Edit: By causality, in this question, I do not mean the traditional mathematical definition in the theory o signals and systems; I mean causality as in an intuitive 'what's moving/pushing what notion'...
I'm having trouble understanding how causality fits into our intuitive ideas of inputting our output back into the system as feedback. What does it mean physically that y, the output, is dependent on the previous y values?
I understand the control/feedback engineering intuition, but once I get into the math, what I see are neat differential equations that govern how every single component should vary under such constraints. But, I don't see how we get to talk about how a certain component's behavior is caused by others.
Take exponential growth, for example, the output's behavior is caused by the behaviors of its rate of change and of the input force. Is this causality statement really the case, or is it just nature doing its thing, or am I just mixing ideas and being way too pedantic?
Either way, I want to understand this concept to be able to fully grasp what it really means when, for example, a servomotor gives feedback information about its rotation, and how this relates to the mathematical/physical differential equation framework.