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Questions Considered

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?. Why is a Turing machine a universal computing device?

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Questions Considered

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  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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