I found this to be an extremely interesting read and decided that I'd share. Its fairly long but well worth it imo. No advanced math necessary.

My favorite part is his discussion of Busy Beaver numbers (btw, definitely the best mathematical term ever).

My favorite quote of his is not totally related to the topic of his article however here it is:

quote: But exponentials have a drearier side as well. The human population recently passed six billion and is doubling about once every forty years. At this exponential rate, if an average person weighs seventy kilograms, then by the year 3750 the entire Earth will be composed of human flesh.

quote: A biggest number contest is clearly pointless when the contestants take turns. But what if the contestants write down their numbers simultaneously, neither aware of the other’s? To introduce a talk on "Big Numbers," I invite two audience volunteers to try exactly this. I tell them the rules: You have fifteen seconds. Using standard math notation, English words, or both, name a single whole number—not an infinity—on a blank index card. Be precise enough for any reasonable modern mathematician to determine exactly what number you’ve named, by consulting only your card and, if necessary, the published literature.

posted
I think the cognitive principles of analyzing this stuff is the most interesting part. When I was reading through I grasped tetration just fine, but when I started thinking about pentation I couldn't get it to click, and I started thinking about my brain thinking (metacognation) and did some kind of mental yoga and everything worked. I think it's intensely cool how advanced a machine our brains are, and this article is a great exercise to test that, thanks for sharing.

Edit: I just realized I haven't posted in a while and my count must have been sitting at the mark of the beast for some time.
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There are a few other good ones, mostly much more obscure.

Also, I really like how the article mentioned Cantor's work on different sizes of infinities - it really is a mind boggling idea. The only thing more mind boggling than the fact that there is more than 1 infinity is the following:

there are SO many different infinities, that NONE of the infinities is large enough to describe the number of infinities there are.

Also, something not really mentioned in the article, there are 2 other ways of describing large numbers (that I'm familiar with):

posted
Awesome article! Thanks for linking. I sent it to 2 friends.

"Set a tape head loose on a sequence of symbols, and it might stop eventually, or it might run forever—like the fabled programmer who gets stuck in the shower because the instructions on the shampoo bottle read "lather, rinse, repeat.""
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posted
Don't know about the biggest number but I know the most powerful number. "4"

Name anything at all. Lets say penguins. How many letters in that: 8(eight) How many letters in that: 5(five) How many letters in that: 4(four) How many letters in that: 4(four) How many letters in that: 4(four) How many letters in that: 4(four)

Works for anything.
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