iSoul In the beginning is reality.

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 etherance n and lenticity u. The etherance of a body is a scalar, though not necessarily a constant. Lenticity is a vector equal to the stance rate of change of chronation, u = dt/ds.

The stance 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 retardation, b.

If etherance 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 two-way 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.

Word of Faith, part 3

One of the main teachings of the Word of Faith movement concerns one’s “confession.” This teaching goes back to E. W. Kenyon, but before looking at what he wrote, let’s consider what a leader of the movement, Kenneth E. Hagin, wrote about it in his exposition of Mark 5:25-34 in his book “Exceedingly Growing Faith,” Chapter VI.

The story concerns a woman with “an issue of blood” who touched the hem of Jesus’ garment while he was in a crowd. Hagin points out the steps she took: (1) She said it: “For she said, If I may touch but his clothes, I shall be whole.” (Mark 5:28) (2) She did it: she got close enough to Jesus to do it. Because she was unclean she was supposed to stay away from others, so by this action she was taking a risk. (3) She received it: she received the healing from Jesus. (4) She told it: Jesus asked, “Who touched my clothes?” (Mark 5:30) She again took a risk by telling her story publicly.

Hagin also references the story of David and Goliath as an example of the importance of saying what one believes: (I Samuel 17):

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Word of Faith, part 2

E. W. Kenyon is widely considered the originator of what is now called the Word of Faith. A previous series of posts showed that Kenyon’s teachings about divine healing were in line with the 19th century faith-cure movement (see here). Theological issues that arise concerning E. W. Kenyon’s writings include his theory of the atonement.

Although theories of the atonement are often considered a part of the orthodox core of Christianity, they are not. Through the centuries Christians have disagreed about the particular reasons for the death of Christ, what its significance is, and what it accomplished. For example, several theories of the atonement are given here.

E. W. Kenyon has his own variation, which combines the Ransom and Substitutionary theories of the atonement, as described in his book “What Happened from the Cross to the Throne” (Seventh Edition, 1969). Here are some excerpts (combining his one sentence paragraphs):

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Word of Faith, part 1

This post begins a series on the Word of Faith movement (also known as word-faith, faith, or by its critics the prosperity gospel or health and wealth gospel). The purpose of this series is to clarify the biblical teachings of this movement. Because many of its expositors lack formal theological education, it is not uncommon for their words to raise theological red flags. But many reject the Word of Faith teachings with little understanding of them, or by taking passages out of context.

While there certainly have been excesses, this series of posts will provide reasons why core Word of Faith teachings are within the broad range of orthodox Christianity. That said, this series of posts does not justify lavish lifestyles, deceptive practices, or false claims. The focus is on the core teachings of the Word of Faith and their biblical justification.

It is important to know from the outset that there are three independent 19th century movements that have some similarities but are radically different: (1) the nature cure, (2) the mind cure, and (3) the faith cure. All sought healing apart from the allopathic medicine that was considered mainstream.

(1) “Nature cure, or natural care refer to methods of self-healing, often using fasting, dieting, rest, or hydrotherapy.” Also included are orthopathy and naturopathy. (Wikipedia)

(2) Mind cure is a “healing system according to which feelings or thoughts are the most important factor in human health. Negative thinking is believed to cause disease, whereas good health results from positive thoughts.” (Free Dictionary) “William James used the term ‘New Thought’ as synonymous with the ‘Mind cure movement.'” (Wikipedia)

(3) Faith cure is “a method or practice of treating diseases by prayer and exercise of faith in God.” (Merriam-Webster)

The teachings of the Word of Faith movement grew out of the faith cure (3) movement, not the others.


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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

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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 a metreloge here.

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

Falling projectile

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. The vertical component represents the dependent variable, which has the form of a semi-parabola. The uniform horizontal motion, which could be any in direction, is the independent variable in units of either length or duration.

To interchange length and duration in an equation with a parametric function of time requires four steps: (1) with a change of variables switch the independent and dependent variables, time and stance; (2) linearize the stance, that is, break its dependent relation; (3) bring time under a functional relation with the new parameter, stance; and (4) 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, stance. The constant acceleration of the vertical component is re-conceived to represent the dependent duration variable with constant lenticity. 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 stance. In that sense it would be best to abstract a functional representation that applies to both length and duration, time and stance.

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 Galileo Reciprocity Principle, the convention that an observed frame has the opposite orientation as the frame from which it is observed, which ensures that corresponding velocities are equal. It is the opposite of the Einstein Reciprocity Principle, the convention that an observed frame has the same orientation as the frame from which it is observed.