IC please clarify for us

[Immanuel Can]

If there is a countably infinite number of planets in the universe, the probability of ideal conditions for life on at least one of them, is high.

Actually, no, it's not -- at least, not mathematically. And that's because "infinity" isn't merely a high-but-limited number, but rather an unlimited non-number concept. It never ends, never exhausts itself, is never constrained by only-so-many recursions. It always has infinitely more.

No matter how many recursions of something there are in an infinity, there are always still infinite "other ways" things could have been. This means that any single outcome remains infinitely improbable, no matter how many there might be or not be.

But not everybody can get his/her head around what "infinite" means. It's a very strange concept, really. We all tend to lapse into number-thinking about it, whereas that is the one thing one cannot do with infinity as a concept, and get it right.

[MikeNovack]

When I said "other states" I did not have in mind "other planets with life" etc. I was not thinking of states that DID exist but other states that COULD exist as alternatives to the one we are in. IC, when you say this state incredibly improbable you are not saying any less probable than any other (possible) state.

But what did I mean by states? Our planet, as it exists, let's call that state zero. Now consider ten things true about state 0 that could easily be different:
1) there remain extant two species in the genus of the gray fox -- so a difference could be three extant species.
2) there remain extant two species in the genus Pan, imagine either chimpanzees or bonobos extinct.
3) there remains one species in genus Homo, imagine there were still two (were two until maybe 50,000 years ago -- H. floresiensis is no longer considered to be a case of island size shrinking -- now not even thought to be in the same "line of descent" within Homo.
etc, till we have ten variations

Now, how many states (including our own). Well if you know about binomials, 1024 states (2 to the 10th power) How many ways can 0-10 things be selected from 10 things.

A hundred such state variations, would be 2 ** 100 states (a rather big number) If we found ourselves in any of these states, we might consider it improbable, but we would say the same in any of the others. EQUAL.

It's your same "a" vs "the" problem IC. That we wold be in a state (any one of these states) is not improbable. It may be very unlikely that YOU, IC, will be struck by a meteorite in your lifetime (about 1 in 2 million) but it is VERY LIKELY that somebody in the US will be hit by a meteorite in their lifetime (about 150 will experience that ) and so more likely than not, somebody in the US will be hit by a meteorite every year.