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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Instead of deck of cards, I prefer to use “paragraphs of text in English”.
Take a page of a book. What is numbers of all the possible combination of sentences (grammatically correct, that make some sense) that could be written on that page? Already more than the number of atoms on earth.
The number of things you can describe is absurdly high. It’s like all the alternate universe that could be, which is significantly more than what a single universe has to offer.
And that’s the same thing with a deck of card. Sure, the deck of card looks small, but we’re talking about all the alternate universe where the deck of card is in a different order. That’s a lot. On the other hand, you’re only counting the atoms of the earth of a single universe.
If you were to count the atoms of all the alternate universes too, obviously it would be more than the number of permutations of cards. But outside of extreme cases, counting the things “in one universe” will lead to smaller numbers than counting the things “in all possible universes”.
And that’s because if you add a single object in the universe, the number of possible universes increases exponentially. In the same way that if you add a single word to English, that word can be combined in all the other words to craft an immense amount of new potential sentences.
So if you add enough objects, “all possible universes” will always win over “the content of one universe”.
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