What We've Learned from NKS Chapter 11: The Notion of Computation

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 0:55 Stephen begins talking 3:49 Section 1: Computation as a Framework 4:43 Section 2: Computations in Cellular Automata 10:15 Section 3: The Phenomenon of Universality 14:41 Section 4: A Universal Cellular Automaton 20:57 Section 5: Emulating Other Systems with Cellular Automata 30:54 Section 6: Emulating Cellular Automata with Other Systems 41:17 Notes from Sections 1 - 7 51:13 Section 7: Implications of Universality 53:14 Section 8: The Rule 110 Cellular Automaton 59:43 Notes 1:02:36 Section 9: The Significance of Universality in Rule 110 1:03:14 Section 10: Class 4 Behavior and Universality 1:05:25 Section 11: The Threshold of Universality in Cellular Automata 1:19:10 Notes 1:22:56 Section 12: Universality in Turing Machines and Other Systems 1:31:53 Notes 1:40:32 Wrapping up Chapter 11 1:42:52 Are "all universal cellular automatons irreducible?" i.e is it impossible to jump ahead to know the answer of the computation? 1:43:58 What is the longest computation on any one rule? 1:45:07 What's the difference between computation that takes place in nature and computation in manmade machines? 1:47:20 This is fascinating, just as a concept. Computing systems being universal seems logical, what would it even mean if it wasn't. Or if a new computing system could emulate the regular ones but not the other way around? 1:49:13 Is there a relationship between computational universality and Penrose's triangle of mind, mathematics, and the physical world? In his world, a tiny part of each world encompasses all of the next world, bound into an impossible triangle. Are each of these worlds somehow a representation of computational universality? 1:50:58 Is there "anything" that a universal computer cannot do? Or is "everything" defined by that which can be computed by a universal computer? 1:51:13 ​Rule 110 can emulate rule 54 ​but can rule 54 emulate rule 110? 1:51:29 What would be required to prove the Universe is Turing complete? 1:55:36 Looking forward 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/