After reading your summary of the difference (maybe just a difference in emphasis) between ‘Paul slow’ vs ‘continuous’ takeoff, I did some further simulations. A low setting of d (highly continuous progress) doesn’t give you a paul slow condition on its own, but it is relatively easy to replicate a situation like this:
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.)
What we want is a scenario where you don’t get intermediate doubling intervals at all in the discontinuous case, but you get at least one in the continuous case. Setting s relatively high appears to do the trick.
Here is a scenario where we have very fast post-RSI growth with s=5,c=1,I0=1 and I_AGI=3. I wrote some more code to produce plots of how long each complete interval of doubling took in each scenario. The ‘default’ rate with no contribution from RSI was 0.7. All the continuous scenarios had two complete doubling intervals over intermediate time frames before the doubling time collapsed to under 0.05 on the third doubling. The discontinuous model simply kept the original doubling interval until it collapsed to under 0.05 on the third doubling interval. It’s all in this graph.
Let’s make the irresponsible assumption that this actually applies to the real economy, with the current growth mode, non-RSI condition being given by the ‘slow/no takeoff’, s=0 condition.
The current doubling time is a bit over 23 years. In the shallow continuous progress scenario (red line), we get a 9 year doubling, a 4 year doubling and then a ~1 year doubling. In the discontinuous scenario (purple line) we get 2 23 year doublings and then a ~1 year doubling out of nowhere. In other words, this fairly random setting of the parameters (this was the second set I tried) gives us a Paul slow takeoff if you make the assumption that all of this should be scaled to years of economic doubling. You can see that graph here.