5 ms·

In the real world all exponentials are sigmoids eventually, so what we actually get is is a recession with a drastic reallocation of resources (creative destruc

In the real world all exponentials are sigmoids eventually, so what we actually get is is a recession with a drastic reallocation of resources (creative destruction).

duped 4y ago
Not really, there are plenty that are sinusoids which are just complex exponentials. The real trouble with sigmoids is when the saturation point is beyond physically meaningful quantities of the system. See the tacoma narrows bridge collapse.
- deleted 4y ago
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- regularfry 4y ago
  Isn't it true to say that a theoretical exponential becomes a practical sigmoid precisely because some property of the system has become saturated and gone nonlinear?
  - LeonB 4y ago
    (Just trying to get this clear in my own head by writing it down.) When a real world system goes non linear (like the Tacoma Narrows case) you don’t get a sigmoid but something catastrophic. (If you graph the amplitude of the vibrations they increase and increase — and then — if it was a sigmoid they’d level out and stay at the max amplitude… but in reality they go to zero as there is no bridge left to vibrate.) When a company is “growing exponentially” it may saturate the market and then the growth slows in a nice sigmoid function. That’s common. But if, for example, the investors insist that the company must maintain the growth at all costs… it breaks laws, gets destroyed and there’s no company left to grow. No exponential curve, no sigmoid, no signal at all. Both the sigmoid and the total collapse are typical real world results of what a simple model would expect to be an unbounded exponential curve.
    - TheOtherHobbes 4y ago
      Control theory assumes the system is linear. As soon as you get saturation the system stops being linear. So in trad undergrad control theory instability implies "And then the system blows up" - numerically, literally, or sometimes both. But depending on the system you can end up in regions of recursive instability which are better modelled by logistic/chaos theory: https://en.wikipedia.org/wiki/Period-doubling_bifurcation https://en.wikipedia.org/wiki/Period-doubling_bifurcation

In the real world all exponentials are sigmoids eventually, so what we actually get is is a recession with a drastic reallocation of resources (creative destruction).

duped 4y ago

Not really, there are plenty that are sinusoids which are just complex exponentials. The real trouble with sigmoids is when the saturation point is beyond physically meaningful quantities of the system. See the tacoma narrows bridge collapse.

deleted 4y ago
[deleted]
regularfry 4y ago
Isn't it true to say that a theoretical exponential becomes a practical sigmoid precisely because some property of the system has become saturated and gone nonlinear?
- LeonB 4y ago
  (Just trying to get this clear in my own head by writing it down.) When a real world system goes non linear (like the Tacoma Narrows case) you don’t get a sigmoid but something catastrophic. (If you graph the amplitude of the vibrations they increase and increase — and then — if it was a sigmoid they’d level out and stay at the max amplitude… but in reality they go to zero as there is no bridge left to vibrate.) When a company is “growing exponentially” it may saturate the market and then the growth slows in a nice sigmoid function. That’s common. But if, for example, the investors insist that the company must maintain the growth at all costs… it breaks laws, gets destroyed and there’s no company left to grow. No exponential curve, no sigmoid, no signal at all. Both the sigmoid and the total collapse are typical real world results of what a simple model would expect to be an unbounded exponential curve.
  - TheOtherHobbes 4y ago
    Control theory assumes the system is linear. As soon as you get saturation the system stops being linear. So in trad undergrad control theory instability implies "And then the system blows up" - numerically, literally, or sometimes both. But depending on the system you can end up in regions of recursive instability which are better modelled by logistic/chaos theory: https://en.wikipedia.org/wiki/Period-doubling_bifurcation https://en.wikipedia.org/wiki/Period-doubling_bifurcation