NEW VIDEO: Goodstein Sequence
Added 2024-11-26 18:41:31 +0000 UTChttps://www.youtube.com/watch?v=0Le7NgS-wO0
Comments
I see. So, I made a mistake in the order of operation for the exponent. Thank you!
Hitoshi Yamauchi
2024-11-27 18:48:50 +0000 UTC3^3^3 is 3^27 - not 27^3
Numberphile
2024-11-27 17:55:04 +0000 UTCUnfortunately, I didn't get this. At 1:35, Is 3^3^3 equal to 19,683? It's just 27^3, which should be less than 100^3, which is one million. I think 3^3^3^3 is equal to 7,625,597,484,987. Is it really 3^3^3?
Hitoshi Yamauchi
2024-11-26 22:48:42 +0000 UTCThe Wikipedia page mentions Dr. Goodstein! https://en.wikipedia.org/wiki/Knuth%27s_up-arrow_notation
Patrick W. Gilmore
2024-11-26 20:28:39 +0000 UTCI never did get "arrow notation" (Knuth arrows). Now I have to go back and watch the Graham's Number video to learn about them.
Patrick W. Gilmore
2024-11-26 20:24:52 +0000 UTCNice video! It reminded me of the recently discovered "Antihydra" sequence, of which it is unknown - unlike the Goodstein sequences - whether it will ever halt or not: "Starting with the number 8, repeatedly add the number, divided by 2 (rounded down) to itself. So 8 -> 12 -> 18 -> 27 -> 40 -> 60 -> ... The resulting numbers are either even or odd. Will you eventually reach a number where you have generated more than twice as many odd as even numbers? If so, stop." If it does, this may take even more steps than any of the numbers mentioned in the video! It is the first/shortest unsolved turing machine (with only 6 states) and its mathematical and programmatic descriptions are equally very short. Yet, none of the researchers I've talked to expect it to be solved within the next 5 years! https://bbchallenge.org/antihydra https://www.sligocki.com/2024/07/06/bb-6-2-is-hard.html
coda
2024-11-26 19:38:43 +0000 UTC
