iSoul Time has three dimensions

Tag Archives: Transportation

Transportation symmetry

An experimenter turns on a device and transmits a signal from point A to point B. Two people play catch and toss a ball from one at point A to the other at point B. A truck transports its cargo from the terminal at point A to the terminal at point B. All these are cases of transportation.

Because of translational symmetry the laws of physics are invariant under any translation, that is, rectilinear change of position. But transportation is something more than translation. Motion is outgoing from one point and incoming at the other point. From the perspective of an observer at point A in the above examples, the translation is an outgoing motion. From the perspective of an observer at point B, the translation is an incoming motion.

Time-reversal symmetry (or T-symmetry) is valid in some cases but not in general, so it cannot be the same as transportation symmetry, which is valid in general, A return trip interchanges the sender and receiver but it is a different trip, and has nothing to do with reversing time.

Because of rotational symmetry the laws of physics are invariant under any rotation. If an observer is translated from point A to point B, and then rotated so they’re facing back, that is not the same as a transportation from point A to point B. The perspective must change, not merely the position.

This change of perspective is a physical change. Outgoing and incoming motions are not the same. Transmission of a signal differs from reception of a signal. Throwing a ball differs from catching a ball. Departing a truck terminal differs from arriving at a truck terminal.

But there is a symmetry between these motions. The laws of physics are invariant under a transformation from the perspective of an observer at the sending point A to the perspective of an observer at the receiving point B. This is transportation symmetry. Because of Noether’s theorem, a conservation law corresponds to transportation symmetry.

Length clock

A time clock is a device that measures a constant rate of internal motion. Time clocks are synchronized to a common event and rate of internal motion. A time clock is used by correlating its internal measure with other motions and events. The unit of measure for a time clock is normally a unit of time but even if it is a unit of length, the constant rate means the length correlates to a time.

A length clock, also called an odologe, is a device that measures a constant rate of external motion. Length clocks are symmacronized to a common event and rate of external motion. A length clock is used by correlating its external measure with other motions and events. The unit of measure for a length clock is normally a unit of length but even if it is a unit of time, the constant rate means the time correlates to a length.

In general, a device to measure length need not run at a fixed rate, or “run” at all, such as a ruler. An orientation toward length rather than time is comparable to the Myers-Briggs-Jung perceptive rather than judging personality type (e.g., see here), in which “time” is perceived less by a time clock and more by something like the tasks remaining or the distance remaining on a trip (as measured by landmarks).

Modern cultures run on a time clock but ancient cultures ran on a different sense of time. I hypothesize that their sense of time is what the length clock measures. They measure what “time” it is by their length from a reference site, for example, how close they are to Jerusalem for the holy days. It is the same with any trip: one can measure the progress by either the elapsed time or the length of distance remaining to the destination.

Natural cyclical movements such as the positions of migrating birds could be used for an informal length clock. A consistent length clock requires a repeatable motion at a fixed rate. There is a constant relationship with such a device and a time clock, so in a sense they are interchangeable.

Mean speed and pace

Speed of a motion is the time rate of length change, that is, the length interval with respect to a timeline interval without regard to direction. Pace of a motion is the space rate of time change, that is, the time interval with respect to a locusline interval without regard to direction.

The symbol for speed is v = Δst and for pace is u = Δts. Instantaneous speed is ds/dt. Punctaneous pace is dt/ds.

There are two kinds of mean speed or pace: the time mean and the space mean. The time mean is the arithmetic mean if the denominators are a common time interval. The space mean is the arithmetic mean if the denominators are a common space interval. The time mean is the harmonic mean if the denominators are a common space interval. If the denominators are a common time interval, the space mean is the harmonic mean.

The time mean speed (TMS) is the arithmetic mean of speeds with a common time interval. The time mean pace (TMP) is the harmonic mean of paces with a common time interval. For example, the travel distance for vehicles on a highway during a time period is measured. The time mean speed or pace may then be calculated.

The space mean pace (SMP) is the arithmetic mean of paces with a common space interval. The space mean speed (SMS) is the harmonic mean of speeds with a common space interval. For example, the travel time for vehicles over a length of highway is measured. The space mean speed or pace may then be calculated.

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Rest in space and time

Rest means no motion, or at least no motion detected by an observer.

We know what rest in space means: staying in the same place. That is, rest means no change of position, no travel distance, no length of motion. So at rest the numerator of the speed is zero.

Yet clocks tick on. The denominator of speed is not zero. The speed of rest then equals zero, that is, a zero length of motion divided by a non-zero quantity of time. Speed v = Δxt = 0/Δt = 0.

What is rest in time? It means staying at the same time. That is, rest means no duration of motion, no travel time. So at rest the numerator of the pace is zero.

In this case, is the length of motion zero, too? No. For pace the length is the independent quantity. It doesn’t depend on the motion. It depends on the given length or unit of length. So the pace of rest is zero, that is, a time of zero divided by a non-zero length. Pace u = Δtx = 0/Δx = 0.

Yet a zero pace seems to say one gets a change of place with no lapse of time. What gives?

Length of motion in the pace ratio is the independent variable. Whether length is conceived to be continually increasing, as if it were a clock, or just a quantity of length for comparison, it is independent of the motion measured. The numerator, the time, is what is measured and compared with a quantity of length to determine the pace.

It is similar with speed. Whether or not there is a clock ticking away, the denominator is a quantity of time compared with a quantity of length. All the clocks in the world could be broken, yet the denominator of speed, the change in time, would still be non-zero.

Consider a vehicle with an odometer and a stopwatch that is running whenever the vehicle is in motion. Both the odometer and the stopwatch would record no additional time for a vehicle at rest. This could not be represented as a ratio since 0/0 is not a valid ratio. Such a state has an indeterminate rate of motion.

Timelines and locuslines

Events may be ordered in various ways (see here). Events ordered by time form a timeline, which is:

1. a linear representation of important events in the order in which they occurred.
2. a schedule; timetable.

This may be generalized to the following definition:

A timeline is an ordering of events by time or duration.

For example, below is a timeline of a Project Mercury flight:

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3D time video series

I’ve posted a video series on 3D time online on Youtube. See the playlist 3D Time here:

It’s also on Vimeo here.

3D Time: From Transportation to Physics



Part 1: Show Me

Part 2: Objections

Part 3: Kinematics I

Part 4: Kinematics II

Part 5: Dynamics

Part 6: Orbits

Part 7: Relativity

Part 8: 6D spacetime

Observation and transportation

Impossible objects such as the Necker cube above are drawings that appear as two different objects, in this case either a box standing out toward the lower left or toward the upper right. It can be seen as one or the other but not both simultaneously.

3D space and 3D time are like this. One can see either 3D space or 3D time but not both simultaneously. One may develop a unified 6D geometry for both of them but to measure rates either space or time must be reduced to a scalar or 1D quantity.

It is the same with observation and transportation. One can view a motion from the perspective of an observer (whether one is moving or on the sidelines) or from the perspective of a traveler (whether one is traveling or on the sidelines).

The observer sees motion taking place in 3D space ordered by scalar time. The traveler sees motion taking place in 3D time ordered by scalar space, that is, the stations.

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Speed of information

Nowadays, we say that the speed of information is the speed of light. That is justified by the rôle of the speed of light in relativity, in which it is the speed of causation. But it is also justified by the use of electromagnetic waves to transmit information between people.

It was not always so. It took much longer for information to travel in the past.

A day’s journey in pre-modern literature, including the Bible, ancient geographers and ethnographers such as Herodotus, is a measurement of distance. In the Bible, it is not precisely defined; the distance has been estimated from 32 to 40 kilometers (20–25 miles). Wikipedia

A critical fact in the world of 1801 was that nothing moved faster than the speed of a horse. No human being, no manufactured item, no bushel of wheat . . . no letter, no information, no idea, order, or instruction of any kind moved faster. Nothing ever had moved any faster.  Stephen E. Ambrose, Undaunted Courage (Simon & Schuster, 1996), p. 52.

The book A Farewell to Alms includes a table showing how long it took for news of sig­nif­i­cant events to reach London. Faster speeds resulted from the in­ven­tion and de­ploy­ment of the telegraph by 1880:

Speed of Information Travel to London, 1798-1914
Event Year Distance (miles) Days until report Speed (mph)
Battle of the Nile 1798 2073 62 1.4
Battle of Trafalgar 1805 1100 17 2.7
Earthquake, Kutch, India 1819 4118 153 1.1
Treaty of Nanking 1842 5597 84 2.8
Charge of the Light Brigade, Crimea 1854 1646 17 4.0
Indian Mutiny, Delhi Massacre 1857 4176 46 3.8
Treaty of TienSin (China) 1858 5140 82 2.6
Assassination of Lincoln 1865 3674 13 12
Assassination of Archduke Maximilian, Mexico 1867 5545 12 19
Assassination of Alexander II, St. Petersburg 1881 1309 0.46 119
Nobi Earthquake, Japan 1891 5916 1 246


Physics of subjects

If a stone rolls down a hill, we would say it is simply following the law of gravitation. It is not “going somewhere” as if it had a destination – that would require nature to have a soul, a view that died out in the early modern period. But if a person or an animal or even a seed pod moves down a hill, we expect it to be going somewhere, to have a destination or purpose.

That is the difference between a subject in motion and an object in motion. At a minimum, an object must have some starting point, at least from our observation, but need not have a destination or purpose for all we know. On the other hand, a subject need not have a known starting point but at a minimum there must be some movement toward a destination or end, else they would not be a subject.

This simple difference leads to a different formulation of space, time, and matter for subjects and objects. Modern physics has been entirely focused on bodies as objects, particles, or waves. In contrast, the physics of subjects will focus on bodies as subjects (somebodies), transicles, and networks.

Since there is a destination, something about its location must be known. At a minimum there must exist a route or path for the subject to traverse to reach their destination. Even if the length of the path is not known, one can at least measure the progress made toward reaching the destination by measuring the space rate of movement, called the pace.

The difference between speed, the time rate of motion, and the pace is the difference between taking space or time as the independent variable. For objects their motion from a point in time is what is given and so time is the independent variable. For subjects space is the independent variable since their movement toward a destination in space is given.

That means for subjects the dependent variable is time, which is measured along with the direction of movement, which results in three dimensions of time. Space is confined to the path of movement, which may be rectified as a line for linear referencing. Examples of a linear reference are the milepoint (MP) and kilometric point (PK) on a map or sign.

Objects have chronologies. Subjects have a destinations. But subjects are like objects in some ways, and objects are like subjects in some ways. For example, a projectile is an object that has been launched by a subject toward a destination.

Mechanistic sciences such as physics study objects. Teleological sciences such as economics study subjects. The physics of subjects is physics for the social sciences.

For more, see the other posts on this website about time-space, with 3D time and 1D space.

Space and time as references

A clock provides a linear reference to measure duration of motion. Similarly, there is a linear reference to measure length of movement. What is this linear reference?

In mapping and geographic information systems (GIS) a linear referencing system (LRS) “is a method of spatial referencing, in which the locations of features are described in terms of measurements along a linear element, from a defined starting point, for example a milestone along a road.”

This may be extended to 3D space by a reference frame, “a space-time coordinate system and set of reference points in space-time that assigns unique space positions and reference durations.” From such a reference frame, one can derive linear references from path lengths.

Alternately, one may attach an odometer (cyclometer, pedometer) to each vehicle or subject in motion, and measure their transit length directly.

Thus there is a strict parallel between the reference provided by a clock and a linear reference such as an odometer. As the former is said to constitute time, an ordering by duration, so the latter constitutes an ordering of space by length.