Could you say the following: If you get 10M active users you can get 100M or 200M, because you have a mainstream service?

I don't know what the numbers are or if this is even a valid concept. Just throwing out a half-baked idea.

Seems like this depends greatly on the definition of "active users". Are these lean-forward visitors? People who've got an app on their phone's homescreen? Creators who actually make content?

More than raw numbers, I think the question about whether you're on a trajectory to mainstream service depends on the traits of the users you've got. Do *they* value having a reach or audience, and see building your platform as part of achieving their own goals?

In the "escape velocity" metaphor, user acquisition might be analogous to your velocity, but the type of user might be your angle of ascent. Question is if you're trying to leave the atmosphere or just move quickly through it. :)

I'll bet the number's tricky to pin down and fluctuates over time because you're competing for people's attention, and this seems to be more scarce at the moment (at the peak of a consumer Internet cycle, with lots of new startups) than in 2005, say.

I think the answer here depends on two things:
1) how strong and active the "core users" are -- i.e. people who actively use the product and are retained, not just casual visitors)
2) how strong the "tractor beam" of the product is -- i.e. how much do the core users draw in others -- either because they aggressively invite them (e.g. LinkedIn, Zynga) or because others are missing out on conversations if they aren't on the service (e.g. Twitter, Facebook, Pinterest) and by signing up there is an easy onramp to see them and get involved

I think if you have between 1-2M core users and a strong tractor beam or network effects you can start to map out how to get to 100M and beyond.

I dont think you can make any of those statements because for each service it depends what escape velocity means, which I take to mean when do network effect set in. When they do set in, then I think services start to feed upon themselves (and get internal combustion if you will) where they grow and grow. Use skype as an example, when 5 of your contacts were on it, it was useful. But then when 15 were on, it was super useful, which led to 50 joining. Those, to me, are network effects and that's where you see the big growth surge come into play.

Besides active users as a tipping point, other escape velocity metrics might be (a) LTV of a user > cost of acquisition of a user, (b) viral coefficient > 1, (c) each new user leads to > 1 DAU (bec they are creating activity which reactivate previously acquired users).