The Entire History of Large Numbers

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Sources and music:
demonin.com/math/historyOfLar...
Videos linked to in this video:
• How To Count Past Infi...
• The Boundary of Comput...
• how floating point works
• Monumentality
Chapters:
00:00:00 Introduction
00:01:20 Section 1: Early History (Pre-1200 AD)
00:02:19 I: Notched bones (44,200 BC - 3400 BC)
00:03:26 II: Sumer (3400 BC - 1500 BC)
00:06:02 III: Assyrian Babylon (1500 BC - 300 BC)
00:06:57 IV: Ancient Egypt (3000 BC - 300 BC)
00:08:23 V: Roman Numerals (500 BC)
00:10:00 VI: Vinculum (~40 BC)
00:12:58 VII: Greek Numerals (600 BC - 0 AD)
00:15:29 VIII: The Sand Reckoner (~250 BC)
00:17:47 IX: Indian Texts (1200 BC - 250 AD)
00:19:54 X: Buddhāvataṃsaka Sūtra (20 AD - 800 AD)
00:27:28 XI: JAIN: THE NUMERABLE (Part 1)
00:30:22 XII: JAIN: THE INNUMERABLE (Part 2)
00:33:42 XIII: JAIN: THE INFINITE (Part 3)
00:36:09 XIV: Some Notes
00:38:49 Section 2: Early Modern History (1200-1970)
00:39:10 XV: The Wheat and Chessboard Problem (1256)
00:40:27 XVI: π
00:43:02 XVII: The computer era of pi
00:45:46 XVIII: Googol and Googolplex (1920)
00:47:46 XIX: The -illions (1270)
00:50:06 XX: Extended -illions
00:52:26 XXI: Tetration (1874)
00:56:56 XXII: Hyperoperators, Ackermann, and Steinhaus (1928)
01:00:49 XXIII: Goodstein Sequences (1944)
01:03:44 XXIV: The Fast-Growing Hierarchy (1970)
01:04:57 Intermission: Infinity and Ordinals
01:05:46 XXV: The Fast-Growing Hierarchy (Again)
01:09:01 Section 3: The Post-Computer Era (1970 onwards)
01:09:47 XXVI: Graham’s Number (1977)
01:11:11 XXVII: When the Beaver is Busy 😳 (1962)
01:16:58 XXVIII: Floating Points and Number Libraries (1985)
01:21:14 XXIX: The Bignum Bakeoff (2001)
01:25:36 XXX: Array Notation (2002)
01:28:43 XXXI: Rayo’s Number (2007)
01:33:29 XXXII: Some Other Things that are Confusing™
01:37:24 XXXIII: Limits in the Garden of Large Numbers
01:41:53 XXXIV: So Long, and Thanks for All the Fish

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Опубликовано:

17 июл 2024

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Комментарии : 63

@idonothavealife Месяц назад

This feels like an upload from a 1M sub channel, not 1.5K.

@Patashu 7 месяцев назад

Guess what I'm going to be doing for the next 1 hour, 43 minutes and 15 seconds exactly

@kekevids134 7 месяцев назад

hi ad and baba is you person

@tylerlarsen1842 2 месяца назад

A few years ago, I engaged in a comment thread with the creator of the LNGN to try and gain even the smallest understanding of what the hell it was even trying to do. As stated in the video, Rayo's number diagonalizes over the first-order logical deductions of set theory. Even when limiting ourselves to ten thousand first-order characters, the numbers that can be defined GREATLY surpass the maximum shifts function, and Rayo's number calls for a googol characters. Now, it is stated in the video that this could also be defined for second-order logic, third-order logic, and so on and so forth. What the LNGN does is group all of those nth-order theories into a "universe", and then uses that as the base for another hierarchy of set theory logic to be grouped into another universe, rinse and repeat. The creator calls this "First-Order Theory Beyond Higher-Order Set Theory", as in, it completely TRANSCENDS traditional set theory. He literally created the set theory multiverse just to define this one unfathomable number. The scale of this number is so far beyond even Rayo's number that whichever set theory you decide to use as the base for the LNGN calculations literally doesn't even matter, as opposed to Rayo's number where it does have a significant impact. And I can confirm that the creator is VERY picky about formal definitions.

@mrredshark77 7 месяцев назад

*woah big number dude* and the video is perfect

@godofnumbersakausername5226 6 месяцев назад

Balance RGCI

@jaytout2224 6 месяцев назад

Omg it’s mrredshark77

@MrMrPurple 2 месяца назад

The views on this video should be a large number

@asheep7797 Месяц назад

The first large number was 2. So yeah, I'd say 2,701 is large.

@godofnumbersakausername5226 11 дней назад

@@asheep7797 Well that's what Sbiss Saibian calls "Large" but the meaning of a "Large Number" is arbitrary as it depends on what you are measuring. If it is the amount of money you make per second, 0.1 would be super large. But if you are measuring the volume of different planets with cubic planck lengths, then something like a decillion would be a tiny number. However, in the context of being the views of a RU-vid video, a large number would probably be a number = or > than 1M.

@MrMrPurple 6 дней назад

@@asheep7797fair enough

@BusybeaverG64 14 дней назад

Esto necesita mas visitas, esta es una joya, muy completo video y calidad en cada instante

@shiaidk 7 месяцев назад

i blinked and i'm in late 2023 with a near 2 hour demonin video what timeline am i in

@LiMetzo 29 дней назад

Greatest video about Large Numbers, G.O.A.T. video

@BusybeaverG64 14 дней назад

This video is a gem, it deserves much more support

@crannmarbh8559 12 дней назад

genuinely incredible video. introduced me to an entirely unfamiliar field of study that, while i don’t comprehend most of it, is nonetheless utterly fascinating to me. i definitely see the solar sands influence, and i would say this holds up to the quality of monumentality.

@justagoosethatsall 14 дней назад

this video is so 💀💣❗🎺ing amazing you dont even know this needs more views, you need more subs, please keep doing awesome videos like this. you have earned my subscription.

@Wendroners Месяц назад

Has to be the highest quality large number related video I've seen on this site, enjoyed the thorough research+trivia and it came as a surprise that you were the one who wrote the JPA article lol Although here's a thing I noted: You've noted in the video that deep-end of the ordinals were a bit out of scope knowledge-wise and I'd say the wiki user Hyp cos' "comparison to ordinal collapsing function" blog post series gives enough grasp to explain (understand at the very least maybe?) how the ordinals collapse imo - a tiny introduction to ordinals in googological context would have been nice, when I delved my feet into this whole jazz, Vsauce vid was of no help. Great presentation nonetheless 🍻