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Core Cognition: Number

Susan Carey

in The Origin of Concepts

Published in print:
2009
Published Online:
September 2009
ISBN:
9780195367638
eISBN:
9780199867349
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780195367638.003.0004
Subject:
Psychology, Cognitive Psychology, Developmental Psychology

This chapter lays out the evidence for two distinct systems of core cognition with numerical content—analog magnitude representations of number and parallel individuation of small sets— contrasting ... More


Behavioral Signatures of Numerical Cognition

Elizabeth M. Brannon, Kerry E. Jordan, and Sarah M. Jones

in Primate Neuroethology

Published in print:
2010
Published Online:
February 2010
ISBN:
9780195326598
eISBN:
9780199864904
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780195326598.003.0008
Subject:
Psychology, Neuropsychology, Evolutionary Psychology

The ability to represent number approximately has been documented in animals as diverse as lizards, rats, pigeons, ferrets, raccoons, dolphins, lemurs, monkeys, and apes. This chapter focuses on ... More


Endangered Number Systems: Counting to Twenty on Your Toes

K. David Harrison

in When Languages Die: The Extinction of the World's Languages and the Erosion of Human Knowledge

Published in print:
2007
Published Online:
January 2010
ISBN:
9780195181920
eISBN:
9780199870622
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780195181920.003.0006
Subject:
Linguistics, Historical Linguistics

This chapter discusses that human languages, when counting, not only have different names for the numbers but also use a wide variety of mathematical strategies. It explores unusual counting systems ... More


Pure Mathematics

E. Brian Davies

in Science in the Looking Glass: What Do Scientists Really Know?

Published in print:
2007
Published Online:
September 2008
ISBN:
9780199219186
eISBN:
9780191711695
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199219186.003.0005
Subject:
Physics, History of Physics

This chapter seeks to demolish the myth that mathematics is uniquely free of controversy, and therefore a guaranteed source of objective and eternal knowledge. Topics discussed include the origins of ... More


The Egyptian Number System

Annette Imhausen

in Mathematics in Ancient Egypt: A Contextual History

Published in print:
2016
Published Online:
January 2018
ISBN:
9780691117133
eISBN:
9781400874309
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691117133.003.0003
Subject:
Mathematics, History of Mathematics

This chapter describes the ancient Egyptian number system. The system can be described in modern terminology as a decimal system without positional (place-value) notation. The basis of the number ... More


Certain Ancient Number Systems

Joseph Mazur

in Enlightening Symbols: A Short History of Mathematical Notation and Its Hidden Powers

Published in print:
2016
Published Online:
January 2018
ISBN:
9780691173375
eISBN:
9781400850112
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691173375.003.0002
Subject:
Mathematics, History of Mathematics

This chapter discusses ancient number systems, beginning with the Babylonian system. Almost every history of early Western mathematics begins with the Babylonian conception of number, a so-called ... More


Summary

Annette Imhausen

in Mathematics in Ancient Egypt: A Contextual History

Published in print:
2016
Published Online:
January 2018
ISBN:
9780691117133
eISBN:
9781400874309
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691117133.003.0005
Subject:
Mathematics, History of Mathematics

This chapter summarizes key discussions in chapters 1 to 3. Writing was developed in Egypt at the end of the fourth millennium BCE. Therefore, it is not surprising to find representations of numbers ... More


Enlightening Symbols: A Short History of Mathematical Notation and Its Hidden Powers

Joseph Mazur

Published in print:
2016
Published Online:
January 2018
ISBN:
9780691173375
eISBN:
9781400850112
Item type:
book
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691173375.001.0001
Subject:
Mathematics, History of Mathematics

While all of us regularly use basic mathematical symbols such as those for plus, minus, and equals, few of us know that many of these symbols weren't available before the sixteenth century. What did ... More


The Indian Gift

Joseph Mazur

in Enlightening Symbols: A Short History of Mathematical Notation and Its Hidden Powers

Published in print:
2016
Published Online:
January 2018
ISBN:
9780691173375
eISBN:
9781400850112
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691173375.003.0004
Subject:
Mathematics, History of Mathematics

This chapter discusses the legacy of Indian mathematics. With very few archaeological clues, the origins of the Indian numbers must rely on a small wealth of writing that survives almost exclusively ... More


Silk and Royal Roads

Joseph Mazur

in Enlightening Symbols: A Short History of Mathematical Notation and Its Hidden Powers

Published in print:
2016
Published Online:
January 2018
ISBN:
9780691173375
eISBN:
9781400850112
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691173375.003.0003
Subject:
Mathematics, History of Mathematics

This chapter discusses the important role played by the Silk and Royal roads in the spread of teaching and knowledge of philosophy, science, and mathematics during ancient times. The Silk Road was a ... More


Uses of Numbers and Their Contexts in Predynastic and Early Dynastic Times

Annette Imhausen

in Mathematics in Ancient Egypt: A Contextual History

Published in print:
2016
Published Online:
January 2018
ISBN:
9780691117133
eISBN:
9781400874309
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691117133.003.0004
Subject:
Mathematics, History of Mathematics

This chapter reviews evidence on the use of the ancient Egyptian number system. There have been only three types of signs used in writing a number: a vertical stroke, a horizontal stroke, and a rope. ... More


Foundation of Mathematics

Annette Imhausen

in Mathematics in Ancient Egypt: A Contextual History

Published in print:
2016
Published Online:
January 2018
ISBN:
9780691117133
eISBN:
9781400874309
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691117133.003.0011
Subject:
Mathematics, History of Mathematics

This chapter discusses arithmetic techniques. At the heart of a mathematical culture that develops mathematical techniques are basic arithmetical operations that allow the numerate scribe to ... More


Arrival in Europe

Joseph Mazur

in Enlightening Symbols: A Short History of Mathematical Notation and Its Hidden Powers

Published in print:
2016
Published Online:
January 2018
ISBN:
9780691173375
eISBN:
9781400850112
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691173375.003.0005
Subject:
Mathematics, History of Mathematics

This chapter examines how our current number system reached Europe. There is a dispute over whether or not the person most responsible for introducing Hindu-Arabic numerals to Europe was Leonardo ... More


<i>Liber Abbaci</i>

Joseph Mazur

in Enlightening Symbols: A Short History of Mathematical Notation and Its Hidden Powers

Published in print:
2016
Published Online:
January 2018
ISBN:
9780691173375
eISBN:
9781400850112
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691173375.003.0007
Subject:
Mathematics, History of Mathematics

This chapter discusses the role played by Leonardo Fibonacci's Liber abbaci in introducing modern arithmetic to the West. In the prologue of Liber abbaci, Fibonacci says he learned the nine Indian ... More


Epistemic Limitations and Precise Estimates in Analog Magnitude Representation

Justin Halberda

in Core Knowledge and Conceptual Change

Published in print:
2016
Published Online:
August 2016
ISBN:
9780190467630
eISBN:
9780190611965
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780190467630.003.0010
Subject:
Psychology, Cognitive Psychology

This chapter presents a re-understanding of the contents of our analog magnitude representations (e.g., approximate duration, distance, number). The approximate number system (ANS) is considered, ... More


The Arab Gift

Joseph Mazur

in Enlightening Symbols: A Short History of Mathematical Notation and Its Hidden Powers

Published in print:
2016
Published Online:
January 2018
ISBN:
9780691173375
eISBN:
9781400850112
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691173375.003.0006
Subject:
Mathematics, History of Mathematics

This chapter focuses on the Arabs' contributions to the modern number system. It first considers the role played by Abu Jafar Muhammad ibn Musa al-Khwārizmī, the greatest Arab mathematician of his ... More


Further Aspects of Mathematics from New Kingdom Sources

Annette Imhausen

in Mathematics in Ancient Egypt: A Contextual History

Published in print:
2016
Published Online:
January 2018
ISBN:
9780691117133
eISBN:
9781400874309
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691117133.003.0016
Subject:
Mathematics, History of Mathematics

This chapter proposes the following scenario: mathematics not only played a huge role within the education and work life of a scribe, but it also held an important role within ancient Egyptian ... More


Concepts of Colour and Limits of Understanding

Barry Stroud

in Seeing, Knowing, Understanding: Philosophical Essays

Published in print:
2018
Published Online:
July 2018
ISBN:
9780198809753
eISBN:
9780191859205
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198809753.003.0016
Subject:
Philosophy, Metaphysics/Epistemology, Philosophy of Mind

This chapter examines some puzzling reflections by Ludwig Wittgenstein on the possibility of understanding concepts of the colours of things different from those already familiar to us. It begins ... More


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