A Rational Cosmology: Continuous and Intermittent Motion

Here, we shall address the distinction between continuous and discontinuous motion, as Newton's calculus provides the most direct investigation of the former of these.

If we were to define continuous motion, we would need to take into account the fact that, if continuous motion is the opposite of intermittent motion, it is motion not interrupted by periods of stasis between an entity's departure from and arrival at, respectively, the two points of reference selected by the observer.

If there are no periods of stasis involved in continuous motion, then, by extension, this must mean that, were we to select any number of particular combinations of spatiotemporal parameters pertaining to a continuously moving object, we would never see the correspondence of the same spatial parameters to different temporal parameters unless the object's motion entails passing through the same point several times, as would be characteristic of an object traveling in a loop, for example. In that case, if the number of times a continuously moving object passes through a given point C is n, we can never encounter more than n sets of the spatial coordinates of C plus some temporal coordinate, different for each set.

In contrast with continuous motion, were we to examine intermittent motion during which an object has stopped at point C, we could find any number of sets which each have the spatial coordinates of C plus some temporal coordinate, different for each set.

Let us presume, for example, that the object stops at C for a mere second, 4 seconds after it has initiated its motion. We shall also let (Cx, Cy, Cz) be the set of point C's spatial coordinates. Though the object lingers at C for only a finite amount of time, it is possible to take an indefinite amount of valid spatiotemporal coordinates for such a condition.

(Cx, Cy, Cz, 4.1), (Cx, Cy, Cz, 4.01), (Cx, Cy, Cz, 4.001), and (Cx, Cy, Cz, 4.0000000000001) are, among others, all correct spatiotemporal parameters describing the object during the static stage interrupting its motion from A to B.

Since it is possible to conceive of an indefinite number of decimals between any two integers, or any two rational numbers, and it is possible to create a time scale based on units of any conceivable magnitude, whenever an object is not involved in continuous motion, there is no exhausting the valid spatiotemporal parameters that might describe it.

However, we must also add that motion which is intermittent using some two points of departure and arrival as points of reference will be continuous using, in this manner, some other two points of departure and arrival. For example, an object moving from A to B and stopping only once in the process at C can be said to move intermittently from A to B, but continuously from A to C and from C to B.

The phenomenon of intermittent motion is, therefore, nothing more than continuous motion interspersed with rest, and, during the process of intermittent motion, the time intervals over which the object actually moves cannot be characterized by anything but continuous motion.

Thus, continuous and intermittent motion are not truly contrary or mutually exclusive states. The latter designation is better attributed to continuous motion and rest, or spatial stasis.

Nevertheless, the phenomenon of "intermittent motion" is still one that needs to be described within the context of the proper frame of reference. If we are concerned about a car traveling from Chicago to New York, we will treat the situation differently if the car undertakes the ride without ever halting until it reaches New York than we will if the car makes a stop in Cleveland, or two stops in Cleveland and Philadelphia. Some parameters are different among these entire experiences of the car along its trip, and this difference is the number of times, if at all, that the car comes to rest. Another difference might be in the length of the time period during whichthe car remains at rest in each case.

In summation:

An object in continuous motion may be described as exhibiting any three particular spatial parameters only a limited number of times during its motion.

An object at rest, be this rest a part of some phenomenon of intermittent motion or pertaining to an entirely spatially static object, may be described as exhibiting some three particular spatial parameters an inexhaustible number of times during its state of rest. Read other parts of "A Rational Cosmology" by clicking here.