I understand the math behind it, I just can’t wrap my head around the fact that something so common and limited like a deck of cards can have more ways to be arranged than something so massive like the earth with all its oceans and mountains has atoms.
In my mind it would make more sense that even a little pond has more atoms than there are deck arrangements.
Could it be due to the fact that atoms have a lot of empty space in them?
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I think you’re getting caught up in the comparison of two different things.
The ‘arrangements’ boosts the cards massively, but the Earth is just, like, there, and unboosted.
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Let’s try this to regain perspective:
Imagine getting an aeroplane, and then making a list of every country, and you’ll travel to each country on earth.
Well, there are 195. Thats more than 52. So there are more possible iteneraries we can plan than there are ways to shuffle a deck of cards.
(It is way way way more, like 300 more digits than a number with ‘only’ 67 digits. Each digit making it 10 times more, so exponentially larger. Like each country past 52 means the list of possible iteneraties dwarfs the amount of ways to shuffle the deck, and we do that dwarfing over 100 times, each time dwarfing it by a larger factor than before.)
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Or, imagine all the ways you could arrange the atoms on earth in a line. That would be probably have something like 50 septillion digits in it. Truly absurdly large.
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The large number comes from the mathematics we’re doing, in order to come up with how many things we could *imagine* being possible.
However, the ‘atoms in the earth’ is not a list of all the possible imaginable things, but instead some actual things.
There is one deck of cards, and it is in one (1) arrangement. It *could* have many arrangements, and that potential number of *different* situations is large. But the deck of cards remains tiny and small physically, despite its mathematical potential.
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