Continuous and Discrete Phenomena

For this subject you have to think somewhat abstractly. Consider any system you like.3 At any distinct moment in time, the elements of the system may be characterized by an exact condition, or “state.” The state may be viewed as the values of a set of variables, which could (practically or theoretically) be measured. We can talk about those variables as being independent or dependent. For example, if the subject under consideration is elevations of the Earth’s surface, the elevation of a point might be described by the dependent variable “height above sea level” based on the independent variables “position coordinates” (e.g., latitude and longitude) and “time.” The terms independent and dependent are a little misleading, because cause and effect is suggested, where none exists. The idea is, rather, that we (independently) specify place and time, which corresponds to a particular elevation. The answer depends on the specifications, but the place and time do not cause the elevation.

(I should say here that the difference between discrete and continuous phenomena has been the source for much debate in philosophy, mathematics, and physics for centuries. Look, for instance, at Zeno’s Paradox (check the Internet). At very small sizes, a mixture of the continuous and the discrete apply to many phenomena. Electromagnetic radiation (e.g., light) comes both in packets (discrete objects) and waves (continuous phenomena). In theory, every moving object has ...

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