At some stage in victorian culture the Vortex as a philosophical model took off. The eastern philosophies are often, tritely, characterized by their circular notions of time. while the modernish western, certainly Zoroastrian philosophies are described by the arrow of time . So it is not surprising that in combining the 2 a spiral or vorticular philosophy naturally arises.
Quite often one is surprised at how widespread the notion of a vortex or a spiral is in human consciousness and history. But it is really the most natural and prevalent form or experience in nature. The apparent supremacy of the circle is in fact a fairly recent trend. Important as the circle appears , it is only a particular ,specialist form of spiral.
Much of life's experience is simplified if a spiral or vorticular basis of motion and sequence is adopted, accepted and used to guide expectations.
If an object, in classical physics, is in motion it has momentum. And in the context of the relative force fields in which it has motion, this momentum is conserved. To most, this implicitly means the motion will continue in a straight line. The caveat "unless", distorts the true situation and hides the fundamental corollary" Angular momntum is also conserved! In classical physics this was understood, particularly by Newton, and thus not all conserved motion was in a straight line! In fact Celestial motion was decidedly curved, a fact on which Newton commented. Thus motion relative to the force field in which it occurs is of any sort , and in any manner so long as both translational and angular momenta are conserved.
Newton could not understand force at a distance. He did not have the empirical based notion of a field of force to support continuing and sequential action. Few today even take the position he accepted, that though there appeared to be the finest of materials in space, nevertheless there was sufficient to represent frictional drag on objects which would eventually dissipate there motion. This was in fact a rudimentary notion of a field of force, it being a field of frictional force.
Nor did Newton's heirs take the conservation of angular momentum to its obvious application, the conservation not only of the rotation of planeets about their axes, but also the orbital motion of planets around there star centres. Thus an object once tethered, to move around an object ,if that tether is broken the object flies away, apparently, and the angular momentum is redistributed to the tether, but also to the objects axial rotation. Why does the object not remain in orbit around the centre?
The vorticular nature of motion is the explanation, within the context of the relative force field.Motion is neither straight nor obvious, but an innate apprehension of the vorticular governance of it makes it more amenable to comprehension.
Einstein's proposition of the curvature of space-time is a common idea today, but it merely allows us to see the geometry of motion in space in an analogous "space" called space time, much a mahematicians hace drawn the complex numbers in a plane called the "complex-plane". These analogies allow us to talk about the actions in space in terms of familiar geometry. But the geometry of the spiral is the true spatial geometry that universally applies.
The Lagrangian view, very much supersedes, the common traditional treatment, in that it holds that the relative force field provides the constraints for equilibrium. Thus, by defining the constraints, one defines the relative force field, The idea is then to seek those solutions to the constraints that show "invariance". This means, constancy, periodicity or nullity.
Tese more general solutions provide the key field and potential notions of modern physics. Because the field is defined by the constraints, one may have little or no apprehension of the field geometry by the constraints, except in a few limited circumstances.
Very well! We have no need to be blind or ignorant of the geometry, as it is in the form of the space in which we defined the constraints. Thus space-time is curved, because we have principally defined the restraints in a polar coordinate form.
All analysis is deemed to be based on essential tautologies. These tautologies are viewed in cyclical terms, as if they evidence the circularity of their relations. But experience shows that each recourse brings new insights and depths of meaning and significance; new applicability and a greater sense of understanding. This represents a iterative, incremental increase or change that exposits the vorticular nature of tautologies.