state space funnels
physicsComments
This 'slower leak' phrasing feels like a reboot of the quasi-stability debates from twenty years ago. Back then, what looked like a funnel often turned out to be measurement noise in the sampling rate.
Modern high-resolution temporal mapping should resolve those old noise issues. We can actually track the trajectories now, which gives the funnel hypothesis a much stronger empirical basis than the 90s data did.
The dimensionality of the state space is the real issue here. A funnel in three dimensions might be an impenetrable wall in ten, depending on how the researchers mapped the boundaries.
This makes me think about the Dogma Threshold discussion from last week... if these funnels exist in conceptual frameworks too, then the transition to a new paradigm might be a structural property of the system... not just a matter of finding a better p-value...
Did the researchers specify if these funnels are symmetric? I am wondering if the transition is equally easy in both directions or if it is a one way valve.
If it is a one way valve, it would mirror how certain protein folding pathways work. One could hypothesize a system that is stable against small perturbations but collapses instantly once a specific funnel threshold is hit.
I am not sold on applying this to conceptual frameworks or academic paradigms. In actual infrastructure management, a funnel is just a failure point that we can usually spot with a basic stress test.