***** To join INSNA, visit http://www.insna.org ***** Loet: > I would be inclined to think of the vectors as providing the variation and > the matrix as containing the structure ("eigenstructure"). The structure is > determining since selective. Variation can be random, but selection is > deterministic. In addition to eigenstructure at each moment of time, one > would have to define an eigen-dynamics over time. > > The eigenvectors and eigenfrequencies can be recombined by a self-organizing > system because it contains one more degree of freedom for the reflection. In > sum: a vector is a one-dimensional probability distribution, a matrix a > two-dimensional one, a system which develops over time would need to be > modeled as a three-dimensional probability distribution, and a > self-organizing system as a four-dimensional one. The entropy statistics of > probability distributions of more than one are not different from the simple > ones. Thus, one can move this forward. > > The cybernetic expectation is that the systems are constructed bottom-up, > but that control tends to emerge at the next-order level. Ryan: Two comments: 1. This approach creates fairly rigid boundaries between system and external. The rigidity is lessened by the introduction of probabilities, but made no less autonomous. These boundaries are necessarily arbitrary...they do not allow for partial inclusion outside of the probability measure. 2. The notion of scale would also need to have (presumably) probabilistic boundaries. It would also create nested levels of dimensions...implausibly complex. Dynamics will require a systemic approach like evolution that is an open system. That is why there are no probabilistic models of mutation worth much. Context is part of the equation--inherently. I have made little progress, but I am inclined to focus on the situation rather than the "network" because of this. SNA might be "over" because it cannot deal with context in any systematic way. This is because it focuses on systems rather than focusing on contexts. I think this is a general flaw of prior generation social science. In short, we modeled closed systems and that was a red herring. We should have been thinking about environments, but instead we thought about species. We literally did not see the forest for the trees. Ryan Lanham _____________________________________________________________________ SOCNET is a service of INSNA, the professional association for social network researchers (http://www.insna.org). To unsubscribe, send an email message to [log in to unmask] containing the line UNSUBSCRIBE SOCNET in the body of the message.