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Of course, but we are without a doubt experiencing exponential technology change. All models are approximations, and an exponential approximation is far better

Of course, but we are without a doubt experiencing exponential technology change. All models are approximations, and an exponential approximation is far better than whatever is going into EIA and IEA advice to policy makers. We have not yet hit the linear part of the sigmoid, and are not close. But the good modes out there take that sigmoid shape into account. (Also, why don't Singularity advocates know about sigmoids?)

kelseyfrog 4y ago
Since the early parts of sigmoid and exponential curves are indistinguishable, the singularity advocates opt for the more interesting of the two. The question people are most interested in "what's the saturation level?" of sigmoids has such a large prediction interval that it's next to useless to estimate from data.
- graycat 4y ago
  Right, extrapolation from the present and past where the growth has been exponential is not promising. But if somehow know the saturation level, upper asymptote, then what are doing is more like interpolation than extrapolation. Then the sigmoid curve is the solution to the differential equation I posted here a few minutes ago here at https://news.ycombinator.com/item?id=31429475 https://news.ycombinator.com/item?id=31429475 and there is just the one free parameter k. Sometimes in practice have a shot at estimating k.
flir 4y ago
> (Also, why don't Singularity advocates know about sigmoids?) They think the curve goes so far up the y axis before it flattens off that it might as well be exponential to us monkeys stuck at the bottom of the slope.
- ben_w 4y ago
  While I think this, I have definitely seen at least one attempt to argue that progress follows a doubling time itself regularly halves and will actually reach infinite “real soon now”. I also see, as a common trope, people talking about “the knee of the exponential”; as they clearly don’t know how the exponential function works, I have no idea what they think.
  - flir 4y ago
    Oh well that's just nuts. Can't help those guys.

kelseyfrog 4y ago

Since the early parts of sigmoid and exponential curves are indistinguishable, the singularity advocates opt for the more interesting of the two. The question people are most interested in "what's the saturation level?" of sigmoids has such a large prediction interval that it's next to useless to estimate from data.

graycat 4y ago
Right, extrapolation from the present and past where the growth has been exponential is not promising. But if somehow know the saturation level, upper asymptote, then what are doing is more like interpolation than extrapolation. Then the sigmoid curve is the solution to the differential equation I posted here a few minutes ago here at https://news.ycombinator.com/item?id=31429475 https://news.ycombinator.com/item?id=31429475 and there is just the one free parameter k. Sometimes in practice have a shot at estimating k.

flir 4y ago

> (Also, why don't Singularity advocates know about sigmoids?) They think the curve goes so far up the y axis before it flattens off that it might as well be exponential to us monkeys stuck at the bottom of the slope.

ben_w 4y ago
While I think this, I have definitely seen at least one attempt to argue that progress follows a doubling time itself regularly halves and will actually reach infinite “real soon now”. I also see, as a common trope, people talking about “the knee of the exponential”; as they clearly don’t know how the exponential function works, I have no idea what they think.
- flir 4y ago
  Oh well that's just nuts. Can't help those guys.