[Balgair]

> The symbiosis event that created Eukaryotes from a random combination of Archaea and Bacteria appears to have happened only _once_ in the entire history of the earth.

That story is very much in flux still. We're not very certain on how that occurred, let alone how many times over those billions of years.It's linked to the Great Oxygenation Event, likely, but we're still in the very early stages of understanding that era.

> A practically infinite universe means potentially infinite diversity, including phenomenon that may not recognize as life at all to us, but should be equally interesting.

As is usual in science, it depends. If you are dealing with matter like us, then there are only a few universal solvents (5? I can't find the citation). In those solvents, there are a countable amount of ways that the chemistry will allow for 'life' to 'evolve'. The ways that the life can then evolve are really complicated and diverse, but there does seem to be a evolution/development trade-off, where you have to go through developmental 'keyholes' to get to a new level of complexity. Is that infinite? I've no idea, but it feels like a different ordinal of infinity.

https://en.wikipedia.org/wiki/Timeline_of_the_evolutionary_h...