Paul Christiano's definition of slow takeoff may be too narrow, and sensitive to a choice of "basket of selected goods".

(I don't have a background in economy, so the following may be nonsense.)

Paul Christiano operationalized slow takeoff as follows:

There will be a complete 4 year interval in which world output doubles, before the first 1 year interval in which world output doubles. (Similarly, we’ll see an 8 year doubling before a 2 year doubling, etc.)

My understanding is that "world output" is defined with respect to some "basket of selected goods" (which may hide in the definition of inflation). Let's say we use whatever basket the World Bank used here.

Suppose that X years from now progress in AI makes half of the basket extremely cheaper to produce, but makes the other half only slightly cheaper to produce. The increase in the "world output" does not depend much on whether the first half of the basket is now 10x cheaper or 10,000x cheaper. In both cases the price of the basket is dominated by its second half.

If the thing we care about here is whether "incredibly powerful AI will emerge in a world where crazy stuff is already happening (and probably everyone is already freaking out)"—as Paul wrote—we shouldn't consider the above 10x and 10,000x cases to be similar.