Struggling to Understand Causality in Input-Output Relationship

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Understanding causality in the input-output relationship y(t) = x(|t|) is challenging, particularly in determining if the system is causal. Causality requires that the output at time t depends on current or past inputs, but the equation suggests that negative values of t yield outputs based on future inputs. The confusion arises when plugging in values, as the output appears to be independent of past inputs. The discussion highlights the complexity of interpreting the relationship, especially when considering the integral form x=∫y, which implies past dependencies. The conclusion emphasizes the need for clarity in defining causality within this context.
cybernoodles
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Hi All,

So I'm at the point where my brain is numb. I've been struggling for the past few hours trying to understand causality. Specifically, I have an input-output relationship y(t) = x(|t|). Determining if this is causal has been very difficult. Causal means that the output at any given time t is dependent on either the current input (present) or past input. So, if I plug in 5 to my output equation, I just get 5. How is that dependent on the past? I'm being told that this system is NOT causal, I.E. dependent on the past, which is really killing me.
 
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Consider the value of y when the parameter of y is negative. The value would be equal to the value of x with a positive parameter, which you may interpret as the output of the system depending on the future value of the system input.
 
x=y seems present tense.

x=∫y would include past?
 
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