheartedly into a philosophical expository of how mathematicians of the past were silly to have attributed the apparent design of the mind to match the universe numerically to a God, when evolution is an available alternative. However, this small distasteful thread didn’t really detract from the research. (In fact, in practically all other maters the author is refreshingly objective and unbiased, examining counterpoints to his theories and conclusions.)
In all, the book still earns its five stars for rigor, fascinating material, objective examination, and clear presentation. Well worth the read, well worth the purchase.
Summary: Quality science, excellent entertainment
Rating: 5
I received this book as a gift. I skimmed it and left it unread for months. I thought it was a cash-in on Steven Pinker’s excellent The Language Instinct. But no!
When I finally read it was as impressed with Dehaene’s science as with his literary flair - not to mention the excellence of his self-translation. His thesis is fascinating, his references authoratitive and his story telling masterful.
This book should fascinate everyone who can count up to two or beyond. Dry it is not. Beyond the interest he develops in the subject are the insights he gives into the ingenuity with which psychological experiments can be designed to eliminate the flaws that a layperson would think unavoidable.
There is a darker side, however. Like that other fellow with his lethal experiments with chicks to test for chemical changes relating to memory, there are allusions to intrusive experiments on living subjects . True, these were some time ago and Dehaene exhibits a proper degree of unease about them. None the less I am much more comfortable with the ingenious ape and baby tests. In my view, no matter how intriguing the question, and how beguiling arguments of research potential leading to new therapies, there is a line that should not be crossed. Dehaene, I’m glad to say, seems aware enough not to cross it.
Fascinating. Highly recommended.
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