Featuring Tony Padilla. See all three videos in this Apocalyptic Trilogy ā https://bit.ly/ApocalypticTrilogy
More links & stuff in full description below āāā
The other two videos in this trilogy are:
Apocalyptic Numbers ā https://youtu.be/0LkBwCSMsX4
Primes and Fibonacci with 666 digits ā https://youtu.be/KXO2l7Kh60A
Extra James Stirling snippet ā https://youtu.be/I8qAp-DXWjw
Tony Padilla on Amazon ā https://amzn.to/3U6DRSM
(Check out āFantastic Numbers and Where to Find Themā)
See our 666 Playlist ā https://www.youtube.com/playlist?list=PLt5AfwLFPxWKqO-8qvPGPbYfLfzcdruBc
Bibledex ā https://www.youtube.com/user/bibledex
Big Numbers Playlist ā https://www.youtube.com/playlist?list=PLt5AfwLFPxWJ_FwchNAjB3xa8UnoKdmQI
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The picture of demon legions were AI generated and are not real demons.
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All three videos in this little trilogy at https://bit.ly/ApocalypticTrilogy
Proving 666!^(666!) > (100^666)! without using Stirling's formula.
Since 666! > 100*101*102…*666 > 100^500 = 10^1000 > 10^666, so 666!^(666!) > (100^666)^(10^666) > (100^666)!
That was awesome, i love these very huge numbers!
where i can i learm more
0:57 brother in christ please save that poor cable charger from that position
Go home math you're drunk
I get goofing around with devil numbers, but what use is super factorial?
Is there a paper on finding goliath numbers that is accessible?
Wow I found it. What? The number that I said to be significant only to let others know I found it.
It bothers me when people say stuff like that about doppelgangers. Assuming there were infinite universes, there's no reason to assume that you would have all possible configurations of matter. You could simply have an infinite number of universes with a single hydrogen atom, or any other arbitrary configuration.
"I went to the place where it happened." Well, no, no you didn't.
The way that phone charger is folded next to the laptop is so uncomfortable
Imagine if you subtract 1 from the smallest known Goliath number, you get a mersenne prime lol
I recognize that symbol for Goliath numbers- it's Gandalf's signature from Lord Of the Rings!
I love Tony Padilla and his big numbers. One of my favorite bits of numberphile
Hail Satan. 666
Wish I could clip the part about the devil 8:52 – 9:01 kinda epic line
Please, not with AI "art".
Interesting to see Dr. Rickert in this video. I studied under him, very briefly – never took a full class, but he went over answers to a Putnam competition and I watched him do math way over my head for about an hour.
So, does G666 catch up to Tree(3)? If not, do G of any of these numbers pull it off?
Of course, Tree(666), Tree(Leviathan), Tree(Legion), etc. are worth considering…
ANd perhaps Busy Beaver of 666 should be called Behemoth if that name isn't already taken among numbers or there's a demon associated with working hard.
This is just mathematical naval gazing. Imagining very large numbers isn't novel, it's an indication of the decline of academia if this is what passes for PhD material.
Why did Tony not round the Sterling approximation to 666×10^666?!?!
Iām kinda surprised nobody commented on (6^6)^6 as an apocalyptic number.
I laughed out loud at the definition of a super factorial. That's just ridiculous
Why aren't there any Behemoth numbers? If you are talking Biblical monsters and mention Leviathan, surely Behemoth should get a mention.
When people talk about the inevitability of duplicates in a sufficiently large universe (or similarly, the idea that every possible digit sequence might appear in pi), I'm never satisfied with the argument. I understand that a sufficiently large universe will have SOME duplicates… but then the next claim after that is that EVERYTHING has a duplicate. What's the missing step? I remain unconvinced. What's the problem here? Is it that there IS a rigorous proof but it's too hard to explain in informal ways so nobody's managed to communicate it yet?
Since Tony mentioned the Stirling approximation, this video ought to give an inspiration for another series of videos: interesting approximations in the world of mathematics. I know some approximations were covered in previous numberphile videos, but why not make a series out of them? Brady please do your magic!
John Rickert was once a professor of mine! He is such a sharp guy and a wonderful teacher. I remember that he held his students to a high standard, and his enthusiasm for math was very infectious to me.
Are there an infinite number of weird numbers and sequences?
Battle of David and Goliath happened? Nah it didnt. The bible is just fairy tales
People complaining about "this is too arbitrary" are missing the point. These exercises are for finding ways to work with large numbers in a way our minds can understand. Like…infinity is really, really, really big. There's an infinite number of infinities within infinite. Picking a number like 666 can help us look for patterns in something that's otherwise complete gibberish to the human brain.
There's obviously practical applications for infinite, but it often becomes so abstract we forget what it actually means. Taking a tiny, teeny sliver of it helps our understanding of large numbers.
It's nice to know even Tony crashes computers trying to compute numbers. It's not just me! He even crashed his paper…
New numbers dropped š„š„š„
Hey, those images for the legion numbers seem to have been created with generative AI. Is that so?
Since it appears in the last 3000 digits, and they don't know if it's the smallest. I'm guessing that they discovered it by only keeping the last ~3000 digits for each multiplication of 2, and they just kept going until the goliath sequence appeared? So it's proof of a goliath number, but they only checked the last ~3000 digits of each value of 2^n. Probably used a higher digit count than 3000 to check, but it illustrates my point.
I think there is an easier proof that super legion is bigger than leviathan
10^666! < (10^666)^(10^666)<(666!)^(666!)
7:20 Since we're just looking for a comparison, there's a much easier approach that doesn't require Sterling's approximation. By considering the expanded form, one can see (1E666)! is significantly less than (1E666)^(1E666). Then we can take the logarithm: log((1E666)^(1E666)) = 1E666 * log (1E666) = 1E666 * 666, which is clearly less than the other log value, ~1.6E1596 (at 7:02).
I wonder what this channel is going to do on April 20
Another fun way of generating these devilish numbers would be 666 pentated 666 times. Should be a much bigger number!
EDIT: 11:00 Side note, looks like the Superfactorial is just a specific type on tetration, one stage lower than pentation!
I have solved continuum hypothesis problem , please refer to research gate with title : Foundation and logic of set theory , replacing all relevant axiomatic system (ZFC or arithmetic) with solution to Russell's paradox , solving continuum hypothesis , DOI: 10.13140/RG.2.2.23990.31045
INDETERMINACY OF All-Power Measurement. Correct me if Im wrong š
10:42 sums up the whole video
Please don't use AI art. It's made through theft of artists' labour. The only way for to get a data pool large enough to create them is by scraping the internet, which not only violates the rights of artists, but also leads to the data pool including private and sensitive images, medical records, as well as material like CSEM. Nothing about how AI art is made is ethical.
"My name is legion" appears somewhere in the bible. (Lucifer is speaking, or one of his minions, as I recall.)
It was stated that Graham's Number is larger than the numbers mentioned in this video, but Graham's Number is notated as G64 because it is the sixty-fourth number in the defining sequence. Would there be any apocalyptic significance of the number G666 in that defining sequence? Would there be any apocalyptic significance in using the number 666 rather than three in defining the sequence analogous to the sequence used in defining Graham's Number?
"Devil sized region of space" would be a great album name