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Survey of COMP 006

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

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Survey of COMP 006

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  1. Survey of COMP 006 Time to Remember …

  2. 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

  3. 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)

  4. 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

  5. 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)

  6. 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

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

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

  9. 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

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