Are the nature of numbers changing? Or to put it more accurately; is it our relationship with numbers that is changing?
I believe our new found discovery of really big numbers, has affected society on a subtle level, and if you'll allow me a moment's digression we can explore this frivolous phenomena together.
Kid Numbers
Do you recall being a child and counting to a million? I do. Well clearly I didn't count to a million, I thought I did, really, I genuinely believed when I was about 7 years old that I had counted to a million.
I remember it well, I proudly announced to all my friends that I was going to start counting at the beginning of break time (not even lunch!), and that I would use the entire playtime to reach the giddy heights of one million.
Word got around the school that this crazy kid was going to attempt to count past 100, past 1000, past 10,000 even, is he mad?! I must witness a boy this crazy!
Break started and off I went, 1, 2, 3, 4, 5 . . . and so on, until 15 minutes later . . . 1,000,000!
The kids went wild, I was a minor celebrity for possibly the rest of that day.
"Did you hear? Cryptogee counted to a million!"
"No way! I didn't think that was possible!"
Just a few years later, I realised that there was no way I could have counted to a million in 15 minutes. In fact counting at the rate of 1 number per second, it would take 16,667 minutes, which is 694 days, that's almost two years . . .
Billionaires Are Messing Up Our Calibration
OK, so when I was a child a million was a huge number, Bill Gates didn't exist; or rather he did, it's just most of the world weren't aware of him.
I mention that because once the world did find out about Bill Gates, the word billion tended to be used when talking about him.
Yet now there are many billionaires in the world, quite literally hundreds. We throw around the word as if it is common place.
A Recursive Journey
A billion is big though, if you were given a dollar for every second you've been alive, you'd have been a millionaire by the time you were 2 years old, however you would have to wait another 29.7 years to become a billionaire!
Let's go bigger now, let's talk national debts, last time I was aware, America's national debt was in the region of 20 Trillion Dollars, if you hear a newscaster say it, sure they emphasise it, but they don't say it with the hushed awe a figure that size deserves.
Let's revisit your generous benefactor; this time he has upped the $1 he is giving you, to $10,000 dollars for each and every second you're alive.
You would need to wait till you were 63 before you got to 20 trillion dollars, if you wanted it by your 30th birthday, you'd have to be given $20,000 for every single second you're alive; wow!
Bitcoin's Cryptographic Numbers
OK, but those numbers are nothing compared to the numbers in cryptography. Bitcoin addresses are typically 160 bit (20 bytes) long, that doesn't sound very big, however the amount of unique addresses that can be created with 20 bytes is phenomenal.
This is the number: 1.46 x 10^48
Or alternatively we could write it like this:
1,461,501,637,330,902,918,203,684,832,716,283,019,655,932,542,976
Right so let's try and quantify that number, if you took all of the 7 billion, billion grains of sand on earth, and turned each one into an exact copy of earth. If you then added up all of the grains of sand on each of those new 7 billion billion earths, you would finally get to an approximation of that number.
In other words, from the moment of birth you would have to be given hundreds of trillions of dollars per second to get anywhere near that figure by the time you are 30!!!
To put it yet another way, from the moment of the big bang, to the time the universe dies a heat death 150 trillion years from now, there won't have been as many seconds to have passed, as there are possible bitcoin addresses . . .
!
Respect For A Billion
OK, so with all that being said, can we regain our respect for the word billion, please? It's huge, sure it isn't anywhere near the number of bitcoin addresses huge, however it is big enough that we shouldn't ever disrespect it by putting the word just, or only in front of it.
I HOPE YOUR HEAD HURTS SUFFICIENTLY FROM THINKING ABOUT THESE HUGE NUMBERS AND YOU ARE NOW PONDERING THE VASTNESS OF THE UNIVERSE. IF SO, LET ME KNOW BELOW!