I meant: conditional on it growing faster, why expect this is attributable to a small number of technologies, given that when it accelerated previously it was not like that (if I understand)?
If throughout most of history growth rates have been gradually increasing, I don't follow why you would expect one technology to cause it to grow much faster, if it goes back to accelerating.
1) Even if it counts as a DSA, I claim that it is not very interesting in the context of AI. DSAs of something already almost as large as the world are commonplace. For instance, in the extreme, the world minus any particular person could take over the world if they wanted to. The concern with AI is that an initially tiny entity might take over the world.
2) My important point is rather that your '30 year' number is specific to the starting size of the thing, and not just a general number for getting a DSA. In particular, it does not apply to smaller things.
3) Agree income doesn't equal taking over, though in the modern world where much purchasing occurs, it is closer. Not clear to me that AI companies do better as a fraction of the world in terms of military power than they do in terms of spending.
The time it takes to get a DSA by growing bigger depends on how big you are to begin with. If I understand, you take your 30 years from considering the largest countries, which are not far from being the size of the world, and then use it when talking about AI projects that are much smaller (e.g. a billion dollars a year suggests about 1/100,000 of the world). If you start from a situation of an AI project being three doublings from taking over the world say, then most of the question of how it came to have a DSA seems to be the question of how it grew the other seventeen doublings. (Perhaps you are thinking of an initially large country growing fast via AI? Do we then have to imagine that all of the country's resources are going into AI?)