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What we might experience are sociological/economic "tipping points" that might be local in origin but consequential well beyond mere territorial boundaries. It doesn't take all that much to send societies/economies into chaos. An extended drought. Crop failure. Water wells running dry. It doesn't take much to set populations in motion, fleeing from disaster. We've seen it happen many times. The consequences vary. Should the disruption in providing for basic human needs be large enough in a population large enough, the economic and political consequences could be significant enough to warrant the moniker "tipping point."

Your description is based on the assumption that we are currently in the basin of an attractor, and near to a stable equilibrium, in socio-economic terms. I don't think that is the case. All of human society seems to me to be rather dramatically far away from the nearest equilibrium -- hence the rapid rate of social change. Even if nothing in our environment were to change, human society would still be changing rapidly, moving towards an unknown equilibrium somewhere out there in a state space of unknown dimensions. But our environment is in fact changing, in part due to our own economic activity and population growth, so that distant equilibrium -- wherever it is -- is itself moving.

None of that invalidates your point that tipping points are the saddle points that separate attractors. It's just a slightly different way of looking at the potential function which determines the "most likely" direction of movement for human society. I see us a located far away from the bottom of any basin, on a potential function that is itself moving in response to our impact on the planet.

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