iSoul In the beginning is reality

Centrism and extremism

I’ve written on my understanding of centrism here and here.

The essence of centrism is an acceptance of a limit for everything. This means there are limits in all directions. The image of this is a closed convex curve with a center in the middle of the region enclosed.

Without limits, there is no center. A center is always within limits. If there is any direction without a limit, the curve is not closed and there is no center.

Non-centrists are extremists in at least one way. They reject a limit in at least one direction. They are not only not in the center, but they reject the existence of a common center.

The slogan “No enemies on the Left” is a left-wing motto that goes back at least to the 1930s. It reflects an attitude that in the direction of leftist politics, there is no limit. Because it lacks a limit in at least one direction, it is extremist in at least one direction.

Most political groups promote some cause or idea that takes precedence over all other causes or ideas. They may hold these in a limited way, but unless they have ways of limiting the range of their support, they will tend to go further and further in that direction. They are or will become extremists.

Linear references and 3D time again

This post is related to previous ones about 1D space + 3D time, such as here and here.

Time is measured in terms of the annual calendar and the daily clock. Clocks are based on the apparent motion of the Sun and other celestial bodies across the sky, divided into 24 hours. The calendar is based on the annual cycle of the Sun’s declination (the angular distance north or south of the celestial equator), divided into 12 months and 365 (or 366) days. Thus time is measured in terms of the Earth’s orbital and rotational periods.

Length may be measured similarly. The original definition of the metre (meter) in 1793 was one ten-millionth of the distance from the equator to the North Pole. What is required for linear references is a motion whose travel length may be accumulated indefinitely. What corresponds to the clock could be the motion of the night shadow across the face of the Earth at the equator:

So the evening and the morning were the [Nth] day. Genesis 1

The circumference of the Earth is 40,075,000 m. This is the distance moved by the edge of the day-night boundary in 24 hours. Then one hour is equivalent to 1,669,792 m and one second is equivalent to 464 m. The shadow motion may be accumulated indefinitely to make reference length, similar to reference time.

Whichever dimension is limited to 1D is the measure of a motion from the perspective of the body in motion, whether this is measured by the length or duration. Since the 1D variable is the independent variable, this is selected as a standard motion available (in principle) to everyone. So the 1D variable becomes a universal length or time against which to measure motions in 3D of time or space, respectively.

Measuring mass and vass

A mass may be measured by a scale with a fulcrum, such as this:

mass1 at distance a to the left of the fulcrum is balanced by mass2 at distance b to the right

If the mass of M1 is a standard mass such as a kilogram, then the gravitational mass of M2 can be determined from the law of the lever as follows:

M2 = M1 × a ÷ b.

Such a scale can also be used to measure the inverse mass, 1/M2, which I’m calling the vass), L2:

L2 = 1/M2 = b ÷ (M1 × a) = L1 × b ÷ a.

The mass and the vass are related properties of a physical body. They can be measured together. The scale for vass is the inverse of the scale for mass: the scale for minimum to maximum mass corresponds to the scale for maximum to minimum vass.

A balance

Anisotropy and reality

This follows posts on synchrony conventions such as here.

Astronomers say things like this: “it takes sunlight an average of 8 minutes and 20 seconds to travel from the Sun to the Earth.”

The statement above assumes the Einstein convention that the one-way speed of light is isotropic and so equal to one-half of the two-way speed of light. However, it is possible that the one-way speed of light could be anywhere in the range of c/2 to infinity as long as the two-way speed of light equals c. So the speed of light could be c/2 one direction and infinity in the opposite direction.

The possibility seems strange until we consider how we ordinarily speak. We see the sun in the sky and its position now is taken as the position where it appears to be. It turns out there is nothing wrong with that manner of thinking and speaking. It is the same as saying the incoming speed of light is infinite, which is perfectly acceptable as long as the outgoing speed of light is c/2.

And so it is with all the comets, moons, planets, and stars: where they appear to be now is where we ordinarily speak of them as being. If there were something wrong with this manner of speaking, we should correct it, but there is nothing wrong with it.

There is something similar happening down on Earth with measurements of the travel time of commuters. The time and location of multiple travelers may be compiled by a traffic data office from electronic communications or from recordings made at the time of measurement. Travel times are then presented with tables and maps such as this isochrone map:

The travel times are taken as they were at one instant, as if vehicles all arrived at the isochrone lines simultaneously. That is how we think and speak about it, whether or not it is exactly true.

Effectively this says that the speed of each commuter or signal they transmit is infinite in one direction – the direction to the traffic data office – and a finite measured value in the travel direction. In this case the round-trip speed is finite but irrelevant.

Anisotropy is more common than we realize.

Numbers large and small

Consider this example, from Funding Science in America by James D. Savage (Cambridge University Press, 2000), p. 165:

Since receiving their first $1 million or more in earmarks, seven institutions increased their rank by eight or more places….

When we talk of increasing a number, we usually mean making it larger, but in some cases making the number smaller is called an increase. Why? Because ranks are ordinal numbers, and the highest ordinal number is first, even though it is numerically the smallest number.

This applies to some qualities and ratios as well, such as duration and pace. The object of a racer is to improve their time at covering a given distance, which means to achieve a smaller number for their duration and pace. So a higher speed means a smaller value for time and pace.

If we take this to the mathematical extreme, zero and infinity can have different meanings, too. A racer with a time of zero would instantaneously arrive at the finish line. Their pace would be zero and their speed effectively infinite. So zero can be the highest number as well as the lowest number.

It’s all a matter of perspective.

Dynamic time-space

Two key expressions for space-time dynamics are the momentum and the kinetic energy. Here we derive the corresponding expressions for time-space, which are called the fulmentum and the kinetic invertegy.

The momentum and kinetic energy are the force through time or space:

momentum = mv = F Δt, an

kinetic energy = mv²/2 = F Δs,

where m = mass, v = velocity, F = force, t = duration, and s = distance.

Since F = ma, these formulae come from the related kinematic formulae without mass:

v = a Δt and /2 = a Δs,

where a = acceleration, with initial distance and velocity zero.

For time-space the corresponding kinematic formulae are these:

u = b Δs and /2 = b Δt,

where u = legerity and b = expedience, with initial duration and legerity zero.

These formulae may be multiplied or divided by mass to get the desired result. Since velocity and legerity are inversely related, the form of mass should also be inversely related. Thus these formulae should be divided by the mass, or multiplied by the inverse of the mass, which I’m calling the vass.

Since Γ = b/m = nb, the corresponding dynamic formulae for time-space are:

fulmentum = u/m = nu = Γ Δs, and

kinetic invertegy = /2m = nu²/2 = Γ Δt,

where Γ = rush, the time-space form of force and  = vass, the inverse of mass.

The kinetic energy and kinetic invertegy are related:

1/kinetic energy = 2/mv² = 2nu² = 4(nu²/2) = 4 × kinetic invertegy.

Four rates of motion

The speed of a motion is its distance per unit of duration. Symbolically, speed is Δrt. Pace is its duration per unit of distance. Symbolically, pace is Δtr. In both of these ratios, the denominator is chosen independently of the numerator. That is, the denominator is selected first, and then the numerator is measured in relation to it. The denominator may equal any positive number.

There is another way to measure motion: by comparing the measurand motion to a standard motion. Then the independent variable is from the standard motion. One can select either a distance or a duration from the standard motion, and then measure a corresponding distance or duration from the measurand motion.

The standard motion should be something easily reproduced, as with a clock. It may also be a maximum motion, as with the speed of light. Or it may be a typical motion, as is often done in transportation. Whatever motion is chosen, its rate of motion is what I’ve called the modal rate.

One could then measure the speed of a motion as the ratio of its distance per unit of distance in a standard motion. Symbolically, that would be ΔrR, where R equals cΔt, for example. That would have the advantage of a dimensionless ratio. Other than that, it amounts to the same thing as speed.

Similarly, one could measure the pace of a motion as the ratio of its duration per unit of duration in a standard motion. Symbolically, that would be ΔtT, where T equals (1/cr, for example. That would have the advantage of a dimensionless ratio. Other than that, it amounts to the same thing as pace.

Thus there are four rates of motion; symbolically, Δrt, Δtr, ΔrR, ΔtT.

No motion as zero speed or pace

What does “no motion” mean for the measurement of speed or pace? There are two cases of no motion: either (1) the trajectory distance is zero or (2) the trajectory duration is zero.

Consider first the speed ratio (Δr/Δt).

(1) the trajectory distance is zero: then the speed is zero because it equals zero distance divided by the nonzero duration of the independent motion.

(2) the trajectory duration is zero: this possibility is excluded by the independence of the duration.

Consider the pace ratio (Δt/Δr).

(3) the trajectory distance is zero: this possibility is excluded by the independence of the distance.

(4) the trajectory duration is zero: then the pace is zero because it equals zero duration divided by the nonzero distance of the independent motion.

Case (4) seems strange but consider a stopwatch that is clicked on, and then immediately clicked off. There would be no motion in that instant. But the distance interval for the pace is independent of this and the unit of distance is nonzero. So the pace would be a zero duration divided by a nonzero distance, which equals zero.

Simple motion in space and time

This post continues the discussion here and here.

Simple motion is “a motion in a straight line, circle or circular arc, or helix”. Since a helix and all other motions are a combination of linear and circular motions, simple motion may be considered as linear or circular motion.

There are two basic measures of simple motion: distance and duration. Linear distance is a length of space. Linear duration is a length of time. Circular distance is an angle of space. Circular duration is an angle of time.

Linear measurements use a measuring rod, and circular measurements use a measuring angle. Other devices that produce the same results may also be used. The convention is to measure distance by linear motion and duration by circular motion, but one could just as well measure distance by circular motion (a measuring wheel) and duration by linear motion (a clock with reciprocating motion).

The linear distance of a linear motion is measured by a measuring rod moving parallel to the linear motion. The linear duration of a linear motion is measured by a measuring rod moving synchronously with the linear motion.

The circular distance of a circular motion is measured by a measuring angle moving in parallel with the circular motion. The circular duration of a circular motion is measured by a measuring angle moving synchronously with the circular motion.

A stopwatch or chronometer is needed to measure time. The continuous motion of a clock provides a convenient source for synchronous measurement but is not necessary to measure time. A clock, calendar, and epoch (starting point) are needed for chronology, which is part of history.

Space is the set of all possible linear and circular distances. Time is the set of all possible linear and circular durations. Mathematically, space and time are metric spaces.

A direction is “the line or course on which something is moving or is aimed to move or along which something is pointing or facing”. A direction angle is the angle made by a given linear motion with a reference linear motion.

A dimension is one of a set of coordinates that are mutually independent or orthogonal. A dimension angle is one of a set of direction angles that are mutually orthogonal. There are three dimension angles in the physical world, so there are three dimensions of distance and duration, that is, of space and time. Since space and time are independent, there are a total of six dimensions of motion in space and time.

Textual realism and anti-realism

Anti-realists always begin with reality – and reject it. Because, they argue, it is obscure, misleading, and subject to different interpretations. So anti-realists begin again, this time with an idea of theirs. Even materialists begin with an idea, the idea of materiality. Thus anti-realists substitute their ideas for reality.

In contrast, realists begin with reality and accept it. Because, we argue, it is reality whether we like it or not; it is sufficiently perspicuous; careful observation and reflection can overcome misleading appearances; and interpretations should be based on reality.

All of this applies to writings as well. Anti-realists turn away from the inherent meaning of the text in favor of their interpretations of the text. Realists accept the inherent meaning of the text, yet are also free to discuss its significance and application.

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