iSoul In the beginning is reality

Definition of vass

See also the related post on the Center of vass. Relativity has been addressed before, such as here.

Isaac Newton called mass “the quantity of matter”, which is still used sometimes, although Max Jammer points out how it has been criticized for centuries (see Concepts of Mass in Classical and Modern Physics, 1961). Other definitions arose in the 19th century. One is the ratio of force to acceleration, which assumes that force can be defined independently of mass.

Another approach is to define the equality of masses. For some such as Saint-Venant, “two bodies have equal masses if their velocity increments after impact are equal.” (ibid., p.91) For Ernst Mach equal masses “induce mutually equal and opposite accelerations.” (ibid., p.94)

Is there an independent definition of vass, the inverse of mass? One could modify these definitions of mass to define vass or equality of vasses:

Definition 1: Vass is the ratio of the surge to the prestination of a body.

Definition 2: Two bodies have equal vasses if their celerity increments after impact are equal.

Definition 3: Two bodies have equal vasses if they induce mutually equal and opposite prestinations.

In relativity theory, mass is dependent on velocity as follows:

m = γ m0,

with mass m, invariant mass m0, velocity v, speed of light c, and γ = (1 – v²/c²)–1/2.

It is easily verified that vass is dependent on celerity as follows:

ℓ = ℓ0 / γ,

with vass ℓ, invariant vass ℓ0, celerity u, pace of light ç, and γ = (1 – ç²/u²)–1/2.

From time to space and back

One question is how to translate from time rates to space rates and vice versa. Consider scalar space and scalar time, and designate the spatial position, s, initial spatial position, s0, temporal position, t, initial temporal position, t0,, velocity, v, initial velocity, v0, acceleration a (assumed constant over time), celerity, u, initial celerity, u0, and prestination, b (assumed constant over space). Then the linear equations of motion are as follows (see also the equations of motion at the top menu or here):

s = s0 + vt; v = v0 + at; s = s0 + v0t + ½at²; = v0² + 2a(s s0);

t = t0 + us; u = u0 + bs; t = t0 + u0s + ½bs²; u² = u0² + 2b(t t0)

From these we have the following derivatives:

ds/dt = v = 1/u; dv/dt = a; dt/ds = u = 1/v; du/ds = b;

du/dv = –1/v² = –u² and dv/du = –1/u² = –v².

If we are given the acceleration, a, what is the prestination, b? This may be determined as follows:

b = du/ds = dv/dt * dt/ds * du/dv = a * (1/v) * (–1/v²) = –a/v³ = –a/(v0 + at)³.

If v0 = 0, then b(t) = –1/(a²t³).

So the prestination is a function of scalar time.

Similarly, if we are given the prestination, b, what is the acceleration, a? This may be determined as follows:

a = dv/dt = du/ds * ds/dt * dv/du = b * (1/u) * (–1/u²) = –b/u³ = –b/(u0 + bs)³.

If u0 = 0, then a(s) = –1/(b²s³).

So the acceleration is a function of scalar space.

Variation is a fact

One of the characteristics of post-modernism is the overlap between facts and theories. In modern science theories were based on facts, theories explained facts, and theories connected facts together. But post-modernism blurs the distinction between facts and theories. For example:

In science, a “fact” typically refers to an observation, measurement, or other form of evidence that can be expected to occur the same way under similar circumstances. However, scientists also use the term “fact” to refer to a scientific explanation that has been tested and confirmed so many times that there is no longer a compelling reason to keep testing it or looking for additional examples. Because the evidence supporting it is so strong, scientists no longer question whether biological evolution has occurred and is continuing to occur. Instead, they investigate the mechanisms of evolution, how rapidly evolution can take place, and related questions. The National Academies – Evolution Resources [The National Academies is also known as the (U.S.) National Academy of Sciences.]

It is easily seen that the term “evolution” is used in (at least) two different senses. Under Definitions, the above website provides the following:

Evolution: Evolution consists of changes in the heritable traits of a population of organisms as successive generations replace one another. It is populations of organisms that evolve, not individual organisms.

That is the factual part. But there is another part, the theory part, which is obscured by not distinguishing fact from theory. For example, their entire website only mentions common descent once, and that in reference to additional resources:

With the publication in 1859 of On the Origin of Species by Means of Natural Selection, Charles Darwin established evolution by common descent as the dominant scientific explanation for nature’s diversity. The National Academies – Darwin’s Gift to Science and Religion

Note also the reification of nature (“nature’s diversity”) and evolution as a “gift” (as if Darwin brought it down from Mt. Science).

But in the context of Darwin’s The Origin of Species by Means of Natural Selection and the modern theories of evolution, “evolution is a fact” may tend to block a full view of the major theories and the hundreds of subtheories found in the study of evolution (Lewis, 1980). NCSE – Theory and the Fact of Evolution.

What does the theory part of evolution include? U. Kutschera and K.J. Niklas list the principal propositions of Darwin’s theory:

1. Supernatural acts of the Creator are incompatible with empirical facts of nature
2. All life evolved from one or few simple kinds of organisms
3. Species evolve from pre-existing varieties by means of natural selection
4. The birth of a species is gradual and of long duration
5. Higher taxa (genera, families etc.) evolve by the same mechanisms as those responsible for the origin of species
6. The greater the similarities among taxa, the more closely they are related evolutionarily and the shorter their divergence time from a last common ancestor
7. Extinction is primarily the result of interspecific competition
8. The geological record is incomplete: the absence of transitional forms between species and higher taxa is due to gaps in our current knowledge
Naturwissenschaften (2004) 91:255–276

All of these propositions are theoretical. The modern synthesis version of evolution adds the genetics of populations to this (Systematics and the origin of species: An introductiom – Hey, Fitch, and Ayala).

So the “fact of evolution” is quite different from the propositions claimed about evolution. The fact – “changes in the heritable traits of a population of organisms as successive generations replace one another” – is better described as variation. It consists of differences observed between the generations. These are the variations that naturally occur.

The term “evolution” implies progress- etymologically, it means an unrolling. Evolution was applied by Herbert Spencer first to society. “Social progress is in fact viewed as a natural evolution”. He was “the first to work out a comprehensive philosophical system … on the basis of the principle of Evolution.” (Herbert Spencer and the Doctrine of Evolution)

But progress is not observed between the generations. What is observed is variation. It is misleading to use the word “evolution” to describe the observation of variation.

From 1D to 3D in two ways

Among the instruments on a vehicle there may be a speedometer, an odometer, a clock, and a compass, which provide scalar (1D) readings of the vehicle’s location. But what is the location of the vehicle in a larger framework? The compass shows two dimensions must exist on a map of this framework, but of what are they dimensions?

The identity of the two dimensions depends on whether the dimensions are associated with the odometer reading (the travel distance) or the clock reading (the travel time). Let’s represent the travel distance by s, the travel time by t, the speed by v, and the travel direction by angle α clockwise from North.

Consider a simple example in which the vehicle is traveling at a constant speed and not changing direction. Then the ratio of the travel distance to the travel time is a constant, which equals the reading on the speedometer: v = s / t.

The vehicle location may be envisioned in two different kinds of maps: (1) In the first kind of map, which is the familiar one, the travel direction is associated with the travel distance. Then the odometer and compass determine the vehicle location, which may be specified by the polar coordinates (s, α) = s. This ordered pair represents a spatial position vector, s. A velocity vector may be constructed from it as v = s / t.

(2) However, we could just as well associate the travel time with the travel direction. So for the second kind of map, the clock and compass determine the vehicle location, which may be specified by the polar coordinates (t, α) = t. This ordered pair represents a temporal position vector, t. A celerity vector, u, may be constructed from it as u = t / s.

Let’s look at another simple example. Consider a vehicle on a curve that turns for an angle θ at a constant angular velocity of ω with a turning radius of r. The travel distance on the curve is s = = ωt. The travel time is t = /ω = s/ω. In the first case the spatial vector is s = (r cos(ωt), r sin(ωt)). In the second case the temporal vector is t = (r cos(s), r sin(s)), which is found by reparameterizing by the arc length.

Note that in the first kind of map the travel time remains a scalar, which is not associated with any particular position on the spatial map and so is a universal time. Note that in the second kind of map the travel distance remains a scalar, which is not associated with any particular position on the temporal map and so is a universal distance.

The question, “What time is it?” refers to scalar time, which is associated with all points of 3D space. Similarly, one could ask, “what space is it?” referring to the scalar distance, a 1D space, which is associated with all points of 3D time.

Physics and theology

The 19th century physicist Ernst Mach is known for his view that all motion is relative, which influenced Albert Einstein. Mach is also known for his book The Science of Mechanics (1883 in German, 1893 in translation), from which the following excerpts about physics and theology are taken (Open Court edition, 1960):

Consolation, [Pascal] used to say, he could find nowhere but in the teachings of Christianity; and all the wisdom of the world availed him not a whit. p.543

Every unbiased mind must admit that the age in which the chief development of the science of mechanics took place, was an age of predominantly theological cast. Theological questions were excited by everything, and modified everything. No wonder, then, that mechanics is colored thereby. p.546

In Leibniz’s correspondence with John Bernoulli, theological questions are repeatedly discussed in the very midst of mathematical disquisitions. Their language is not unfrequently couched in biblical pictures. p.549

Maupertuis, the famous president of the Berlin Academy, and a friend of Frederick the Great, gave a new impulse to the theologizing bent of physics by the enunciation of his principle of least action. In the treatise which formulated this obscure principle … the author declared his principle to be the one which best accorded with the wisdom of the Creator. p.549

Euler magnanimously left the principle [of least action] its name, Maupertuis the glory of the invention, and converted it into something new and really serviceable. … The theological point of view, Euler retained. He claims it is possible to explain phenomena, not only from their physical causes, but also from their purposes. “As the construction of the universe is the most perfect possible, being the handiwork of an all-wise Maker, nothing can be met with in the world in which some maximal or minimal property is not displayed. There is, consequently, no doubt that that all the effects of the world can be derived by the method of maxima and minima from their final causes as well as from their efficient ones.” p.550

Similarly, the notions of the constancy of the quantity of matter, of the constancy of the quantity of motion, of the indestructibility of work or energy, conceptions which completely dominate modern physics, all arose under the influence of theological ideas. The notions in question had their origin in an utterance of Descartes, before mentioned, in the Principles of Philosophy, agreeably to which the quantity of matter and motion originally created in the world–such being the only course compatible with the constancy of the Creator–is always preserved unchanged. The conception of the manner in which this quantity of motion should be calculated was very considerably modified in the progress of the idea from Descartes to Leibniz, and to their successors, and as the outcome of these modifications the doctrine gradually and slowly arose which is now called the “law of the conservation of energy.” But the theological background of these ideas only slowly vanished. p.551

During the entire sixteenth and seventeenth centuries, down to the close of the eighteenth, the prevailing inclination of inquirers was, to find in all physical laws some particular disposition of the Creator. But a gradual transformation of these views must strike the attentive observer. Whereas with Descartes and Leibniz physics and theology were still greatly intermingled, in the subsequent period a distinct endeavor is noticeable, not indeed wholly to discard theology, yet to separate it from purely physical questions. Theological disquisitions were put at the beginning or relegated to the end of physical treatises. Theological speculations were restricted, as much as possible, to the question of creation, that, from this point onward, the way might be cleared for physics. p.551-552

Towards the close of the eighteenth century a remarkable change took place,–a change which was apparently an abrupt departure from the current trend of thought, but in reality was the logical outcome of the development indicated. After an attempt in a youthful work to found mechanics on Euler’s principle of least action, Lagrange, in a subsequent treatment of the subject, declared his intention of utterly disregarding theological and metaphysical speculations, as in their nature precarious and foreign to science. He erected a new mechanical system on entirely different foundations, and no one conversant with the subject will dispute its excellencies. All subsequent scientists of eminence accepted Lagrange’s view, and the present attitude of physics to theology was thus substantially determined. p.552 [Lagrange’s Mécanique analytique was published in 1788.]

Newton never, despite his profound religiosity, mingled theology with the questions of science. … The same may be said of Galileo and Huygens. p.552

It stands to reason that in a stage of civilization in which religion is almost the sole education, and the only theory of the world, people would naturally look at things from a theological point of view, and that they would believe that this view was possessed of competency in all fields of research. p.553 #

… the theological conception of nature itself owes its origin to an endeavor to obtain a more comprehensive view of the world;–the very same endeavor that is at the bottom of physical science.  p.556

In fact, science can accomplish nothing by the consideration of individual facts; from time to time it must cast its glance at the world as a whole. p.556

But now, after a century has elapsed, after our judgment has grown more sober, the world-conception of the encyclopaedists appears to us as a mechanical mythology in contrast to the animistic of the old religions. p.559

Physical science does not pretend to be a complete view of the world; it simply claims that it is working toward such a complete view in the future. The highest philosophy of the scientific investigator is precisely this toleration of an incomplete conception of the world and the preference for it rather than an apparently perfect, but inadequate conception. p.559

# One might update this sentence as follows: It stands to reason that in a stage of civilization in which science is almost the sole education, and the only theory of the world, people would naturally look at things from a scientific point of view, and that they would believe that this view was possessed of competency in all fields of research.

Time and space as scalars or vectors

We need to distinguish between scalar (1D) and vector (3D) versions of both time and space. Motion in scalar (1D) time and scalar (1D) space is measured by clocks and odologes, respectively, and apply throughout the associated vector space or vector time (in Newtonian mechanics).

Scalar space is like scalar time. They are proportional if an odologe with constant pace is used. If celestial bodies are used, they may be not quite proportional.

Motion in vector (3D) time and vector (3D) space is measured as points on a curve (trajectory), which may be decomposed into components. The position vector to each point is its distimement or displacement, respectively.

Each instance of vector space is associated with one point of scalar time, and each instance of vector time is associated with one point of scalar space. A value of scalar time is called the time. A value of scalar space may be called the space because it answers the question, ‘which instance of space is it?’

The travel time of a body between two points of vector time, A and B, may be measured with a stopwatch accompanying the body starting simultaneously with A and ending simultaneously with B. The travel distance of a body between two points in vector space, C and D, is measured with a measuring wheel (odometer) accompanying the body starting at location C and ending at location D.

The speed of a body is the travel distance per unit of travel time. The pace of a body is the travel time per unit of travel distance. The velocity and celerity include the vector travel direction of the body with the ratios given.

Since the travel time or travel distance may not be available to an observer not on the body, the velocity and celerity may make use of the scalar time or space in the denominator, respectively.

For the velocity one can substitute the vector travel distance per unit of scalar time. The speed uses the magnitude of the vector travel distance per unit of scalar time.

For the celerity one can substitute the vector of travel time per unit of scalar space. The pace uses the magnitude of the vector travel time per unit of scalar space.

Synopsis of the Gospel

A previous post here gave a summary of the Gospel. The following comes from Rev. David Harper’s blog entry, The power of story:

Here’s a synopsis.

1. God created humankind in His image for fellowship and partnership, entrusting to us stewardship of His earth. (Gen. 1:28)  

2. Because of sin, in which we all participate, our fellowship with God and one another has fractured (Gen. 3:1-19, 4:8; Rom. 3:23).

3. God sent His Son, Jesus, as the promised Messianic King and Son of God, come to earth in human form to become one with us. (Rom. 1:3-4; Phil. 2:4ff.).

4. By his death and resurrection, Jesus atoned for our sin, and secured our justification by grace, (1 Cor. 15:3ff.). He has broken the dominion of sin and evil over us (Col. 2:13-15), restored us to right relationship with the Father, and made us the firstfruits of His new creation. (James 1:18)

 5. He has given us His Holy Spirit to empower us to do the works that Jesus did, enlisting us in His plan and purpose to make the whole creation new. (John 14:12ff, Acts 2:1ff, Eph. 1:9-10, 3:8-12

6. At his return, Jesus will complete what he began by the renewal of the entire material creation, and the resurrection of our bodies (Rom 8: 18ff.).)

For more from Rev. Harper, see his website Things New & Old. One thing he is known for is expressed in his talk on Three Streams, One River.

Design illustrated

This post continues thoughts about design, last posted here.

Here is a description of how cement is made from the Portland Cement Association:

In its simplest form, concrete is a mixture of paste and aggregates, or rocks. The paste, composed of portland cement and water, coats the surface of the fine (small) and coarse (larger) aggregates. Through a chemical reaction called hydration, the paste hardens and gains strength to form the rock-like mass known as concrete.

The key to achieving a strong, durable concrete rests in the careful proportioning and mixing of the ingredients. A mixture that does not have enough paste to fill all the voids between the aggregates will be difficult to place and will produce rough surfaces and porous concrete. A mixture with an excess of cement paste will be easy to place and will produce a smooth surface; however, the resulting concrete is not cost-effective and can more easily crack.

The design in this case is the proportion of ingredients in the mixture. It might happen that the ingredients formed naturally but they would be in the correct proportion only by design. That is, the particular application entails a goal, which the design meets.

Certainly concrete can and does happen naturally in aggregate rock formations. But it does not meet a need without a design. And that doesn’t happen naturally. Roads built with concrete only happen because engineers and construction crews built them. There’s nothing natural about that.

Time space and and space length

I’ve been revising the glossary lately, see above. This required adjusting the post on Foundations of mechanics for time-space, among others. Here is an explanation:

Ordinary 3D space is measured by distances. Correspondingly, 3D time is measured by durations. That is, 3D time is a space of times. Call this time space.

Ordinary 1D time is an independent duration. Correspondingly, 1D space is an independent distance, like time composed of distance. However, there is not necessarily a “flow” – the distance is increased as needed. Call this a space length. 1D time is then a time length.

1D time is that which is measured by a clock. What is 1D space measured by? We need a measure of distance that continues indefinitely. A measuring wheel would do if it keeps going. Or the Voyager 1 spacecraft continuing into space, see here. Call this an odologe, from Greek odo(s), way/path + (horo)loge, clock.

Mechanics studies the motion of bodies in 3D space over 1D time. Correspondingly, mechanics can study the motion of time bodies in 3D time over 1D space. What is a time body? It’s a body but its dimensions are durations, not lengths. That is, it is a body for motion, or a vehicle.

A body in dynamics is conceived as a collection of particles. What is a time body composed of? A time body is conceived as a collection of eventicles. An eventicle is a point vass, as a particle is a point mass.

Inertia is the resistance of a body to any change in its state of motion. Correspondingly, an alacrity is the nonresistance of a time body to a change in its state of motion. Inertial reference frames move at constant speed in a straight line. Alacrital reference timeframes move at constant pace in a straight line. Because of the inverse relation between speed and pace, inertial and alacrital frames are equivalent.

Terms for science controversies

Controversies are more difficult than they need be. I have written about this before here and here. One challenge for dealing with controversies is that terminology is misleading, inaccurate, or loaded. Here are some examples from the creation-evolution controversy.

The term ‘evolution’ originally meant an unrolling, and was applied by Charles Lyell and Herbert Spencer to the idea that there was a natural progression over time from lower to higher organisms. Charles Darwin did not originally call his theory ‘evolution’ but others prevailed on him to use the term. Ever since people have confused the idea of progress with Darwin’s theory of unguided evolution.

Historically, Darwin’s theory is one of several theories of transmutation, which is any natural sequence of changes over time from lower to higher organisms. Darwin’s particular theory was that the natural variability of generations over a long time might result in some populations of lower species transmutating into higher species. In other words, varieties could become new species, which could become new genera, and so on.

The process Darwin theorized is not an unrolling as the term evolution would imply, and even transmutation gives it a direction which is not part of the undirected process. A better term would be “variationism” because it posits that every species starts as a variety, or variation of an existing species. It’s like a chemist who asserts that isotopes can become new elements.

A naturalist refers to person who studies nature. But it can also refer to one who promotes naturalism, the teaching that nature is all there is. It would be better to call the first kind of naturalist a ‘naturist’ since it is nature, not ‘the natural’ that they study.

Naturalism is the foundation of transmutationism, including the variationism known as evolution. Some would call a change “from molecules to man” evolution but evolutionists don’t like to address the origin of life. And cosmic evolution refers to the ideas of Pierre Teilhard de Chardin. It is naturalism that leads people to support stellar evolution, and other ideas in which ‘nature’ explains the whole history and condition of the universe.

Naturalism is opposed by creationism, though creationism is often paired against evolution. Creationism originally meant that God created the universe, without addressing what has happened since the creation. This is not a bad usage but what about the character of the original creation? It is not part of a natural progression, and is more than mere creation. The key issue is the creation of kinds of things, particularly populations that can vary only within created limits.

The question then is the existence of ‘natural kinds’ which are kinds of things that possess a fixed nature. To include creation in the concept, a ‘natural kind” would be a ‘created kind’. And someone who accepts ‘created kinds’ should be called a, well, ‘creationist’ in the sense that includes created kinds. At least this is not far from the common meaning today.

The term ‘scientist’ is problematic, too. It would literally mean someone who studies knowledge. That would refer to every discipline that concerns knowledge, including history, philosophy, theology, etc. But the term is meant for a restricted class of people who study empirical science. The correct term would seem to be ’empiricist’. However, empiricism is a teaching that all knowledge is based on sense experience. That usually means ‘scientism’ so we seem to be going in circles.

The solution is to broaden the definition of scientist to include all those who study the sciences, as distinct from the arts. The restricted usage would then be ’empirical scientist’. Since one does not need a license to practice science, unlike the medical or engineering professions, the term ‘scientist’ seems to be available for wider usage. So historians, philosophers, and theologians are scientists, too.