ON COMPUTABLE NUMBERS, WITH AN APPLICATION TO THE ENTSCHEIDUNGSPROBLEM (Turing 1936 paper)
Topics Related to Turing Machines
*Formal Definition of Turing Machines
*Transition Function, Instantaneous Descriptions, and Moves
*Turing Machines as Transducers
Turing Machines implemented in JavaScript (Examples)
TuringKara - two-dimensional Turing machines
Wolfram's Version of Turing machines
Two Dimensional Turing Machines (from Wolfram)
Langton's Ant (A two-dimensional Turing machine)
A random pattern produced by a Turmite
Turing Machine implemented in Conway's Game of Life
Patterns, Programs, and Links for Conway's Game of Life
*Variations on Turing Machines, Universal Turing Machines, Church-Turing Thesis
Recursively Enumerable Languages
!The Halting Problem and Other Unsolvable Problems
Uncomputable Functions and Church's Thesis
Uncomputability in the work of Turing and Penrose
Discussion of unsolvability of Hilbert's tenth problem
Bounds on the Busy Beaver Function
Proof of Uncomputability of the Busy Beaver Function
References on the Busy Beaver Function
Busy Beaver Function (Wolfram's Version)
Busy Beaver Candidates for 4-tuple Turing machines
Hypercomputation: computing more than the Turing machine
Decoherence in Large Molecules
Quantum computation: a tutorial
Quantum Leaps May Solve Impossible Problems
Quantum Algorithm for Hilbert's Tenth Problem
The quantum algorithm of Kieu does not solve the Hilbert's tenth problem
Light Exceeds Its Own Speed Limit, or Does It?
Is Faster Than Light Travel or Communication Possible?
Quantum Entanglement On A Chip Is Demonstrated
Applications of Quantum Entanglement
The Axioms of Euclid and Hilbert
Twenty Four Valid Categorical Syllogisms
First-order predicate calculus
Higher-order logic and nonstandard models
Gödel's incompleteness theorem
Gödel's Incompleteness Theorem
Discussion of Gödel's theorem and other incompleteness results
Algorithmic information theory
Gödel's Theorem and Information (Chaitin's View)
A Century of Controversy over the Foundations of Mathematics (Chaitin)
THE UNKNOWABLE (Ad for Chaitin book)
The Emperor's New Mind (Penrose book attaching foundations of AI)
Minds, Machines, and Mathematics
The Non-Algorithmic Character of Human Consciousness
Consciousness Involves Noncomputable Ingredients
Why Penrose is Wrong about the Computability of Human Mathematics
Questions Considered in This Course
Decidability and Partial Decidability
