This joke maybe good in any other site but not on Lesswrong which is based on idea of unlimited AI self-improving. Of cause Ebola will end it exponential growth—I just interested to know how and when. Will it burn out in Africa, or we get herd immunity after 100 million victims, or effective vaccine will be created, or we will nuke all places with Ebola?
This joke maybe good in any other site but not on Lesswrong which is based on idea of unlimited AI self-improving.
Some people here, including the founder, believe that recursive AI self-improvement is a realistic possibility, but I’m pretty sure that even the most hardcore believers acknowledge that there are physical limits, and that you can’t just expect an exponential function to be a good fit for a trend when you get close to the limit.
The basic function you should be looking for modelling this kind of phenomena is the logistic function. It’s the basic model for phenomena that include both positive feedback mechanisms (e.g. self-replication) and negative feedback mechanisms (e.g. resource constraints).
If you look at the graph of the logistic function, you may notice that initially, when positive feedback is dominant, it very closely resembles an exponential, then it becomes about linear around the middle point and then, negative feedback is dominant, it becomes close to a negative exponential.
If a disease had a constant basic reproduction number$R_0>1$, and it could infect anyone, and infected people never died because of the infection and remained infectious for life, then the prevalence of the disease over time would be well approximated by a logistic function, with the world population size as the supremum value (the “capacity”).
In an actual epidemic, of course, people can die or heal, and the R factor varies over time as the disease spreads to different places, people and institution change their behavior, better treatment becomes available, and so on, thus you don’t really get an exact logistic trend, but that’s the first-order model for forecasting the long-term prevalence disease, not an exponential model that neglects feedback loops. An exponential model is only useful when the disease prevalence is still quite far from the capacity, that is, when a typical infected person is mostly surrounded by uninfected (and infectable) people.
...and 40 billion cases by December 2016. Beware exponential extrapolation.
This joke maybe good in any other site but not on Lesswrong which is based on idea of unlimited AI self-improving. Of cause Ebola will end it exponential growth—I just interested to know how and when. Will it burn out in Africa, or we get herd immunity after 100 million victims, or effective vaccine will be created, or we will nuke all places with Ebola?
Some people here, including the founder, believe that recursive AI self-improvement is a realistic possibility, but I’m pretty sure that even the most hardcore believers acknowledge that there are physical limits, and that you can’t just expect an exponential function to be a good fit for a trend when you get close to the limit.
The basic function you should be looking for modelling this kind of phenomena is the logistic function. It’s the basic model for phenomena that include both positive feedback mechanisms (e.g. self-replication) and negative feedback mechanisms (e.g. resource constraints).
If you look at the graph of the logistic function, you may notice that initially, when positive feedback is dominant, it very closely resembles an exponential, then it becomes about linear around the middle point and then, negative feedback is dominant, it becomes close to a negative exponential.
If a disease had a constant basic reproduction number $R_0>1$, and it could infect anyone, and infected people never died because of the infection and remained infectious for life, then the prevalence of the disease over time would be well approximated by a logistic function, with the world population size as the supremum value (the “capacity”).
In an actual epidemic, of course, people can die or heal, and the R factor varies over time as the disease spreads to different places, people and institution change their behavior, better treatment becomes available, and so on, thus you don’t really get an exact logistic trend, but that’s the first-order model for forecasting the long-term prevalence disease, not an exponential model that neglects feedback loops.
An exponential model is only useful when the disease prevalence is still quite far from the capacity, that is, when a typical infected person is mostly surrounded by uninfected (and infectable) people.
So, do you think that half of the population will be infected?
No.