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The reason it is hard is that it is using a stateless model to approximate an inherently stateful and often chaotic process. Take tech adoption for example. Of

The reason it is hard is that it is using a stateless model to approximate an inherently stateful and often chaotic process. Take tech adoption for example. Often incorrectly represented as s-curves, they are the result of the inherent cost/benefit of the technology combined with the stateful diffusion process of communication and inherently human resistance to change. And being inherently stateful, you can have chaotic influences in that diffusion process. For example, the idea of microservice architecture had an absolutely massive diffusion jump the moment Amazon sent out that now-famous email mandating adoption. It wasn't linear, it wasn't exponential...it was a discrete step, and a very large one at that. These are everywhere too, because communication doesn't propogate like bacteria grows, it propagates due to extremely non-linear levels of influence. Bill Smith, 45 year old mid-level programmer for a tiny Midwest bank, will never have the tech-adoption influence levels of a Steve Jobs or Alan May or Linus Torvalds. A better option for modeling would be to use Monte Carlo methods or systems methods. Something that acknowledges the inherent statefulness of the process.

KarlKemp 7y ago
> Often incorrectly represented as s-curves, they are the result of the inherent cost/benefit of the technology [...] You're taking from two completely different levels of abstraction here. Tech adoption rather obviously happens in an S-shaped curve, at least sometimes. See the article for examples. And of course that shape, and its exact parameters, are the result of some underlying processes. These two things aren't contradictory. Outside air temperature follows a roughly sinusoid curve. It's the result of the earth turning and therefore alternating between night and day. But it's still sinusoid. And the S-curve does acknowledge state, or it would just be exponential. Yes, there are different approaches to disease modelling, such as agent- and rule-base simulations. Unfortunately, they tend to be really bad because we just don't enough data to satisfactorily simulate societies at the level necessary for this application.
- darksaints 7y ago
  But having an s-shaped curve is not the same thing as being a sigmoid function, in the same way that having a bell-shaped density is not the same thing as having a gaussian distribution. There a tons of processes out there that can approximate well with either of those two, while being extremely different in extrapolation. One thing that can immediately disprove mathematical sigmoid modeling: curve symmetry. If the early adoption exponential growth is not exactly the same shape as the late adoption slowdown, then you don't have a sigmoid function. And that's the problem: if you're using a single function to model the result of two (or more) separate processes with distinct mechanics and parameters, you're going to have the same exact pitfalls as you would trying to model a bimodal process with a single probability distribution. Namely that they might fit well with interpolative methods, but completely fail with extrapolative methods (like forecasting!).

KarlKemp 7y ago

> Often incorrectly represented as s-curves, they are the result of the inherent cost/benefit of the technology [...] You're taking from two completely different levels of abstraction here. Tech adoption rather obviously happens in an S-shaped curve, at least sometimes. See the article for examples. And of course that shape, and its exact parameters, are the result of some underlying processes. These two things aren't contradictory. Outside air temperature follows a roughly sinusoid curve. It's the result of the earth turning and therefore alternating between night and day. But it's still sinusoid. And the S-curve does acknowledge state, or it would just be exponential. Yes, there are different approaches to disease modelling, such as agent- and rule-base simulations. Unfortunately, they tend to be really bad because we just don't enough data to satisfactorily simulate societies at the level necessary for this application.

darksaints 7y ago
But having an s-shaped curve is not the same thing as being a sigmoid function, in the same way that having a bell-shaped density is not the same thing as having a gaussian distribution. There a tons of processes out there that can approximate well with either of those two, while being extremely different in extrapolation. One thing that can immediately disprove mathematical sigmoid modeling: curve symmetry. If the early adoption exponential growth is not exactly the same shape as the late adoption slowdown, then you don't have a sigmoid function. And that's the problem: if you're using a single function to model the result of two (or more) separate processes with distinct mechanics and parameters, you're going to have the same exact pitfalls as you would trying to model a bimodal process with a single probability distribution. Namely that they might fit well with interpolative methods, but completely fail with extrapolative methods (like forecasting!).