Rolling and running aren't different degrees of something as far as I can tell. They're qualitatively different. What do you mean?
The technical term is "
Degrees of Freedomwiki". Although used slightly different in mechanics, dynamics (used in physics and chemistry), and statistics, these differences really just come down to different perspective of the of how the symmetries are specified. Not only are they quantitatively different, they fundamental define the distinction between all systems. That is why modern physics has a coordinate independent approach, where these symmetries are all that is important in distinguishing physical law.
The running verses rolling can be made analogous with the translational verses rotational degree of freedom F
0 of mechanics. Even the waveforms through a medium are the result of this, such as through a gas (with rotation F
0) verses a solid (no rotation F
0). The F
0 even defines the energy dispersion in a system as kinetic energy E = 1/2mV
2. Thus ideal gas law, classical thermodynamics, is a direct result.
As westprog noted, it is a matter of perspective, but a change of perspective does not invalidate the symmetry which provided that perspective with validity. The symmetry defines the perspectival rotations that are valid. It's not like the social relativist position, where position is as true as any other. Only those positions that corresponds to a valid symmetry transform is valid. It's even valid when definitions are reversed with that transform, so long as the symmetry is maintained. Relativity was built off a deeper understanding of this symmetry of degrees of freedom. Social relativism was a simple minded bastardization of those symmetries, falsely claiming validity irrespective of any symmetry.
Degrees of freedom are
the fundamental distinction between things.