iSoul In the beginning is reality.

Category Archives: Science

Science particularly as related to creation and the creation-evolution controversy

Terminology contexts

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; vass is like mass; levitation is the opposite of gravitation; and oldtons are the units for rush, analogous to newtons for force. Metreloge is like horologe, which is a clock.

One context is racing. The term pace is used, particularly in running and (bi)cycling to mean the time interval per unit distance, which is the inverse of speed. The direction is ignored or assumed to follow the course of the race so a new term is needed to indicate the vector version of pace. For this I have chosen legerity, which is an old literary term for lightness of movement.

The second context is transport, such as package delivery. Consider an order to expedite a delivery. That means to reduce the time of transport, analogous to acceleration. A package stamped with “RUSH” gets a greater effort to reduce the time of delivery. Rush is analogous to a force applied. To hustle means to apply a rush over a distance, analogous to a force applied over time (which is called impulse). Surge is a rush applied over a dischronment, which is the inverse of work. Reserve is the capacity for surge, which is analogous to energy.

Intentional and extensional causes

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 causality is inverse of bottom-up causality.

The Inverse Correspondence Principle states that intentional motion is the inverse of extensional motion and experimentation is the inverse of observation. Similarly, transmission is the inverse of reception, developmental is the inverse of empirical, and time is the inverse of space.

The goal of science is empirical theory. The goal of engineering is development of something practical.

Goal and action go together like form and content or matter.

Consider Galileo dropping two balls, one wooden and one metal, from the tower of Pisa. One observer says it’s a race to the ground. Another observer says it’s an experiment. What is the nature of the balls? Or what does Nature do?

Final and formal causes are the inverse of efficient and material causes.

Science and history, part n

Science is inherently dualistic because it is based on distinctions, and cannot keep denying one side of a distinction without denying the distinction altogether.

Duality is as far as science can go. Unification is a temporary state, to be superseded by a more abstract duality.

Low-entropy science seeks fixed relations. High-entropy science seeks stochastic relations.

Science cannot properly speak of the universe because that ventures into metaphysics. Science can only speak of cosmos and chaos. Cosmos has low entropy. Chaos has high entropy. Also called law and chance.

Scientific history is potential history. Historical science is potential science.

Science boosters add metaphysics to science.

Life to a Darwinian is noise that happened to produce some harmonious sounds.

To a materialist chaos predominates. To an idealist cosmos predominates.

Science is a method, not a metaphysics. Science is the duality of induction and deduction.

Science is empirical mathematics. History is multi-experiential narrative.

Science is synchronic, so physics can replace time with a kind of length. History is diachronic, so history can replace space with a kind of duration.

The first scientist was Euclid. Classical geometry is the theory of length.

Half-duplex relativity

Galilean relativity requires the speed of light to be instantaneous (i.e., zero pace). Because the one-way speed of light is not known, it may be instantaneous as long as the mean speed of light is finite. Such a situation is possible if light is conceived as in half-duplex telecommunications: one direction at a time is observed or transmitted, but never both simultaneously.

Consider a light clock in this context:

light at restSaw-tooth light path

Let Δt be the time for one cycle of light at rest (top diagram). Let Δt’ be the time for one cycle of light traveling at relative velocity v (bottom diagram). The mean speed of light is c. Then

Read more →

Interchange of length and duration

Length and duration are independent measures of the extent of motion, which are measured by comparing the target motion to a uniform reference motion. Although uniform linear motion is simpler in theory, uniform circular motion is simpler in practice – especially for unstopped motion. With one addition, the classic circular clock with hands serves as a reference motion. The addition is to mark the circumference in length units along with the duration units of the angles between the hands and the vertical. See post on arcloge here.

Galileo uses horizontal uniform linear motion to mark length and duration below (from his Dialogues Concerning Two New Sciences, Fourth Day):

Galileo parabola

The horizontal uniform motion of a particle coming from the right at a-b is continued with b-c-d-e as the horizontal component of the particle descending with uniform acceleration b-o-g-l-n. Because the horizontal motion is uniform, it can represent either the length or duration of the target motion. The vertical component represents the dependent variable, which has the form of a parabola.

To interchange length and duration in an equation with a parametric function of time requires five steps: (1) replace length components with their radial distance, which becomes the base; (2) switch time and base, that is, switch the independent and dependent variables; (3) linearize the base, that is, break its dependent relation; (4) bring time under a functional relation with the new parameter, base; and (5) expand time to include angular components. Functions are inverted and the independent and dependent status of variables is switched. An inversion and a kind of re-inversion return to the same function.

In the example above, the horizontal uniform motion which was taken by Galileo to represent time is re-conceived to represent the independent length variable, base. The constant acceleration of the vertical component is re-conceived to represent the dependent duration variable with constant legerity. The quadratic sequence in units of length becomes a sequence in units of duration at a constant rate.

The result of this interchange process is that the equations of motion for length and duration are interchangeable without functional change. All of the equations of physics in terms of parametric functions of time may be adopted as parametric functions of base. In that sense it would be best to abstract a functional representation that applies to both length and duration, time and base.

Galileo’s reciprocity

From Galileo’s Dialogue Concerning the Two Chief World Systems, translated by Stillman Drake (UC Press, 1967):

Salv. Now imagine yourself in a boat with your eyes fixed on point of the sail yard. Do you think that because the boat is moving along briskly, you will have to move your eyes in order to keep your vision always on that point of the sail yard and to follow its motion?

Simp. I am a sure that I should not need to make any change at all; not just as to my vision, but if I had aimed a musket I should never have to move it a hairsbreadth to keep it aimed, no matter how the boat moved.

Salv. And this comes about because the motion the ship confers upon the sail yard, it confers upon you and also upon your eyes, so that you need not move them a bit in order to gaze at the top of the sail yard, which consequently appears motionless to you. [And the rays of vision go from the eye to the sail yard just as if a cord were tied between the two ends of the boat. Now a hundred cords are tied at different fixed points, each of which keeps its place whether the ship moves or remains still.] p.249-250

Galileo is portraying motion as viewed by a human observer. The implication is that the observer in another ship would be observing the same kinds of things. Then two observers in motion with respect to one another who observe one another must face one another. That is, they are positioned opposite one another, effectively each turned 180º from the other.

This is the Galilean Reciprocity Principle, the convention that an observed frame has the opposite orientation of the frame from which it is observed, which ensures that corresponding velocities are equal.

Relativity of orientation

The Principle of Relativity states that the laws of physics are the same in all inertial frames of reference (IRF). Since a frame of reference includes an orientation, that is, a convention as to which rectilinear semi-axes are positive (and so which are negative). Since there is no preferred frame of reference, each frame has its own orientation, not the orientation of a particular frame. That means IRF orientations are what is called “body-fixed” orientations.

A frame of reference is called “body-fixed” if it is conceptually attached to a rigid body, such as a vehicle, watercraft, aircraft, or spacecraft. Body-fixed frames are inertial frames if the body to which the frame is affixed is in inertial motion. The body is usually referenced in anthropomorphic terms, such as its left, right, face, or back, although some craft have their own terms, notably, ships with port, starboard, fore, and aft.

Consider the following scenario of cars in five lanes, oriented so that their forward direction is positive, with their unsigned speeds shown relative to the two parked cars in the middle lane:Six cars in five lanesCompare the direction of cars B, C1, C2, and D according to the frames attached to the five cars:

Read more →

Velocity reciprocity clarified

This is a follow-on to posts here and here.

It is common to derive the Lorentz transformation assuming velocity reciprocity, which seems to say that if a body at rest in frame of reference is observed from a frame of reference S that travels with relative velocity +v, then a body at rest in frame of reference S will be observed from the frame of reference to be traveling with velocity –v. But that’s not the case.

Consider the typical scenario in which a person standing on the earth (embankment, station) with frame of reference S observes a person sitting in a railway car with frame of reference . Say they are both waving their right hands and their frame of reference follows a right-hand orientation: the positive direction is toward their right.

Person waves to train

The first illustration shows the scenario from behind the observer standing on the earth in frame S, who observes the passenger sitting in the train moving to their right with velocity +v. The scenario is typically presented from only this perspective, that of an observer at rest in frame A, even if the perspective of an observer at rest in frame is described.

Read more →

Galilean relativity defended

Galilean relativity is a relational theory of motion as a function of time, which leads to the Galilean transformation. Here is a defense of Galilean relativity from two postulates:

(1) The Galilean principle of relativity, which states that the laws of mechanics are invariant under a Galilean transformation.

(2) A convention that rectilinear coordinates for frames of reference follow the right-handed rule: the unit vectors i, j, and k are related as i × j = k.

The Galilean transformation for constant motion on the x axis is x´ = xvt,  and t´ = t. Postulate (2) means if the extended right-hand thumb points to the positive X axis and the extended right-hand first finger points to the positive Y axis, then the right-hand middle finger points orthogonally to the positive Z axis.

The standard configuration for derivations of the Lorentz transformation consists of two inertial frames of reference moving relative to each other at constant velocity, with Cartesian coordinates such that the x and x′ axes are collinear facing the same direction:

Axes with same orientation

In this case the velocity of S´ relative to S is +v and the velocity of S relative to S´ is –v. This is called the principle of velocity reciprocity.

Read more →

Conventions and properties

Everything in science is a combination of conventions and properties. For example, frames of reference have certain conventions in common and particular properties that each individual frame has. The definition of a frame of reference is the first convention. Every frame of reference has an origin and at least the possibility of one or more coordinate axes. But the particular origin of a frame need not be in common with other frames; it is a particular property of one frame.

Definitions and postulates are conventions. Stipulations and measurements are properties. Physical laws are conventions with the appropriate supporting definitions and postulates. Interpretations of events become conventions when they are widely accepted.

The SI metric system is the international convention for measurement (i.e., metrology). Individual measurements are properties of things. Kinematics and dynamics have a convention for simultaneity (as well as simulbaseity). The orientation of orthogonal axes follows a convention for the order of the axes and the direction of positivity.