iSoul In the beginning is reality.

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.

Ratios of length and duration

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) below with horizontal and vertical rulers added :

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 and the sequence b-o-g-l-n to represent the height of the projectile above the Earth. The sequence b-i-f-h represents the parabolic path of the falling projectile.

Any uniform motion can serve as a reference motion. There are two uses of a reference variable: (i) as a parametric variable, or (ii) as a measurement variable. A parametric variable is an independent variable that provides ordered input for any dependent variable. A measurement variable is a variable that is dependent on the independent variable being measured. In the figure above the parametric variable is the time (duration) of the uniform motion on the horizontal axis, and the measurement variable is the height (length) of the uniform acceleration on the vertical axis.

Combine this with the two measures of motion, length and duration, and there are four possible cases: (1) independent duration variable with dependent length variable; (2) independent length variable with dependent duration variable; (3) independent length variable with dependent length variable; and (4) independent duration variable with dependent duration variable.

The figure above is an example of case (1). Its complement is case (2). Cases (3) and (4) include only one measure, length or duration, and so cannot express a rate of motion. Galileo expresses case (1) as a proportion between ratios of the variables at different times: s1 : s2 :: t12 : t22, which avoids combining different units in a single ratio, consistent with Eudoxian proportionality.

Consider case (2) in which the independent variable is length. This variable is a baseline for locating other motions, which is like a timeline except that it expresses an independent length as the order parameter. The dependent reference variable in this case is duration, which measures any independent variable, in this case projectile height. This could be expressed as a proportion between ratios of the variables at different times: t1 : t2 :: s12 : s22, avoiding different units in a single ratio.

Case (1) enables multiple length variables dependent on one independent variable, the timeline. Case (2) enables multiple duration variables dependent on one independent variable, the baseline. Rates of motion in case (1) are in units of the independent timeline, which is duration. Rates of motion in case (2) are in units of the independent baseline, which is length.

From length to duration and back

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 its inverse:

s = f(t) = f(f-1(s)) = t,

t = f-1(s) = f-1(f(t)) = s.

Function f takes t-units into s-units, and function f-1 takes s-units into t-units. The vector versions are as follows:

s = f(t) = f(f-1(s)) = t,

t = f-1(s) = f-1(f(t)) = s.

Motion space is an ordered pair of vectors s and t: (s, t), resulting in their direct sum vector space. Addition is conducted by components: (r, w) + (s, t) = (r + s, w + t). Scalar multiplication is also by component: (a, b) (s, t) = (as, bt). To multiply a scalar and only one component requires the other component to be unity. Thus additive unity is (0, 0) and multiplicative unity is (1, 1).

There are two ways to mask an ordered pair of vectors: left mask (s, t) = (s, t) and right mask (s, t) = (s, t), where s = |s| and t = |t|. What was described here as expansion and contraction may now be shown more clearly as masking and unmasking. A parametric length vector function is converted to a parametric duration vector function as follows:

r(t) = masked r(t) ↑ unmasked r(t) ↔ (inverted) = unmasked t(r) ↓ masked t(r) = t(r).

r(t) = [r(t), θ(t), φ(t)] ↑ [(t´, χ´, ψ´), θ´(t´, χ´, ψ´), φ´(t´, χ´, ψ´)] ↔ ((r´, θ´, φ´), χ´(r´, θ´, φ´), ψ´(r´, θ´, φ´)) ↓ [t(r), χ(r), ψ(r)] = t(r).

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.

Duality as a convention

Is color an absorption phenomena or an emission phenomena? The answer is that it’s both. But absorption works subtractively whereas emission works additively. The question then is whether color is subtractive or additive. Again the answer is that it’s both. Color is a duality.

Does an artist work with subtractive colors or additive colors? Here the answer is one or the other. A painter works with pigments that are subtractive, whereas a glass artist works with stained glass that is additive. Even though absorption and emission are operating in both cases, working with color requires picking one or the other (except for mixed media).

A simultaneity convention can also be a duality. What has been called apparent simultaneity is the convention that the backward light cone is simultaneous. But it is possible to adopt a complementary convention in which the forward light cone is simultaneous (see here). Either of these is something of a combination of Newton’s and Einstein’s physics.

One could recover Newtonian physics by adopting a combination of the backward and forward light cone simultaneity conventions. For an absorption event the backward light cone is simultaneous. For an emission event the forward light cone is simultaneous. This is like half-duplex communication (push to talk, release to listen). Such a duality convention recovers Newtonian physics because it is as if the speed of light is instantaneous in all directions.

Newton and Einstein compared

Isaac Newton expanded on what is now called the Galilean transformation (GT). The GT encapsulates a whole approach to physics. Length and duration are independent variables, and accordingly are universal, and may be measured by any observer. The length of a body is a universal value. The duration of a motion is a universal value. These values are independent of the control or condition of an observer.

Albert Einstein expanded on what is now called the Lorentz transformation (LT). The LT encapsulates a whole approach to physics. There are two universal constants: the speed of light in a vacuum and the orientation of reference frames. These constants are independent of any observer, though the speed of light may be measured by any observer. The orientation of reference frames is assumed to be the same universally, as if all are aligned with the fixed stars according to a universal convention.

Galileo described the relativity of speed, so that inertial observers do not have a universal speed but have speeds relative to other inertial observers. There is no universal maximum one-way speed. The two-way speed of light is a universal constant, but one leg of its journey may be instantaneous by convention, consistent with common ways of speaking. The orientation of reference frames is also relative, so that two frames view each others’ velocities as having the same direction.

Einstein described the relativity of length and duration, depending on their relative speed, which is always less than the speed of light in a vacuum. By convention, the mean of the two-way speed of light is assigned to every leg of its journey. Since the orientation of reference frames is the same, two frames view each other’s velocities as opposite in direction.

The strength of Newton’s vision is his mechanics and its continuity with common ways of speaking. The strength of Einstein’s vision is its continuity with Maxwell’s equations of electromagnetism.

Note: The Galilean transformation is related to the Lorentz transformation in one of three ways: (1) as c → ∞, (2) as v → 0, or (3) as the simultaneity of the backward (or forward) light cone (i.e., c0 = ∞) [see here].

Word of faith, part 4

In this final post on the Word of faith movement, I specifically want to address the claims of D. R. McConnell in his book, A Different Gospel (updated edition 1995). He concludes on p.185:

There are many peculiar ideas and practices in the Faith theology, but what merits it the label of heresy are the following: (1) its deistic view of God, who must dance to men’s attempts to manipulate the spiritual laws of the universe; (2) its demonic view of Christ, who is filled with “the satanic nature” and must be “born-again” in hell; (3) its gnostic view of revelation, which demands denial of the physical senses and classifies Christians by their willingness to do so; (4) its metaphysical view of salvation, which deifies man and spiritualizes the atonement, locating it in hell rather than on the cross, thereby subverting the crucial Christian belief that it is Christ’s physical death and shed blood which alone atone for sin.”

I have addressed in part 2 here the idea that a particular theory of the atonement is part of Christian orthodoxy; it is not. Each theory has its advantages and disadvantages. The ransom theory has the particular disadvantage of making the atonement seem to be paying off Satan, but the other theories have their disadvantages, too. McConnell’s objections (2) and (4) thus reflect his sectarianism.

Objection (1) is a common objection to the Word of faith teachings, but it is a misunderstanding. The God of the Bible is a God of laws. Does that mean God is bound by His own laws? That is an old theological conundrum. Are there spiritual laws? See Bill Bright’s famous Four Spiritual Laws here. Where are the books claiming heresy for these spiritual laws? There is no more problem with spiritual laws then with physical laws. The idea that we could get spiritual laws working for us should be no more problematic than getting physical laws working for us.

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Dual dynamics equations

(1) Newton’s Second Law

Momentum is defined as the product of mass m and velocity v. The mass of a body is a scalar, though not necessarily a constant. Velocity is a vector equal to the time rate of change of location, v = ds/dt.

The time rate of change in momentum is dp/dt = m dv/dt + v dm/dt = ma + v dm/dt by the rules of differential calculus and the definition of acceleration, a.

If mass is constant, then v dm/dt equals zero and the equation reduces to dp/dt = ma. If we define F = dp/dt, then we get Newton’s famous F = ma.

The dual equation is derived similarly:

Fulmentum is defined as the product of vass n and legerity u. The vass of a body is a scalar, though not necessarily a constant. Legerity is a vector equal to the base rate of change of chronation, u = dt/ds.

The base rate of change in fulmentum is dq/ds = n du/ds + u dn/ds = nb + u dn/ds by the rules of differential calculus and the definition of expedience, b.

If vass is constant, then u dn/ds equals zero and the equation reduces to dq/dt = nb. If we define R = dq/ds, then we get the dual of Newton’s second law, R = nb.

(2) Work and kinetic energy

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Mean speed of light postulate

Einstein stated his second postulate as (see here):

light is propagated in vacant space, with a velocity c which is independent of the nature of motion of the emitting body.

Since the one-way speed of light cannot be measured, but only the round-trip (or two-way) speed, let us modify this postulate to state:

The measured mean speed of light in vacant space is a constant, c, which is independent of the nature of motion of the emitting body.

This is the most that can be empirically verified. Then for convenience sake, let us adopt the following convention:

The final observed leg of the path of light in empty space takes no time.

Since the (harmonic) mean speed of light is c, the speeds of the other legs of light travel are at least c/2 such that the mean speed equals c. In this way, the Galilean transformation is preserved for the final leg. And interchanging length and duration leads to an alternate version of the Galilean transformation.

This accords with common ways of speaking. Even astronomers speak of where a star is now, rather than pedantically keep saying where it was so many years ago. Physical theory should be in accord with observation of the physical world as much as possible. This is an example of how amateur scientists can help re-integrate science and common life.