iSoul Time has three dimensions

Isaiah Berlin on history and science

The following (long) excerpts are from Isaiah Berlin’s article “History and Theory: The Concept of Scientific History”, published in History and Theory 1 (1):1 (1960). Republished in Concepts and Categories: Philosophical Essays. NY: Viking Press, 1979. (online here).

HISTORY, according to Aristotle, is an account of what individual human beings have done and suffered. In a still wider sense, history is what historians do. Is history then a natural science, as, let us say, physics or biology or psychology are sciences? And if not, should it seek to be one? And if it fails to be one, what prevents it? Is this due to human error or impotence, or to the nature of the subject, or does the very problem rest on a confusion between the concept of history and that of natural science? These have been questions that have occupied the minds of both philosophers and philosophically minded historians at least since the beginning of the nineteenth century, when men became self-conscious about the purpose and logic of their intellectual activities. But two centuries before that, Descartes had already denied to history any claim to be a serious study. Those who accepted the validity of the Cartesian criterion of what constitutes rational method could (and did) ask how they could find the clear and simple elements of which historical judgements were composed, and into which they could be analysed: where were the definitions, the logical transformation rules, the rules of inference, the rigorously deduced conclusions? While the accumulation of this confused amalgam of memories and travellers’ tales, fables and chroniclers’ stories, moral reflections and gossip, might be a harmless pastime, it was beneath the dignity of serious men seeking what alone is worth seeking – the discovery of the truth in accordance with principles and rules which alone guarantee scientific validity.

Read more →

History and science combined

For previous posts on history and science, see here.

History and science are different kinds of knowledge. History is based on the particulars that go into narratives. Science is based on the universals that go into theories.

History is focused on the matter and science is focused on the form, in the Aristotelian sense. The nature of something is its essence, its participation in universals, which is why there are natural sciences. Social sciences look at the form of human interaction. The term natural history is an older term for a scientific investigation into the natural world, especially biology, not a history in the modern sense.

The matter of something is its key particulars. Physical history is the investigation of the key particulars of physical objects in the past resulting in a narrative. This might be called natural history, but that term has meant science so it would be confusing. The investigation of the key particulars of documents in the past resulting in a narrative is simply called history.

History and science can be combined to explain something in the past. Yes. This is often called science but it is mainly history, with science assisting. For example, the investigation leading to the conclusion that the extinction of the dinosaurs was caused by a large asteroid or volcano is physical history that is commonly called science. Key particulars explain what happened. Science provides support. The result is a narrative, not a theory. (See here.)

The explanation of an event or series of events is history, since the particulars of events are history, even if science takes a supporting rôle. The explanation of a phenomenon or multiple phenomena is science, since their explanation depends on their nature, even if history takes a supporting rôle.

Repeating events entail universals that require science for explanation. Non-repeating events entail particulars that require history for explanation. Ancient mythology tried to explain repeating events through particulars, e.g., Zeus’ anger explains lightening, as if their nature was irrelevant. Modern mythology tried to explain unique events through universals, as if their substance was irrelevant.

“Creation science” concerns created universals. “Creation history” concerns created particulars.

Length contraction and time dilation

These derivations follow that in ‘Hyperphysics’ here.

Length Contraction

The length of any object in a moving frame will appear foreshortened in the direction of motion, or contracted. The length is maximum in the frame in which the object is at rest.

Fixed and moving reference frames

If the length L0 = x2´ − x1´ is measured in the moving reference frame, then L = x2x1 in the rest frame can be calculated using the Lorentz transformation.

Read more →

Length and duration in space and time

The following derivations are based on the exposition by G. G. Lombardi here.

Time Dilation

Time dilation with a light clock

A clock is made by sending a pulse of light toward a mirror at a distance L and back to a receiver. Each “tick” is a round-trip to the mirror and back. The clock is shown at rest in the “Lab” frame in Fig. 1a, or any time it is in its own rest frame. Consequently, it also represents the clock at rest in Rocket #1. Figure 1b is the way the clock looks in the Lab when the clock is at rest in Rocket #1, which is moving to the right with velocity v and legerity u, hence speed v and pace u.

Read more →

Lorentz from light clocks

Space and time are inverse perspectives on motion. In space length is measured by a rigid rod at rest, whereas duration is measured by a clock that is always in motion. In time duration is measured by a clock at rest relative to the time frame, whereas length is measured by a rigid rod in motion that counteracts time as it were.

This is illustrated by deriving the Lorentz factor for time dilation and length contraction from light clocks. The first derivation is in space with scalar time and the second is in time with scalar space.

light clock with height hlight clock in motion

The first figure above shows a light clock in space as a beam of light reflected back and forth between two mirrored surfaces. The height that the light beam travels between the surfaces is h. Let one time cycle Δt = 2h/c = 2 or h = cΔt/2 = Δt/(2¢), with mean speed of light c and mean pace of light ¢.

The second figure shows the light clock as observed by someone moving with velocity v and pace u relative to the light clock; the length of each leg is d; and the length of the base of one triangle-shaped cycle is b.

Read more →

Linear clocks and time frames

The idea of a linear clock was mentioned before here, here, and here.

One bar on top of anotherOne bar shifted on another

Consider two bars or rods, one on top of the other (left), each with a zero point aligned at first. The top one moves at a constant rate relative to the other, which is at rest. After a time T, the top bar has moved an interval measured by the difference between the zero points of the bars (right). The length that B moved relative to A measures the time of motion.

Side note: a 12-inch ruler turned into a circle would form the markings for a 12-hour clock. The hours of time would correspond to inches of length.

A time frame of reference (TFR), or time frame, is a frame of reference for time. Like a space frame of reference (SFR) it is composed of rigid bars or rods that can in principle be extended indefinitely.

Read more →

Types of information

One type of information is surprise. If a message is surprising, then it is news and informative to the extent that it is new or unexpected. The opposite of this is the ordinary and expected, which can be filtered out like the carrier of a signal. This type of information is measured by entropy: the greater the entropy of a signal or series of messages, the greater its unpredictability. For n = 2,

H = −p log2(p) − (1−p) log2 (1−p),

which is a minimum at p = 0 or 1 and a maximum at p = 1/2.

The greatest unpredictability is noise, which is a random message. As the news media produces updates by the minute (and social media runs wild), the flood of surprise approaches noise. The news media has become the noise media.

This leads to information as unsurprise. In a flood of noise the presence of something recognizable is a reduction of surprise and entropy. Sufficiently reduce the noise and the result is a coherent signal. With the expansion of mass and social media today, there is an increasing need for filters and editors to extract meaning. This is measured by shifted entropy, in which noise is the minimum and a constant signal the maximum. For n = 2,

N = −|p−1/2| log2(|p−1/2|) − (1 − |p−1/2|) log2(1 − |p−1/2|),

which is a minimum at p = 1/2 and a maximum at p = 0 or 1.

The fullest information is both surprising and meaningful, a mean between the expected and the unexpected, the carrier and the noise of a channel of communication. This is measured by the mean of entropy and shifted entropy. For n = 2,h

M = ½( −p log2(p) − (1−p) log2(1−p) − (|p−1/2|) log2(|p−1/2|) − (1 − |p−1/2|) log2(1 − |p−1/2|),

which is a minimum at p = 0, 1/2, or 1 and a maximum at p = 1/4 or 3/4.

Observers in motion

A rigid rod or other device that measures length is at rest relative to itself, even if part moves such as a measuring wheel, because it moves relative to other objects, not relative to itself. A concept of simulstanceity enables an observer to determine length at other times (e.g., they are the same point on the stance line).

A clock measures time, but what is a clock? It is a device with a part that moves relative to a part that is at rest. So a clock is an object in motion relative to itself (yes, this is possible). The part that moves indicates the time. A concept of simultaneity enables an observer to determine time at other places (e.g., they are the same instant on the time line).

Let there be a rigid reference frame associated with each observer or object (e.g., they are attached). An observer may be at rest or in motion relative to their frame. If the observer is at rest, then their frame is a length frame and what they observe is in space. Time is the independent variable and length in three dimensions is the dependent vector variable.

If the observer is going somewhere, they are not at rest but in motion. Their reference frame for rest is not their own frame but a different frame, such as one located on the surface of the earth. In this case the observer and rest frame system are like a clock, that is, a clock frame, and what is observed is in time. A clock frame is moving in the opposite direction of a rest frame. Length is the independent variable and time in three dimensions is the dependent vector variable.

Frames in motion

For Galilean inertial frames the observer is at rest and the moving frame transmits the current stance in an instant of the time line, instantaneously. For dual Galilean inertial frames the observer is in motion and the rest frame transmits the current time in a point of the stance line, punctstanceously.

The rest frame observer has three dimensions in space. The observed frame in motion is effectively reduced to the one dimension of its motion in time. The moving frame observer is like a clock with space and time exchanged: the dimensions of the observer’s frame are in motion so the three dimensions are in time. The rest frame that is observed appears to move and is effectively reduced to the one dimension of its path in space.

Time and simultaneity

There are several ways of understanding the time of remote events. What follows is a summary of the basic ways of determining simultaneity.

As a way of comparing the different ways consider transmitting a light signal to a remote location where it is reflected back. What is the time when the signal is reflected back?

Observation time is an extension of ordinary perception. When we observe an event, we say that it is happening at the time of observation. So when a light signal is reflected and received back, the reflection observed is considered to have happened when it was observed. In effect the light observed is instantaneous. By implication the one-way speed of light transmitted is c/2 in order for the two-way speed of light to equal c.

Observation time is thus the projection of the time of observation to the entire observable universe. This way of understanding time is characterized by the Galilean transformation.

Transmission time is an extension of the ordinary transmission of light. When we shine a light on an event, we say that it is happening at the time of transmission. So when a light signal is aimed toward a reflector, the event of reflection is considered to have happened when the light was transmitted. In effect the light transmitted is instantaneous. By implication the observed one-way speed of light is c/2 in order for the two-way speed of light to equal c.

Transmission time is thus the projection of the time of transmission to the entire transmittable universe. This way of understanding time is characterized by the dual Galilean transformation.

Probe time is an extension of measurement by a probe (a “small, unmanned exploratory craft”) to the entire probeable universe. See previous post here. An event is said to occur when intersected by a probe that measures the duration of probe movement since a reference event. So when a probe comes upon the reflection of light, the probe measures the time of reflection as the time of the probe. If the probe is not moving at the speed of light, there may need to be multiple probes.

Consider a series of probes moving at a speed v over a distance d to the reflection event. The probe that leaves at time (d/c) – (d/v) is the probe that intersects the reflection event. If v = c, then the time is zero.

Because probes can measure the length or duration of motion, probe time is characterized by the Lorentz or dual Lorentz transformation.

Reference frame time measures time by a rigid reference frame that has clocks which were previously synchronized spread throughout. See the Relativity of Simultaneity and Einstein Synchronisation. These synchronizations are characterized by the Lorentz transformation.

Reference probes and systems

A reference frame is in principle a rigid structure embodying a 3D coordinate system. It represents an observer at rest with complete access to rods and clocks to measure length and duration in any direction:

Such a reference frame may be the framework or infrastructure for a reference probe moving like a miniature aerial tram in any direction. A probe is a “small, unmanned exploratory craft”. Such a reference probe compared with a target motion can measure either the extent of the framework crossed by the target, which is the length, or the extent of the framework crossed by the reference probe, which is the duration. The rate of the target motion is the ratio of the length to the duration or the ratio of the duration to the length.

Alternatively, the reference frame may be the framework or infrastructure for a reference system of probes jmoving in all directions. The motion of such a system can be given by a table of changes, which are the intersections of consecutive trips, called “times”, and consecutive stations, called “stances”:

Table of Changes


Trip 1

Trip 2


Location 1

change 1,1 change 1,2

Location 2

change 2,1 change 2,2

A target motion can be measured as the number of stances, which is the length, or as the number of times, which is the duration. The rate of the target motion is the ratio of the length to the duration or the ratio of the duration to the length.

What if one reference framework is moving with respect to another reference framework? The motion of a framework is no different than the motion of an object as observed by a reference framework. How can one compare the observation of an object from one framework with that of another framework? That requires applying the appropriate transformation, Galilean, dual Galilean, Lorentz, or dual Lorentz.