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A placebo button is a push-button that appears to do something, but actually has no effect, like a placebo. In other cases a control like a thermostat may not be connected. Although non functional they can give the user an illusion of control. In some cases the button may have been functional, but may have failed or been disabled during installation or maintenance. Only in relatively rare cases will the button have been deliberately designed to do nothing. (via @rieg)