What happens at the Boundary of Computation?

The machine learning consultancy: https://truetheta.io Join my email list to get educational and useful articles (and nothing else!): https://mailchi.mp/truetheta/true-theta-email-list In this video, we look inside the bizarre busy beaver function. SOCIAL MEDIA LinkedIn : https://www.linkedin.com/in/dj-rich-90b91753/ Twitter : https://twitter.com/DuaneJRich Github: https://github.com/Duane321 Enjoy learning this way? Want me to make more videos? Consider supporting me on Patreon: https://www.patreon.com/MutualInformation REFERENCE NOTES As mentioned, [1] was the primary source. The first video and this one were originally inspired by reading [1], so many of the ideas can be traced to that point. Anyone still interested should continue their search there. Sources [3]-[4] were essential for understanding the exact nature of the busy beaver and champion machines. In fact, I should have also thanks Pascal Michel in the video. He has maintained a detailed recorded of which machines were champions at which points and I found myself referencing it regularly. Sources [5]-[7] plus some conversations with the author were essential for my understanding of the Collatz-like behavior. REFERENCES [1] S. Aaronson, "The Busy Beaver Frontier", https://www.scottaaronson.com/papers/bb.pdf [2] T. Radó. "On non-computable functions". Bell System Technical Journal. 41 (3): 877–884, 1962 [3] P. Michel. "The Busy Beaver competition: a historical survey". 2019. https://arxiv.org/abs/0906.3749 [4] P. Michel. "Problems in Number Theory from the Busy Beaver Competition". Logical Methods in Computer Science Vol. 11(4:10), pp. 1–35, 2015 [5] S. Ligocki, "BB(6, 2) is greater than 10^10...^10", 2022, https://www.sligocki.com/2022/06/21/bb-6-2-t15.html [6] S. Ligocki, "Collatz-like behavior of Busy Beavers", 2021, https://www.sligocki.com/2021/07/17/bb-collatz.html [7] S. Ligocki, "BBB Complex Collatz-like Behavior", 2021, https://www.sligocki.com/2022/02/22/collatz-complex.html TIME CODES 0:00 Introduction 0:42 Reviewing the Basics 2:11 How does it grow faster than anything computable? 2:58 Using Collatz for Absurd Growth 3:59 Collatz in the 5-state machine 7:31 Exponential Collatz in the 6-state machine 9:05 The Busy Beavers answer famous open problems 11:23 The Busy Beavers are unknowable by any mathematical system 14:10 The Conjectures 14:26 Thank You's