fantastic article about how fucking huge numbers can get.

for physicists, exponentials (eg 2^77) are usually considered very large, basically as big as things get/as fast as things grow. even in thermodynamic calculations i think i've only ever used a doubley nested exponential (eg 2^77^34) a few times. for instance, the number of atoms in our universe is approximately 10^80. that is a very, VERY large number. imagine how incomprehensibly hard it would be to count the grains of sand on a beach, or the number of leaves in a forest. then compare the size of that task to the semi-absurdity of counting the number of atoms in the univers, and you may start to appreciate the insanely vast size of that number.

now, consider the number of PAIRS of atoms in the universe that you could make, which is (10^80)! which is approximately 10^80^(10^80) up to minor corrections. this number is almost as easy to write down, but is so much bigger that i'm not really sure i can think about it correctly. so nesting exponentials lets you write down numbers so big that they have no conceivable physical analogue, in that you could never ever point to something and say "there are about 10^80^(10^80) of those" the way you could with the number of grains of sand on the beach or even the number of atoms in the universe.

the numbers in this article dwarf exponentials (even nested ones) the ways exponentials dwarf the number 83. it pretty much blew my mind how big they were.

so, anyone want to take up the biggest number challenge? before you read the article, write down your biggest number in the comments box, according to the rules:

You have fifteen seconds. Using standard math notation, English words, or both, name a single whole number—not an infinity—[in the comments box]. 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.

go! (and no looking at other people's answers before you write your's down)