What We've Learned from NKS Chapter 12: The Principle of Computational Equivalence [Part 1]

In this episode of "What We've Learned from NKS", Stephen Wolfram is counting down to the 20th anniversary of A New Kind of Science with [another] chapter retrospective. If you'd like to contribute to the discussion in future episodes, you can participate through this YouTube channel or through the official Twitch channel of Stephen Wolfram here: https://www.twitch.tv/stephen_wolfram/ Read all of NKS here: https://www.wolframscience.com/nks/ 00:00 Stream Begins 1:30 Stephen begins talking 7:36 Section 1: Basic Framework 9:20 Section 2: Outline of the Principle 15:14 Section 3: The Content of the Principle 27:03 Section 4: The Validity of the Principle 41:40 Notes from Sections 1-4 1:00:45 Section 5: Explaining the Phenomenon of Complexity 1:01:57 Section 6: Computational Irreducibility 1:10:11 Notes 1:18:53 Section 7: The Phenomenon of Free Will 1:24:53 Notes 1:33:28 Section 8: Undecidability and Intractability 1:55:04 Notes 2:15:45 What's the difference between computation and physical process? 2:16:14 Does computational equivalence imply an mathematical equivalence between the observer and the universe? 2:16:29 Is computational irreducibility related to entropy? 2:17:03 ​Strange that there are no general methods for proving universality yet. Since for example NAND operation is universal, its easy to prove that by constructing other gates. So why is it so difficult? 2:17:46 ​What is the field of science that creates all those Curves they tried expanding Ruler and compass with? - Conchoid of Nicomedes. I saw Kempe linkages in the notes 2:18:39 Wrap Up 2:20:48 Stream Ends Follow us on our official social media channels. Twitter: https://twitter.com/WolframResearch Facebook: https://www.facebook.com/wolframresearch Instagram: https://www.instagram.com/wolframresearch/ LinkedIn: https://www.linkedin.com/company/wolfram-research/ Contribute to the official Wolfram Community: https://community.wolfram.com Stay up-to-date on the latest interest at Wolfram Research through our blog: https://blog.wolfram.com Follow Stephen Wolfram's life, interests, and what makes him tick on his blog: https://writings.stephenwolfram.com/