When I was a kid. maybe 6 years old, we went to visit my uncle who lives in a small town with unpleasant-tasting water, and this was a big local issue at the time. We drank from a Brita filter, and I made some comment about how the town should just install a really big Brita for the whole town. In my youthful enthusiasm, I said something to the effect of "It'll cost like a thousand dollars". My uncle's reply was "If it cost a thousand bucks, they'd have done it already". And this confused me quite a lot at the time. That was a huge amount of money - I don't think I'd ever had more than $20 to my name in my life. How could $1000 not be enough to afford everything?
I've spent a lot of time dealing with math and big numbers over the years since then. I was the kind of kid who learned what a googol is, and then doubled down on nerdiness in my teen years to learn about Skewes' number and Graham's number(which is so big you need whole new types of notation even to write it down). I scroll through pages called "A Tediously Accurate Scale Model of the Solar System". And bringing it back to the concrete, I routinely debate the breakdown of a budget in the trillions, and I work a job where I get to tell people "A million dollars isn't nearly as much as you think it is" on a regular basis.
In other words, I've trained my brain out of the mistake I made as a kid. Not consciously, but it looks the same in the end, I've been immersing myself in orders of magnitude for twenty years now. And I still catch myself making this mistake sometimes.
It makes sense, though. Big numbers are tough, because our brains aren't really wired that way - nobody on the East African savannah in 100,000 BC needed to know what a trillion was, or "100,000 BC" either. Even with experience, even with a pro-mathematical disposition, a lot of numbers ending in "illion" still sound the same and create the same gut reaction.
This habit of mind, this insensitivity to the actual scale of large numbers, explains a few things. The one I find most interesting is how people deal with big sums of money. Look at lottery winners. About 2/3 of them go bankrupt within 5 years. That's bonkers! This is something people dream of all their life, and when it finally happens, it destroys them. The dynamics of it are simple, though. Someone who's lived on $50,000 a year(and never had more than a few grand in one place at any given time) gets $5,000,000, and they see it as "Holy shit, I have ALL THE MONEY IN THE WORLD". So they spend like it. Buy a million dollar house and another one for your mother, get his&hers Ferraris, give $10k to everyone you know on Facebook, invest a quarter mil in your brother-in-law's surefire success of a bar that he wants to open, and so on, and so on. And it's gone.
Lotto-winner bankruptcy doesn't generally happen because the lottery payout is too small. It happens because a lot of people don't understand that any number over a million actually has limits. Why would they? They've never needed to bother with it. It's not $5M, it's $Lots, and therefore they spend money on all the things that a person with $Lots can afford. As it turns out, a big number is not actually infinite, and there's few piles of money so large that you can't blow through them with dedicated spending.
A lot of other problems in how humans deal with big numbers are explained pretty well by this phenomenon as well. CEO pay is $Lots, some wasteful government program you dislike is $Lots, and rich people all have $Lots. If you think the problem is not enough money for you or things you like, just take some from $Lots - that'll be enough to provide for it. Right?
Sadly, the real world demands real numbers, both on the small scale and the large. Fudging it all into an "illion" somewhere doesn't work when you need to solve real problems, not even when you really want it to. Even if you don't care about math, math cares about you.
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