Dear Michael,
If we go by the dictionary meaning of consciousness ("state of being aware of and responsive to one's surroundings"), in a way in each mathematical function, the dependent variable is conscious of its independent variables. For instance, in case of z=f(x,y), z is aware and is responsive to x, and y.
If we consider the psychology definition of consciousness capturing "extent of information integrated among the different parts of the brain", then the time dimension also comes into play and becomes prominent. The time dimension adds the dynamic perspective. Let me explain.
Revisiting z = f(x,y,..)
It will take the form z = f(x(t), y(t),..)
which can be approximated as
Integration of f(x(0), y(0),..),...f(x(m), y(m) ..)..
Thus, z at any point of time also contains the integrated information (not summation) of past z values. Extrapolating this analogy further, the differentiated information memorized/existing in various part of brain reflect the lived life experience of the individual/biological entity. In a way consciousness can be seen as emergent phenomenon of the mathematical dynamics which takes place as the different part of brain interacts based on triggers coming from sensory signals.
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