This continues the series of posts, see here. Let’s begin with Galileo’s figure for uniform motion and uniform accelerated motion: Let the horizontal uniform motion be situated in a 2D x, y coordinate system: The dependent uniform acceleration moves in an additional dimension, z, and so has 3D coordinates. If the independent uniform motion is […]
This continues posts about Galileo such as here. Look again at this figure from Galileo: The horizontal line represents the independent variable, which is the horizontal component of a projectile with an initial speed that falls with uniform acceleration. The independent variable need not be horizontal, so let us represent it vertically with the vertical
A kinematic frame of reference is a mathematical method to determine the position of points in abstract 3D space and scalar time. An inertial frame of reference is a physical method to measure the position of bodies in physical 3D space and scalar time. The latter is often envisioned as three mutually-perpendicular rigid rods attached
Time is like a river that flows on indefinitely, as observed from a place on its bank. The flow of time is downstream. Place does not change in this way but the time keeps changing. Space is like a river that flows on indefinitely, as observed from a platform floating down the river. The flow
This relates to the post here. There are three dimensions of motion with two measures of the extent of motion, which makes a total of six metric dimensions of motion. But these six metric dimensions collapse into two structures of one and three dimensions as the conversion factor approaches infinity. With the pace of light,
This post is related to an old post here. Broadly speaking, there are three kinds of empirical science, which correspond to three views of nature. (1) The ancient view of empirical science is represented by Aristotle, which includes the careful observation of undisturbed nature. Motion, for example, meant natural motion, not “violent” motion in which
This post continues the one here. While I avoid coining new terms or new definitions, some have been necessary. To have a consistent vocabulary, I try to imagine contexts in which they easily fit. Some words are simply variations of words in use: distime is like distance; dischronment is like displacement; chronation is like location;
This post relates to others such as this. Consider Galileo’s figure (see his Dialogues Concerning Two New Sciences, tr. Crew & De Salvio p.249 Fig. 108 or Drake’s translation p.221): A projectile moves with uniform velocity horizontally to the left and begins to descend at point b. Galileo used the sequence a-b-c-d-e to represent time
Let’s start with one-dimensional, i.e., scalar, functions, f, g, h, and k. Say there is the following functional relation: s = f(t) = f(h(s)) ≡ g(s) = t, t = g(s) = g(k(t)) ≡ f(t) = s, in which s and t are parameters with different units. By implication the functions are either f or
This post continues previous posts on causes, especially the one here. Final and formal causes constitute top-down causality, which may lead to efficient and material causes. Material and efficient (mechanism) causes constitute bottom-up causality, which may lead to formal and final causes. Top-down is intentional. Bottom-up is extensional. The Inverse Causality Principle states that top-down
