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NancyLebovitz comments on If there IS alien super-inteligence in our own galaxy, then what it could be like? - Less Wrong
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It may have discovered some property of physics which enabled it to expand more efficiently across alternate universes, rather than across space in any given universe. Thus it would be unlikely to colonize much of any universe (specifically, ours).
If physics allows for the spreading across alternative universes at a rate greater than that at which you can spread across our universe, the Fermi paradox becomes even more paradoxical.
Not necessarily - See Hilbert's Paradox.
https://en.wikipedia.org/wiki/Hilbert%27s_paradox_of_the_Grand_Hotel
If an infinite number of aliens have the potential to make contact with us (which I realize isn't necessarily implied by your comment) then some powerful subset must be shielding us from contact.
Infinity is really confusing.
This is only a paradox under naive definitions of infinity. Once one starts talking about cardinality, the "paradoxical" nature of the thought experiment fades away.
In other words, this is not really responsive to James_Miller's comment.