The size of 52 Factorial
Published 11/10/24 - Alex
Humans are quite bad at processing huge numbers
Now yes I know you might be saying oh but I can name super large numbers like Googol or TREE(3) and although people interested in mathematics or in a feild are aware of these numbers chances are they dont fully apprechiate how big these numbers are!
In this article we will be investigating a particular number called 52 Factorial written "52!". The exclamation point symbol donotes this factorial operation and it couldnt be more accurate because this function rises at a super fast rate
First lets establish what factorial means exactlly and why we are using 52
All factorial means is we take the number behind it lets call it n where n is a natrual number (0, 1, 2, 3...) and multiply this by every natrual number below until we reach 0. For example. 5! = 5x4x3x2x1 = 120
If you are familiar with statistics in probability you may have used factorial before or in advanced mathematics as it is helpful in many cases for respresenting a shorthand way of doing things
Factorial can also be written as product notation
Why 52 Factorial?
52! factorial is equal to the number of permutations of a deck of playing cards or the different ways they can be ordered. So 52 factorial already seems pretty large. 52x51x50x49x48... x1 = ???
52! factorial happens to be equal to exactally: 80658175170943878571660636856403766975289505440883277824000000000000
Written with commas it looks like: 80,658,175,170,943,878,571,660,636,856,403,766,975,289,505,440,883,277,824,000,000,000,000. Im not even gonna try to read that!
So why are we looking at this
Well 52! on the scale of numbers in math is pathetically small. But even then in human terms its hard to comprehend to us how large this actually is so were gonna take a look at how we might underestimate the power in these numbers!
Lets hear a story
There is a very famous story used to talk about the size of 52! Credit to this story goes to czap.net. We Will summarize it to give you an idea
How long is 52 Factorial seconds? We start by picking a random point along the equator of earth. And take 1 step... about every billion years! Each time you complete a trip around the ENTIRE WORLD. Keep in mind assuming 1 step is 1 feet this will be 131,477,280 steps walked so already 131,477,280,000,000,000 years have passed
Each time you go around the world remove a drop of water from the pacific ocean. Continue this till the ocean is completly empty. Take one sheet of paper and place it on the ground each time you empty the ocean assuming it refills each time. Do this until the stack reaches THE SUN
This dosnt quite cut it though. We have a long ways to go! Do this about 3000 more times and that still wouldnt quite be enough. A little more and maybe 52! seconds will pass. Assuming the universe still exists then :)