[tacticalogic]

Maybe there's more than one opposite pole, more than one axis of symmetry. Doesn't work for the dialectic, of course. Null, chaos, which parallels maximum entropy?

I'd think the opposite of information would be chaos, and the opposite of data would be null, providing of course that you differentiate between information and data.

[RightWhale]

Turns out there is information in chaos. It might be that information is entirely subjective, which would make it malleable to scientific methods. By opposite pole is not meant mathematical opposite, but conceptual opposite or complement, the negate of information. Null would just be a location along the axis.