Remember Huge Numbers, a book I posted about in August? Graham’s Number is several chapters from the end.
I hadn’t then finished the book to get to Fish 7, which has a rigorously defined generation. Elwes works hard to try to convey a graspable sense of how such hugeness is mathematically conceived and developed, but the process becomes more and more abstract.
An interesting question is whether AI can develop an original way of generating even larger numbers. That to me would be more astounding than finding proofs of already known hypotheses.
At that scale one is no longer “generating” numbers, one is defining them. Such numbers count as integers only because they are provably finite, are the answer to a specific mathematical conjecture, and their magnitude can be defined. They’re beyond human comprehension otherwise. A few people claim that such mathematical entities aren’t really numbers in the common sense.
Indeed, Elwes addresses these concerns in his book. He takes them seriously as pathways into interesting mathematical issues, yet acknowledges that hugeness beyond hugeness can’t now be translated into anything meaningful outside of math.
Some of the concepts given in @Pardel-Lux’s link grew out of a bet between mathematicians over who could create a larger number. Recreational math has in the past led to deeper insights.
Look at John Horton Conway, who invented one of the ways to express extremely huge numbers on a page. He also crated the Game of Life, which led to cellular automata, and the surreal numbers, important to game theory, among a lifetime full of out-of-the-box insights.
IANAM, but I don’t think we can simply dismiss huge numbers as meaningless mathematical masturbation.
In fact, Graham’s Number is so big that if you were to continually repeat that process (# of digits in Graham’s Number, then the number of digits in that number, and so on), the number of steps it would take to finally get a result that would fit in the universe - wouldn’t fit in the universe.
For comparison, a Googolplex (1 followed by a googol of zeros) which is a fantastically large number, takes only two of the above steps to get a result that fits in the universe.
Pistachio shells go pop and split open as part of the ripening process. I always assumed the split shell happened as part of the post-harvesting process.
I’m pretty clueless about many showbusiness things, so this is not intended as a dig.
Doja Cat is a pop singer / performer. Yes, it’s a stage name.
I know of her only because her music plays now and again on my car’s entertainment system. Which like all modern systems, includes words and pictures about who / what is playing. So it told me that was “Doja Cat” singing. Who sounds good and looks kinda cute too.
I’m curious how you came to be aware of the name, but with no context? How else would one hear or read of “Doja Cat” without knowing who / what it was?
I’m one of those luddites who watches sports, not the shows about sports or the twitter feeds about sports or the [whatevers] about sports. Same with other sorts of entertainment and also factual stuff like news. I take mine straight from the source, or as close as I can get.
So I tend to forget there’s this ginormous overhang of people talking about what other people are talking about about something else happening and there’s a huge audience watching / reading all that talking about talking about.
Now that you remind me, yeah sure it makes sense that someone tracking a talking about talking about people talking source would tend to throw all sorts of new factoids your (or my) way with no context.
Truly we live in a strange and increasingly unfamiliar world.
I’m not suggesting my way is the better way. Just that it’s the one I use. So far.
