Haha, wow! Thanks for a really well thought out reply :) I think you nailed down where we were talking past each other, and I had no idea that the math world was divided on the sizes of uncountable infinities. Like you, I’m going to say that if the mathematicians are divided, I’m probably just going to accept that.
As for the “number of universes”: I agree on the possible ways we could have multiple universes, without having one for every possibility. But I want to spin a bit back to what we mean by “multiple universes”. I like the idea that if we assume that the universe is infinite, but we know that our observable universe is finite, that implies (without the assumption that “multiple universes” were created in the Big Bang) that there can be en infinite number of “observable universes” that fit within our infinite universe, that are simply moving so fast away from each other that they are completely separated (space between them is expanding faster that the speed of light).
That, in a way, leads back to one of your (our) questions: Does an infinite universe contain a countable or uncountable number of finite, observable, universes? Intuitively I would think the answer is “uncountable”, just like there is an uncountable number of finite, non-overlapping intervals on the real numbers (I think?). That leads us back to your (our) other question/condition: Can uncountable infinities have different sizes? And like you said: If the mathematicians are divided on that, I’m not even going to try to answer.
So I don’t think we’ll get much further until the mathematicians conclude, but it’s fun thinking about the possibilities :)
I also like the idea that these “other universes” might be within the realm of our infinite universe, beyond the reach of our finite observable universe. And I agree that we’ve probably reached as far as our logic can take us :) thanks for taking the time and effort to think this through with me, it was very fun!
Haha, wow! Thanks for a really well thought out reply :) I think you nailed down where we were talking past each other, and I had no idea that the math world was divided on the sizes of uncountable infinities. Like you, I’m going to say that if the mathematicians are divided, I’m probably just going to accept that.
As for the “number of universes”: I agree on the possible ways we could have multiple universes, without having one for every possibility. But I want to spin a bit back to what we mean by “multiple universes”. I like the idea that if we assume that the universe is infinite, but we know that our observable universe is finite, that implies (without the assumption that “multiple universes” were created in the Big Bang) that there can be en infinite number of “observable universes” that fit within our infinite universe, that are simply moving so fast away from each other that they are completely separated (space between them is expanding faster that the speed of light).
That, in a way, leads back to one of your (our) questions: Does an infinite universe contain a countable or uncountable number of finite, observable, universes? Intuitively I would think the answer is “uncountable”, just like there is an uncountable number of finite, non-overlapping intervals on the real numbers (I think?). That leads us back to your (our) other question/condition: Can uncountable infinities have different sizes? And like you said: If the mathematicians are divided on that, I’m not even going to try to answer.
So I don’t think we’ll get much further until the mathematicians conclude, but it’s fun thinking about the possibilities :)
I also like the idea that these “other universes” might be within the realm of our infinite universe, beyond the reach of our finite observable universe. And I agree that we’ve probably reached as far as our logic can take us :) thanks for taking the time and effort to think this through with me, it was very fun!