What We've Learned from NKS Chapter 6: Starting from Randomness

Описание: 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:   / stephen_wolfram  

Read all of NKS here: https://www.wolframscience.com/nks/


00:00 Stream Begins
4:19 SW begins talking
7:30 Section 1: The Emergence of Order
11:30 Section 2: Four Classes of Behavior
33:08 Section 3: Sensitivity to Initial Conditions
40:30 Section 4: Systems of Limited Size and Class 2 Behavior
51:01 Section 5: Randomness in Class 3 Systems
1:00:09 Section 6: Special Initial Conditions
1:12:49 Section 7: The Notion of Attractors
1:24:25 Section 8: Structures in Class 4 Systems
1:35:10 Wrap up Chapter 6
1:36:50 For rule 110 the growth is polynomial. The universe itself does not seem to be ergodic and does not trace out an exponential space of possibilities, given that the data that we do encode is very "compressible". Could it be the case that P!=NP, yet we can solve problems efficiently because the universe does not sample phase space exponentially but polynomially?
1:37:34 ​Do you know which rules make random behaviour, is there some pattern in the rule itself, such that; when you look at the rule, you know that it must produce some random behaviour?
1:38:54 Would a black hole be an attractor in this case in a literal sense?
1:40:05 Imagine a plane of random black and white cells. Could you create a CA type program which applies its rules by looking into the unpredictable future of a neighborhood instead of the determined past?
1:41:06 Those cellular evolve vertically according to deterministic rules. What if we read them horizontally? Is there some randomness arising from that ?
1:41:43 Because of Gödel's 1st & 2nd incompleteness theorems, is a continuous structure always mathematically ambiguous?
1:42:25 Have you noticed any cellular automata that display Penrose tiling characteristics?
1:43:02 if it's truly random can you actually assign meaningful value/ nomenclature to it?

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