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Without numbers, modern civilization would
not exist. But until now, no one has explained where numbers
exist in the mind, how they got there, or how we use them.
In What Counts, Brian Butterworth combines his unique
expertise in cognitive neuroscience with his broad knowledge
of mathematics to offer a completely original picture of
how our brains do math.
Butterworth's pioneering research into the
behavior and genetics of mathematical ability has led him
to discover that we all possess a fundamental number sense,
which he calls "numerosity." This inherent ability
is even more basic to human nature than language is. Numbers
do not exist inside our heads the way words do; they are
a separate kind of intelligence with their own brain module.
This module, located in the left parietal lobe, is where
math happens.
We all know that some of us are good at
math and some of us are not. But, as Butterworth shows,
the reason a person falters at math is usually not because
of the wrong gene or "engine part" in the left
parietal lobe, but because he or she has not fully developed
the sense we are all born with. The left parietal lobe is
also where fingers are registered in our brain -- a fact
that Butterworth demonstrates is an important clue to the
evolution of our sense of numerosity -- and interestingly,
it is the reason we count on our fingers. The nonlinguistic
nature of math explains why cultures that have no words
for numbers have still managed to develop market economies
throughout history with all the counting that buying and
selling require. Butterworth argues that counting is so
basic a facet of our biology that, with practice, most people
could become mathematical prodigies.
Butterworth illustrates his cognitive model
of math with enlightening examples from the history of mathematics
and its many anomalies. He shows us the numerical world
of the Neanderthals, Cro-Magnons, and Stone Age peoples.
He recounts the case of the Italian woman who suffered a
stroke that left her unable to count beyond four, as well
as the extraordinary story of zero. He describes how the
great math prodigy Ramanujan emerged from a childhood of
poverty and astonished the world with his brilliance. He
presents surprising research demonstrating that infants
can add and subtract even when they are only a few weeks
old, and that people afflicted with Alzheimer's have unexpected
numerical abilities.
The implications of Butterworth's advances
in fundamental concepts of mathematical thinking are profound
-- for our understanding of how our minds work, how we can
lead our children to a deeper understanding of mathematics,
and even how formal education could be better structured
on the basis of what counting really is. What Counts
is the first book to provide a complete picture of how and
why our mathematical brain evolved and what this new knowledge
means in our everyday lives. No one who reads it will ever
think about math in the same way again.
Brian Butterworth is Professor of Cognitive
Neuropsychology in the Institute of Cognitive Neuroscience
at University College in London. In 1993 he launched the
scientific journal Mathematical Cognition, which
publishes studies on the psychology and neuropsychology
of numbers. He lives in London.
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