How similar would an alien intelligence* be to our intelligence?
PLEASE NOTE: Answers along the lines of "we cannot know" etc are of course true. They are also -- as any reasonably intelligent alien would presumably know -- dull, boorish, obvious, and unimaginative. Please do not pollute this thread with such boring answers.
My own thoughts on this are that we would have more in common with an alien who evolved in an environment similar to ours than we would have in common with an alien who evolved in a dissimilar environment to ours.
For instance, I think anything approaching a sensible answer to the question would necessarily begin by first taking into account the life-form's external environment. For instance, did it evolve to live in social groups? Did it evolve to live as a surface creature like us? Did it evolve on a rocky world like us? e.g. we are a social species whose brain grew (relatively) huge primarily in order to deal with our living in larger and larger social groups.
Assume the Universe has a purpose. And that purpose is evolution. And purpose of evolution is to produce ever more complex lifeforms that experience the Universe in ever increasing deeper and more interesting ways. We are the Universe's way of experiencing itself. Our consciousness questioning existence and thinking about God is an expression of how a result of evolution creates a particular way to appreciate God.
I think we can assume there are extraterrestrial lifeforms that exist that are millions of years perhaps billions of year more advanced than we are in terms of evolution and how they would appreciate God and existence. Just like I can imagine some lifeforms would use a different liquid for blood that remains a liquid at much lower or higher temperatures, and just like I can imagine lifeforms that have metabolisms not bases on processing sugar for energy, I can also imagine extraterrestrial lifeforms with many more additional senses over reality experiencing reality a much deeper and profound way that is beyond what I am capable of imagining.
Regardless of our depth of perception and experience of God's created existence, I would imagine our extraterrestrial friends would have to deal with the four great existential questions:
1. Who am I?
2. Why am I here?
3. What does it all mean?
4. What is going to happen to me when I die?
I think these four essentially unaswerable questions we would have in common and a common ground of conversation.
I found this really great video on the Fermi paradox and reasons why we do not experience a Universe teeming with extraterrestrial life: