Putting Data into Orbit. Part One: Examples from (almost-)everyday Life

The most intuitive example of an orbit (Section 1) is Carnot's cycle represented on the ${p, V}$ plane: it is a path formed by time-ordered ${p, V}$ pairs. Since the \underline{model} of the Carnot engine is known, then the orbit is a \underline{model-driven} result. Examples provided herewith are either model-driven or \underline{data-driven}. The latter are met whenever no model is available of the process which produces the data. Section 2 deals with application to single-cell mRNA sequencing: data have been heuristically represented by many Authors on a phase plane in order to display the dynamics of cell differentiation; the author's contribution consisted of synthesising a dynamical system which could explain the process, thus providing a model-driven application. Section 3 describes an application to groundwater hydraulics: sequences of water column data collected by a hydrometer network are put into orbit; the response of two seepage wells to a rainstorm can be compared. Applications to Public Health include the display of data from the SARS-CoV-2-caused disease (Subsection 4.1) and the dynamics of drinking water contaminants (Subsection 4.2). Finally, an application to Economics (Section 5): normalised balance of payments data from Italy and Germany are compared. In conclusion (Section 6), putting experimental data into orbit may add further insight and suggest a model of the underlying process. However, not all models are systems of just two ordinary differential equations: problems posed by higher dimensional systems are outlined.