Hi Sara,
(Thanks for your very fascinating questions that you posted on my page, which as mentioned just above I'm addressing in a separate comment here).
That's an excellent distinction regarding requiring the self-reference to be manifest at a given instant versus allowing it to dynamically distribute through time. Since a system can be analysed from the perspective of other observables besides time, perhaps a way to generalize this distinction then is to consider whether the self-reference applies to a specific state, or instead manifests as an emergent phenomena throughout a distribution of states and their paths. The former scenario can be more active; that is a self referential 'operator' can be applied to a given state, and this physically can be accomplished by a specific physical event like the half pulse of laser light shining on the rubidium atom. Looking at it that way - from instantiating self reference at a given state - quantum superposition lends itself as a compelling description because it can explain efffects that we observe. The latter scenario (emerging through a distribution of states and paths) seems more passive, but need not necessarily be the case. In a path dependent multi-state system like that described in your paper, perhaps the particular state path (which may be nonlinear, as your paper suggests) in which a self reference emerges can be looked at as one macrostate M. The key would be what defines the self reference for such a macrostate, and what physical phenomena led to it. Did it evolve and if so is there any way to predict or assign probability to it happening? Could it be 'pushed' or 'tweeked' to emerge that way from an added physical event? That macrostate M applied to itself would be a NOT function of itself, but there would be many possibilities in a path dependent system that could satisfy NOT [M]. It may be that if such a self reference were interpreted to yield a quantum superposition, or a system of superpositions of the particular microstates involved, then it would have to be so complex that the observable effect yielded could perhaps be inferred as many discernible effects. This could be difficult if they in some way interfere with each other or are not fully addressed depending on the measuring environment. Even more revealing is if together they could indeed be perceived as one phenomena or concept. I'm thinking out loud at this point and would need to consider this much more, but needless to say your question has been very inspiring! It's an intriguing suggestion that self reference is a defining feature of living systems. I approached it from the idea of consciousness and its connection to causality, and this is a good example where the specific consideration of time (i.e. self reference manifest at an instant in time versus distributed in time) would especially apply. The analysis in this discussion here adds yet another dimension; perhaps there are environments in which the complex macrostate superposition mechanism described would yield phenomena that yet triggers other self referencing. If so, a modifed defining feature of life could be not just self reference, but a framework in which self reference is constantly or iteratively being invoked in a coordinated manner, (for example such as by these complex mechanisms).
Thanks again Sara for some very thought provoking questions; these are just some of my thoughts on it, and I definitely want to explore this distinction of instant versus emergent self reference much more!
Kindly, and best regards,
Steve Sax
