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The Math Gene: How Mathematical Thinking Evolved And Why Numbers Are Like Gossip (First Published in Great Britain in 2000 by Weidenfeld & Nic)

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Devlin's "The Math Gene" is a wonderful book, well worth reading if you've an interest in how we think, and absolutely essential if your interest extends further to why we can do mathematics.

This is an intriguing question. After all, it's a fairly new part of human behavior - having been around maybe 10,000 years - that we all can do, at least a bit, and the rest of the animal kingdom can't, at least as far as we know.

Devlin's the first mathematician I know of who's looked deeply into this subject using recent research in the area; he's done a great job fitting the available data to a theory that starts to answer the question, how it is we can do mathematics?

First, though, you have to understand what mathematics really is. Devlin's definition is the "science of patterns" and he explains clearly and convincingly why it's the right one.

His premise, roughly, is that however we acquired language, and he stays mostly on the sidelines of the heated debates about that, mathematical ability came along for the ride. His reasoning is that "off-line reasoning" is an essentially equivalent to language, as you can't have one without the other, and that this plus some other abilities, such as a number sense and spatial reasoning, give us the ability to do mathematics.

He then explains why so many of us find the subject difficult. A simplified version is that we use language mainly to talk about interpersonal relationships. In a word, gossip. Note he's not claiming this to have been the purpose for it's development, just that it's what we mostly do with it now. And we're very good at gossiping. In fact, it's so easy we consider it to be a form of relaxation. To Devlin, you need to have the same kind of relationship with mathematical objects in order to be able to work with them.

The book's greatest strength, to my mind, is its gathering of results in cognitive psychology into a coherently developed thesis regarding the origins of mathematical ability. It's a worthy contribution to the discussion, even if the theory proposed is completely wrong, as it may well be. Devlin's open and clear about it being highly speculative.

I do have quibbles, but they're just that. Its major weakness, if the book can be said to have any, is that it doesn't make much by the way of predictions based on his theory, which would make it far more convincing. But this is a terrific starting point for other work.

"The Math Gene" presents a theory of how mathematical ability and language are related, and how they might have evolved. Devlin starts by separating "number sense" from mathematical ability. Many animals as well as humans can estimate the quantity of something; rats can be taught to press a lever about sixteen times to get a reward. The "about" is significant though; it's an estimate, not an exact count, as far as the rats are concerned. So if number sense and mathematical ability are not the same, what else is needed for mathematics? Devlin lists eight other attributes, including algorithmic ability, a sense of cause and effect, and relational reasoning ability.

Then there's a fairly long discussion of mathematics from the inside--are mathematician's brains different? What is it mathematicians do?--including a moderately detailed description of the basics of mathematical groups. I think Devlin does this to provide non-mathematicians with a sense of what mathematics is about, to make the rest of the book more plausible. This section is well-written and fluent, but I found myself getting a little impatient for the meat of his argument, which comes in the last half of the book. I suspect any reader with a good mathematics background would react the same way.

The next piece of the argument is to demonstrate that language is unlikely to have developed solely as a result of evolutionary pressure towards communication. This is a subtle point I haven't seen made before, but Devlin (who acknowledges his debts to other workers in this area) makes the case quite convincing. In summary: apart from extremely simple messages like "Danger!" and "Mammoth here" you can't communicate what you don't have a mental representation of. The evolution of communication can't have driven representation; it must have always lagged a half-step behind. So mental representation must have evolved first. I am not doing this argument justice here, but Devlin buttresses it well.

The inference is that language is simply a natural but lucky result of our ability to represent the world in our minds. Devlin's key point, however, is that since mathematics is essentially the ability to construct and work with increasingly abstract representations, the same mental changes that gave rise to language have also given rise to mathematics. His conclusion is that we all have the ability to do mathematics: there is no "math gene" except in the same way there is a "language gene": it's universal.

As a side note, not critical to his main argument, he points out that the most likely reason for the growth of representational ability in human brains was to foster understanding of other humans in the group; to encourage a sense of group-ness. For a creature that was more effective in group actions (e.g. hunting) there would have been a strong evolutionary advantage to having an emotional investment in the success of the group. Hence much of the early use of this ability would have been to represent others in the group; when language was added, it would have enabled people to talk about each other. In Devlin's words, "Having arisen as a side-effect of off-line thinking, language was immediately hijacked to facilitate gossip." (Off-line thinking is used to mean representational thinking that doesn't result in or from actions in the immediate environment.)

Two particular items in the book are worth mentioning. One is a followup to some famous experiments done by child psychologist Piaget in the 1930's. Piaget thought he'd demonstrated that children don't acquire a fully-developed number sense till around six years old. More recent work has demonstrated that children are much smarter than Piaget realized: there was a subtle and fascinating methodological flaw in Piaget's experiment. The second item is a little test of logical reasoning, presented with four cards on a table. Even mathematicians, who will probably get the test right, may be surprised at the coda to the test, which forms one of the few methods of direct verification of Devlin's claim that everyone can do mathematics.

The case is well-argued, but one problem with theories like these is that there *are* so few ways of finding out if they're true. "The Math Gene" is reminiscent of Julian Jaynes' "The Origin of Consciousness in the Breakdown of the Bicameral Mind" in this way; a fascinating argument that we may never be able to test. However, it's thought-provoking and plausible, and left me, at least, convinced of its likely truth.

The Math Gene is a wonderful insight into mathematics and how humans may have evolved the ability for mathematical thought. Dr Devlin gives a powerful argument for his theory in three parts. He begins with an explanation of the nature of mathematics, and dispells many misconceptions about math held by people outside of the mathematics community. He then spends the bulk of his text describing the nature and evolution of language and communication in humans and their differences with animals in that respect. He explains what pressures in the environment would be necessary to cause an evolutionary change in language and thought in a way that is understandable by a layperson and plausable to someone with a strong scientific background. He ends his book with a comparison of the mind's mathematical and language processes, why language (particularly gossip) must have preceded mathematical thought, and why mathematical thought is a direct product of any consciousness capable of language.

I thoroughly enjoyed this book, and have recommended it to friends and colleages alike. I would also recommend another one of Devlin's books, The Language of Mathematics, for a glimpse into the diverse and beautiful world of math any person could understand and appreciate.

This is a book from a well-known and respected popular science writer and mathematician, Professor Keith Devlin, on a very intriguing question: how and why did people acquire the skill of doing mathematics. Unfortunately, many readers will probably still be looking for more after finishing this one.

Devlin starts with our sense for numbers. Not all numbers are the same: we instantly recognize one or two objects; beyond that number, we have to count them. But counting itself is not yet mathematics. So what is mathematics? Devlin fancies the answer that it is a science of patterns, and spends a whole chapter on what he really means by the extended concept of pattern. In order to describe abstract patterns, mathematics has developed a specialized language. So is it possible to learn anything about mathematics from what the linguists have already learned about the generalized structural grammar, underlying every known language? How did the full language - with grammar - evolve at all from the "momma hungry" protolanguage? And why?

The above arguments pose a grandiose ouverture for Devlin's thesis, which we are finally ready for in the second-but-last chapter: in order to be able to plan and predict, human ancestors have some 300.000 years ago developed what Devlin calls "off-line" thinking. With off-line thinking came grammar and language. Language is, and always was, used predominantly to build the "team spirit" among humans, or, with other words, for gossip. Mathematicians can avoid one unnecessary level of abstractions if they visualize the entities they are working with. So for them, doing mathematics is like gossiping. Well, sort of.

And that is it. The book is actually quite a pleasant read, with lots of interesting stuff. On the other hands, Devlin drags us on and around general linguistics and the evolution of speech and God knows what else before getting to the promised topic. The final thesis comes then rather unculminating. On the plus side, Devlin is fair at citing books and articles he had learned from. I wish I could say the same about some other popular science authors.

In the book The Math Gene, author Keith Devlin stated that math is just a special use of our language faculty and every one should be able to do math. The basic structure of the book is Prologue, what is math, what is language, and from language to math( the point). We can see this clearly from the last sentence of the prologue," Once you know what mathematics is really about, and once you see how our brains create language, you should find it far less surprising that thinking mathematically is just a specialized form of using our language facility."

He spends the first 4 chapters talking about what math is: the science of pattern.
Chapter 2 and 3 is mostly boring to me, maybe people with little math background will appreciate it. Chapter 4 is not bad, especially when he cited the research on animal coating, it is really interesting that the coating of a leopard could be generated by solving math equations. Other examples are also very interesting.

In chapter 5, the author talked about math thinking. It is abstract thinking. Then he used the house metaphor to compare it with daily life. Make it simple to understand for the readers. He also talked about the high concentration you need in doing math problems, this kind of concentration is very hard for ordinary people who are busy worrying about their daily life. And that¡¯s one of major hurdle preventing most people from being good at math. This chapter is quite good.

Again chapter 6 and 7 is a bit uninteresting. It talked about what language is. Then in chapter 8 he talked about how math thinking evolved and the idea of offline thinking, how important it is to human, etc. It is an important chapter, though I don¡¯t find it interesting.

The best part of the book for me, also the whole point of the book comes last in chapter 9. It tells "why numbers are like gossip". I am very interested to read about it.
It first cited a very common fact: that people like to talk about other people, also they are interested in other people¡¯s lives, it¡¯s like a need for them. Then he said the usefulness of this is that it will benefit the group, make its members more close to each other.
Then he said the same thinking involved could be used in math thinking. How relationship between people in real world could also be applied to the relationships between abstract objects in the imaginary world created by human brain. Then he said why most people can not do math even they have this faculty in them. It is because it takes training most people don¡¯t have. Once those people get training, they will also be able to do math. However most people are not motivated.
And he said how mathematicians are able to do it and how wonderful the math world is. Only people that has reached the summit of one of the many math mountains can see the whole picture and the very picture motivate them to go further. While amateurs and outsiders only walk around the valley and never see the whole picture, and that is why they think math is difficult and uninteresting.

Chapter 10 is just citing about some other people¡¯s opinion and his viewpoint on it.

The epilogue of the book " how to sell soap" is also quite funny.

Overall, it is a worth reading book. It is something new for me. Gives me more insight in language, math and gossip. The idea of the author is quite convincing. Some chapters of the book serve as background knowledge and could be skipped if you already have them. Mainly chapter 2, 3, 6, also chapter 10 could be skipped.

The author presents a carefully crafted theory of how language developed in humans, and links our innate mathematical abilities to this skill with language. Although his position is that everybody has some level of mathematical skill beyond number sense, he never really addresses in detail why some people have an aptitude for math and others don't, other than to mention the mathematician's ability to cope with abstraction.

This is the second book by Devlin I've read, and I'm impressed by his boldness in escorting the reader through difficult mental terrain. If you find the topic of language development interesting, and you're willing to exert some mental effort to keep up with his arguments, you'll find this book a thought-provoking read. However if you want to know why high-school algebra gave you such trouble, you'll have to look elsewhere for the answer.

Let's face it. Most people have trouble with math, and are delighted when they don't have to figure out any more when two trains are going to collide or pass each other. Personally, I always liked problems, so I found math interesting. My friends always thought that was one of my more peculiar characteristics.

Dean Keith Devlin deplores the fact that the way math (that which we learn after arithmetic is mastered) is taught obscures access to the most interesting parts of the subject. I agree with him on that. In this book, he tries to take away some of the fog for the reader by showing you thought processes that mathematicians use in some simple situations and problems that most people can grasp. These examples are nicely designed to build on one another, so you get a cumulative learning experience from them of how a mathematician may think. The "nested" design of the examples was impressive to me as an author.

This book is for those who think of themselves as nonmathematical and want to understand more about why they experience a weak skill set in that way. Mathematicians will probably find the book much too elementary to be interesting, except as a model of how to explain mathematics to the lay person. Those who study mind development will find the book full of logical proofs, but modest insight.

The author also tries to build a plausible scenario for how mathematical ability developed in primitive humans. I applaud his ambition. His speculations are interesting, but certainly did not persuade me. I think his problem was that he did not look far enough into the scientific research on how we learn.

Everyone has problems with something where we have no experience. As David Ingvar pointed out, we simply draw a blank until we can create experience in that area or connect to an existing experience. To help people learn, give them experience in the new thing that is structured to be connected to some familiar thing. This point is made indirectly by an example Dean Devlin provides: Children who have trouble doing simple arithmetic can make change perfectly well. The best educational techniques create simulations that encourage this approach focused in relevant experiences. Unfortunately, those who teach math are mostly immune to using this method. Higher math is taught in the way that makes it most difficult to understand -- as abstractions unconnected to other math or ordinary situations and people. You will often "feel" an underlying unity in math, but I never had a teacher who addressed it. The closest I came was in a calculus class where we wrote software programs to solve problems. Putting a virtually infinite set of rectangles together and adding their areas to approach the answer for the area under the curve was fascinating and useful to me.

The other problem with his arguments about the origins of mathematical ability is that he concentrates on the "formal proof" parts of this thinking which are conscious. Many people report that math for them is more unconscious and intuitive. I am one of those people. I can see the solution in a nonverbal, nonmathematical form. After I know the answer, then I sit down and painstakingly translate it into formal proofs. But that is merely for communication purposes. It doesn't help me at all. I was not surprised that Dean Devlin sees conscious mathematical thinking as being like language -- because that's the exact same purpose it serves. The more important question of how mathematical insight can be developed is not really addressed, as I understood the book. Dean Devlin alludes to those moments of inspiration, but doesn't tie them into his main themes. I suspect that "knowing" the answer in this unconscious way is much like "knowing" where to throw a rock to hit something, an example that Dean Devlin uses.

Reading this book made me realize that there are many disciplines where I do not understand the fundamental thought processes involved. Perhaps that is true of you, too. Since we often rely on other people to help us in these areas, we cannot hope to understand their advice if we do not understand the mental processes for how they arrive at that advice. I suggest that you and I start spending some time over lunch and drinks getting some more understanding of medicine, engineering, pscyhology, and teaching in this same way from professionals in those disciplines. I suspect we will be greatly helped by what we learn.

Peer out from the other person's mind from time to time to see more!

Like a lot of people, I've been augmenting my reading lately with many of the scientific popularizations that have been coming out on neuroscience, biology, linguistics and information processing theory. These books generally fall into four camps: good science with bad prose (Edelman, Calvin, Llinas); bad science with good prose (Pinker, Bickerton, Lakoff & Johnson); good science with good prose (Deacon, Damasio's first effort, Tomasello, Ramachandran) and bad science with bad prose (anything to do with "memes" - and this book!)

Quite simply: no good argument here is new, and no new argument here is good (to paraphrase Samuel Johnson). For the "math gene" itself turns out to be nothing more than the "math version" of Chomsky's moribund and increasingly untenable "deaux ex machina" - an Innate and Universal Grammar, made even more implausible - if such a thing is possible at this late date - by the addition of Derek Bickerton's "catastrophic adaptation" model of how the "miraculous mutation" that "endowed" us with "syntax" (and thus with Universal Grammar and its "mathematical equivalent") took place.

Far worse from an intellectual standpoint is the uncredited and wholly superficial regurgitation of far more insightful authors' works, in particular Terrance Deacon, whose "Symbolic Species" is all but plagarized in the few coherent chapters of this book.

Too, it soon becomes obvious that the author of THE MATH GENE obviously never bothered to read any of the source materials. To give just one of many possible examples, the American philosopher C.S. Pierce posited eleven - not three - levels of interpretation between icon and symbol - but since Terrance Deacon (who is never credited anywhere in this book, not even in the bibliography, despite the many examples and their arguments - communication vs. language, symbol vs. index, the whole discussion of vervet alarm calls, etc. - that have been lifted whole from his work) deliberately limited his own discussion in The Symbolic Species to three, the author of THE MATH GENE dutifully reports that Pierce's orginal formulation was likewise three.

Lev Vygotsky similarly gets a perfunctory mention in the last two pages, though at no time throughout this book is any evidence whatsoever offered that would lead on to conclude that the author of THE MATH GENE has ever actually read any of Vygotsky's work (Vygotsky in that sense is becoming today what Freud was fifty years ago).

Finally, the author spends an unconscionable amount of time promising, heralding, and foreshadowing the upcoming appearance of his revolutionary explanatory "thesis" that - hold onto your hats for a mind-blowing challenge to 2500 years of received wisdom here - human beings are good at math beacuse the species has evolved a talent for "what I call 'off-line' thinking."

307 poorly written pages for that!

In short, I've read undergraduate students' term papers that had more original and well-argued thought.

And they cite their sources.

As an avid teacher and student of Mathematics, I was excited by the title of this book. It seemed like it would demonstrate why all humans have an aptitude for Math, and maybe how those who are 'innumerate' could tap into this inborn potential.

Unfortunately, this is not at all what the book delivered. It was basically a description of the evolution of the Human brain, specifically with regard to language acquisition.

With about 30 pages left in the book, he finally launches into his Thesis, which is that we are natrually good gossips, and that Math, to real Mathematicians, is very much like gossip. Mathematicians know numbers like they are people, and know their properties and relationships deeply.

That was it. No clue as to how people who have struggled with Math can use this gossip ability to help them learn and appreciate Math at any level.

Really a disappointing book. Don't waste your time, as I did mine.

In the book The Math Gene, author Keith Devlin stated that math is just a special use of our language faculty and every one should be able to do math. The basic structure of the book is Prologue, what is math, what is language, and from language to math( the point). We can see this clearly from the last sentence of the prologue,¡± Once you know what mathematics is really about, and once you see how our brains create language, you should find it far less surprising that thinking mathematically is just a specialized form of using our language facility.¡±

He spends the first 4 chapters talking about what math is: the science of pattern.
Chapter 2 and 3 is mostly boring to me, maybe people with little math background will appreciate it. Chapter 4 is not bad, especially when he cited the research on animal coating, it is really interesting that the coating of a leopard could be generated by solving math equations. Other examples are also very interesting.

In chapter 5, the author talked about math thinking. It is abstract thinking. Then he used the house metaphor to compare it with daily life. Make it simple to understand for the readers. He also talked about the high concentration you need in doing math problems, this kind of concentration is very hard for ordinary people who are busy worrying about their daily life. And that¡¯s one of major hurdle preventing most people from being good at math. This chapter is quite good.

Again chapter 6 and 7 is a bit uninteresting. It talked about what language is. Then in chapter 8 he talked about how math thinking evolved and the idea of offline thinking, how important it is to human, etc. It is an important chapter, though I don¡¯t find it interesting.

The best part of the book for me, also the whole point of the book comes last in chapter 9. It tells ¡°why numbers are like gossip¡±. I am very interested to read about it.
It first cited a very common fact: that people like to talk about other people, also they are interested in other people¡¯s lives, it¡¯s like a need for them. Then he said the usefulness of this is that it will benefit the group, make its members more close to each other.
Then he said the same thinking involved could be used in math thinking. How relationship between people in real world could also be applied to the relationships between abstract objects in the imaginary world created by human brain. Then he said why most people can not do math even they have this faculty in them. It is because it takes training most people don¡¯t have. Once those people get training, they will also be able to do math. However most people are not motivated.
And he said how mathematicians are able to do it and how wonderful the math world is. Only people that has reached the summit of one of the many math mountains can see the whole picture and the very picture motivate them to go further. While amateurs and outsiders only walk around the valley and never see the whole picture, and that is why they think math is difficult and uninteresting.

Chapter 10 is just citing about some other people¡¯s opinion and his viewpoint on it.

The epilogue of the book ¡° how to sell soap¡± is also quite funny.

Overall, it is a worth reading book. It is something new for me. Gives me more insight in language, math and gossip. The idea of the author is quite convincing. Some chapters of the book serve as background knowledge and could be skipped if you already have them. Mainly chapter 2, 3, 6, also chapter 10 could be skipped.