From 1,000,000 to Graham’s Number
Numbers are fascinating, and truly gargantuan numbers are even more fascinating. Thanks to Wait but Why for this description of a "google". Read it, and then click here to learn about Graham's number. The name googol (redefined by Larry Page and Sergey Brin) came about when American mathematician Edward Kasner got cute one day in 1938 and asked his 9-year-old nephew Milton to come up with a name for 10100—1 with 100 zeros. Milton, being an inane 9-year-old, suggested “googol.” Kasner apparently decided this was a reasonable answer, ran with it, and that was that.
So how big is a googol?
It’s the number of grains of sand that could fit in the universe, times 10 billion. So picture the universe jam-packed with small grains of sand—for tens of billions of light years above the Earth, below it, in front of it, behind it, just sand. Endless sand. You could fly a plane for trillions of years in any direction at full speed through it, and you’d never get to the end of the sand. Lots and lots and lots of sand.
Now imagine that you stop the plane at some point, reach out the window, and grab one grain of sand to look at under a powerful microscope—and what you see is that it’s actually not a single grain, but 10 billion microscopic grains wrapped in a membrane, all of which together is the size of a normal grain of sand. If that were the case for every single grain of sand in this hypothetical—if each were actually a bundle of 10 billion tinier grains—the total number of those microscopic grains would be a googol.
We’re running out of room here on both the small and big end of things to fit these numbers into the physical world, but three more for you:
10113 – The number of hydrogen atoms it would take to pack the universe full of them.
10122 – The number of protons you could fit in the universe.
10185 – Back to the Planck volume (the smallest volume I’ve ever heard discussed in science). How many of these smallest things could you fit in the very biggest thing, the observable universe? 10185. Without being able to go smaller or bigger on either end, we’ve reached the largest number where the physical world can be used to visualize it.