Based on the hypothesis as it is so far developed, we have the impression of an energy field in which fluctuation events are occurring within a limited range of energy but with a range of dimensions varying from one to an infinite number, and a variety of rates, sizes and topologies, many of which are toroidal, which I have likened to a sea with swells and waves upon waves flowing and surging in all directions. I am reminded of a blinding storm at sea in which all differentiation between sea and sky is lost in the confounding melee of churning waves, slashing sea spray and pelting rain, the unremitting violent motion depriving one of all sense of structure . . . This is the image I have of the world that we have so far hypothesised. It is a world of close to maximum entropy so obviously further development is required to achieve the ordered structure that the world so obviously has.
The complex structure of space
Regardless of whether they are comprised of atoms in the void or of space crumpled up as matter, it is obvious that many kinds of structures of widely varying complexity exist. In the first case we would say that structures exist in space and in the latter we say that space itself has structure. To be quite clear, I am talking here about all structures from the Planck scale on up through the scales of some twenty orders of magnitude to the sub-atomic elements such as quarks, electorns, protons and neutrons, that comprise atoms, to molecules, familiar objects, planets, stars, systems, galaxies, clusters of galaxies and ‘great walls’ of galaxies; objects that would commonly be regarded as being in space, and I am saying that they are of space.
The structure of the world is formed in accordance with the ontological principle that we have hypothesised and the ratio of the slopes of the contracting and expanding phases of the toroidinos is the basis of the ontological principle which is manifested through the curvature of space as gravity. Moreover, as we will see, every aspect of the behaviour of space and everything comprised of space, that is the structure of the world, occurs according to the ontological principle.
In our analysis of the structure of space we will start with why it must have at least three dimensions.
The three dimensions of space
Fluctuating into and out of existence at various frequencies, space could have any number of dimensions, all but three of which are beyond the reach of our perception. This might be because all but the familiar three are too small or too brief for us to recognize or because they don’t exist at all, so let us concentrate for the present on the ones we know do exist.
A line is one dimension in that it has linear extension, it cannot have any width or thickness. Let’s be clear, we are not talking about a line in space, just a line by itself, so there can be no space there. Of course it may be argued that since we can build a bridge using elements that are essentially one dimensional, we should be able to construct space with elements that are one dimensional. However, we would need to overlook the fact that a three dimensional space would be required in which to construct the bridge. Nevertheless, it seems that the people who postulate string “theory” do believe it is possible to construct a world of one dimensional strings. This is despite the palpable fact that it is impossible for strings with only one dimension to amount to anything more than a longer piece of string. Since one dimensional strings have no width or thickness, stacking even an infinity of them in any way would still amount to nothing more than a single, one dimensional string.
The same logic applies to two dimensional planes which, having no thickness, may be stacked one on top of the other ad infinitum without increasing the thickness one iota. So, it would seem that three dimensions is the minimum required for the world as we know it.
Since we have hypothesised that things are not in space but are of space, it must be that whatever comprises space is what causes it to have three dimensions. It may be argued that three dimensional space must have existed prior to the energy field from which the toroidinos arise. However, remember that we are talking about an iterative process in something that has always existed and it is this process that gives rise to the world as we know it and toroidinos are an intinsic part of the process.
As I indicated above, it is possible that the fluctuation events occur in an infinity of dimensions but we cannot perceive any more than three dimensions either because they are two small or because they do not survive long enough. Although it is possible that the world may have more than three dimensions, if we invoke the practice of making the least assumptions necessary and assuming the higher probability of simple systems, it is more likely that the simplest possible concept of space is correct: that space just has the three dimensions necessary to make the space with which we are familiar.
Patterns of space
Now we will see how it might be that an energy field comprised of apparently random toroidinos is transformed according to the ontological principle into the dynamic patterns that are the things, all the objects and phenomena, with which we are familiar.
Nodes, modes and properties
Continued at top of right column . . .
Central to the idea of patterns are nodes and modes; for example in a vibrating string on a musical instrument fixed at both ends, any vibration of the string must have nodes at each end. In the example shown at the top of the right column, the string with length L could have a standing wave with wavelength twice as long as the string, that is, the wavelength = 2L.
|This gives a node at either end and an antinode in the middle. This is one of the modes of vibration of the string—‘mode of vibration’ meaning just a style or way of vibrating. Other modes are allowed on a string fixed at both ends and several are shown occurring at different fractions of the fundamental wave length (λ).
This is a drawing of the first four modes of vibration of an idealised stretched string with a fixed length. The vertical axis has been exaggerated.
Nodes and modes in a vibrating string or wire
I also use the word ‘node’ as a verb; as in to node is to form an entity with significant topological characteristics. Because of tiny random variations in the formation of nodes, not all nodes will be the same and this is what gives rise to the different modes of the nodes. The modes of nodes, as indicated above, are the ways the nodes are, that is, their properties. Various aspects of modes are their shape; frequency of oscillation—which is determined by the energy in the mode—and complexity, or the number of harmonics in the oscillation frequency.
Because it is important to have a clear idea of what I mean by the words ‘node’, ‘mode’ and ‘property’, I define a node (noun) as a knot or knotty formation or, more generally, an entity with significant topological characteristics. The toroidinos are themselves modes of nodes and will form into more complex modes according to the ontological principle.
The way I mean the word ‘mode’ is as the accidental property of a substance and, according to the hypothesis we are developing, this means all properties because, on the basis that random fluctuations are at the root of all events, all properties of things must be accidental. According to the OED, other important definitions of the word ‘mode’ are: any of the distinct kinds or patterns of vibration that an oscillatory system can sustain; a manner or state of being of a thing; a thing considered as possessing certain non-essential attributes which may be changed without destroying its identity (my italics).
Particular modes are particular properties of things, which determine not only that we are able to distinguish between things, that is we do not live in an undifferentiated world, the modes also determine the way we perceive things as particular events, objects and things.
In summary, nodes are individual types of events that are the basis for things and objects and it is the modes of the nodes that are the specific properties of things. That is, the dynamic pattern of space that we perceive as things and objects are really the properties of the objects.
Since the fluctuations of space are about a nominal mean, there will be a regularity in the fluctuations in that the resulting toroidinos will all be within a certain range of size and energy intensity. The justification for the supposition of regularity is that, as we have hypothesised, the existence of space is the natural state of the world and space is independent, therefore there is only the inherent instability of space to cause changes in the intensity of space and this inherent instability will only occur over a limited range of scales.
As explained above, the ratios of the contracting and expanding cells will determine the properties of space such as its curvature, elasticity and density. It stands to reason that the regularity of space will result in the formation of regular coagulations or clusters which form the regular patterns of space. Although not necessarily representative of the regularity of space, the illustration below shows a regular pattern with patterns of nodes that are intrinsic to the main pattern.
Recall that the most probable ontology of the world is that there is only one entity, space, and one principle according to which it is organised along one path to what we perceive as matter, therefore, according to the hypothesis as it has been developed so far, this means that all objects, things and phenomena are events that are intrinsic to the dynamic pattern of space. It follows from this that, because the pattern of space is dynamic, the nodes and their modes are dynamic at every scale. It is a world of events within events within events, in which there are no ontological levels and no distinct parts. This process is summarised in the figure below.
Nodes and modes of nodes in a pattern
A regular pattern with nodes forming intrinsic patterns to the main pattern. The nodes are indicated by the red and blue arrows. The red arrows point to one mode of a node and the blue arrows another mode of node. That is, all of the intrinsic patterns are nodes and the differences between them are determined by their modes.
Continued below figure . . .