Science and Information Theory

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A classic source for understanding the connections between information theory and physics, this text was written by one of the giants of 20th-century physics. Topics include the principles of coding, coding problems and solutions, the analysis of signals, a summary of thermodynamics, thermal agitation and Brownian motion, plus an examination of Maxwell's demon. 81 figures. 14 tables.
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Science and Information Theory: Second Edition

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Overview


A classic source for understanding the connections between information theory and physics, this text was written by one of the giants of 20th-century physics. Topics include the principles of coding, coding problems and solutions, the analysis of signals, a summary of thermodynamics, thermal agitation and Brownian motion, plus an examination of Maxwell's demon. 81 figures. 14 tables.
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Product Details

  • ISBN-13: 9780486439181
  • Publisher: Dover Publications
  • Publication date: 9/7/2004
  • Series: Phoenix Edition Series
  • Edition description: REV
  • Edition number: 2
  • Pages: 368
  • Product dimensions: 6.22 (w) x 9.10 (h) x 0.94 (d)

Table of Contents

Preface v
Introduction vii
Chapter 1 The Definition of Information 1
1 Definition of Information 1
2 Unit Systems 2
3 Generalization and Examples 3
4 Information Using the Alphabet 4
5 Information Content in a Set of Symbols with Different a priori Probabilities 5
6 General Remarks 8
Chapter 2 Application of the Definitions and General Discussion 11
1 Definitions 11
2 Property A 12
3 Property B 13
4 Property C 14
5 Joint Events 17
6 Conditional Information 19
Chapter 3 Redundancy in the English Language 21
1 Correlation and Joint Events 21
2 Correlation in Language 22
3 Redundancy in Language 23
4 Some Typical Experiments 25
5 Coding Devices 26
Chapter 4 Principles of Coding, Discussion of the Capacity of a Channel 28
1 Introduction 28
2 Definition of a Channel and its Capacity 28
3 Symbols, Words, and Messages in Sequential Coding 30
4 Discussion 32
5 Examples 34
6 Computation of the Capacity of a Channel 37
7 Matching a Code with a Channel 38
8 General Problem: Symbols with Different Lengths 41
9 The Matching Problem 44
10 Problems of Word Statistics (Mandelbrot) 44
11 Solving the Matching Problem 47
Appendix 49
Chapter 5 Coding Problems 51
1 Alphabetic Coding, Binary System 51
2 Alphabetic Coding, Ternary System 53
3 Alphabet and Numbers 54
4 Binary Coding by Words 55
5 Alphabetic Coding by Words 58
6 Coding Based on Letter Groups and on Correlation 58
Chapter 6 Error Detecting and Correcting Codes 62
1 Error Detecting Codes 62
2 Single Error Detecting Codes 63
3 Single Error Correcting and Double Error Correcting Codes 66
4 Efficiency of Self-Correcting Codes 67
5 The Capacity of a Binary Channel with Noise 69
Chapter 7 Applications to Some Special Problems 71
1 The Problem of Filing Using a Miscellaneous Cell 71
2 Filing with Cross Referencing 73
3 The Most Favorable Number of Signals per Elementary Cell 75
Chapter 8 The Analysis of Signals: Fourier Method and Sampling Procedure 78
1 Fourier Series 78
2 The Gibbs' Phenomenon and Convergence of Fourier Series 80
3 Fourier Integrals 83
4 The Role of Finite Frequency Band Width 87
5 The Uncertainty Relation for Time and Frequency 89
6 Degrees of Freedom of a Message 93
7 Shannon's Sampling Method 97
8 Gabor's Information Cells 99
9 Autocorrelation and Spectrum; the Wiener-Khintchine Formula 101
10 Linear Transformations and Filters 103
11 Fourier Analysis and the Sampling Method in Three Dimensions 105
12 Crystal Analysis by X-Rays 111
Appendix Schwarz' Inequality 113
Chapter 9 Summary of Thermodynamics 114
1 Introduction 114
2 The Two Principles of Thermodynamics; Entropy and Negentropy 114
3 Impossibility of Perpetual Motion; Thermal Engines 117
4 Statistical Interpretation of Entropy 119
5 Examples of Statistical Discussions 121
6 Energy Fluctuations; Gibbs Formula 122
7 Quantized Oscillator 124
8 Fluctuations 125
Chapter 10 Thermal Agitation and Brownian Motion 128
1 Thermal Agitation 128
2 Random Walk 129
3 Shot Effect 132
4 Brownian Motion 134
5 Thermal Agitation in an Electric Circuit 137
Appendix 139
Chapter 11 Thermal Noise in an Electric Circuit; Nyquist's Formula 141
1 Random Impulses Model 141
2 The Nyquist Method 143
3 Discussion and Applications 145
4 Generalizations of Nyquist's Formula 146
5 Thermal Agitation in a Rectifier 148
Chapter 12 The Negentropy Principle of Information 152
1 The Relation between Information and Entropy 152
2 The Negentropy Principle of Information; Generalization of Carnot's Principle 153
3 Some Typical Physical Examples 156
4 Some General Remarks 159
Chapter 13 Maxwell's Demon and the Negentropy Principle of Information 162
1 Maxwell's Demon: Historical Survey 162
2 The Demon Exorcised 164
3 Discussion 166
4 The Demon's Operation as a Transformation of Information into Negative Entropy 168
5 The Negentropy Required in the Observation 172
6 Szilard's Problem: The Well-Informed Heat Engine 176
7 Gabor's Discussion 179
Appendix I 182
Appendix II 183
Chapter 14 The Negentropy Principle of Information in General Physics 184
1 The Problem of Measurements in Physics 184
2 Observations Made on an Oscillator 185
3 High-Frequency Resonator and the Cost of an Observation 188
4 Experiments Requiring Many Simultaneous Observations at Low Frequencies 190
5 Problems Requiring High Reliability 194
6 A More Accurate Discussion of Experiments Using High Frequencies 196
7 An Example Showing the Minimum Negentropy Required in an Observation 198
Chapter 15 Observation and Information 202
1 Experimental Errors and Information 202
2 Length Measurements with Low Accuracy 204
3 Length Measurements with High Accuracy 206
4 Efficiency of an Observation 209
5 Measurement of a Distance with an Interferometer 210
6 Another Scheme for Measuring Distance 213
7 The Measurement of Time Intervals 217
8 Observation under a Microscope 219
9 Discussion of the Focus in a Wave Guide 223
10 Examples and Discussion 226
11 Summary 228
Chapter 16 Information Theory, the Uncertainty Principle, and Physical Limits of Observation 229
1 General Remarks 229
2 An Observation is an Irreversible Process 231
3 General Limitations in the Accuracy of Physical Measurements 232
4 The Limits of Euclidean Geometry 235
5 Possible Use of Heavy Particles Instead of Photons 236
6 Uncertainty Relations in the Microscope Experiment 238
7 Measurement of Momentum 241
8 Uncertainty in Field Measurements 243
Chapter 17 The Negentropy Principle of Information in Telecommunications 245
1 The Analysis of Signals with Finite Band Width 245
2 Signals and Thermal Noise: Representation in Hyperspace 246
3 The Capacity of a Channel with Noise 247
4 Discussion of the Tuller-Shannon Formula 248
5 A Practical Example 252
6 The Negentropy Principle Applied to the Channel with Noise 254
7 Gabor's Modified Formula and the Role of Beats 257
Chapter 18 Writing, Printing, and Reading 259
1 The Transmission of Information: Live Information 259
2 The Problem of Reading and Writing 260
3 Dead Information and How to Bring it Back to Life 261
4 Writing and Printing 263
5 Discussion of a Special Example 264
6 New Information and Redundancy 265
Chapter 19 The Problem of Computing 267
1 Computing Machines 267
2 The Computer as a Mathematical Element 269
3 The Computer as a Circuit Element, Sampling and Desampling (Linvill and Salzer) 273
4 Computing on Sampled Data at Time t 275
5 The Transfer Function for a Computer 277
6 Circuits Containing a Computer, The Problem of Stability 279
7 Discussion of the Stability of a Program 281
8 A Few Examples 283
Chapter 20 Information, Organization, and Other Problems 287
1 Information and Organization 287
2 Information Contained in a Physical Law 289
3 Information Contained in a Numerical Table 291
4 General Remarks 293
5 Examples of Problems Beyond the Present Theory 294
6 Problems of Semantic Information 297
Chapter 21 Inevitable Errors, Determinism, and Information 302
1 Information in Science 302
2 Information is Finite 302
3 The Viewpoint of M. Born 303
4 Observation and Experimental Errors 304
5 A Simple Example for Discussion: Laplace's Demon Exorcised 305
6 Some More Examples: Anharmonic Oscillators, Rectifier 308
7 The Anomaly of the Harmonic Oscillator 311
8 The Problem of Determinism 314
9 Information Theory and our Preceding Examples 316
10 Observation and Interpretation 318
11 Conclusions 320
Chapter 22 The Problem of Very Small Distances 321
1 The Difficulties in Measuring Extremely Small Distances 321
2 The Possible Use of These Remarks for the Computation of Diverging Integrals in Physics 322
3 Example: Electromagnetic Mass of the Electron 324
4 A Justification of our Assumptions: Schrodinger's Zitterbewegung 325
5 Discussion and Possible Generalizations 326
Author Index 329
Subject Index 331
Books published by L. Brillouin 349
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