@#468 is truly remarkable science. Wish all sources had the theory of their phenomena and the patient analysis so well developed!

On the other hand, I bet if there wasn't such a rush to application in some of these fields, we might collectively be farther along with understanding.

My system is back, by the way, so I look forward to cranking away on my phase plane plots for COVID-19*with uncertainty clouds about*.

By the way, regarding #457, #458, and #459, the pitfalls of phase plane plots seen as projections on basis vectors corresponding to derivatives has an analogy with projects of data upon singular vectors or eigenvectors. Some of the time (I'm not sure how one says "most of the time") these separate out independent behaviors, say, when depicting these derived from spectral decompositions of circulants of (time) series. But once in a while, there's a phenomenon where two basis vectors are needed to see the actual behavior and they act as a couplet. Presumably, for some series, there might be a need for three or four. Else it's like "shadows on the wall of the cave".

So it's possible that for complicated systems, some behaviors are irreducible to the phase plane.

I'm not sure if this phenomenon is well known in the PCA world.

On the other hand, I bet if there wasn't such a rush to application in some of these fields, we might collectively be farther along with understanding.

My system is back, by the way, so I look forward to cranking away on my phase plane plots for COVID-19

By the way, regarding #457, #458, and #459, the pitfalls of phase plane plots seen as projections on basis vectors corresponding to derivatives has an analogy with projects of data upon singular vectors or eigenvectors. Some of the time (I'm not sure how one says "most of the time") these separate out independent behaviors, say, when depicting these derived from spectral decompositions of circulants of (time) series. But once in a while, there's a phenomenon where two basis vectors are needed to see the actual behavior and they act as a couplet. Presumably, for some series, there might be a need for three or four. Else it's like "shadows on the wall of the cave".

So it's possible that for complicated systems, some behaviors are irreducible to the phase plane.

I'm not sure if this phenomenon is well known in the PCA world.