Science particularly as related to creation and the creation-evolution controversy
This is the latest post in a series on science and metaphysics; the previous post is here. The one and only metaphysical postulate of natural science is this: Everything has a fixed nature. This postulate allows the study of classes or kinds or types of things with a common fixed nature. For example, it allows …
This post is a slight modification of section 2.0 “The Parallel Sum of Vectors” from W. N. Anderson & G. E. Trapp (1987) “The harmonic and geometric mean of vectors”, Linear and Multilinear Algebra, 22:2, 199-210. We will consider vectors in a real N dimensional inner product space, although some of the results given herein …
The difference quotient is the average rate of change of a function between two points: The instantaneous rate of change is the limit of the difference quotient as t1 and t0 approach each other, which is the derivative of f(t) at that point, denoted by f′(t). Derivatives are added by arithmetic addition, i.e., if f(t) …
This post builds on the previous one here. Vector rates rates of change are of two kinds. An ordinary rate for the vector change of f relative to a unit of x is defined as: The reciprocal vector rate is the vector reciprocal of an ordinary rate with a vector change of g relative to …
Rates of change are of two kinds. An ordinary rate for the change of f relative to a unit of x is defined as: The reciprocal rate is the reciprocal of an ordinary rate with a change of g relative to a unit of x is defined as: An ordinary rate has its independent variable …
This post reflects a previous one here. Color (or colour) is both subjective and objective. Objectively, the rays of color light from a glass prism are different wavelengths (or frequencies) of light. The colors we see are those that reflect from objects; the others are absorbed. Colors are additive. Primary colors are red, green, blue; …
The reciprocal difference quotient is or The reciprocal derivative of f(x), symbolized by a reversed prime, is the limit of the reciprocal difference quotient as x1 and x2 approach x: or as h approaches zero: The reciprocal derivative of a linear function, f(x) = ax + b, is The reciprocal derivative of a power function, …
A rate is the quotient of two quantities with different, but related, units. A unit rate is a rate with a unit quantity, usually the denominator. A vector rate is a rate with a vector quantity, usually the numerator. Rates with the same units may be added, subtracted, and averaged. Addition Rates with the same …
This post expands on Reciprocal Algebra posted here. A vector space, or better a vector realm, to avoid connecting it with physical space, is a set V on which two operations + and · are defined, called vector addition and scalar multiplication. The operation + (vector addition) must satisfy the following conditions: Closure: If u …
This post is based on research papers by Anderson and Trapp, Berlinet, and the post on Reciprocal arithmetic. The vector inverse x−1 is defined as with positive norm. For a non-zero scalar k, The reciprocal (or harmonic or parallel) sum is symbolized in various ways, but I prefer a “boxplus” to maintain its relation with addition. The …
