1.17 Value, Slope and Curvature

Science uses mathematics to describe events of physical reality in time. Here is discussed "function of time." Newton viewed reality and its mathematical description to be the same in the limit of very change, short instances in time. At an instance, say at t = t*, physical reality described by a mathematical function has a value, a change of that value (function slope) and a curvature. Value, slope and curvature, that mathematics, explains, physical behaviors at their basis.

Basic Thermodynamics ~ J. Pohl ©

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1.17 Value, Slope and Curvature

Science attempts to describe changes of physical reality. The items that change are called properties. Properties are realized to change in time or space. Consider a hypothetical property notated as, F, which changes only as does time. That property is written symbolically as: F(t). For us, any observation of some F(t) over time must begin at (the beginning of its observation) x = x^*:

A basic idea of calculus is that a function, F(t), has three characteristics at any specified value of t, say x = x^*.  Associated with x^* the function has a a value, a slope and curvature. These ideas are illustrated in the sketches below.