Originally Posted by

**FunBotan**
Yes

In most cases, I'm using a somewhat generalized notion of a limit (except in proposition 3.4) since I don't yet have a strict mathematical model to describe a civilization. Basically, this means that I make all unknown parameters of a civilization (how advanced the technology is, how durable/intelligent/rational are the individuals, how effectively they can colonize space, etc.) approach infinity (although in practice it usually means assigning the theoretically maximal values, e.g. an infinitely advanced reactor only has a 100% efficiency). This ensures that my model provides an upper limit to what can be done by a civilization in principle.

No, it means that whoever can gather the bigger fleet wins.

Now that I think about it... My previous statement actually was incorrect. War is not likely to be the solution.

"In the limit" here means that at least the leaders of the opposing sides are perfectly rational and, knowing at least what we know, can predict the outcome of a conflict with near certainty. So it's unlikely a weaker colony will even attempt a rebellion, knowing they would be destroyed by the metropole. And the metropole will never allow a colony to grow enough to become a threat.

If that assumption breaks down, then yes, war will happen. But again, its outcome is predetermined, so my model holds regardless.

Drawing lessons for interstellar warfare from ancient surface-bound wars is usually a bad idea. They only share some very basic aspects rooted in pure math, like the square law.

And this protects them how?

I'm just using K3 as a commonly accepted measure of scale. It doesn't imply a coherent civilization by itself.