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LessWrong (Curated & Popular)
“A computational no-coincidence principle” by Eric Neyman
Feb 19, 2025
Eric Neyman, author and thinker in mathematics, dives into intriguing ideas about the no-coincidence conjecture. He explores why mathematicians often believe in unproved truths, using the example of pi's normality. The conversation uncovers Neyman’s computational perspective on this conjecture, highlighting its relevance to reversible circuits and theoretical computer science. Listeners are treated to insights on how mathematicians assess probabilities of unconfirmed statements and the philosophical implications that follow.
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Quick takeaways
- The no-coincidence principle suggests that extraordinary coincidences in mathematics require underlying explanations, as seen in the belief surrounding the normality of pi.
- The computational no-coincidence conjecture emphasizes that significant properties in reversible circuits point towards structured explanations, enhancing understanding of surprising computational outcomes.
Deep dives
Understanding the No-Coincidence Principle
The no-coincidence principle posits that if an extraordinary coincidence occurs within mathematics, there should be an underlying reason explaining it. This principle arises in the context of beliefs surrounding mathematical entities, such as the assertion that the number pi is likely normal, despite its unproven status. Specifically, the idea is articulated that, without evidence suggesting otherwise, any anomalies regarding the distribution of digits in pi would be considered unlikely coincidences. This principle is further exemplified through historical mathematical occurrences, like Chebyshev's bias regarding prime numbers, where understanding the heuristic behind the occurrence supports the no-coincidence principle.
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