When I hear the phrase “large numbers” I instantly think of the law of large numbers. That’s just that the average of a large number of results approaches the expected value. And that’s not what I’m talking about here.
What I am talking about is literal large numbers. Things like a million or a billion. I’m not sure anyone really knows what they mean. They are unimaginably large numbers, literally. People cannot imagine a million or a billion. Sure, people know things about them. For instance, a million is the whole number between 999,999 and 1,000,001. But those are just words. No one can see or touch or taste or hear or smell a million things. A million is too abstract to really know.
This leads to a question. What is the smallest large number? What is the smallest number that’s unimaginably big? I once read that seven is the most things people can hold in their minds at a time. I don’t know if that’s true or not (I’m not even exactly sure what it means), but would that make eight a large number? I don’t think so. It seems like I can reasonably imagine a dozen eggs or a dozen donuts.
What about 100? Can I imagine ten tens? I know that there are 100 pennies in a dollar, but can I picture 100 pennies? I can imagine a pile of pennies or two rolls of pennies, but 100 individual pennies is beyond me.
So, how about 50? If I unroll one of those rolls of pennies, can I look at it and know what I have? I think it’s unlikely. 49, 50, and 51 would all look the same to me. That makes me think that the smallest large number is less than 50.
20 seems to be too small to be a large number, but is it? I find that when I imagine 20, I break it into a smaller number of groups. Two groups of ten or five groups of four. I struggle to imagine twenty units.
I already said that I can picture a dozen donuts, but can I do 13? I’m trying right now without success. I keep picturing it as a baker’s dozen, I picture the 12 and then 1. That suggests that the smallest large number, for me at least, is 13. That’s pretty small for a large number.
That’s what makes the millions and billions of the world so unfathomable. Not only can I not imagine a million units, I can’t even break it down into imaginable chunks. 2 chunks of 500,000 doesn’t work because 500,000 is too big. 1,000 x 1,000 doesn’t work either because 1,000 is too big.
I know this is unimportant on every level, but it’s something I like thinking about. It’s humbling to think that my smallest large number is only 13. My brain isn’t as expansive as I sometimes think it is.
What’s your smallest large number?