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taw comments on Folk theories can be useful even when they're entirely wrong - Less Wrong Discussion
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Yes, thermostats are simple on/off devices, with on/off switch based on temperature setting and sensed current temperature ('threshold theory').
Folk theory held by about a third of the public (called "valve theory' in paper) states that they regulate heating in a way linearly proportional to current setting, without any temperature sensing.
Valve theory is trivially demonstrable to be wrong, and yet it has about the same number of successful operational predictions as threshold theory.
It turns out that threshold theory needs a lot of extra complexity until it definitely beats valve theory.
While this is true of thermostats as such, not all heating controls are thermostats. My parents' house had wall-mounted ovens which worked like a kitchen stove: They put out heat proportional to the setting. As an aside, central heating seems to be rare in Norway; instead each room has its own heating. I'm not sure why this should be so.