You may be right that this is more than a ‘tweak’. What I was trying to imply is that the framework is not wildly different. You still have graphs, integrals over time, decomposition into similar variables etc — but they can behave somewhat differently. In this case, the resources approach is tracking what matters (according to the cited papers) faithfully until expansion has ended, but then is indifferent to what happens after that, which is a bit of an oversimplification and could cause problems.
I like your example of speed-up in this context of large-scale interstellar settlement, as it also brings another issue into sharp relief. Whether thinking in terms of my standard framework or the ‘tweaked’ one, you are only going to be able to get a pure speed-up if you increase the travel speed too. So simply increasing the rate of technological (or social) progress won’t constitute a speed-up. This happens because in this future, progress ceases to be the main factor setting the rate at which value accrues.
You may be right that this is more than a ‘tweak’. What I was trying to imply is that the framework is not wildly different. You still have graphs, integrals over time, decomposition into similar variables etc — but they can behave somewhat differently. In this case, the resources approach is tracking what matters (according to the cited papers) faithfully until expansion has ended, but then is indifferent to what happens after that, which is a bit of an oversimplification and could cause problems.
I like your example of speed-up in this context of large-scale interstellar settlement, as it also brings another issue into sharp relief. Whether thinking in terms of my standard framework or the ‘tweaked’ one, you are only going to be able to get a pure speed-up if you increase the travel speed too. So simply increasing the rate of technological (or social) progress won’t constitute a speed-up. This happens because in this future, progress ceases to be the main factor setting the rate at which value accrues.