iSoul In the beginning is reality

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.

Reality and conventions #5

This post continues a series of posts. The previous one was here.

I’ve noted before that the one-way speed of light is a convention (see John A. Winnie, Philosophy of Science, v. 37, 1970). The two-way (round-trip) speed of light is known to equal c, but the one-way speed may vary between c/2 and infinity, as long as the two-way speed equals c. The isotropic convention is the “scientific” one because modern science prefers symmetry.

What do people ordinarily do? As I’ve mentioned before here, people act as though the light from stars is where it is seen, when it is seen. The light is viewed as if it traveled instantaneously. As long as the return trip is considered to travel at the speed of c/2 this is perfectly legitimate.

This is also the approach of Newtonian mechanics, which uses the Galilean (Galilei) transformation in which the time coordinates are universal. This implicitly uses an anisotropic convention for the speed of light. Because no time elapses between light coming from distant stars in this model, time can be universally identical.

As I’ve pointed out before here, there is a dual to this Galilei transformation:

Galilei transformation (3+1): r1´ = r1 – vt1,

Co-Galilei transformation (1+3): t1´ = t1 – r1/v,

where the other coordinates remain unchanged. The co-Galilei transformation implicitly uses the opposite convention: the return trip of light travels instantaneously. The isotropic convention leads to the Lorentz transformation or its dual, which was described here.

The scientific approach then should be to combine the Lorentz transformations into a 3+3 dimensional invariant interval, which I’ve presented here. The problem with all this is that it loses touch with the way people ordinarily live and speak. Science becomes more and more esoteric. Is there a way to be consistent with empirical knowledge and with ordinary life, too?

The answer is yes, but only by sacrificing the single, static answer that modern science so craves. We would have to use the Galilean transformation for observers/receivers and the co-Galilean transformation for transporters/transmitters. There would be a kind of dialectic of the two transformations to represent reality.

Instead of the isotropic center would be the anisotropic center, a dynamic center.

Direction and time

The measurement of the length of a motion follows the course of motion at its own pace. It is a measurement of something passive, and the motion may be past when the measurement takes place.

Cartesian space lacks direction. The independent axes are just coordinates that describe a passive space. The origin is arbitrary and the direction hidden in the coordinates. There are three coordinates, three dimensions to this physical space.

Motion in space is relative to an origin, and so where the motion is coming from. The wind is coming from a certain direction; that is its direction.

Modern natural science excludes teleology. There are no natural goals, no directions. Nature is passive. If there is any goal-seeking, it must come from outside nature.

The measurement of the time of a motion follows the course of motion at its pace. It is a measurement of something active, in motion while the measurement takes place.

A direction is a command and a course. Go West, young man is a course to take and a direction to follow. Trains are distinguished by their destinations. Their direction is indicated by the last stop. The goal and the direction are the same.

Motion in transportation always has a goal, a direction. Motion is physical, but the goal is part of the motion. There’s always a destination.

The destination is some distance away. It takes time to reach the destination. It makes a difference which direction is taken. There are two directions and one distance, which makes three dimensions.

Time in transportation has three dimensions. It is oriented toward the where the vehicle is going, the destination. The train is going toward a certain direction; that is its direction.

Introduction to 3D time with 1D space

Since Newton, time has been the usual and ultimate independent variable for physics. This contrasts with problems in transportation, where time is often optimized. Whether transporting goods across the world, commuters across town, or athletes to the finish line, length is the independent variable against which time is measured and optimized. If length is taken as the independent variable for physics, a mechanics results that is different from Newton’s but equivalent to it. In what follows we explore the basic kinematics and dynamics with length as the independent variable, first in classical, then in relativistic mechanics.

To represent time on a map, one may use isochrones (time contours), as in this map of tsunami travel time in hours:

Or time may be used instead of length, as in this map of European rail travel times in hours:

Note that in this map it is time that is two dimensional, not space. It looks like a distortion of the spatial representation, but it is not a distortion. It is a time map with units of time rather than units of length. The multidimensionality of time will be a main feature of taking distance as the independent variable.

Length could be included as a distance from a particular place, represented by an iso-distance contour. That is, length is reduced to one dimension if time is the dependent variable.

Units such as natural units may be adopted to equalize the units for length and time, i.e., by adopting a constant modal speed dependent on the mode of travel. However, they are still different measurements. Such units allow constant speeds to be represented the same, whether in space or time, which minimizes the seeming distortion of a time map.

As I pointed out here, an independent variable is given to us and so not in our control, and so may seem to flow on independently. A clock is like that, and it gives us a sense that time flows. But a stopwatch starts and stops at our command. Time no longer flows.

Distance can seem to flow if we allow it to. Consider a hop-on, hop-off transit system with a fixed route. It cycles through its various destinations and then repeats the cycle. The distance between two stops may be read from an odometer by subtracting the earlier from the later distance. This is just like finding the time between two points with a clock. Only here it’s the transit system that flows on, accumulating distance indefinitely. Distance flows instead of time.

Units of time-space

The kinematic units of time-space are straightforward opposites of space-time units:

Distimement has units of seconds, minutes, hours, days, or years.

Pace and celerity have units of distance over duration: s/m or min/km or min/mile. Compare speed and velocity with their units of m/s, km/hr, or mi/hr.

Prestination has units of s/m² or min/km² or min/mile². Compare acceleration with its units of m/s² or km/hr².

Angular celerity has units of seconds per radian, seconds per degree, seconds per revolution, etc. Compare angular velocity with its units of radians per second, degrees per second, revolutions per minute, etc.

Strophence is the rate of change of angular celentum of a time body (or vehicle), σ = Iβ, which has units of seconds per radian², seconds per degree², seconds per revolution², etc.


For dynamics time-space units are needed that correspond to mass and force etc.

Vass is the nonresistance of a time body (or vehicle) to a change in its state of motion when a net surge is applied; it is the inverse of mass. Units of kg-1.

Celentum is the vass times the celerity, so it has units of s m–1 kg–1, which is the inverse of momentum.

Surge is the space rate of change of the celentum, so it has units of s m–2 kg–1. Compare the unit of force, the Newton, N, which is the force needed to accelerate one kilogram of mass at the rate of one m/s² in the direction of the applied force. Analogously, we could define an Unton, U, (= UnNewton) as the surge needed to prestinate one kg–1 of vass at the rate of one s/m² in the direction of the applied surge.

Effort is a constant surge, Γ, that moves a time body (or vehicle) the distimement t: V = Γt. The joule, J, is defined as the work expended by a force of one newton through a displacement of one metre. Analogously, we could define the Quoule, Q, (quasi-joule) as the effort expended by an surge of one unton through a distimement of one second.

The watt, W, which is the time rate of work, which is one joule per second. Exertion is the space rate of making effort, with unit of one quoule per metre, which might be called one DeWatt, D.


The gravitational constant, G, equals 6.674 × 10−11 m³⋅s−2⋅kg−1. The levitational constant, H, equals 2.233 × 1017 kg⋅s⋅m−3/2.

Time and light

This post continues on the subject of light conventions, see here.

In ordinary life today clocks are very common and portable. Time is everywhere and is everywhere the same (apart from adjustments for longitude, that is, time zones). It’s as if the signals from clocks arrived instantaneously everywhere, near or far. This is equivalent to a convention about the speed of light: the incoming speed is instantaneous. In order that the round-trip speed of light equal c, the outgoing speed of light must be equal to c/2. And time is 1D because it is a scalar quantity. This is the modern, Newtonian conception of time.

In another convention, the Sun is a global time keeper that casts its light and shadow everywhere, and is everywhere the same (apart from adjustments for longitude). It’s as if the sun sends out its light so that it reaches everywhere at the same time. In order that the round-trip speed of light equal c, any return reflection would be at the speed of c/2. And time is 3D because the position of the Sun is a 3D vector and the relative motion of the Sun is 3D, as observed in its diurnal and annual cycles. This is implicitly the ancient conception of time.

Einstein proposed a new convention: the speed of light is the same everywhere, independent of whether it is being sent or received. This is a middle position between the extremes of instantaneous and c/2 light speeds. However, the invariant interval was developed on 3D space +1D time dimensions, and so is 4D. In order to be completely neutral between the extremes, we would need to affirm 3+3 dimensions with an invariant interval of 6D.

The original creation story

The fact that many creation stories from around the world have been preserved (see here) shows that there is something behind them all. It shows us that something happened at the very dawn of time that human beings were aware of and considered important and tried to pass on.

Now imagine trying to preserve a story for thousands of years. How would you do it? If you wrote it on paper, the paper would disintegrate over time. If you inscribed it on stone, the stones could be buried over time. If you taught it to your children, how would you know if they passed it on correctly? All this and language changes so that the story might be misunderstood.

That is to say it’s not surprising that there are many variations of the creation story. It’s impossible now to combine them into one account because they are so different. For example, the role of water in the various stories makes some of them creation stories and some more like flood stories. How can we ever sort this out?

When you read of the creation and flood in Genesis, you can start to see how the other creation stories are all related to it. Both creation and flood are covered but in separate narratives. Instead of rivalries between purported gods, there is the orderly creation by the divine creator of a universe that we know is very ordered.

There are unique aspects to the Genesis account, too. This author notes several: Study Bible Shorts: The Uniqueness of the Genesis Creation Story – The Identity of God, No Rival Gods, Creation out of nothing, The Value of Humanity, and The Sabbath.

What about creation stories that are older than the Bible? Writing was not invented in the early days of humanity so stories were passed on orally. It’s of little significance which story was written down first. What counts is the reliability of the source, whether oral or written. The Bible has been zealously preserved for thousands of years. Other written accounts languished in caves and underground, forgotten and rejected.

To preserve a story for thousands of years you’ll need a group of people dedicated to preserve it intact. The Hebrew people have a well-deserved reputation for preserving their oral and written traditions. They (and later the Christians) have been fanatic about preserving the Bible over thousands of years. The Bible contains the original story.

Where does that leave ancient mythologies? They are a combination of corruptions of Genesis and legends about people such as Adam and Noah that sometimes made them into gods or superhuman beings. They indirectly reflect what actually happened, of which the key events are preserved in Genesis.

Law of levitation

This was derived for circular orbits here. In this post it is derived directly from Newtonian gravitation.

The law of gravitation states that the gravitational force is proportional to the product of the masses divided by the square of the semi-major axis, As, of the orbit:

F = G mM / As².

Because of Newton’s second law, the gravitational acceleration is

a = Gm / As².

The object is to transpose this into time-space by expressing it in terms of prestination and vass. The first step is to use Kepler’s third law, which is an estimate that states:

T² ∝ As³, or


where T is the sidereal period. This may be expressed in terms of the radial time, i.e., the corresponding time to traverse the semi-major axis, At = t, estimated as a proportion of the period:

At = tT,

so that


This allows the gravitational acceleration to be expressed in terms of radial time:


The next step is to integrate, with a = dv/dt:

∫ dv = ∫ C1 mt–4/3 dt = –3 C1 mt–1/3 + C2 = v.

Then integrate again, with v = dr/dt:

r = ∫ dr = ∫ –3 C1 mt–1/3 + C2 dt = –(9/2) C1 mt2/3 + C2t + C3,

where the radial distance r = As. For the purposes of stating a law, set C2 = C3 = 0, and then solve for t:

t = –(2/9mC1)3/2 r3/2 = –C4 ℓr3/2,

where ℓ is the vass. Then take the derivative:

dt/dr = –(3/2) C4 ℓr1/2 = u,

where u is the celerity. Take the derivative again to get:

du/dr = –(3/4) C4 ℓ/r1/2 = b,

where b is the prestination of levitation, since the sign is the opposite of gravitation. This leads to

Γ = H ℓN/r1/2,

for vasses ℓ and L, the levitational constant H, and the levitational surge Γ.

Design and entropy

A carrier is the baseline transmission (such as a wave) that is modulated for a signal. Carriers have minimum entropy. Their opposite, noise, has maximum entropy. A signal conveys a message between a sender and a receiver. The entropy of signals is between that of the carrier and noise.

Carriers are the canvas for the artist. The canvas starts out blank. Then paint is added, which is the signal for the viewer. Noise would be like splotches of paint that somehow got put on the canvas. If the canvas were all noise, the signal would be completely covered with random bits of paint. The signal is designed to be between these extremes.

The closer a signal is to looking like the carrier, the lower the entropy and the simpler the message. The closer a signal is to looking like noise, the higher the entropy and the less the complexity of a message that can be transmitted. With the carrier alone or noise alone there is no message.

Design works the same way. A carrier alone or noise alone exhibit no design. A simple design would be similar to a carrier or to noise. A more complex design would be between the extremes of all carrier and all noise.

Entropy is a way to determine the presence of design. The more that entropy is in-between zero and the maximum, the more likely it is a result of design. A simple measure of design may be constructed from entropy as follows:

Define a design index, Ξ (xi) from the entropy, H, as

Ξ := (HHmin) / (HmaxHmin),

which ranges from zero if H = Hmin to one if H = Hmax. If the design index is one-half, then H is the mid entropy. The closer the value of Ξ is to one-half, the more likely the distribution is the result of design.

2015, updated