Cybernetics is a Thing

There is a basic fundamental result in Cybernetics that holds that any self-regulating system must contain a model of itself.  We can examine this in the operation of so simple a self-regulating system as the common household thermostat.

A common design for thermostats is to have a mercury switch attached to a bi-metal ribbon coil.  The two different metals expand and contract with temperature changes to close and open the switch, which then activates or deactivates the heating system.  The coil is adjusted by turning the dial to set the desired temperature.

Now it should be obvious that the coil "measures" the ambient temperature, and can thus be considered an "internal" analog model of the "external" temperature.  (I put "external" in quotes because the entire thermostat is always at that temperature so it is not exactly external, is it?)

It should also be obvious that the angle of adjustment of the dial and the way that that affects the "set point" of the mercury switch is an analog model of the user's desired temperature.

So where is the internal model that Cybernetic theory predicts must exist? The thermostat must contain a model of itself in order to operate, so where is it?

There's a model of the current temperature, that's the current expansion/contraction ratio of the coil.

There's a model of the desired output temperature, that's the angle that the user sets on the dial. That modifies the relationship between the current temperature and the mercury switch which controls the heating system.

Where's the model of the thermostat itself? Switch plus dial plus coil, so simple, how can this system be modelling itself?

I'll give you a hint: I left out the heating system in the above.  The system is properly:

Room + Air + Heater + Thermostat

Here's another hint: Other than the temperature, the only aspect of the system that the thermostat really needs to model to model itself properly is how long it takes to heat up the room.

Figure it out yet?  Once the temperature of the room reaches the desired temperature the thermostat does not cut off immediately.  The heater runs a little while longer and heats the room a little bit past the desired temperature. You can easily adjust the amount of the delay (and in fact there is a little screw in there just for that purpose) but if it's set correctly you generally don't have to.

But how do you know what the "correct" setting for that delay is?  Well, it depends on how long it takes to heat up the room.

That delay is the self-model in the self-regulating system of "Room + Air + Heater + Thermostat"!

That delay prevents the heater from switching on and off too often, which prevents wasting energy and keeps the room at the desired temperature more efficiently.  If the system changes, say between summer and winter, you can adjust that delay (internal model) to re-optimize the efficiency of the heating system.

Isn't Cybernetics cool?