iSoul In the beginning is reality

Tag Archives: Transportation

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.

Measurement of space and time

The various ways of measuring space and time are parallel.

Measuring space:

  1. A ruler measures length, that is, the distance between two points in space (A to B).
  2. An ruler turned upside-down measures length backwards (B to A).
  3. A tripmeter measures the travel distance of a vehicle trip.
  4. An odometer measures the cumulative travel distance.Odometer 12,000
  5. A measuring wheel measures the travel distance of a wheel being pushed.
  6. A road map measures travel distance of a standard vehicle. See Geodistance.

Measuring time:

  1. A stopwatch measures time, that is, the duration between two points in time (A to B).
  2. A timer measures the time counting down from a set time, i.e., backwards (B to A).
  3. A GPS watch or time clock measures the duration of an activity, such as running or working. GPS watch
  4. A GPS watch (or smartphone app) measures cumulative travel time (or flight time).
  5. A measuring wheel with a stopwatch measures the travel time of a wheel being pushed.
  6. A clock measures travel time synchronized with a standard motion.

Note that #2 shows time can be measured backwards. Space and time can both be counted up or counted down. There’s nothing magical about it.

Motion vs. movement

The English words motion and movement are similar. They both have to do with “changing position or going from one place to another.” (Collins English Dictionary)

Then what’s the difference? Here are a few ways of putting it:

motion is used to describe physical properties, while movement is used to describe the qualities of motion. Ref.

motion doesn’t always imply a purpose, and movement usually does. Ref.

The difference is very fine. I would say that movement is déplacement d’un lieu à un autre [displacement from one place to another] whereas motion is le fait de ne pas rester immobile [not to stand still]. But usage and context are crucial. Ref.

People may not be consistent about it but for the purposes here they can be distinguished. Motion is the general term in kinetics, the study of motion. It says nothing about the purpose of a motion, or its origin and destination. Something just happens to change place.

However, movement includes some purpose, some origin and destination. A movement is a complete motion, from beginning to end. So movement would be preferred in the arts and social sciences and motion in the natural sciences.

Physics studies motion. Transportation studies movement. They may both speak about something changing position but there is a different perspective.

A movement is an entity, a thing, not just a change as a motion is. A motion can be studied abstractly but a movement is not fully abstract because it is an entity.

A body has its motion and a movement has its figure. A body is flesh-and-blood 3D, with motion only adding a thin 1D time perspective. A movement has 3D animation and life, with a figure only adding a thin 1D space perspective.

Speed vs. velocity

For some background, see here and here.

Velocity is defined as: “The time rate of change of position of a body; it is a vector quantity having direction as well as magnitude.” Speed is defined as: “The time rate of change of position of a body without regard to direction; in other words, the magnitude of the velocity vector.” (McGraw-Hill Dictionary of Physics, 3rd ed.)

However, it’s not that simple. A common example shows the problem:

When something moves in a circular path (at a constant speed …) and returns to its starting point, its average velocity is zero but its average speed is found by dividing the circumference of the circle by the time taken to move around the circle. This is because the average velocity is calculated by only considering the displacement between the starting and the end points while the average speed considers only the total distance traveled. Wikipedia

So the average speed is not the magnitude of the velocity (which is zero in this case) but something else – the travel distance divided by the travel time.

The question is whether the speed over a finite interval should be the magnitude of the displacement divided by the time interval or the arc length divided by the time interval (i.e., the integral of the norm of the velocity function over the time interval). The answer should be the latter, although the former is implied by the common definition of speed.

It is better to define speed as the ratio of the arc length (length of travel) divided by the arc time (travel time). In short, speed is that which is measured by a speedometer.

Measures of motion

This post follows others such as the one here and here. A background document is here.

One-dimensional kinematics is like traveling in a vehicle, and on the dashboard are three instruments: (1) a clock, (2) an odometer, and (3) a speedometer. In principle the speedometer reading can be determined from the other instruments, so let’s focus on a clock and an odometer. The clock measures time, which will be used to measure travel time. The odometer measures distance, or length, which will be used to measure travel distance.

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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.

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 length) 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 legerity 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.