[HN Gopher] A Straightforward Explanation of the Good Regulator ...
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       A Straightforward Explanation of the Good Regulator Theorem
        
       Author : surprisetalk
       Score  : 41 points
       Date   : 2025-06-14 14:22 UTC (4 days ago)
        
 (HTM) web link (www.lesswrong.com)
 (TXT) w3m dump (www.lesswrong.com)
        
       | amatic wrote:
       | There is a mistake right in the beginning, not sure how it
       | affects the conclusions yet. The variables given are S - System
       | variable (some kind of disturbance), Z is the outcome ( a
       | controlled variable) and R is the action of a controller. The
       | causal relations between them are S affects Z, S affects R, and R
       | affects Z.
       | 
       | > The archetypal example for this is something like a thermostat.
       | The variable S represents random external temperature
       | fluctuations. The regulator R is the thermostat, which measures
       | these fluctuations and takes an action (such as putting on
       | heating or air conditioning) based on the information it takes
       | in. The outcome Z is the resulting temperature of the room, which
       | depends both on the action taken by the regulator, and the
       | external temperature.
       | 
       | The problem here is that the regulator R does not measure
       | external temperature. It just measures the controlled variable -
       | the temperature Z, so the causal arrow should go from Z to R too,
       | and the arrow from S to R does not exist.
        
         | analog31 wrote:
         | I wonder if the theorem is another way of showing how hard
         | control is without feedback. And I can't quite figure out if it
         | addresses dynamic systems as opposed to static ones.
        
         | masfuerte wrote:
         | > The problem here is that the regulator R does not measure
         | external temperature.
         | 
         | Domestic thermostats typically don't but some heating control
         | systems do.
        
       | stanislavzza wrote:
       | This is pedantic, but I don't like the formulation of entropy as
       | sum of p log(1/p). I think of log(p) as information of a single
       | event, for which log base 1/2 gives the answer in bits. This
       | makes the negative sign unnecessary, and technically all these
       | formulas should specify the base of log > 1. Everything is
       | cleaner with log base 1/2 (instead of e.g. using the equivalent
       | negative log base 2). This comes up in log likelihood all the
       | time too. I guess it's a prejudice against fractional bases.
        
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