iSoul Time has three dimensions

Category Archives: Knowing

epistemology, science, kinds of knowledge, methodology

Replicating time

In mathematical finance, a replicating portfolio for a given asset is a portfolio of assets with the same properties. Here we replicate time through motions that have the same properties as time.

Step 1. Consider the motion of a rigid body A with a translation and a rotation around the same axis, such that the translation and rotation begin and end together. Measure the displacement of the translation as a multiple of the rigid body length along the axis. Count the number of rotations and any fractional rotation of the rigid body. The assertion here is that the quantity of rotations is a measure of the distimement, that is, the duration of motion around the axis of rotation.

Step 2. Separate the motion of rigid body A into a translation of rigid body B and a rotation of rigid body C such that the displacement of B and the distimement of C are the same as the displacement and distimement of A in step 1. Then the displacement of B is a measure of the displacement of A, and the distimement of C is a measure of the distimement of A.

Step 3. Construct an independent clock as a rotating rigid body that matches the rotation of rigid bodies A and C but runs continuously. Note the marking on the clock when rigid bodies A and C start and stop moving. The quantity of rotations between the start and stop is equal to the duration of motion of rigid bodies A and C. The reading on the clock is a measure of scalar time.

Conclusion. In order to generalize this the clock needs to move at a constant rate that is standardized for all clocks. Then allow another rotation so that the motion of translation and rotation replicates any rigid body motion per Chasles [shahl] Theorem of kinematics.

Chasles [shahl] Theorem states: Every rigid body motion can be realized by a rotation about an axis combined with a translation parallel to that axis. (Reference)

The independent clock generates a scalar time because it is not associated with any axis or direction. If the clock is associated with an axis of motion, then it generates a vector time, just as a rigid rod along an axis generates a vector length.

All theories are limited

This post continues previous posts on this topic, such as here.

Once a theory becomes established, it is always valid. It is never falsified. What happens is that its limits are discovered. Any pretense to being universal breaks down.

All theories are limited. Theories are analogies, and all analogies have limits. It is the scientific fashion to initially present a theory as universal, but this is a manner of speaking, not to be taken literally. No theory is universal because all theories have their limits.

When the limits of a theory are known, it is what Werner Heisenberg called a closed theory. An open theory is one whose limits are not known. It may be considered universal, even though it is not. But until its limits are known, no one knows its limits so it’s as if there are none. Eventually, limits will be found.

This means for example, there are three valid theories of the figure of the earth: the flat earth, the spherical earth, and the ellipsoidal earth. Each is valid within a certain domain of accuracy and precision.

There are several valid theories of the celestial bodies: simple geocentrism, Ptolemaic geocentrism, Copernican heliocentrism, Tychonic geoheliocentrism, Keplerian heliocentrism, Newtonian barycentrism, and Einsteinian cosmology. They are all valid within their domain of applicability.

Several theories of biological diversity are valid: fixed species, fixed kinds with limited change, and change over time (evolution). None of these are universal. They all have their limits.

Disciples and relatives of Jesus

There are many disciples of Jesus in the Bible, but there are twelve that are particularly the disciples, or simply, the twelve. Some of these are related to each other. In the small town region of Galilee where Jesus lived that would not be surprising.

What follows is a summary of the disciples and relatives of Jesus, given that we don’t have as much detail about them as we would like. First, the twelve disciples, which are listed four times in the New Testament (Mt 10:1–4, Mk 3:13–19, Lk 6:12–16, and Acts 1:13):

Simon Peter and Andrew, brothers who worked with Zebedee’s family fishing business. Jesus gave Simon the nickname Peter.

James and John, sons of Zebedee and Salome, whom Jesus nicknamed Boanerges, “sons of thunder”.

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Creation and evolution intersect

The controversy over creation vs. evolution, or creationism vs. evolutionism (naturalism), is often treated as an either-or, one-or-the-other proposition. In fact the creation models of today contain much that would be classified as ‘evolution’ (change over time).

Before the 19th century, theories of creation accepted a static model in biology, geology, and astronomy. That is, the universe of today was considered virtually the same as it was when first created. Extinction, for example, was widely considered impossible. In the 19th century Georges Cuvier and others showed that fossils were the remains of living beings and extinctions did occur. That upended the static model of creation.

Opponents of creationism, from Darwin to today, define creationism as the static model of creation. However, creationists have included change over time to their model of creation, starting in the 19th century and continuing today. Much of what commonly comes under the heading ‘evolution’ is part of the creation model today: adaptation, natural selection, speciation — all are part of creationism.

It is false to identify creationism with a static model of creation.

What parts of evolution theory are not part of creation theory today? Universal common descent is part of evolution theory but not creation theory. Change over time is limited in creation theories to within life forms or kinds (similar to genus or family), whereas there are no limits to change over time in theories of evolution. The postulate of deep time is necessary for theories of evolution, but not for theories of creation.

Importantly, humans are different only in degree from other animals in theories of evolution, but in theories of creation humans are different in kind from other animals. This point goes beyond mere biology to a statement of what it means to be human. Accordingly, it is open to other disciplines. For example, Mortimer J. Adler’s The Difference of Man and the Difference It Makes makes a philosophical case for humans being different in kind from other animals.

Theories of creation and evolution intersect. Their differences are about the limits to change over time, rather than the existence of change over time.

Time, space, and order

There are three axes (dimensions) of motion with six degrees of freedom. There are two metrics of motion: a length metric and a duration metric. The length metric is the magnitude of the vector between two points, and is called distance. The duration metric is the magnitude of the vector between two instants, and is called distime.

If one conceives of this as two 3D metric geometries of motion, then there is a 3D space geometry with a distance metric and a 3D time geometry with a distime metric. If the speed of light is an absolute conversion between distance and distime (which is essentially Einstein’s second postulate of special relativity), then there is one 6D spacetime metric geometry.

A 3D space coordinate system is built from an origin point and three orthogonal axes with a distance metric. A 3D time coordinate system is built from an origin instant and three orthogonal axes with a distime metric. A 6D spacetime coordinate system is built from an origin event, three space coordinates, and three time coordinates converted to lengths. An equivalent 6D spacetime coordinate system has three time coordinates and three space coordinates converted to durations.

A stance line represents two opposite linear motions with a constant rate (i.e., inertial motions). The positive direction represents distances to events diverging away from the origin point. The negative direction represents distances to events converging toward the origin point (i.e., destination). Apart from motion a point has a distance but its sign is ambiguous. A stance line represents the stance or scalar space of an odologe.

A time line represents two opposite straight motions with constant rate (i.e., inertial motions). The positive direction represents distimes to events diverging from the origin instant. The negative direction represents distimes to events converging toward the origin instant (i.e., destination). Apart from motion an instant has a distime but its sign is ambiguous. A time line represents the time or scalar time of a clock.

Events may be ordered by the stance or the time. Events ordered by stance are macronological. Events ordered by time are chronological. All events that are equal distances (equidistant) from the origin point are simulstanceous with it. All events that are equal distimes (equidistimed) from the origin instant are simultaneous with it.

6D Galilean spacetime

Here we expand 4D Galilean spacetime into 6D Galilean spacetime, based on section 1.3 Galilean spacetime of The Geometry of Relativistic Spacetime: from Euclid’s Geometry to Minkowski’s Spacetime by Jacques Bros (Séminaire Poincaré 1 (2005) 1 – 45).

[p.3] We start with a representation space whose points are interpreted as the “physical events”. Any motion of a particle which is physically possible between two given events A and B is represented by a certain world-line with end-points A and B. There is an absolute orientation of such worldline, which can be called its “time-arrow”: its physical meaning is that one of the end-point events, e.g. B, is in the future of the other one A.

[p.6] From the viewpoint of mathematical physics, the use of geometry in more than three dimensions turns out to be necessary, if one wishes to represent phenomena whose description necessitates more than three independent quantities. A typical example is the six dimensional space Rab6Ra3 × Rb3 of the positions (a; b) of pairs of material points (or pointlike particles) in mutual interaction. Trajectories of such pairs are represented by curves in R6, described in terms of a parameter t by equations of the form a = a(t); b = b(t).

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History of theories of creation

A theory of creation (also known as a creation theory) is an older term that has been overshadowed by the terms creation science and especially creationism since 1980 (see Ngrams here and here). This overlooks the long history of theories of creation, and implies that the subject is of recent vintage, purely a reaction to theories of evolution, which is badly mistaken.

This brief survey shows that there were and are various theories of creation before and after Darwin and Huxley. First, let us show when creationism arose. The Online Etymology Dictionary states about creationism:

1847, originally a Christian theological position that God immediately created out of nothing a soul for each person born; from creation + -ism.

As “science teaching based on a fundamentalist interpretation of the Book of Genesis, the scientific theory attributing the origin of matter and life to immediate acts of God,” opposed to evolutionism, it is attested from 1880. Century Dictionary (1897) defines creationism in this sense as “The doctrine that matter and all things were created, substantially as they now exist, by the fiat of an omnipotent Creator, and not gradually evolved or developed.”

A search of the text of Darwin’s Origin of Species shows that what he called “the theory of creation” is the same as the 1897 definition of creationism. Darwin referenced no exponent of this theory, and yet he made it the sole foil for his “theory of descent with modification”. The conclusion is that Darwin is the originator of the creation theory he has in mind. What for Darwin was bad science was for TH Huxley not science at all, as if he could remove pre-Darwinian biologists from science.

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Conservations of energy

This post is about the conservation of (space) energy and time energy. I wrote about the conservation of fulmentum here. See also the post on Work, effort and energy.

First, here is a derivation of the conservation of (space) energy from classical physics:

The law of the conservation of (space) energy states that the total (space) energy in an isolated system remains constant over time (distime). The total (space) energy over an arbitrary length of distime, Δt, is constant. Let the total (space) energy at two times be E1 and E2. Then:

(E2E1)/Δt = 0.

Since the total energy equals the kinetic space energy (KSE) plus the potential space energy (PSE), we have

(KSE2 + PSE2KSE1PSE1)/Δt = 0

= (KSE2KSE1)/Δt + (PSE2PSE1)/Δt = 0

= (ΔKSE – ΔPSE)/Δt.

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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.

Spiral/helical motion

The outline below is also available in pdf form here.

Spiral/Helical Motion

A helix is the geodesic of a cylinder; if we develop the cylinder on which the helix is traced, the helix becomes a straight line. Radius r (or a or R or A); velocity v, arc length s, arc time, w, pitch length P; pitch time, M; pitch angle α; pitch time angle β

Constants

v = |v| = √(r² + b²)          s = t √(r² + b²)

u = |u| = √(q² + c²)         w = x √(q² + c²)

Pitch and slope

pitch length, P = 2πb     slope, P/S = b/r

pitch time, M = 2πc       time slope, M/T = c/q

Pitch angle

α = atan(P/S) = atan(b/r)       β = atan(M/T) = atan(c/q)

Arc length of one winding    L = √(P² + S²)

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