The impression I get from a (I admit relatively casual) look is that you are saying something along the following lines:
1) there is a big mystery concerning the fact that the rate of growth has been accelerating,
2) you will introduce a novel tool to explain that fact, which is stochastic calculus,
3) using this tool, you arrive at the conclusion that infinite explosion will occur before 2047 with 50% probability.
For starters, as you point out if we read you sufficiently carefully, there is no big mystery in the fact that the rate of growth of humanity has been super-exponential. This can be simply explained by assuming that innovation is an important component of the growth rate, and the amount of innovation effort itself is not constant, but grows with the size of the population, maybe in proportion to this size. So if you decide that this is your model of the world, and that the growth rate is proportional to innovation effort, then you write down some simple math and you conclude that infinite explosion will occur at some point in the near future. This has been pointed numerous times. For instance, as you point out (if we read you carefully), Michael Kremer (1993) checked that, going back as far as a million years ago, the idea that population growth rate is roughly proportional to (some positive power of the) population size gives you a good fit with the data up to maybe a couple of centuries ago. And then we know that the model stops to work, because for some reason at some level of income people stop to transform economic advancement into having more children. I don’t think we should ponder for long about the fact that a model that matched well past data stopped to work at some point. This seems to me to be the natural fate of models of early growth of anything. So instead of speculating about this, Kremer adjusts his model to make it more realistic.
It is of course legitimate to argue that human progress over recent times is not best captured by population size, and that maybe gross world product is a better measure. For this measure, we have less direct evidence that a slowdown of the “naive model” is coming (By “naive model” I mean the model in which you just fit growth with a power law, without any further adjustment). Altough I do find works such as this or this quite convincing that future trends will be slower than what the “naive” model would say.
After reading a (very small) bit of your technical paper, my sense is that your main contribution is that you fixed a small inconsistency in how we go about estimating the parameters of the “naive model”. I don’t deny that this is a useful technical contribution, but I believe that this is what it is: a technical contribution. I don’t think that it brings any new insight into questions such as, for instance, whether or not there will indeed be a near-infinite explosion of human development in the near future.
I am not comfortable with the fact that, in order to convey the idea of introducing randomness into the “naive model”, you invoke “E = mc2″, the introduction of calculus by Newton and Leibnitz, the work of Nobel prize winners, or the fact that “you experienced something like what [this Nobel prize winner] experienced, except for the bits about winning a Nobel”. Introducing some randomness into a model is, in my opinion, a relatively common thing to do. That is, once we have a deterministic model that we find relatively plausible and that we want to refine somewhat.
The impression I get from a (I admit relatively casual) look is that you are saying something along the following lines:
1) there is a big mystery concerning the fact that the rate of growth has been accelerating,
2) you will introduce a novel tool to explain that fact, which is stochastic calculus,
3) using this tool, you arrive at the conclusion that infinite explosion will occur before 2047 with 50% probability.
For starters, as you point out if we read you sufficiently carefully, there is no big mystery in the fact that the rate of growth of humanity has been super-exponential. This can be simply explained by assuming that innovation is an important component of the growth rate, and the amount of innovation effort itself is not constant, but grows with the size of the population, maybe in proportion to this size. So if you decide that this is your model of the world, and that the growth rate is proportional to innovation effort, then you write down some simple math and you conclude that infinite explosion will occur at some point in the near future. This has been pointed numerous times. For instance, as you point out (if we read you carefully), Michael Kremer (1993) checked that, going back as far as a million years ago, the idea that population growth rate is roughly proportional to (some positive power of the) population size gives you a good fit with the data up to maybe a couple of centuries ago. And then we know that the model stops to work, because for some reason at some level of income people stop to transform economic advancement into having more children. I don’t think we should ponder for long about the fact that a model that matched well past data stopped to work at some point. This seems to me to be the natural fate of models of early growth of anything. So instead of speculating about this, Kremer adjusts his model to make it more realistic.
It is of course legitimate to argue that human progress over recent times is not best captured by population size, and that maybe gross world product is a better measure. For this measure, we have less direct evidence that a slowdown of the “naive model” is coming (By “naive model” I mean the model in which you just fit growth with a power law, without any further adjustment). Altough I do find works such as this or this quite convincing that future trends will be slower than what the “naive” model would say.
After reading a (very small) bit of your technical paper, my sense is that your main contribution is that you fixed a small inconsistency in how we go about estimating the parameters of the “naive model”. I don’t deny that this is a useful technical contribution, but I believe that this is what it is: a technical contribution. I don’t think that it brings any new insight into questions such as, for instance, whether or not there will indeed be a near-infinite explosion of human development in the near future.
I am not comfortable with the fact that, in order to convey the idea of introducing randomness into the “naive model”, you invoke “E = mc2″, the introduction of calculus by Newton and Leibnitz, the work of Nobel prize winners, or the fact that “you experienced something like what [this Nobel prize winner] experienced, except for the bits about winning a Nobel”. Introducing some randomness into a model is, in my opinion, a relatively common thing to do. That is, once we have a deterministic model that we find relatively plausible and that we want to refine somewhat.