How big is a billion?
Sounds like a simple question, right?
One that has a simple answer, probably.
You may think you already know!
But if you’re human, and I assume that you are, translating this knowledge of a billion
from an idea into a real world size is almost impossible.
Let me show you.
I need something small.
The dime is the smallest of all the US coins, only 1.35mm thick.
So let’s use a dime’s thickness as a unit of measurement to help us understand really
big numbers by taking a stack of dimes, laying it on its side, and seeing how far away the
top of the stack ends up from our starting point.
I’m in Salt Lake City, Utah, at the Utah State Capital.
And here is our starting point, 0.
Which puts 1-dime thickness almost right next to it.
Ten-dimes is still pretty close by, right about here, and 100 dimes is still within
a hand’s reach.
1000 dimes is right here.
A little further away, but still pretty close.
This tube has 1000 dimes in it, so I’m going to keep it with me as a reference as we move
further away.
Here’s the ten thousand mark.
One hundred thousand.
Way over there you can still see our starting point.
But say goodbye, because that’s the last time we’ll see it on this trip.
Let’s take a walk.
One million dimes.
Our starting point is a kilometer and a half, or 0.8 miles, back that way.
Which would put a billion dime mark…
I’m going to need my car.
Welcome to Iowa Western Community College, in Council Bluffs, Iowa – one billion dimes
away from Salt Lake City.
That’s a distance of 1350km, or 839 miles, about that way.
To put that in perspective, let’s go to a map:
The billion dime circle centered on Salt lake City runs from the heart of the Midwest into
the Pacific Ocean, and from central Alberta Canada, to northern Mexico, covering an area
of 5.7 million square kilometers, or 2.2 million square miles.
So why is it, then, that when we look at the edge of a dime, we can easily figure out how
big a stack of ten or a hundred would be, but can’t immediately figure out where a
stack of a billion of them would end?
The answer is, we’re complicated.
Our brains can’t make sense of really big numbers because for hundreds of thousands
of years of evolution, they haven’t had to.
Until the last 4,000-5,000 years or so, at human scale there’s never really been more
than a couple hundred of something that actually mattered.
So instead our brains evolved to understand that beyond a certain point it’s not how
many of something that matters, but that there is many of something.
But as math and science have progressed, we needed to describe just how big or how small
a numbers really is, and whether it’s comparable to another number.
Part of the solution is to describe a numbers as being of a certain order of magnitude.
A number that is ten times bigger or smaller than another differs by 1 order of magnitude,
a hundred times bigger or smaller is 2 orders, a thousand is three, and so on.
Orders of magnitude give us sliding scale that we can use to center our brain’s natural
understandings, in tens and hundreds.
But while convenient, this creates the problem that it’s hard to bring our understanding
back into a context of real scale.
It’s easy to assume that one million makes a big difference in the context of a billion,
or a trillion, because to our brains they’re all really big numbers, and only differ by
a few orders of magnitude.
But in reality, a million to a billion is like one dime to this thousand-dime stick,
almost unnoticeable.
And a million to a trillion, well that’s like this stick to the total distance back
to Utah.
Which is to say… basically nothing.
For Tech Laboratories, I’m Tech Adams, saying keep thinking, and thanks for watching.
So where’s a billion dime thicknesses from you?
I’ve put a link in the description where you can click on a map and find out.
Let me know on Facebook, Twitter and Instagram, and then subscribe to Tech Laboratories for
more videos on science and technology.
See you next time!
So where’s ten billion?
Australia!
Are we driving?