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.
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.
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 🍻
@@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.
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.
