god nos
so the other day i was talking to b about a contest scientific american ran a long time ago. martin gardner convinced the magazine to offer up to a $1 million dollar prize. which was huge amount of money 30 years ago. you can enter as many times as you want. type a positive integer on a 3x5 card using a typewriter and normal spacing and kerning. alternatively type an expression that evaluates to a positive integer. that number is the number of chances you have to win. the prize amount actually awarded to the winner is the $1m maximum divided by the sum of all of the numbers sent in. if the sum is zero then the magazine keeps the dough. as mg expected, it quickly turned into a contest to see who could send in the biggest number. the sun is some 150 million kilometers away. that's an astronomical number by definition. even in meters it's also a measly 12 characters, 150000000000. easily fits on a 3x5 card. if any one person sent in an astronomical number, the prize awarded would be a tiny fraction of a penny. b came up with filling the card with 9s. the number of particles in the universe is something like 10^90. 90 such nines would easily fit on a 3x5 card. presumably normal word (number?) wrap rules apply. this would be a universe sized number. however, people sent in numbers much larger than that. much much much larger. the one i remember is a 9 followed by as many exclamation points as would fit. a few hundred bangs. as in 9 factorial factorial factorial factorial factorial factorial. google says 9!! is infinity. i estimate it has some 10,000 digits. much much much larger than a universe scale number. on the spot, i coined the phrase a god sized number. which is any number bigger than a universe sized number. readers sent in many god-sized numbers. which was the biggest? i have no idea. neither did the mathematical gamer. and sciam was off the hook for prize money.