Obligatory: https://www.scottaaronson.com/writings/bignumbers.html
(Yes, I know this gets posted every time one of these topics comes up, but there's always someone new who hasn't read it yet.)
(Yes, I know this gets posted every time one of these topics comes up, but there's always someone new who hasn't read it yet.)
https://czep.net/weblog/52cards.html
Start a timer that will count down the number of seconds from 52! to 0. Then walk around the world along the equator, at the very leisurely pace of one step every billion years. The equatorial circumference of the Earth is 40,075,017 meters. After you complete your round the world trip, remove one drop of water from the Pacific Ocean. Now do the same thing again: walk around the world at one billion years per step, removing one drop of water from the Pacific Ocean each time you circle the globe. The Pacific Ocean contains 707.6 million cubic kilometers of water. Continue until the ocean is empty. When it is, take one sheet of paper and place it flat on the ground. Now, fill the ocean back up and start the entire process all over again, adding a sheet of paper to the stack each time you’ve emptied the ocean.
Do this until the stack of paper reaches from the Earth to the Sun. Take a glance at the timer, you will see that the three left-most digits haven’t even changed.
Sorry.
> Of course, in reality none of this could ever happen. Sorry to break it to you. The truth is, the Pacific Ocean will boil off as the Sun becomes a red giant before you could even take your fifth step in your first trek around the world. Somewhat more of an obstacle, however, is the fact that all the stars in the universe will eventually burn out leaving space a dark, ever-expanding void inhabited by a few scattered elementary particles drifting a tiny fraction of a degree above absolute zero. The exact details are still a bit fuzzy, but according to some reckonings of The Reckoning, all this could happen before you would've had a chance to reduce the vast Pacific by the amount of a few backyard swimming pools.
>Every thousand years This metal sphere Ten times the size of Jupiter Floats just a few yards past the earth You climb on your roof And take a swipe at it With a single feather Hit it once every thousand years 'Til you've worn it down To the size of a pea Yeah, I'd say that's a long time But it's only half a blink In the place you're gonna be
"Sure, Graham's Number is okay. ... If you like your big numbers computable."
"And in Go, which has a 19-by-19 board and over 10150 possible positions, even an amateur human can still rout the world’s top-ranked computer programs." -- that needs to be updated, though.
Completely aside, I do not when this article is from but the update I mention above shows how we have changed in the way we approach some problems (brute force vs. ML)