The Structure Of The Mathematical Brain
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The Structure Of The Mathematical Brain
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Author : Tudor Popescu
language : en
Publisher:
Release Date : 2014
The Structure Of The Mathematical Brain written by Tudor Popescu and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014 with categories.
The Structure Of Intelligence
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Author : Ben Goertzel
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-07
The Structure Of Intelligence written by Ben Goertzel and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-07 with Psychology categories.
0. 0 Psychology versus Complex Systems Science Over the last century, psychology has become much less of an art and much more of a science. Philosophical speculation is out; data collection is in. In many ways this has been a very positive trend. Cognitive science (Mandler, 1985) has given us scientific analyses of a variety of intelligent behaviors: short-term memory, language processing, vision processing, etc. And thanks to molecular psychology (Franklin, 1985), we now have a rudimentary understanding of the chemical processes underlying personality and mental illness. However, there is a growing feeling-particularly among non-psychologists (see e. g. Sommerhoff, 1990) - that, with the new emphasis on data collection, something important has been lost. Very little attention is paid to the question of how it all fits together. The early psychologists, and the classical philosophers of mind, were concerned with the general nature of mentality as much as with the mechanisms underlying specific phenomena. But the new, scientific psychology has made disappointingly little progress toward the resolution of these more general questions. One way to deal with this complaint is to dismiss the questions themselves. After all, one might argue, a scientific psychology cannot be expected to deal with fuzzy philosophical questions that probably have little empirical signifi cance. It is interesting that behaviorists and cognitive scientists tend to be in agreement regarding the question of the overall structure of the mind.
The Number Sense How The Mind Creates Mathematics
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Author : Stanislas Dehaene Research Affiliate Institut National de la Sante et de la Recherche Medicale
language : en
Publisher: Oxford University Press, USA
Release Date : 1997-11-06
The Number Sense How The Mind Creates Mathematics written by Stanislas Dehaene Research Affiliate Institut National de la Sante et de la Recherche Medicale and has been published by Oxford University Press, USA this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-11-06 with Mathematics categories.
Our understanding of how the human brain performs mathematical calculations is far from complete. But in recent years there have been many exciting scientific discoveries, some aided by new imaging techniques--which allow us for the first time to watch the living mind at work--and others by ingenious experiments conducted by researchers all over the world. There are still perplexing mysteries--how, for instance, do idiot savants perform almost miraculous mathematical feats?--but the picture is growing steadily clearer. In The Number Sense, Stanislas Dehaene offers general readers a first look at these recent stunning discoveries, in an enlightening exploration of the mathematical mind. Dehaene, a mathematician turned cognitive neuropsychologist, begins with the eye-opening discovery that animals--including rats, pigeons, raccoons, and chimpanzees--can perform simple mathematical calculations, and he describes ingenious experiments that show that human infants also have a rudimentary number sense (American scientist Karen Wynn, for instance, using just a few Mickey Mouse toys and a small puppet theater, proved that five-month-old infants already have the ability to add and subtract). Further, Dehaene suggests that this rudimentary number sense is as basic to the way the brain understands the world as our perception of color or of objects in space, and, like these other abilities, our number sense is wired into the brain. But how then did the brain leap from this basic number ability to trigonometry, calculus, and beyond? Dehaene shows that it was the invention of symbolic systems of numerals that started us on the climb to higher mathematics, and in a marvelous chapter he traces the history of numbers, from early times when people indicated a number by pointing to a part of their body (even today, in many societies in New Guinea, the word for six is "wrist"), to early abstract numbers such as Roman numerals (chosen for the ease with which they could be carved into wooden sticks), to modern numbers. On our way, we also discover many fascinating facts: for example, because Chinese names for numbers are so short, Chinese people can remember up to nine or ten digits at a time--English-speaking people can only remember seven. Dehaene also explores the unique abilities of idiot savants and mathematical geniuses, asking what might explain their special mathematical talent. And we meet people whose minute brain lesions render their mathematical ability useless--one man, in fact, who is certain that two and two is three. Using modern imaging techniques (PET scans and MRI), Dehaene reveals exactly where in the brain numerical calculation takes place. But perhaps most important, The Number Sense reaches many provocative conclusions that will intrigue anyone interested in mathematics or the mind. Dehaene argues, for instance, that many of the difficulties that children face when learning math, and which may turn into a full-blown adult "innumeracy," stem from the architecture of our primate brain, which has not evolved for the purpose of doing mathematics. He also shows why the human brain does not work like a computer, and that the physical world is not based on mathematics--rather, mathematics evolved to explain the physical world the way that the eye evolved to provide sight. A truly 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.
Structure Of Matter Structure Of Mind
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Author : William L. Abler
language : en
Publisher:
Release Date : 2005
Structure Of Matter Structure Of Mind written by William L. Abler and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Psychology categories.
"Structure of Matter, Structure of Mind provides a complete, clear, unified theory of the foundations of mathematics, language, and the human mind. Mind in the human sense is no longer distinguished by a few chance details of zoological classification, but, like physics, is based directly in first principles. Because sentences share all functional mechanisms with equations - a main verb, linguistic deep-structure, recursion, discretencess, linear delivery, truth and falsity - language shares a common source with arithmetic and algebra. Because truth or falsity of equations depends on their symmetry about the "equals", equations are self-regulating, not arbitrary, and reflect the founding properties of matter. Sentences of ordinary language are formed from equations by the turning of a single key - that of symmetry - unlocking the human mind into the fascinating non-Euclidean world of 21[superscript st] century physics and beyond."--BOOK JACKET.
The Number Sense
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Author : Stanislas Dehaene
language : en
Publisher: OUP USA
Release Date : 2011-04-29
The Number Sense written by Stanislas Dehaene and has been published by OUP USA this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-04-29 with Mathematics categories.
"Our understanding of how the human brain performs mathematical calculations is far from complete. In The Number Sense, Stanislas Dehaene offers readers an enlightening exploration of the mathematical mind. Using research showing that human infants have a rudimentary number sense, Dehaene suggests that this sense is as basic as our perception of color, and that it is wired into the brain. But how then did we leap from this basic number ability to trigonometry, calculus, and beyond? Dehaene shows that it was the invention of symbolic systems of numerals that started us on the climb to higher mathematics. Tracing the history of numbers, we learn that in early times, people indicated numbers by pointing to part of their bodies, and how Roman numerals were replaced by modern numbers. On the way, we also discover many fascinating facts: for example, because Chinese names for numbers are short, Chinese people can remember up to nine or ten digits at a time, while English-speaking people can only remember seven. 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 math can open up a window on the human mind"--Provided by publisher.
Neuroscience
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Author : Alwyn Scott
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-12-14
Neuroscience written by Alwyn Scott and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-12-14 with Science categories.
This book will be of interest to anyone who wishes to know what role mathematics can play in attempting to comprehend the dynamics of the human brain. It also aims to serve as a general introduction to neuromathematics. The book gives the reader a qualitative understanding and working knowledge of useful mathematical applications to the field of neuroscience. The book is readable by those who have little knowledge of mathematics for neuroscience but are committed to begin acquiring such knowledge.
Associations Between Reading And Mathematics Genetic Brain Imaging Cognitive And Educational Perspectives
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Author : Sarit Ashkenazi
language : en
Publisher: Frontiers Media SA
Release Date : 2017-10-05
Associations Between Reading And Mathematics Genetic Brain Imaging Cognitive And Educational Perspectives written by Sarit Ashkenazi and has been published by Frontiers Media SA this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-10-05 with categories.
Converging evidence demonstrates a strong link between reading and mathematics: multiple cognitive processes are shared between reading and mathematics, including the representation and retrieval of symbolic information, attention, working memory, and cognitive control. Additionally, multiple brain networks are involved in both math and reading, and last, common genetic factors might influence both reading and math. Hence, it comes as no surprise that there are meaningful associations between (aspects of) math and reading abilities. Moreover, comorbidity rates between math learning disabilities (MD) and reading disabilities (RD) are high (up to 66%) and prevalence rate of the comorbid condition is reported to be more common than the prevalence rate of isolated math learning disabilities. Accordingly, the goal of the research topic is to explore the underline mechanisms of this overlap between reading and math. The research topic aims to include the following topics: • Genetics - it has been found that both RD and MD are based on genetic factors and run in families. Moreover, math problem solving shares significant genetic overlap with general cognitive ability and reading decoding, whereas math fluency shares significant genetic overlap with reading fluency and general cognitive ability. Hence, this topic will explore the shared and unique genetic risk factors to RD and MD, In addition to shared and unique genetic influence on reading and math. • Neural perspective - converging evidence from both structural and multiple functional imaging studies, involving a wide range of numerical tasks, points to the intraparietal sulcus (IPS) as a core region that involve in quantity manipulation. However, several additional brain areas, such as frontoparietal and temporoparietal areas were found to be involved in numerical tasks. Individuals with MD show deficits in a distributed, set of brain regions that include the IPS, fusiform gyrus in posterior brain regions and pre frontal cortex regions. Similarly, converging evidence indicate that the left hemisphere regions centered in the fusiform gyrus, temporoparietal cortex, and pre frontal cortex regions are strongly involve in typical reading and present lower activity, connectivity or abnormal structure in RD. Thus, there is a meaningful neural overlap between reading and math. Hence, the authors can submit empirical studies on the role of several of brain regions that are involved in math and reading (commonality and diversity) both in the typical and a-typical development. • Cognitive factors that play role in mathematics and reading, and comorbidity between RD and MD - There is a long lasting debate whether MD and RD originate from unique cognitive mechanisms or not. Multiple cognitive processes are shared between reading and mathematics. Therefore, impairments in any one of domain-general skills could conceivably play an important role in both pure and comorbid conditions. Moreover, it has been suggested that phonological processing has a significant role in some aspects of numerical processing such as retrieval of arithmetical facts. • Education - it will be interesting to look at the effect of interventions that aim to improve reading (such as phonological awareness) and there transfer effect on improving mathematical processing. Alternatively, it will be good to test whether math interventions will improve reading.
Mathematical Structures Of Natural Intelligence
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Author : Yair Neuman
language : en
Publisher: Springer
Release Date : 2017-12-01
Mathematical Structures Of Natural Intelligence written by Yair Neuman and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-12-01 with Mathematics categories.
This book uncovers mathematical structures underlying natural intelligence and applies category theory as a modeling language for understanding human cognition, giving readers new insights into the nature of human thought. In this context, the book explores various topics and questions, such as the human representation of the number system, why our counting ability is different from that which is evident among non-human organisms, and why the idea of zero is so difficult to grasp. The book is organized into three parts: the first introduces the general reason for studying general structures underlying the human mind; the second part introduces category theory as a modeling language and use it for exposing the deep and fascinating structures underlying human cognition; and the third applies the general principles and ideas of the first two parts to reaching a better understanding of challenging aspects of the human mind such as our understanding of the number system, the metaphorical nature of our thinking and the logic of our unconscious dynamics.
Mathematical Cognition
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Author : Brian Butterworth
language : en
Publisher: Psychology Press
Release Date : 1996
Mathematical Cognition written by Brian Butterworth and has been published by Psychology Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996 with Cognition categories.
This volume is a collection of all papers published in Volume One of the journal "Mathematical Cognition". The aim of the journal is to provide a forum for explorations of how we understand mathematics and how we acquire and use mathematical concepts. The journal encourages an interdisciplinary approach to the field, and publishes advances in the study of the mental representation and use of mathematical concepts from a range of disciplines.; This first volume features contributions from cognitive psychology, developmental psychology, philosophy, neuroscience, education, computational modelling, and neuropsychology.
What Counts
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Author : Brian Butterworth
language : en
Publisher:
Release Date : 1999
What Counts written by Brian Butterworth and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with Mathematics categories.
Though he admits to not being particularly good at math, Butterworth (cognitive neuropsychology, U. College, London), the founder of the Mathematical Cognition journal, contends that we all possess an inherent "numerosity" sense--developed to different degrees of course. The author bases his case on empirical research and historical speculation. Annotation copyrighted by Book News, Inc., Portland, OR
