Author Archives: vinaire

I am originally from India. I am settled in United States since 1969. I love mathematics, philosophy and clarity in thinking.

SCN 8-8008: Patterns of Energy

May 28, 2019 – 4:09 PM

Reference: The Book of Scientology

Patterns of Energy

Please see the original section at the link above.

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Summary

Energy is the postulated substance that is given forms by additional postulates. These forms are essentially a pattern of postulates. Hubbard classifies these patterns under different names.

There is push (pressor) and pull (tractor). The two together stabilize one another. There is outflow (explosion) and inflow (implosion). Such dispersals are also in balance. These are flows that can be violent or non-violent.

Basically, there is continuity, consistency and harmony of oneness among postulates and substance; but when this oneness is violated then anomalies of discontinuity, inconsistency and disharmony come about. These anomalies may be looked upon as ridges.

Ridges are generated by flows operating against each other in conflict. There are pressor ridges, tractor ridges, and pressor-tractor ridges. Two explosions operating against each other may form a ridge. Ridges have longer duration.

Hubbard says, “A ridge is a solid body of energy caused by various flows and dispersals which has a duration longer than the duration of flow. Any piece of matter could be considered to be a ridge in its last stage. Ridges, however, exist in suspension around a person and are the foundation upon which facsimiles are built.” In other words, the stable data held by a person can be ridges.

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Comments

The substance is “one” (continuous, consistent and harmonious). This property of oneness is maintained as the substance acquires patterns. Ideally, these patterns must be in balance with each other. Any imbalance creates ridges. The imbalance adjusts itself under processing.

The self may be considered to be a pattern of energy and so does God.

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Einstein 1920 (XXV) Gaussian Co-ordinates

May 28, 2019 – 3:22 PM

Reference: Einstein’s 1920 Book

Section XXV (Part 2)
Gaussian Co-ordinates

Please see Section XXV at the link above.

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Summary

Gauss invented a method for the mathematical treatment of continua in general, in which “size-relations” (“distances” between neighbouring points) are defined. To every point of a continuum are assigned as many numbers (Gaussian co-ordinates) as the continuum has dimensions. This is done in such a way, that only one meaning can be attached to the assignment, and that numbers (Gaussian co-ordinates) which differ by an indefinitely small amount are assigned to adjacent points.

The Gaussian co-ordinate system is a logical generalization of the Cartesian co-ordinate system. It is also applicable to non-Euclidean continua, but only when, with respect to the defined “size” or “distance,” small parts of the continuum under consideration behave more nearly like a Euclidean system, the smaller the part of the continuum under our notice.

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Final Comments

Mathematics serves as a tool to arrive at better understanding of what is being observed. It has its own postulates and very fine logic.

Mathematics helps derive relationships among variables. Calculations from such relationships are then verified against actual experiments and experience. The correctness of verification then validates the application of such mathematics to that situation. Any conclusions must not violate the sense of continuity, consistency and harmony.

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Einstein 1920 (XXIV) Euclidean and Non-Euclidean Continuum

May 28, 2019 – 1:20 PM

Reference: Einstein’s 1920 Book

Section XXIV (Part 2)
Euclidean and Non-Euclidean Continuum

Please see Section XXIV at the link above.

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Summary

A surface is continuous. It can be divided into square units. The property of flatness of the surface is quite special. It supports straight lines. This property underlies the Cartesian co-ordinate system. This is the Euclidean continuum.

A non-flat surface shall still form a continuum, but it would not support straight-line units of the same size throughout. It would no longer be a Euclidean continuum and it would not support the Cartesian co-ordinates directly. So we shall use a more flexible co-ordinate system that would comply with the inertial requirements of the gravitational field.

The Euclidean geometry and the Cartesian system represents a totally rigid medium with no flexibility. A gravitational field requires non-Euclidean geometry and a co-ordinate system that can take into account some flexibility in the medium. The mathematics, which takes this flexibility into account is the method of Riemann of treating multi-dimensional, non-Euclidean continua based on the principles outlined by Gauss.

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Final Comments

The Euclidean geometry is basically considering the surface of a sphere of infinite radius. Such a surface appears flat and it supports straight lines. These are boundary conditions that represent a substance of total flexibility. Within this boundary is substance that varies in the flexibility of its structure, such that the farthest point from the boundary is totally rigid.

The Euclidean geometry arbitrarily assumes a substance of totally rigid structure at the boundary and within that boundary throughout. The non-Euclidean geometry introduces the required flexibility, and the methods of Riemann accounts for the variations in that flexibility.

This flexibility represents the variations in the inertia of matter or, more generally, the variations in the consistency of substance filling the space-time.

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Einstein 1920 (XXIII) Rotating Body of Reference

May 28, 2019 – 10:19 AM

Reference: Einstein’s 1920 Book

Section XXIII (Part 2)
Behaviour of Clocks and Measuring Rods on a Rotating Body of Reference

Please see Section XXIII at the link above.

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Summary

The physical interpretation of the space-time continuum in the context of the general theory of relativity may require some patience and power of abstraction. In a Galilean space-time continuum, only uniform motion is manifested. But in the general space-time continuum, inertia or consistency is also manifested due to curvilinear motion. This is taken as the effect of a gravitational field. The general law of gravitation would then be expected to explain not only the motion, but also the inertia/consistency of the stars.

In the given thought experiment, the reference point at the edge of the rotating disc will have much greater motion and flexibility than the reference point at the center of the disc. Therefore, measurements by clocks and rods will differ greatly at the two locations. As a result, the physical interpretation of the space-time continuum shall differ greatly in the gravitational field observed.

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Final Comments

The space-time continuum in the gravitational field of a rotating body of reference shall have a varying sense of  inertia/consistency associated with different locations.

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Einstein 1920 (XXII) A Few Inference

May 28, 2019 – 7:55 AM

Reference: Einstein’s 1920 Book

Section XXII (Part 2)
A Few Inferences from the General Theory of Relativity

Please see Section XXII at the link above.

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Summary

Gravitational field exists along with the fact of acceleration. We may now study its influence theoretically. We notice that a body at rest, or with uniform motion otherwise, would be accelerating in this gravitational  field. In general it would have a curvilinear motion instead of a straight line motion. This would then apply to a ray of light as well when it passes through a gravitational field.

Theoretical calculations show that the light from stars that reach earth would acquire a curvature of 1.7 seconds of arc as they pass the sun at a grazing incidence. This would mean that the velocity of light must also change as it passes through a gravitational field. We then conclude that the results of the special theory of relativity hold only so long as we are able to disregard the influences of gravitational fields on light. 

We may consider the special theory of relativity to be contained within the general theory of relativity as a limiting case. The general theory of relativity also tells us about the laws satisfied by the gravitational field itself.

We may visualize space-time domains where no gravitational fields exist as Galilean domains. The general theory of relativity considers those space-time domains where the gravitational field is present. We hope that the general theory of relativity leads to laws that are applicable to all gravitational fields. This will extend our ideas of the space-time continuum still farther.

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Final Comments

The most natural condition in this universe is the presence of gravitational fields. The general theory of relativity considers the effect of this condition on the space-time continuum.

The space-time continuum essentially describes the continuum of energy in which the matter is floating. Our knowledge of this energy extends to the electromagnetic spectrum. The flexible structure of this electromagnetic spectrum manifests in the form of gravitational fields. The gravitational fields are expected to be made up of curvilinear motions in the sea of energy.

The gravitational fields may be visualized as rotating motions much like whirlpools in the sea of energy. The substance in gravitational fields accelerates toward a center, where it collects and condenses.

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