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That’s a tricky question because “emergent” is a very controversial term and people mean very different things when they use it. Nevertheless, there is an obvious sense in which consciousness is emergent: the spatio-temporal scale at which our conscious experiences “run” seem to involve neurons or groups of neurons (rather than atoms or quarks etc.) and time scales of tens of milliseconds. Accordingly, the physical substrate of our consciousness is not to be found at the micro level of physics. However, “emergent” is often paired or contrasted with epiphenomenal, or associated with some dynamically emergent pattern that is observer-dependent. Consciousness is observer-independent, so it cannot be emergent in the mere sense of “level of description”. There has to be an observer-independent reason why consciousness runs at the specific spatio-temporal scale it runs at. In that sense, consciousness is not like a flock of birds. It is real, meaning it exists in a fundamental way.
For more see my interview with David Garofalo on David Garofalo’s Corner.
The assumption in IIT is that micro mechanisms are indeed Markovian with order 1. Handwaivingly, this is because memory requires a mechanism, and if the micro elements had mechanisms within themselves they would not be micro.
Such micro system (described by micro transition probability matrices) can be mapped into supervening macro systems with fewer elements and smaller state spaces, which often end up non-markovian (or at least > order 1). For now, we have two ways worked out how this can be done: coarse-graining and black-boxing. Both can produce non-markovian macro-tpms. However, this non-markovianity of the macro level is due to the micro information that was averaged or disregarded at the micro level. When we search for the optimal spatio-temporal scale, we also search over the number of micro time steps that are grouped into a macro time step and evaluate the macro elements’ interaction at that time scale. All other influences are causally marginalized, as they are not intrinsic to the scale that we are evaluating.
Recorded data can also appear non-markovian because the spatio-temporal scale of the recording device averages or makes snapshots at a particular macro time scale of the system. Again, such non-markovian dependencies are not intrinsic to the system and should be discounted.