Discussion Overview
The discussion revolves around the existence of computable normal numbers, specifically whether any known examples exist and the implications of their existence on mathematical conjectures. The scope includes theoretical aspects of normal numbers and computability.
Discussion Character
- Debate/contested
- Technical explanation
Main Points Raised
- One participant questions the clarity of Wikipedia regarding known computable normal numbers and references a paper that may not be peer-reviewed.
- Another participant introduces the Champernowne constant as an example of a known normal number, asserting its computability and noting that it is normal in base 10.
- A later reply clarifies the definition of "computable" and discusses the existence of a super-exponential-time algorithm for computing Sierpinski's construction, while inquiring about polynomial-time computable normal numbers.
- One participant speculates that the existence of a polynomial-time computable normal number would not significantly impact existing mathematical conjectures, suggesting that many familiar constants are conjectured to be absolutely normal.
Areas of Agreement / Disagreement
Participants express differing views on the existence of computable normal numbers and their implications, with no consensus reached on whether a polynomial-time computable normal number is known.
Contextual Notes
Unresolved issues include the definitions of computability and normality, the status of the referenced paper, and the implications of the existence of computable normal numbers on conjectures.
Who May Find This Useful
Readers interested in theoretical computer science, number theory, and the properties of normal numbers may find this discussion relevant.