Notes

Chapter 10: Processes of Perception and Analysis

Section 1: Introduction

Section 2: What Perception and Analysis Do

Section 3: Defining the Notion of Randomnesshttps://www.wolframscience.com/nks/chap-10--processes-of-perception-and-analysis--notes#sect-10-3--defining-the-notion-of-randomness

Algorithmic information theory

History [of randomness definitions]

Inevitable regularities and Ramsey theory

Section 4: Defining Complexityhttps://www.wolframscience.com/nks/chap-10--processes-of-perception-and-analysis--notes#sect-10-4--defining-complexity

History [of complexity definitions]

Section 5: Data Compressionhttps://www.wolframscience.com/nks/chap-10--processes-of-perception-and-analysis--notes#sect-10-5--data-compression

Practicalities [of data compression]

History [of data compression]

Number representations

Lengths of [number] representations

Completeness [of number representations]

[Number representations in] practical computing

Run-length encoding

Maximal block compression

Arithmetic coding

Pointer-based encoding

Recursive subdivision [encoding]

2D run-length encoding

Section 6: Irreversible Data Compressionhttps://www.wolframscience.com/nks/chap-10--processes-of-perception-and-analysis--notes#sect-10-6--irreversible-data-compression

History [of irreversible data compression]

Orthogonal bases

Walsh transforms

Hadamard matrices

Image averaging

Practical image compression

Fourier transforms

JPEG compression

Sound compression

Section 7: Visual Perceptionhttps://www.wolframscience.com/nks/chap-10--processes-of-perception-and-analysis--notes#sect-10-7--visual-perception

The visual system

Feedback [in visual processing]

Scale invariance [in vision]

History [of vision research]

Implementation [of texture perception model]

Testing the [texture perception] model

Related [texture perception] models

Image processing

Statistical methods [for texture analysis]

Generating textures

Perception and presentation

Section 8: Auditory Perceptionhttps://www.wolframscience.com/nks/chap-10--processes-of-perception-and-analysis--notes#sect-10-8--auditory-perception

$Diffraction patterns$

Auditory system

History [of auditory perception]

Implementation [of sound]

[Sounds based on] time variation

[Sounds based on] musical scores

Recognizing repetition [in sounds]

Sound compression

Spectra [of sequences]

Spectra of substitution systems

[Sequences with] flat spectra

Nested vibrations

[Spectra of] random block sequences

Spectra of cellular automata

Diffraction patterns

Section 9: Statistical Analysishttps://www.wolframscience.com/nks/chap-10--processes-of-perception-and-analysis--notes#sect-10-9--statistical-analysis

History [of statistics]

Practical statistics

Origin of probabilities

Probabilistic models

Binomial distribution

Estimation of parameters [in probabilistic models]

Complexity of models

Markov processes

[Models involving] non-local processes

Block frequencies [in sequences]

Entropy estimates [for sequences]

Tests of randomness

Difference tables

Randomized algorithms

Section 10: Cryptography and Cryptanalysishttps://www.wolframscience.com/nks/chap-10--processes-of-perception-and-analysis--notes#sect-10-10--cryptography-and-cryptanalysis

History [of cryptography]

Basic theory [of cryptography]

[Redundancy in] text

Linear feedback shift registers

LFSR cryptanalysis

Rule 30 cryptography

[Cryptographic] properties of rule 30

Directional sampling [in cellular automata]

Alternative rules [for cryptography]

Nonlinear feedback shift registers

Backtracking [in cellular automata]

Deducing cellular automaton rules

[Cryptanalysis of] linear congruential generators

Digit sequence encryption

Problem-based cryptography

Factoring integers

RSA cryptography

Quadratic residue sequences

Section 11: Traditional Mathematics and Mathematical Formulashttps://www.wolframscience.com/nks/chap-10--processes-of-perception-and-analysis--notes#sect-10-11--traditional-mathematics-and-mathematical-formulas

Practical empirical mathematics

Difference tables and polynomials

Implementation [of repetitive array]

Nested patterns and numbers

Implementation [of finite automata for nested patterns]

[Patterns from] arbitrary digit operations

Generating functions [for nested patterns]

Pascal's triangle

Nesting in bitwise functions

Trinomial coefficients

Gegenbauer functions

Standard mathematical functions

[Generating functions for] 1D sequences

Multidimensional additive rules

Continuous generalizations [of additive rules]

Nested continuous functions

Power cellular automata

Computing powers [of numbers]

Complex powers [of numbers]

[Algebraic computation of] additive cellular automata

The more general case [of computation speed ups]

Evaluation chains

Boolean formulas

DNF minimization

[Boolean] formula sizes

Cellular automaton [Boolean] formulas

Primitive [Boolean] functions

Multilevel [Boolean] formulas

Nand expressions

Cellular automaton [Nand] formulas

Binary decision diagrams

History [of Boolean functions]

Reversible logic

[Reduced formulas in] continuous systems

Section 12: Human Thinkinghttps://www.wolframscience.com/nks/chap-10--processes-of-perception-and-analysis--notes#sect-10-12--human-thinking

History [of ideas about thinking]

The future [of machine thinking]

Pointer encoding [and memory]

[Identifying] similar words

[Memory analogs with] numerical data

Error-correcting codes

Matrix memories

Neural network models

[Cognitive] child development

Computer interfaces

Context-free languages

[Computer and human] languages

Computer language fluency

Human generation of randomness

Games between programs

Section 13: Higher Forms of Perception and Analysishttps://www.wolframscience.com/nks/chap-10--processes-of-perception-and-analysis--notes#sect-10-13--higher-forms-of-perception-and-analysis

Biological [forms of] perception

Evolving to predict [data]

Familiar features [of perceived data]

Relativism and postmodernism