## The Mathematical Theory of Information (The Springer International Series in Engineering and Computer Science)

### Kåhre, Jan

4.5 avg rating
( 2 ratings by GoodReads )

The general concept of information is here, for the first time, defined mathematically by adding one single axiom to the probability theory. This Mathematical Theory of Information is explored in fourteen chapters: 1. Information can be measured in different units, in anything from bits to dollars. We will here argue that any measure is acceptable if it does not violate the Law of Diminishing Information. This law is supported by two independent arguments: one derived from the Bar-Hillel ideal receiver, the other is based on Shannon's noisy channel. The entropy in the 'classical information theory' is one of the measures conforming to the Law of Diminishing Information, but it has, however, properties such as being symmetric, which makes it unsuitable for some applications. The measure reliability is found to be a universal information measure. 2. For discrete and finite signals, the Law of Diminishing Information is defined mathematically, using probability theory and matrix algebra. 3. The Law of Diminishing Information is used as an axiom to derive essential properties of information. Byron's law: there is more information in a lie than in gibberish. Preservation: no information is lost in a reversible channel. Etc. The Mathematical Theory of Information supports colligation, i. e. the property to bind facts together making 'two plus two greater than four'. Colligation is a must when the information carries knowledge, or is a base for decisions. In such cases, reliability is always a useful information measure. Entropy does not allow colligation.

"synopsis" may belong to another edition of this title.

Product Description:

The Mathematical Theory of Information presents a new mathematical theory of information, built on a single powerful postulate: the Law of Diminishing Information. The concept of information is here, for the first time, defined mathematically by adding this postulate to the axioms of the probability theory. The Law of Diminishing Information is founded on a fusion of two fundamental ideas: Carnap and Bar-Hillel's `Ideal Receiver' and Shannon's `Noisy Channel'.

The Law of Diminishing Information is applied to information technology, game theory, legislation, logic of research, algorithmic information, chaos theory, control engineering, medical tests, and biological evolution. In physics, both the Second Law of Thermodynamics and Schrödinger's wave function are derived from the Law of Diminishing Information. Conventional information theory, that of telecommunications, is analyzed as a special case, and eight conditions for its applicability are listed.

The reader will get the essential ideas to understand and use the concept of information. The Mathematical Theory of Information is suitable as a textbook in general information theory for students of technical, scientific, and mathematical subjects. The book is ideal as a supplementary textbook in traditional courses on telecommunications information theory at all levels.

The website of the book is www.matheory.info.

List Price: US\$ 69.95
US\$ 66.79

Shipping: FREE
From United Kingdom to U.S.A.

Destination, Rates & Speeds

## 1.The Mathematical Theory of Information (Paperback)

ISBN 10: 1461353327 ISBN 13: 9781461353324
New Paperback Quantity Available: 10
Print on Demand
Seller
The Book Depository
(London, United Kingdom)
Rating

Book Description Springer-Verlag New York Inc., United States, 2013. Paperback. Book Condition: New. 235 x 155 mm. Language: English Brand New Book ***** Print on Demand *****.The general concept of information is here, for the first time, defined mathematically by adding one single axiom to the probability theory. This Mathematical Theory of Information is explored in fourteen chapters: 1. Information can be measured in different units, in anything from bits to dollars. We will here argue that any measure is acceptable if it does not violate the Law of Diminishing Information. This law is supported by two independent arguments: one derived from the Bar-Hillel ideal receiver, the other is based on Shannon s noisy channel. The entropy in the classical information theory is one of the measures conforming to the Law of Diminishing Information, but it has, however, properties such as being symmetric, which makes it unsuitable for some applications. The measure reliability is found to be a universal information measure. 2. For discrete and finite signals, the Law of Diminishing Information is defined mathematically, using probability theory and matrix algebra. 3. The Law of Diminishing Information is used as an axiom to derive essential properties of information. Byron s law: there is more information in a lie than in gibberish. Preservation: no information is lost in a reversible channel. Etc. The Mathematical Theory of Information supports colligation, i. e. the property to bind facts together making two plus two greater than four . Colligation is a must when the information carries knowledge, or is a base for decisions. In such cases, reliability is always a useful information measure. Entropy does not allow colligation. Softcover reprint of the original 1st ed. 2002. Bookseller Inventory # AAV9781461353324

US\$ 66.79
Convert Currency
Shipping: FREE
From United Kingdom to U.S.A.
Destination, Rates & Speeds

## 2.The Mathematical Theory of Information (Paperback)

ISBN 10: 1461353327 ISBN 13: 9781461353324
New Paperback Quantity Available: 10
Print on Demand
Seller
The Book Depository US
(London, United Kingdom)
Rating

Book Description Springer-Verlag New York Inc., United States, 2013. Paperback. Book Condition: New. 235 x 155 mm. Language: English . Brand New Book ***** Print on Demand *****. The general concept of information is here, for the first time, defined mathematically by adding one single axiom to the probability theory. This Mathematical Theory of Information is explored in fourteen chapters: 1. Information can be measured in different units, in anything from bits to dollars. We will here argue that any measure is acceptable if it does not violate the Law of Diminishing Information. This law is supported by two independent arguments: one derived from the Bar-Hillel ideal receiver, the other is based on Shannon s noisy channel. The entropy in the classical information theory is one of the measures conforming to the Law of Diminishing Information, but it has, however, properties such as being symmetric, which makes it unsuitable for some applications. The measure reliability is found to be a universal information measure. 2. For discrete and finite signals, the Law of Diminishing Information is defined mathematically, using probability theory and matrix algebra. 3. The Law of Diminishing Information is used as an axiom to derive essential properties of information. Byron s law: there is more information in a lie than in gibberish. Preservation: no information is lost in a reversible channel. Etc. The Mathematical Theory of Information supports colligation, i. e. the property to bind facts together making two plus two greater than four . Colligation is a must when the information carries knowledge, or is a base for decisions. In such cases, reliability is always a useful information measure. Entropy does not allow colligation. Softcover reprint of the original 1st ed. 2002. Bookseller Inventory # AAV9781461353324

US\$ 72.06
Convert Currency
Shipping: FREE
From United Kingdom to U.S.A.
Destination, Rates & Speeds

## 3.The Mathematical Theory of Information

ISBN 10: 1461353327 ISBN 13: 9781461353324
New Paperback Quantity Available: 1
Seller
Herb Tandree Philosophy Books
(Stroud, GLOS, United Kingdom)
Rating

Book Description Springer, 2013. Paperback. Book Condition: NEW. 9781461353324 This listing is a new book, a title currently in-print which we order directly and immediately from the publisher. Bookseller Inventory # HTANDREE0406954

US\$ 62.20
Convert Currency
Shipping: US\$ 10.28
From United Kingdom to U.S.A.
Destination, Rates & Speeds

## 4.The Mathematical Theory of Information

ISBN 10: 1461353327 ISBN 13: 9781461353324
New Quantity Available: > 20
Print on Demand
Seller
PBShop
(Wood Dale, IL, U.S.A.)
Rating

Book Description Springer-Verlag New York Inc., 2013. PAP. Book Condition: New. New Book. Shipped from US within 10 to 14 business days. THIS BOOK IS PRINTED ON DEMAND. Established seller since 2000. Bookseller Inventory # IQ-9781461353324

US\$ 68.58
Convert Currency
Shipping: US\$ 3.99
Within U.S.A.
Destination, Rates & Speeds

## 5.The Mathematical Theory of Information

ISBN 10: 1461353327 ISBN 13: 9781461353324
New Quantity Available: > 20
Print on Demand
Seller
Books2Anywhere
(Fairford, GLOS, United Kingdom)
Rating

Book Description Springer-Verlag New York Inc., 2013. PAP. Book Condition: New. New Book. Delivered from our UK warehouse in 3 to 5 business days. THIS BOOK IS PRINTED ON DEMAND. Established seller since 2000. Bookseller Inventory # LQ-9781461353324

US\$ 61.58
Convert Currency
Shipping: US\$ 11.56
From United Kingdom to U.S.A.
Destination, Rates & Speeds

## 6.The Mathematical Theory of Information

ISBN 10: 1461353327 ISBN 13: 9781461353324
New Paperback Quantity Available: 1
Print on Demand
Seller
Ria Christie Collections
(Uxbridge, United Kingdom)
Rating

Book Description Springer, 2016. Paperback. Book Condition: New. PRINT ON DEMAND Book; New; Publication Year 2016; Not Signed; Fast Shipping from the UK. No. book. Bookseller Inventory # ria9781461353324_lsuk

US\$ 69.65
Convert Currency
Shipping: US\$ 4.27
From United Kingdom to U.S.A.
Destination, Rates & Speeds

## 7.The Mathematical Theory of Information (The Springer International Series in Engineering and Computer Science)

ISBN 10: 1461353327 ISBN 13: 9781461353324
New Softcover Quantity Available: 15
Print on Demand
Seller
Rating

Book Description Springer, 2013. Book Condition: New. This item is printed on demand for shipment within 3 working days. Bookseller Inventory # LP9781461353324

US\$ 68.70
Convert Currency
Shipping: US\$ 6.05
From Germany to U.S.A.
Destination, Rates & Speeds

## 8.The Mathematical Theory of Information (The Springer International Series in Engineering and Computer Science)

ISBN 10: 1461353327 ISBN 13: 9781461353324
New Paperback Quantity Available: 20
Print on Demand
Seller
Murray Media
(North Miami Beach, FL, U.S.A.)
Rating

Book Description Springer, 2017. Paperback. Book Condition: New. This item is printed on demand. Bookseller Inventory # 1461353327

US\$ 79.86
Convert Currency
Shipping: US\$ 2.99
Within U.S.A.
Destination, Rates & Speeds

## 9.The Mathematical Theory of Information (The Springer International Series in Engineering and Computer Science)

ISBN 10: 1461353327 ISBN 13: 9781461353324
New Paperback Quantity Available: 1
Seller
Irish Booksellers
(Rumford, ME, U.S.A.)
Rating

Book Description Springer, 2013. Paperback. Book Condition: New. book. Bookseller Inventory # 1461353327

US\$ 83.94
Convert Currency
Shipping: FREE
Within U.S.A.
Destination, Rates & Speeds

## 10.The Mathematical Theory of Information

ISBN 10: 1461353327 ISBN 13: 9781461353324
New Paperback Quantity Available: 20
Seller