Turing Diagrams: Systems of Calculus Based on Ordinal Logics Pubblico
Haig, Asher Dreskin (2014)
Published
Abstract
Alan Turing effectively created the foundation for the modern computing age. The imitation game, more commonly known and frequently dismissed in a severely reduced form as the "Turing Test", is the heart of Turing's endeavors. The imitation game consolidates Turing's previous work with computability, universal machines, ordinal logic, cryptography, and intelligent machines. It also functions as the predecessor to Turing's subsequent work in applied biochemistry known as "morphogenesis". This text examines Turing's imitation game in detail, following its cumulative development through eight distinct iterations. The iterations are shown to be developmentally related, and the imitation game is shown to be a problem of determination that constitutes the core of Turing's work with artificial intelligence by extending his earlier work with the universal machine to a context that concerns the space of interaction between multiple machines.
Table of Contents
Introduction
Turing Machines 1
The Universal Machine
λ: A Definition for "Algorithm" 12
A: Problem 15
B: Structure 28
C: Condition 45
The Imitation Game
Mλ0: A Mathematical Meta-Model 54
Diagram: Turing's Imitation Game 57
A: Dynamic 58
Diagram: Figure A 60
B: Distribution 66
Diagram: Figure B 66
C: Context 70
Diagram: Figure C 72
Chapter 1
Actuality 76
Diagram: An n-Bodies Problem 79
Diagram:Nodes of Adhesion 81
Diagram: Incommensurate Modes 83
System
Mλ1: Computability 85
Diagram: Iteration A 87
Diagram: Substitution A 89
A: Consistency 91
Diagram: Machine A 94
B: Dimension 98
Diagram:Figure B 100
C: Direction 112
Diagram: Figure C 114
Syntax
Mλ2: Computation 116
Diagram: Iteration B 118
Diagram: Substitution B 119
A: Reference 120
Diagram: Machine A 121
B: Action 126
Diagram: Machine B 129
C: Intelligibility 131
Diagram: Figure C 131
Statement
Mλ3: Computable Number 135
Diagram: Iteration C 138
Diagram: Substitution C 142
A: Composition 143
Diagram: Figure A 143
Diagram: Machine A 144
Diagram: Machine C 145
Diagram: Machine C--A 146
B: Contingency 148
Diagram: Figure B 152
Diagram: Figure C 153
C: Expression 159
Diagram: Machine C 159
Diagram: Machine A 163
Chapter 2
Potentiality 165
The Image of Thought
M: The Pivot 167
A: Indeterminacy 170 B: Model 174 C: Ordinal Topology 178
Selection
Mλ4: Ramified Time 185
Diagram: Iteration C` 188
Diagram: Substitution C` 190
A: Incompleteness 191
Diagram: Machine A--B 192
Diagram: Machine A--C 193
B: Intuition 198
Diagram: Machine B--A 200
Diagram: Machine B--C 205
C: Reversibility 210
Diagram: Machine C--A 211
Diagram: Machine C--B 213
Chapter 3
Potential 228
Intrinsic Consistency
Mλ5: Terms of Dialogue 240
Diagram: Iteration C--C` 243
A: Artifice 247
Diagram: Machine A--B--Å 249
Diagram: Machine A--C--Å 250
B: Edifice 254
Diagram: Machine B--A--B 254
Diagram: Machine B--C--B 255
C: Intellection 262
Diagram: Machine C--B--C 264
Diagram: Machine C--A--C 265
Extrinsic Consistency
Mλ6: Encapsulation 270
Diagram: Iteration M--M` 274
A: Domain 275
Diagram: Machine A--B--C--B 276
Diagram: Machine A--C--B--C 278
Diagram: A-Type Machines 288
Diagram: B-Type Machines 289
B: Institution 290
Diagram: B-Type Machines Linearized 290
Diagram: B-Type Machine Example 294
Diagram: Machine B--A--C--A 295
Diagram: Machine B--C--A--C 298
C: Encounter 301
Diagram: Machine C--A--B--A 303 Diagram: Machine C--B--A--B 305
Conclusion
Turing Circuits 313
Halting Conditions
Mλ7: Iteration 316
Diagram: Iteration M`--M`` 318
A: Zero 333
Diagram: Machine A Extrinsic Articulation 334
Diagram: Machine A Intrinsic Determination 336
B: Non-Zero 340
Diagram: Machine B Extrinsic Articulation 342
Diagram: Machine B Intrinsic Determination 344
C: Continuity 349
Diagram: Machine C Extrinsic Articulation 352
Diagram: Machine C Intrinsic Determination 359
Synchronization
Mλ8: Iterability 360
Diagram: M--M`--M``--M 362
A: Catalysis 373
Diagram: Machine A Intrinsic Consistency 380
Diagram: Machine A Extrinsic Consistency 383
B: Reaction Potential 385
Diagram: Machine B Intrinsic Consistency 397
Diagram: Machine B Extrinsic Consistency 399
C: Opinion 412
Diagram: Machine C Intrinsic Consistency 417
Diagram: Machine C Extrinsic Consistency 422
Works Cited 432
Other Relevant Works 436
Endnotes 441
About this Dissertation
School | |
---|---|
Department | |
Degree | |
Submission | |
Language |
|
Research Field | |
Parola chiave | |
Committee Chair / Thesis Advisor | |
Committee Members |
Primary PDF
Thumbnail | Title | Date Uploaded | Actions |
---|---|---|---|
|
Turing Diagrams: Systems of Calculus Based on Ordinal Logics () | 2018-08-28 12:44:01 -0400 |
|
Supplemental Files
Thumbnail | Title | Date Uploaded | Actions |
---|