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Gestalt hag
Existence is the natural state of the universe.

space objects
Nature of something.

all is flux
Nature of space

events cell
Creation of event cells

toroidino
Topology of event cells

universal principle
The universal organising principle

curvature of space
Determination of the curvature of space

gravity scape
Cumulative effects of event cells

mass and weight
The creation of ‘gravity’ and ‘mass’

dynamic patterns
The dynamic patterns of space

matter from energy
The production of ‘matter’ from energy

energy gradient
About energy gradients

motion without movement
;About ‘motion without movement’

lightning
The speed of light

force without force
About ‘force without force’

ball on table
Inertia and momentum

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This site is frequently updated. The date-line below indicates when it was last worked on.

12 February 2015

© Copyright 2008-2015 GERRY NOLAN

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Determination of the curvature of space
Changes in the internal energy intensity of a toroidino will cause changes in the size of the toroidino in such a way that the energy intensity increasing from the mean will cause the cell to expand, while the intensity decreasing back to the mean will cause the cell to contract, as indicated in (c) below.
Profiles of a toroidino

fluctuation-event intensity

(a)

fluctuating intensity vs time

(b)

change in intensity

(c)

Additionally, remembering that the toroidino is intrinsic to space, when it is expanding it must do so against the pressure of the contiguous toroidinos, some of which, perhaps most, will also be expanding, in which case it is reasonable to expect that the expansion of the toroidinos will be slow relative to their rate of contraction which, because the contraction will be assisted by the pressure of the contiguous cells, will result in a more abrupt end to the event, that is, that toroidino will end. It is clear from this that the balance between the rates of expansion and contraction of a toroidino will depend on the incessantly changing environment of the toroidino. There will be occasions when the surrounding environment is predominantly contracting and occasions when it is predominantly expanding. I will describe the effects of this in detail shortly.

It is very important to note that the fluctuation events or ‘toroidinos’, as I have been referring to them, are not fluctuations of the same toroidino. Once the contraction of the toroidino has reached the stage where the changing intensity returns to the mean, that toroidino ends and another begins. That is, there are no cells pulsating up and down in the one location, although the space itself is continuous, each fluctuation in the energy intensity of space is a brand new event. However, we note for later reference that this state of affairs does not preclude the fluctuations occurring in a pattern.

When analysing the effects of the fluctuations of the energy intensity of the toroidinos of space, we will examine the activity at several scales:

— from the fundamental scale of the fluctuating toroidino;

— through the scale of the concentrations of toroidinos; and

— regions of concentrations;

— right up to the cosmological scale.

In the following sub-section we first of all analyse more closely both the expanding and contracting phases of the toroidino to see how they might affect the contiguous space. Secondly, we analyse the slopes of the curves representing the rates of change of the expanding and contracting phases of the individual cells and the effect of the ratio between the slopes. Thirdly, at the scale of the concentrations of toroidinos, keeping in mind their contiguous environment, we evaluate the cumulative effects of the ratios between the slopes on both the rate of change of the size of the region as well as the actual size of the region in which the events are occurring. During the third stage we note for further study the profound implications that both the rates of change and the sizes of the regions of concentrations of toroidinos have for the behaviour of space on the cosmological scale.

Analysing the slopes and ratios of the slopes of the curves representing phases of the individual toroidinos
Recall that the cell on which we are focussed is an event, a fluctuation in a sea of fluctuations, with the result that the cumulative effect of the toroidinos that are contiguous to each toroidino will modify the growth of the individual toroidinos in constantly changing ways. If the toroidino is tightly constrained, the growth will be slower relative to the contraction, which will be more abrupt, as shown below in (a) below.

The state of affairs in (a) will occur in a region of space in which there is an accumulation of events cells, resulting in a crowded environment, the pressure of which will constrain the rate of expansion as well as the size of the individual toroidinos, and assist their rate of contraction.

In (b), we see that the rates of expansion and collapse are close to even. This situation will occur when there is not so much pressure from the adjoining toroidinos, allowing the rate of expansion to be higher and causing the rate of contraction to be slower than in (a).

Varying slopes of toroidino expansion and contraction

event (a)

(a) Due to pressure from the surrounding sea of fluctuating toroidinos, there is a relatively slow expansion and an abrupt contraction.

event (b)

(b) In this case there is not so much pressure from the contiguous toroidinos so the rates of expansion and contraction are about the same.

event (c)

(c) Here there is much less pressure from the contiguous toroidinos so the rate of expansion is higher and the rate of contraction slower.

Illustration (c) above depicts a situation where there is much less pressure from the surrounding sea of toroidinos so the rate of expansion is much higher, possibly to a larger size, and the rate of contraction is relatively slower.

The cumulative effects of concentrations and regions of toroidinos
It is important to remember that the toroidinos are very small, happening very quickly and there are very many of them so, rather than the characteristics of individual toroidinos, we are primarily concerned with the cumulative effect or the statistical averages of their behaviour at increasingly larger scales.

In a concentration of toroidinos, if the contracting phase predominates in the majority of the toroidinos, the space becomes curved around the concentration. The highest degree of curvature will be at the most intense accumulation of cells with the curvature decreasing as the distance from the most intense accumulation of cells increases. In other words, the cumulative effect of the concentrations of cells provides a mechanism for curving space.

It not ‘mass’ that is curving the space but the accumulated contractions of the fluctuating toroidinos of the energy intensity of space.

Creating the curvature of space
curvature of space
The illustration shows the effect of three individual but intrinsic toroidinos on the curvature of their contiguous space. The individual toroidinos illustrated above could just as well be regions of concentrations of contracting or expanding space on a larger scale, the effect on the curvature would be the same only spread over a larger region. The collective effect of a region where the number of toroidinos in which the contracting phase predominates is that space becomes curved in one direction while, in a region where the expanding phase predominates, space will be curved in the opposite direction. In the profile of the cross section A—B illustrated above, the highest degree of curvature is at the maximum accumulated intensity of contractions, as indicated at (a). The steepness of the curvature of contraction decreases as the distance from the maximum intensity of the contractions increases at (b), flattening as the mean is approached and eventually becoming a new curve of expansion at (c), curving more gently in the opposite direction in the region of the expanding cells. There is an obvious comparison between this illustration and the earlier illustrations with the atmospheric pressure analogy.
‘Gravity-scape’

gravity-scape

Overall the effect of this varying curvature is something like the ‘gravity-scape’ image above, although, of course, whereas this image is only in two dimensions, the undulations in the curvature of space are in three dimensions.

The cumulative effect of the individual contracting toroidinos causing space to curve around these toroidinos is that concentrations of individual toroidinos will form regions of space that become curved. This will result in the further accretion of toroidinos, which will further tend to curve the adjoining space, leading to further accretion, leading to a more intense region of curvature, spreading to larger regions and so on . . . but to varying degrees, until the ‘gravity-scape’ resembles an undulating landscape. The ‘gravity-scape’ is in three dimensions and it is constantly changing like a big sea with confused swells of many sizes running in all directions.

It is apparent that the cumulative effects of the toroidinos of fluctuating energy will depend on the following parameters, all of which will be influenced by the proximate environment:

— the absolute energy intensity of each toroidino;

— the ratio between the rate of expansion and the rate of contraction of each toroidino;

— the number and rate of occurrence of the toroidinos;

— the ultimate sizes of the toroidinos.

These effects will accumulate to the next scale of phenomena, which I have referred to as ‘concentrations of toroidinos’ or simply as ‘concentrations’, and then to the next larger scale, the accumulation extends to what we will refer to as ‘regions’, and then on up to the cosmological scale.

Further development of the explanation of the ontological principle
In moving onto the subject of gravity we have jumped ahead from the development of the ontological principle to its application, so we leave gravity here and continue with the development of the explanation of the ontological principle.

The difficulty illustrated by this ‘jumping ahead’ is part of the problem of dealing with a subject in some sort of logical sequence while all of the factors of these incessantly changing, interrelated phenomena affect everything else. This is the reason that some of the descriptions and explanations might appear to be repetitive, it helps to repeat parts as we advance in an iterative process.

We continue with the further analysis of the implications of the cumulative effects of the concentrations of toroidinos on the curvature of space and the implications of these effects for an ontological principle.

KEY IDEAS

  • Changes in the internal energy intensity of a toroidino will cause changes in its size such that the energy intensity increasing from the mean will cause it to expand, while the intensity decreasing back to the mean will cause the toroidino to contract.

  • Because the toroidino is intrinsic to space, when it is expanding it must do so against the pressure of the contiguous toroidinos, which may also be expanding, in which case the rate of expansion of the toroidino will be slow relative to its rate of contraction. Because the contraction will be assisted by the pressure of the contiguous cells a more abrupt end to the toroidino will result.

  • The balance between the rates of expansion and contraction of each toroidino will depend on the incessantly changing environment of the toroidino.

  • If the contracting phase predominates in a majority of the toroidinos in a concentration, the cumulative effect is that space becomes curved around the concentration.

  • It is not ‘mass’ that is curving the space but the accumulating contractions of the fluctuating toroidinos.

  • The cumulative effects of the toroidinos will depend on the absolute energy intensity of each toroidino;the ratio between the rate of expansion and the rate of contraction; their number and rate of occurrence and their ultimate sizes. These effects will accumulate to the next larger scale and then on up to the cosmological scale.

Space is real and substantial and changing incessantly. Things are patterns of space which retain their identity because the patterns persist.