Author: John N. Crossley
Publisher: World Scientific
ISBN: 9789971504144
Category : Mathematics
Languages : en
Pages : 240
Book Description
This book presents detailed studies of the development of three kinds of number. In the first part the development of the natural numbers from Stone-Age times right up to the present day is examined not only from the point of view of pure history but also taking into account archaeological, anthropological and linguistic evidence. The dramatic change caused by the introduction of logical theories of number in the 19th century is also treated and this part ends with a non-technical account of the very latest developments in the area of Gdel's theorem. The second part is concerned with the development of complex numbers and tries to answer the question as to why complex numbers were not introduced before the 16th century and then, by looking at the original materials, shows how they were introduced as a pragmatic device which was only subsequently shown to be theoretically justifiable. The third part concerns the real numbers and examines the distinction that the Greeks made between number and magnitude. It then traces the gradual development of a theory of real numbers up to the precise formulations in the nineteeth century. The importance of the Greek distinction between the number line and the geometric line is brought into sharp focus.This is an new edition of the book which first appeared privately published in 1980 and is now out of print. Substantial revisions have been made throughout the text, incorporating new material which has recently come to light and correcting a few relatively minor errors. The third part on real numbers has been very extensively revised and indeed the last chapter has been almost completely rewritten. Many revisions are the results of comments from earlier readers of the book.
The Emergence of Number
Author: John N. Crossley
Publisher: World Scientific
ISBN: 9789971504144
Category : Mathematics
Languages : en
Pages : 240
Book Description
This book presents detailed studies of the development of three kinds of number. In the first part the development of the natural numbers from Stone-Age times right up to the present day is examined not only from the point of view of pure history but also taking into account archaeological, anthropological and linguistic evidence. The dramatic change caused by the introduction of logical theories of number in the 19th century is also treated and this part ends with a non-technical account of the very latest developments in the area of Gdel's theorem. The second part is concerned with the development of complex numbers and tries to answer the question as to why complex numbers were not introduced before the 16th century and then, by looking at the original materials, shows how they were introduced as a pragmatic device which was only subsequently shown to be theoretically justifiable. The third part concerns the real numbers and examines the distinction that the Greeks made between number and magnitude. It then traces the gradual development of a theory of real numbers up to the precise formulations in the nineteeth century. The importance of the Greek distinction between the number line and the geometric line is brought into sharp focus.This is an new edition of the book which first appeared privately published in 1980 and is now out of print. Substantial revisions have been made throughout the text, incorporating new material which has recently come to light and correcting a few relatively minor errors. The third part on real numbers has been very extensively revised and indeed the last chapter has been almost completely rewritten. Many revisions are the results of comments from earlier readers of the book.
Publisher: World Scientific
ISBN: 9789971504144
Category : Mathematics
Languages : en
Pages : 240
Book Description
This book presents detailed studies of the development of three kinds of number. In the first part the development of the natural numbers from Stone-Age times right up to the present day is examined not only from the point of view of pure history but also taking into account archaeological, anthropological and linguistic evidence. The dramatic change caused by the introduction of logical theories of number in the 19th century is also treated and this part ends with a non-technical account of the very latest developments in the area of Gdel's theorem. The second part is concerned with the development of complex numbers and tries to answer the question as to why complex numbers were not introduced before the 16th century and then, by looking at the original materials, shows how they were introduced as a pragmatic device which was only subsequently shown to be theoretically justifiable. The third part concerns the real numbers and examines the distinction that the Greeks made between number and magnitude. It then traces the gradual development of a theory of real numbers up to the precise formulations in the nineteeth century. The importance of the Greek distinction between the number line and the geometric line is brought into sharp focus.This is an new edition of the book which first appeared privately published in 1980 and is now out of print. Substantial revisions have been made throughout the text, incorporating new material which has recently come to light and correcting a few relatively minor errors. The third part on real numbers has been very extensively revised and indeed the last chapter has been almost completely rewritten. Many revisions are the results of comments from earlier readers of the book.
The Emergence of Meaning
Author: Stephen Crain
Publisher: Cambridge University Press
ISBN: 0521858097
Category : Language Arts & Disciplines
Languages : en
Pages : 307
Book Description
An investigation into the underlying logic of human languages which looks at how children acquire English and Mandarin.
Publisher: Cambridge University Press
ISBN: 0521858097
Category : Language Arts & Disciplines
Languages : en
Pages : 307
Book Description
An investigation into the underlying logic of human languages which looks at how children acquire English and Mandarin.
Uncountable
Author: David Nirenberg
Publisher: University of Chicago Press
ISBN: 022664698X
Category : History
Languages : en
Pages : 429
Book Description
"From the time of Pythagoras, we have been tempted to treat numbers as the ultimate or only truth. This book tells the history of that habit of thought. But more, it argues that the logic of counting sacrifices much of what makes us human, and that we have a responsibility to match the objects of our attention to the forms of knowledge that do them justice. Humans have extended the insights and methods of number and mathematics to more and more aspects of the world, even to their gods and their religions.Today those powers are greater than ever, as computation is applied to virtually every aspect of human activity.But the rules of mathematics do not strictly apply to many things-from elementary particles to people-in the world.By subjecting such things to the laws of logic and mathematics, we gain some kinds of knowledge, but we also lose others. How do our choices about what parts of the world to subject to the logics of mathematics affect how we live and how we die?This question is rarely asked, but it is urgent, because the sciences built upon those laws now govern so much of our knowledge, from physics to psychology.Number and Knowledge sets out to ask it. In chapters proceeding chronologically from Ancient Greek philosophy and the rise of monotheistic religions to the emergence of modern physics and economics, the book traces how ideals, practices, and habits of thought formed over millennia have turned number into the foundation-stone of human claims to knowledge and certainty.But the book is also a philosophical and poetic exhortation to take responsibility for that history, for the knowledge it has produced, and for the many aspects of the world and of humanity that it ignores or endangers.To understand what can be counted and what can't is to embrace the ethics of purposeful knowing"--
Publisher: University of Chicago Press
ISBN: 022664698X
Category : History
Languages : en
Pages : 429
Book Description
"From the time of Pythagoras, we have been tempted to treat numbers as the ultimate or only truth. This book tells the history of that habit of thought. But more, it argues that the logic of counting sacrifices much of what makes us human, and that we have a responsibility to match the objects of our attention to the forms of knowledge that do them justice. Humans have extended the insights and methods of number and mathematics to more and more aspects of the world, even to their gods and their religions.Today those powers are greater than ever, as computation is applied to virtually every aspect of human activity.But the rules of mathematics do not strictly apply to many things-from elementary particles to people-in the world.By subjecting such things to the laws of logic and mathematics, we gain some kinds of knowledge, but we also lose others. How do our choices about what parts of the world to subject to the logics of mathematics affect how we live and how we die?This question is rarely asked, but it is urgent, because the sciences built upon those laws now govern so much of our knowledge, from physics to psychology.Number and Knowledge sets out to ask it. In chapters proceeding chronologically from Ancient Greek philosophy and the rise of monotheistic religions to the emergence of modern physics and economics, the book traces how ideals, practices, and habits of thought formed over millennia have turned number into the foundation-stone of human claims to knowledge and certainty.But the book is also a philosophical and poetic exhortation to take responsibility for that history, for the knowledge it has produced, and for the many aspects of the world and of humanity that it ignores or endangers.To understand what can be counted and what can't is to embrace the ethics of purposeful knowing"--
Bulletin
Author: United States. Bureau of Entomology
Publisher:
ISBN:
Category : Entomology
Languages : en
Pages : 880
Book Description
Publisher:
ISBN:
Category : Entomology
Languages : en
Pages : 880
Book Description
Bulletin
Author:
Publisher:
ISBN:
Category : Entomology
Languages : en
Pages : 314
Book Description
Publisher:
ISBN:
Category : Entomology
Languages : en
Pages : 314
Book Description
The Basic Principles of Insect Population Suppression and Management
Author: E. F. Knipling
Publisher:
ISBN:
Category : Insect pests
Languages : en
Pages : 676
Book Description
Publisher:
ISBN:
Category : Insect pests
Languages : en
Pages : 676
Book Description
The North Kaibab Pandora Moth Outbreak, 1978-1984
Author: J. M. Schmid
Publisher:
ISBN:
Category : Insect pests
Languages : en
Pages : 80
Book Description
A pandora moth outbreak in Arizona was studied from 1979 to 1985 to determine the moth's life cycle, densities, and distribution of life stages, larval and adult behavior, effects of the defoliation, sampling procedures, importance of biotic mortality factors, and the effectiveness of insecticides. This report summarizes the available published and unpublished information on the outbreak.
Publisher:
ISBN:
Category : Insect pests
Languages : en
Pages : 80
Book Description
A pandora moth outbreak in Arizona was studied from 1979 to 1985 to determine the moth's life cycle, densities, and distribution of life stages, larval and adult behavior, effects of the defoliation, sampling procedures, importance of biotic mortality factors, and the effectiveness of insecticides. This report summarizes the available published and unpublished information on the outbreak.
Technical Bulletin
Author:
Publisher:
ISBN:
Category : Agriculture
Languages : en
Pages : 20
Book Description
Publisher:
ISBN:
Category : Agriculture
Languages : en
Pages : 20
Book Description
Miscellaneous Publication
Author:
Publisher:
ISBN:
Category : Agriculture
Languages : en
Pages : 390
Book Description
Publisher:
ISBN:
Category : Agriculture
Languages : en
Pages : 390
Book Description
Biology and Control of the Western Pine Beetle
Author: John Martin Miller
Publisher:
ISBN:
Category : Pine
Languages : en
Pages : 402
Book Description
This publication reviews the results of research on the western pine beetle up to July 1, 1952. It shows the progress that has been made in over a half-century of study of this one bark beetle. It also records the trials and errors--the research that ran into blind alleys. The record of this pioneer effort in the field of forest entomology in the United States should be of great help to research workers who are faced with similar problems.
Publisher:
ISBN:
Category : Pine
Languages : en
Pages : 402
Book Description
This publication reviews the results of research on the western pine beetle up to July 1, 1952. It shows the progress that has been made in over a half-century of study of this one bark beetle. It also records the trials and errors--the research that ran into blind alleys. The record of this pioneer effort in the field of forest entomology in the United States should be of great help to research workers who are faced with similar problems.