Stephen Wolfram's A New Kind of Science | OnlineA New Kind of Science | Online
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Chapter 10
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Preface
1
The Foundations for a New Kind of Science
1
An Outline of Basic Ideas
2
Relations to Other Areas
3
Some Past Initiatives
4
The Personal Story of the Science in This Book
2
The Crucial Experiment
1
How Do Simple Programs Behave?
2
The Need for a New Intuition
3
Why These Discoveries Were Not Made Before
3
The World of Simple Programs
1
The Search for General Features
2
More Cellular Automata
3
Mobile Automata
4
Turing Machines
5
Substitution Systems
6
Sequential Substitution Systems
7
Tag Systems
8
Cyclic Tag Systems
9
Register Machines
10
Symbolic Systems
11
Some Conclusions
12
How the Discoveries in This Chapter Were Made
4
Systems Based on Numbers
1
The Notion of Numbers
2
Elementary Arithmetic
3
Recursive Sequences
4
The Sequence of Primes
5
Mathematical Constants
6
Mathematical Functions
7
Iterated Maps and the Chaos Phenomenon
8
Continuous Cellular Automata
9
Partial Differential Equations
10
Continuous Versus Discrete Systems
5
Two Dimensions and Beyond
1
Introduction
2
Cellular Automata
3
Turing Machines
4
Substitution Systems and Fractals
5
Network Systems
6
Multiway Systems
7
Systems Based on Constraints
6
Starting from Randomness
1
The Emergence of Order
2
Four Classes of Behavior
3
Sensitivity to Initial Conditions
4
Systems of Limited Size and Class 2 Behavior
5
Randomness in Class 3 Systems
6
Special Initial Conditions
7
The Notion of Attractors
8
Structures in Class 4 Systems
7
Mechanisms in Programs and Nature
1
Universality of Behavior
2
Three Mechanisms for Randomness
3
Randomness from the Environment
4
Chaos Theory and Randomness from Initial Conditions
5
The Intrinsic Generation of Randomness
6
The Phenomenon of Continuity
7
Origins of Discreteness
8
The Problem of Satisfying Constraints
9
Origins of Simple Behavior
8
Implications for Everyday Systems
1
Issues of Modelling
2
The Growth of Crystals
3
The Breaking of Materials
4
Fluid Flow
5
Fundamental Issues in Biology
6
Growth of Plants and Animals
7
Biological Pigmentation Patterns
8
Financial Systems
9
Fundamental Physics
1
The Problems of Physics
2
The Notion of Reversibility
3
Irreversibility and the Second Law of Thermodynamics
4
Conserved Quantities and Continuum Phenomena
5
Ultimate Models for the Universe
6
The Nature of Space
7
Space as a Network
8
The Relationship of Space and Time
9
Time and Causal Networks
10
The Sequencing of Events in the Universe
11
Uniqueness and Branching in Time
12
Evolution of Networks
13
Space, Time and Relativity
14
Elementary Particles
15
The Phenomenon of Gravity
16
Quantum Phenomena
10
Processes of Perception and Analysis
1
Introduction
2
What Perception and Analysis Do
3
Defining the Notion of Randomness
4
Defining Complexity
5
Data Compression
6
Irreversible Data Compression
7
Visual Perception
8
Auditory Perception
9
Statistical Analysis
10
Cryptography and Cryptanalysis
11
Traditional Mathematics and Mathematical Formulas
12
Human Thinking
13
Higher Forms of Perception and Analysis
11
The Notion of Computation
1
Computation as a Framework
2
Computations in Cellular Automata
3
The Phenomenon of Universality
4
A Universal Cellular Automaton
5
Emulating Other Systems with Cellular Automata
6
Emulating Cellular Automata with Other Systems
7
Implications of Universality
8
The Rule 110 Cellular Automaton
9
The Significance of Universality in Rule 110
10
Class 4 Behavior and Universality
11
The Threshold of Universality in Cellular Automata
12
Universality in Turing Machines and Other Systems
12
The Principle of Computational Equivalence
1
Basic Framework
2
Outline of the Principle
3
The Content of the Principle
4
The Validity of the Principle
5
Explaining the Phenomenon of Complexity
6
Computational Irreducibility
7
The Phenomenon of Free Will
8
Undecidability and Intractability
9
Implications for Mathematics and Its Foundations
10
Intelligence in the Universe
11
Implications for Technology
12
Historical Perspectives
Notes
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Chapter 10:
Processes of Perception and Analysis
Section 1:
Introduction
https://www.wolframscience.com/nks/chap-10--processes-of-perception-and-analysis#sect-10-1--introduction
Page 547
Notes
Section 2:
What Perception and Analysis Do
https://www.wolframscience.com/nks/chap-10--processes-of-perception-and-analysis#sect-10-2--what-perception-and-analysis-do
Page 548
Page 549
Page 550
Page 551
Notes
Section 3:
Defining the Notion of Randomness
https://www.wolframscience.com/nks/chap-10--processes-of-perception-and-analysis#sect-10-3--defining-the-notion-of-randomness
Page 552
Page 553
Page 554
Page 555
Page 556
Notes
Section 4:
Defining Complexity
https://www.wolframscience.com/nks/chap-10--processes-of-perception-and-analysis#sect-10-4--defining-complexity
Page 557
Page 558
Page 559
Notes
Section 5:
Data Compression
https://www.wolframscience.com/nks/chap-10--processes-of-perception-and-analysis#sect-10-5--data-compression
Page 560
Page 561
Page 562
Page 563
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Page 571
Notes
Section 6:
Irreversible Data Compression
https://www.wolframscience.com/nks/chap-10--processes-of-perception-and-analysis#sect-10-6--irreversible-data-compression
Page 572
Page 573
Page 574
Page 575
Page 576
Notes
Section 7:
Visual Perception
https://www.wolframscience.com/nks/chap-10--processes-of-perception-and-analysis#sect-10-7--visual-perception
Page 577
Page 578
Page 579
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Notes
Section 8:
Auditory Perception
https://www.wolframscience.com/nks/chap-10--processes-of-perception-and-analysis#sect-10-8--auditory-perception
Page 585
Page 586
Page 587
Notes
Section 9:
Statistical Analysis
https://www.wolframscience.com/nks/chap-10--processes-of-perception-and-analysis#sect-10-9--statistical-analysis
Page 588
Page 589
Page 590
Page 591
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Notes
Section 10:
Cryptography and Cryptanalysis
https://www.wolframscience.com/nks/chap-10--processes-of-perception-and-analysis#sect-10-10--cryptography-and-cryptanalysis
Page 598
Page 599
Page 600
Page 601
Page 602
Page 603
Page 604
Page 605
Notes
Section 11:
Traditional Mathematics and Mathematical Formulas
https://www.wolframscience.com/nks/chap-10--processes-of-perception-and-analysis#sect-10-11--traditional-mathematics-and-mathematical-formulas
Page 606
Page 607
Page 608
Page 609
Page 610
Page 611
Page 612
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Page 614
Page 615
Page 616
Page 617
Page 618
Page 619
Notes
Section 12:
Human Thinking
https://www.wolframscience.com/nks/chap-10--processes-of-perception-and-analysis#sect-10-12--human-thinking
Page 620
Page 621
Page 622
Page 623
Page 624
Page 625
Page 626
Page 627
Page 628
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Page 631
Notes
Section 13:
Higher Forms of Perception and Analysis
https://www.wolframscience.com/nks/chap-10--processes-of-perception-and-analysis#sect-10-13--higher-forms-of-perception-and-analysis
Page 632
Page 633
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Page 635
Notes
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