iSoul In the beginning is reality

Modernity and parsimony

I’ve written before about modernity here and parsimony here.

An age begins by repudiating something essential about the previous age. The middle ages started with repudiating the ancient gods and myths (cf. St. Augustine’s City of God). The modern age began with the Reformation, which repudiated the history of the Church and the pagan past of the Gentiles. It continued with scientists repudiating Scholasticism and Aristotle. And it came into its own by starting anew, whether in religion or science or politics.

If modernity starts with breaking free of the past, then what keeps it from flaming out into insignificance? The key for science was parsimony, commonly called simplicity. In contrast with the middle ages, which specialized in ad hoc explanations, the modern age adopted Occam’s razor, the law of parsimony, which privileged the fewest number of assumptions and kinds of entities.

Modernity took the law of parsimony to an extreme. It led to questioning, if not overthrowing, every tradition, every non-empirical entity, every metaphysics. The absolute minimum ontology was considered the best, which turned out to be the physical world.

Even the nature of physical things was questioned as unknowable, until the only nature left was the nature of the physical world. This nature became the idol of modernity, the one thing that could not be questioned. It became Nature, reified as something with a will of its own, something that led to human life, something that substituted for God.

As we break free of modernity, we can see its limitations and failures more and more. One is the bias of the law of parsimony: it meant qualitative parsimony but not quantitative parsimony. That is, only one or a few kinds of things could exist, but the number of them available for explanatory purposes was unlimited. This bias fit well with the use of mathematics as the language of science.

But mathematics is more than the study of quantity. It is also the study of space, structure, and change. And there is no good reason not to apply parsimony to all of them in finding the best explanation. Once we open up to the possibility of a balanced application of the law of parsimony, we can see some of the weaknesses of modern science.

Deep time was invented in the 18th century and exploited in the 19th and 20th centuries to explain the history of the Earth and the universe. What started with geology expanded to human history, biology, and cosmology.

It is all a matter of time scale. An event that would be unthinkable in a hundred years may be inevitable in a hundred million. Carl Sagan

Time is in fact the hero of the plot. … Given so much time, the “impossible” becomes possible, the possible probable, and the probable virtually certain. One has only to wait; time itself performs the miracles. George Wald

The flaw is simple: it’s too easy to “explain” anything. The violation of quantitative parsimony was the Achilles’ heel of modernity. The temptation to explain everything was too much to resist. And so, as with every age, modernity ended in failure. A great failure, but a failure nonetheless.

We can only hope that the current age will learn from the failure of modernity and seek a balanced parsimony.

International English spelling

With the spread of printing and literacy, spelling became standardized. In the U.S. Noah Webster, who wrote the first dictionary of American English, successfully introduced new spellings, which became standard in the U.S. Now that the Internet has facilitated international written communication, there is a need for an international standard of English spelling.

One could say that Americans should just adopt the spellings of the English as written by the English people, that is, British English. That is not likely to happen. For one thing, American idioms are influential internationally. Look at how “OK” became international.

There have been attempts to promote International English that are more concerned with ease of learning than with spelling. While spelling differences are minor, those publishing for an international audience need to have some standards. Editors do, too.

I certainly don’t have the last word on this, but I can at least make some suggestions and adopt them myself. If there are good reasons to retain the British spelling, let’s do so. But if American norms are OK or have advantages, let’s not shy from adopting them instead. Here are a few suggestions for the purpose of this blog:

(1) Metric units. The International System of Units uses British spellings. It also has the advantage of preserving a spelling distinction between a device or instrument for measuring and the other meanings of meter in American English. Adopt the British spelling.

(2) Other distinctions are sometimes obscured in Noah Webster’s shorter spellings. For example, the meaning of the suffixes -er and -or as “one who…” such as carpenter and author are obscured by changing other words to end in -er and -or. Meter is an example of the former; color is an example of the latter (one who cols?). Since the British spelling preserves these distinctions, they should be adopted.

(3) There are many variants of spelling (or terminology) that have no particular advantage one way or the other. Traveling or travelling? The former is American, the latter British. The American rule is “when a multisyllabic word ends in a vowel and a consonant (in that order), you double the consonant when adding a suffix only if the stress falls on the final syllable.” I usually prefer the American usage in that case.

Observers and travelers, continued

This post continues the topic of the previous post here. This is a post about two kinds of people. First a warning:

There may be said to be two classes of people in the world; those who constantly divide the people of the world into two classes, and those who do not. – Robert Benchley

Actually, this post is about two different roles that people take, though some people get stuck in one role or the other. Consider these pairs of complementary roles:

speakers and listeners, writers and readers, artists/performers and viewers, musicians and audiences, programmers/designers and users, producers and consumers, etc.

Scientists and engineers often have complementary roles: engineers making things that work in the world and scientists observing and seeking to understand the world. In the MBTI personality types, there are judgers and perceivers. Combine all these with travelers and observers, transmitters and receivers, of the previous post.

What is the basic distinction here? It’s between an active role and a passive role, between having a goal and a way to get there vs. letting things go and seeing what happens. In terms of Aristotle’s four causes, it’s between the final and formal causes vs. the mechanistic/efficient and material causes.

Aristotle give an example of a sculptor, who starts with a final goal in mind and develops a plan, a design, a form. Then they take some material such as marble or clay and use tools to form it into something. An observer would only see the last two steps: the material and the action on it. They would have to infer the first two steps – or else stick to the empirical and ignore the first two steps.

In terms of studying motion, the distinction is between having a destination and moving there vs. starting somewhere and observing what motion there is. These two roles lead to the two approaches to space and time: 3+1 dimensions and 1+3 dimensions.

These roles are distinct even when they’re combined. For example, scientists do experiments, which requires an active role, but the purpose is to observe, which means to watch what happens.

These roles are different enough so that communication may be a problem. They speak different dialects and some translation may be required for them to understand one another. Knowing about personality types provides a clue as to how to approach those who prefer to take a particular role.

A few favorites of this “different kinds of people” genre:

There are three kinds of people in the world: Those who know math and those who don’t.

There are 10 kinds of people in the world: Those who understand binary and those who don’t.

There are two types of people in this world: Those who can extrapolate from incomplete data

Observers and travelers

Let us distinguish between observer-receivers and traveler-transmitters. Although observers can travel and travelers can observe, insofar as one is observing, one is not traveling, and insofar as one is traveling, one is not observing. The main difference is this: traveler-transmitters have a destination but observer-receivers do not (or at least not as observers).

Compare the roles of the driver and the passengers in a vehicle: the driver is focused on the road and traveling to the destination, whereas the passengers are looking out the window and observing things in the landscape. These are two different roles.

Observer-receivers of motion naturally compare the motion observed with the elapsed time. But traveler-transmitters have a destination and naturally compare the travel motion with the elapsed distance, which measures progress toward the destination. Because of this, the frame of mind for observer-receivers is 3D space + 1D time, whereas it is 1D space + 3D time for traveler-transmitters.

Observers of the sky naturally think of celestial bodies as appearing when they are observed, as with celestial navigation. That is, they act as though the light observed arrives in their sight instantaneously.

Transmitters of light naturally think of light as reaching its destination as they transmit it, as with visual communication. That is, they act as though the light transmitted arrives at its destination instantaneously.

This is consistent with having two conventions of the one-way speed of light (previously discussed here). To be consistent with the round-trip speed of light equaling the value, c, for all observers, that implies the following:

For observers: received light is instantaneous but transmitted light travels at the speed c/2.

For travelers: transmitted light is instantaneous but received light travels at the speed c/2.

Although relativity theory is the scientific approach, for everyday life the above speeds make things simpler, and are fully legitimate.

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 longicty 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 progressity as follows:

n = n0 / γ,

with vass n, invariant vass n0, progressity 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), progressity, u, initial progressity, 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 progressity 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

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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 progressity 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 progressity 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 progressity 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.