3 ms·

Another law of complexity: the Law of Requisite Variety: If a system is to be stable, the number of states of its control mechanism must be greater than or equa

Another law of complexity: the Law of Requisite Variety: If a system is to be stable, the number of states of its control mechanism must be greater than or equal to the number of states in the system being controlled. https://en.wikipedia.org/wiki/Variety_(cybernetics)#Law_of_Requisite_Variety https://en.wikipedia.org/wiki/Variety_(cybernetics)#Law_of_R...

grenoire 8y ago
but who controls the controller?
btrettel 8y ago
Is there a better introduction to these ideas than Wikipedia? It makes intuitive sense, but I'd like to see the proof of this statement. Wikipedia mentions a "good regulator theorem", but the citation is pretty bad: "Conant 1970". Edit: The paper must be this: https://www.tandfonline.com/doi/abs/10.1080/00207727008920220 https://www.tandfonline.com/doi/abs/10.1080/0020772700892022... But I'm still interested if there's a better introduction. Edit #2: Looks like Ashby's 1956 book around page 207 has an argument based on information entropy. I haven't read it, just skimmed it. I'll look more closely later. You can download the book here: http://pespmc1.vub.ac.be/ASHBBOOK.html http://pespmc1.vub.ac.be/ASHBBOOK.html
- sgillen 8y ago
  The whole "cybernetics" field is pretty weird to me, I think the notation and lingo have sort of moved on (I could easily be wrong and biased without realizing). However the theorems you are talking about have useful, well studied analogs in the field of control theory. For example the Law of Requisite Variety is very much related to the concept of under-actuation (https://en.wikipedia.org/wiki/Underactuation https://en.wikipedia.org/wiki/Underactuation). The good regulator theorem becomes the internal model principle. https://en.wikipedia.org/wiki/Internal_model_(motor_control) https://en.wikipedia.org/wiki/Internal_model_(motor_control) I think you'll have much better luck finding good introductions to these topics in control theory than in trying to learn more about cybernetics.
tlb 8y ago
The law only applies when you need to control the system exactly. No real-world controllers attempt that. Intuitively, the theorem says that to control a system exactly you have to see any external disturbances coming in advance, predict their effect (which requires knowing the entire state of the system) and generate control inputs to counteract them. But practical controllers usually don't bother with this, and just apply negative feedback based on the observed state. For instance, to steer a ship exactly you need to know all the waves and wind coming at it in the future. But to steer it adequately, you can just look at the heading and apply a low-pass filter to generate rudder commands. (The low-pass filter might require state consisting of 2-3 numbers). Or to control data transmission over the internet exactly you need to know the size and timing of everyone else's data packets, but you can do an adequate job with TCP just keeping track of ACKed packets.

grenoire 8y ago

but who controls the controller?

btrettel 8y ago

Is there a better introduction to these ideas than Wikipedia? It makes intuitive sense, but I'd like to see the proof of this statement. Wikipedia mentions a "good regulator theorem", but the citation is pretty bad: "Conant 1970". Edit: The paper must be this: https://www.tandfonline.com/doi/abs/10.1080/00207727008920220 https://www.tandfonline.com/doi/abs/10.1080/0020772700892022... But I'm still interested if there's a better introduction. Edit #2: Looks like Ashby's 1956 book around page 207 has an argument based on information entropy. I haven't read it, just skimmed it. I'll look more closely later. You can download the book here: http://pespmc1.vub.ac.be/ASHBBOOK.html http://pespmc1.vub.ac.be/ASHBBOOK.html

sgillen 8y ago
The whole "cybernetics" field is pretty weird to me, I think the notation and lingo have sort of moved on (I could easily be wrong and biased without realizing). However the theorems you are talking about have useful, well studied analogs in the field of control theory. For example the Law of Requisite Variety is very much related to the concept of under-actuation (https://en.wikipedia.org/wiki/Underactuation https://en.wikipedia.org/wiki/Underactuation). The good regulator theorem becomes the internal model principle. https://en.wikipedia.org/wiki/Internal_model_(motor_control) https://en.wikipedia.org/wiki/Internal_model_(motor_control) I think you'll have much better luck finding good introductions to these topics in control theory than in trying to learn more about cybernetics.

tlb 8y ago

The law only applies when you need to control the system exactly. No real-world controllers attempt that. Intuitively, the theorem says that to control a system exactly you have to see any external disturbances coming in advance, predict their effect (which requires knowing the entire state of the system) and generate control inputs to counteract them. But practical controllers usually don't bother with this, and just apply negative feedback based on the observed state. For instance, to steer a ship exactly you need to know all the waves and wind coming at it in the future. But to steer it adequately, you can just look at the heading and apply a low-pass filter to generate rudder commands. (The low-pass filter might require state consisting of 2-3 numbers). Or to control data transmission over the internet exactly you need to know the size and timing of everyone else's data packets, but you can do an adequate job with TCP just keeping track of ACKed packets.