iSoul In the beginning is reality

Transforming 3D space into 3D time

There is a symmetry between space and time. As one can transform an observation by rectilinear motion (translation), or by rotation, or by a timeline change, so one can transform 3D space into an equivalent 3D time. This is not a continuous change so don’t expect a simple equation. There are four things that must be done to transform 3D space into 3D time, that is, 3+1 spacetime into 1+3 timespace:

(1) The ordering of events should be switched between a timeline and a placeline. So a measurement of time, such as the duration from a reference event, should be switched with a measurement of place, such as the distance from a reference place.

(2) Non-directional scalars should be inverted: speed ⇒ pace, mass ⇒ 1/mass (vass), energy ⇒ 1/energy = invergy, work ⇒ 1/work = invork, etc.

(3) Vectors that are ratios of base units or products of base units should switch their numerators and denominators such that (a) the denominator becomes a magnitude of the former numerator and (b) the numerator becomes the vector with units of the former denominator: velocity ⇒ legerity, momentum ⇒ fulmentum, etc. This is similar to an inversion since (1/s)/(1/t) = t/s.

(4) Other units should be derived from these, with new rates relative to the timeline for 3D space and the placeline for 3D time: acceleration ⇒ expedience, force ⇒ rush, power ⇒ exertion, etc.

There should be no time vectors in 3D space and no space vectors in 3D time. The distance from a reference place and duration from a reference event should be the same for both, apart from a change of reference points. The laws of physics should be the same for observation or transportation in each frame.

Equality and hierarchy

The state of nature was invented by Thomas Hobbes to support his idea of a social contract that was (or would have been) entered into by free individuals. In the natural state people would have been totally free but also lacking in security and other goods of society. So they voluntarily entered into a social contract that reduced their rights in exchange for social goods.

This placing of individual rights before social duties is what Harvey Mansfield called the beginning of liberalism. It is an egalitarian liberalism, since everyone is in an equal state of nature and has an equal right to make (or break) a social contract.

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Timelines and placelines

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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From 3D space to 3D time

We observe the sun and the moon traversing the sky. We know that the moon is objectively orbiting the earth but the sun is not. Where then is the sun that is observed traversing the sky in daily and annual cycles? It is not in 3D space. It is in 3D time.

Binary stars orbit their common barycenter. If the sun and earth were the only celestial bodies, it might not be clear as to which was orbiting which. But since there are other planets orbiting the sun, the only objective view is that all the planets are orbiting the sun (more precisely, the barycenter of the solar system, which is in or near the sun).

Compare sun-centered (heliocentric) and earth-centered (geocentric) frames of reference (click to enlarge):


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Direction for expedience and rush

Expedience is the change in legerity per unit of length. Average expedience is (u2u1)/Δs. If the second legerity is faster than the first, the time interval is shorter and the legerity is lower in value, which makes the expedience negative. Since increased motion is the default for expedience (as it is for acceleration), the default direction for expedience is in the direction opposite the motion. Negative expedience, or inexpedience, is in the direction of motion.

Rush, which is vass times expedience, is also in the direction opposite the motion. So the rush of levity is in the opposite direction as well. That is why cyclic motion in 3D time has a centrifugal rush. And that is why there is levity, not gravity, in 3D time although the motion is the same.

Newton’s 3rd law shows that forces (and rushes) come in direction pairs. So it is a matter of convention which direction is the primary one. The force toward the spatial center is primary in 3D space. The rush from the temporal center is primary in 3D time. Both directions are valid but one is primary.

Ordering events

There are many ways to order events. One way is by time. Events happening at the same time are put in an equivalence class, which is then ordered from the earliest time to the latest time. History is usually ordered this way. With the advent of mechanical clocks and watches, modern people typically experience events as ordered by time.

Note: Events ordered by time make up a chronology. In a chronology time is employed to order events. But a chronology should not be confused with time itself. Chronology is an application of time.

Another way to order events is by distance from a particular location, such as a city center. Events happening at the same distance from the city center are put in an equivalence class, which is then ordered from the shortest distance to the longest distance (or vice versa). Commuting events might be ordered this way. Ancient literature such as the Bible exemplifies the place of events being as much or more significant than their time.

Another way to order events is by their importance. One might start with their wedding, then order other events by their significance: having children, remodeling a house, going on a special vacation, etc. Minor events would come last in this scheme. That could be a way of organizing an album of photographs.

The order of events is the sequence of events as they occur in a story. Storytellers – authors, playwrights, screenwriters, speakers, etc. – have many ways to order events. For example:

In J. R. R. Tolkien’s The Two Towers, the narrative switches regularly from events occurring in one location (Gondor) to events occurring almost simultaneously in another (Rohan). Because to offer a play-by-play juxtaposition of events in these two locations with chronological integrity would demand inscrutable dialogue volleying, Tolkien orders these two narrative segments by alternating chapter. Narrative Wiki

Flashbacks fill in the audience with the backstory. Some stories begin with the end and then recount the events leading up to it. Or a story can be retold by different authors in a sequence of stories, as with the four gospel stories in the Bible.

The order of events is not the same as time, although time is often used to order events.

3D time video series

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

Objections to multidimensional time

Multidimensional time is held to be impossible or the stuff of science fiction. Despite this there is an extensive literature on multidimensional time. However, with few exceptions multidimensional time is held to be merely a formalism or undetectable. If multidimensional time is considered to exist, it is something very different from time as is commonly known.

On this website we have shown that multidimensional time is readily understood through elementary transportation and physics. In what follows we present short counter-arguments to some objections to multidimensional time.

Objection #1. Time is measured by clocks, which measure only one dimension.

We can just as well say space is measured by rods or rulers, which measure only one dimension. Both clocks and rods measure one dimension with each use but may be employed to measure multiple dimensions separately – or with three instruments. Three dimensions of time are measured from one-dimensional measurements, as are three dimensions of space.

Objection #2: Direction is a property of space, not of time.

First, this is begging the question. The question is whether temporal direction exists. Second, the association of direction with space it just that: an association. One can just as well associate direction with time. That is, direction can be defined temporally as well as spatially. Third, entities in motion have both spatial and temporal properties that arise together. The difference is in how they are measured.

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Jesus’ brothers and sisters

The Gospel According to John, chapter 7:2-10 reads:

2 Now the Jews’ Feast of Booths was at hand. 3 So his brothers said to him, “Leave here and go to Judea, that your disciples also may see the works you are doing. 4 For no one works in secret if he seeks to be known openly. If you do these things, show yourself to the world.” 5 For not even his brothers believed in him. 6 Jesus said to them, “My time has not yet come, but your time is always here. 7 The world cannot hate you, but it hates me because I testify about it that its works are evil. 8 You go up to the feast. I am not going up to this feast, for my time has not yet fully come.” 9 After saying this, he remained in Galilee. 10 But after his brothers had gone up to the feast, then he also went up, not publicly but in private.

Three times the text mentions “Jesus’ brothers”, or as the footnote states, it can be translated, “Jesus’ brothers and sisters”. Who are these brothers and sisters?

1. Literally speaking, someone’s brother or sister is a person with the same parents. Since Jesus is uniquely the Son of God (John 3:18), he cannot have any brother or sister in the literal sense. Therefore, these verses cannot be read literally.

2. Someone’s half-brother or half-sister has one parent in common. Is it possible that Joseph and Mary had natural children after Mary gave birth to Jesus? John 19:26-27 reads:

26 When Jesus saw his mother and the disciple whom he loved standing nearby, he said to his mother, “Woman, behold, your son!” 27 Then he said to the disciple, “Behold, your mother!” And from that hour the disciple took her to his own home.

This action of Jesus as he was dying makes no sense if either Joseph were still alive or Mary had other children who would take care of her. So Jesus did not have a half-brother or a half-sister.

3. Someone’s step-brother or step-sister is a child of a parent from a previous marriage. Is it possible that Joseph was widowed and had children before marrying the Virgin Mary? The John 19 passage above shows this would make no sense because if either Joseph were still alive or Mary had other children, they would take care of her. So Jesus did not have a step-brother or a step-sister.

4. In some cultures such as first-century Jewish culture another relative such as a cousin may be called a brother or sister. This is the remaining possibility and must be the meaning of the passage. These brothers and sisters were likely cousins of Jesus.

The conclusion is that Jesus of Nazareth was an only child.

Displacement vs. arc length

As pointed out here, average speed does not equal the magnitude of average velocity. But the instantaneous speed does equal the magnitude of instantaneous velocity. For example, the average velocity of one orbit is zero but the average speed is positive.

Consider a section of a curve as below:

The arc length of this section of the curve is Δs. The displacement is Δr. This with the horizontal and vertical differences Δx and Δy makes a triangle. The Pythagorean theorem gives the hypotenuse of the triangle:

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