Survey of COMP 006 Time to Remember …

Turing Machine definition (why TM?) Turmites Conway’s Game of Life Program Turing machines in class –Does input have “a” in it –Is input of form w_w for binary w –Others (including HW 1 - 3) Extensions and Restrictions of TM Decidability Partial Decidability

Church-Turing Thesis Universal Turing Machines Small Universal Turing Machines Undecidability of halting problem Blank tape halting problem Busy beaver function (uncomputable) Busy Beaver machine simulations Chaitin’s omega (uncomputable)

Paradox of consciousness –Loop testing version –Four possible solutions Quotes from Lucas, Penrose, Ramanujan Simulate student’s turmites from hw4 Hypercomputation Wave particle duality Double slit experiment Schroedinger’s Cat Uncertainty Principle

Tunneling and Solar Energy Quantum Superposition Kieu’s Algorithm Decoherence C60, C70 molecules as waves Feynman: Quantum wierdness Faster than light travel Quantum entanglement Quantum computation (brief)

Consciousness and time Left and right brains and consciousness Poincare and Mozart’s inspiration Einstein and nonverbal thought Inspiration in animals Is language necessary for consciousness? Logic Interpretations, models, truth Validity in a logic

Standard Interpretation Theorem Prover for a logic Aristotelian logic (syllogisms) Deciding syllogisms with Venn diagrams Geometry – two axiom systems Propositional calculus Truth Tables

First-order logic –For all –There exists –Translations into English Peano arithmetic and induction Zermelo-Fraenkel set theory Nonstandard interpretations Nonstandard integers Statement  H(T j,j) true but not provable in L, asserts its own unprovability

New form of paradox in terms of logics –We can know a statement L cannot derive Independent statements about program complexity –Large number of them 2001 A Space Odyssey