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Questions Considered

Explore the abstract sense of computation, the capabilities and limitations of computers, the importance of Turing machines, unsolvable problems, Goedel's theorem, and the relationship between human minds and machines.

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Questions Considered

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Presentation Transcript

  1. Questions Considered • What is computation in the abstract sense? • What can computers do? • What can computers not do? (play basketball, reproduce, hold a conversation, …) • What is a Turing machine and why is it important?

  2. Why is a Turing machine a universal computing device? • Why is the halting problem unsolvable by a computer? • Why are other problems unsolvable by a computer? • How can one classify non-halting Turing computations? • Can a computing device be more powerful than a Turing machine?

  3. Could quantum mechanics lead to such a device? • Could faster than light transmission lead to such a device? • How are formal logics inherently limited by Goedel’s theorem? • What are the consequences of this limitation? • How many true, unprovable statements are there?

  4. Why aren’t true, unprovable statements more of a problem for mathematics? • Is the human mind more powerful than a Turing machine? • Is Goedel’s theorem related to this question? • Is human consciousness related to this question? • Do humans have mathematical intuition that cannot be expressed in formal logic?

  5. Why can’t formal logic fully capture the concepts of • finiteness • integers • infinities beyond the integers • Can a computer be conscious? • Can a computer understand?

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