The Incomprehensible Scale of 52! (52 factorial)

[Graybeard]

I love stuff like this. I'm not a math wizard but numbers can be fascinating. Who would ever think that any time you shuffle a deck of cards that it is a unique ordering of the deck that never existed before? Stuff like this almost takes my breath away and makes me dizzy with the immensity of numbers!

One of my favorite fun facts to share with someone is how no matter how implausible it seems, every time you shuffle a deck of cards, you've produced a sequence of cards that has never existed before.

It's of course natural to doubt or even disagree with this. After all, 52! just cannot be fit into any type of visualization with an object we are familiar with. So we cant mentally picture just how immense it is. For this reason I like to say there are an infinite ways to shuffle a deck of cards. Since no human nor humanity itself could ever possibly produce every single combination.

Seriously. If humanity managed to become some kind of card shuffling empire and managed to shuffle a trillion unique decks a second since the start of the universe you legitimately wouldn't accomplish anything.

I cannot explain with words how large 52! is.

As unique as each individual order of cards is, more so is the person you are. Not even considering the genetic possibilities for a person but the life decisions and experiences you've encountered throughout. You may not feel it. But it's pretty crazy that you exist.

The sand calculations I just took as an amalgam of the tons of different rough estimates I can find on the web. It ranges from 10^18 up to 10^25.

Here's the video, I wish I knew how to insert a YT video.

https://youtu.be/hoeIllSxpEU

 

[aja8888]

Yes, that's a BIG number!

 

[Koolau]

Can't recall the circumstance exactly as it was well over 50 years ago and memory fades. In any case, I was in a class and a we were working on a problem that included the concept of Factorials.

The teacher asked a young lady in the class to read the problem in the book. No idea of the actual problem, but it could have gone something like this:

Young Lady: "Shuffling a deck of cards gives a number of possible card combinations given by the simple formula 52! "

I don't know any better way to show the emphasis the young lady placed on the number 52.

 

[latexman]

8.065817517094e67

Ginormous!

 

[Koolau]

8.065817517094e67

Ginormous!

Isn't that something like the number of atoms in the Milky Way galaxy?

 

[stepford]

The really big (but finite) number everyone has heard of is a Googol = 10^100 (10 to the 100th power). Of course most of us only know about it because it was misspelled by some company in the SF Bay Area.

 

[EastWest Gal]

Can you googol that?

 

[latexman]

Googol.

 

[ERD50]

Very well done. Thanks for posting!

I always have to stop and get my head around stuff like this. 3! is 6. 1*2*3 =6. And it's easy to list the 6 combinations of 'cards' A, B, and C. And it's easy to visualize that if I added a fourth card 'D', the # of combinations would be multiplied by that, So you do get 4!, which is 24.

By the time you hit 10 cards, you are up to 3.6 Million combinations!

-ERD50

 

[Graybeard]

Very well done. Thanks for posting!

I always have to stop and get my head around stuff like this. 3! is 6. 1*2*3 =6. And it's easy to list the 6 combinations of 'cards' A, B, and C. And it's easy to visualize that if I added a fourth card 'D', the # of combinations would be multiplied by that, So you do get 4!, which is 24.

By the time you hit 10 cards, you are up to 3.6 Million combinations!

-ERD50

Sort of like would you want $1M or a penny a day doubled for 30 days? It seems like a no brainer but those last 2 or 3 days the value rockets up.

 

[ERD50]

Sort of like would you want $1M or a penny a day doubled for 30 days? It seems like a no brainer but those last 2 or 3 days the value rockets up.

Right, that example came to mind. I recall one way it was expressed was doubling grains of rice on a checkerboard with each square, starting with one grain, so [-]64[/-] 63 doublings by the time you got to the last square.

9.2 X 10^18

and google says 1.4 X 10^7 grains of rice per ton (who counted? long grain, short grain, jasmine?). But almost a trillion tons. That's... a lot!

-ERD50

 

[youbet]

Who would ever think that any time you shuffle a deck of cards that it is a unique ordering of the deck that never existed before?

https://youtu.be/hoeIllSxpEU

Hmmmm......... Isn't it also possible that when you shuffle a deck of cards it might result in the very same ordering you had the last time you shuffled it? The probability of that happening, while it's completely possible, also calls for some pretty large numbers!

Unique does not equal low probability.