A Small Problem With Big Numbers
The human mind is exceptionally bad at interpreting large numbers.
Don’t get me wrong, anyone with an elementary education can count as high as their heart desires — or until they realise the futility of the task or life in general. The real challenge is to understand what those big numbers mean.
For example, we know that a million, a billion and a trillion are massive numbers — but most people have a hard time understanding how significant the difference is between them.
It’s a little easier to understand this in terms of time.
1 million seconds is 11 and 1/2 days
1 billion seconds is to 31 and 3/4 years
1 trillion seconds is 31,710 years
Unless you are one of those people that math textbooks talk about — the kind that purchases hundreds of watermelons so that kids can practice their algebra — you aren’t dealing with big numbers daily.
Even from an evolutionary perspective, our palaeolithic ancestor did not have to worry about large numbers … or numbers. Early humans only really needed to get a basic sense of small batches of quantities, like the number of people in the clan, or how many animals might occupy a certain area or other cavemanly concerns.
We managed to get better at counting (again, shoutout to the people buying those watermelons, couldn’t have done it without you) but big numbers still baffle us.
Despite this cognitive set-back, we are surrounded by ginormous numbers every day and are expected to make sense of it. Be it the latest pandemic figures, budget proposals by your government, the latest news, scientific research and other things that we pretend to read and understand to sound smart.
Now, this would be a great and useful post if it was about how to really understand big numbers.
But it’s not.
It’s to help you realise how much you suck at understanding big numbers.
How many ways can a deck of cards be arranged?
Every time you shuffle a deck of cards, chances are that you have put them in an order that has never been seen in the history of the universe. But how many ways can you do it?
Anyone who has ever taken a beginner’s course in probability will tell you that it’s simple — the answer is 52!
For the uninitiated, a standard deck of cards has 52 unique cards, and the “!” at the end is not because the number is particularly exciting, it’s read as “52 Factorial”. That’s math for multiply it with numbers less than it.
52! = 52 * 51 * 50 … 3 * 2 * 1
=80658175170943878571660636856403766975289505440883277824000000000000
With your astute observation skills, I’m sure you must have figured out that it is a massive number. But how big is this number really?
Here’s a creative way to look at it.
Set a timer so that it would take 52! seconds for it to reach 0.
Now, choose any spot on the equator. You have to walk around the Earth along the equator. But there’s a catch — you can only take one step every billion years.
After you complete one journey around the equator and reach the point where you started, remove one drop of water from the Pacific Ocean.
Now repeat the whole process — walk around the Earth at one billion years per step, removing one drop of water from the Pacific Ocean every time you circle the globe. Continue until the ocean is empty.
After you have emptied the Pacific Ocean, take one sheet of paper and place it flat on the ground.
Fill the ocean back up and start the entire process all over again, adding a sheet of paper to the stack every time you empty the ocean.
Do this until the stack of paper reaches the Sun.
Once the stack reaches the Sun take it down and… you guessed it, do it all over again.
One thousand times more.
Surely the timer must have reached 0 by now?
Nope.
You’re only done with one-third of the time!
That’s how big 52! really is.
Further Reading
