# Varieties of Matter

In the preceding sections, we have considered both photons and atoms merely as general classes of objects. This is sufficient so far as the photons are concerned, as there are no individual differences in this class of objects other than in frequency. There is, however, a large amount of variability in the atoms of matter, and our next undertaking in the exploration of the theoretical universe of the Reciprocal System will be to examine the nature of this variability and the reason for its existence.

This investigation will be concerned largely with the magnitudes of the various motions involved, and some points concerning these magnitudes should benoted before proceeding with the development. As stated in Section B, the natural datum, or reference level, for physical phenomena is unit speed, not zero. The true magnitude of any absolute quantity (one that is not arbitrarily related to some selected reference datum) is therefore the deviation from the unit value, rather than the mathematical total. In the case of the combinations of rotational motion that constitutes matter, the magnitudes with which we will be primarily concerned are the rotational speeds.

But inasmuch as we will be dealing with units of deviation from unit speed, rather than with speeds measured in the usual manner from the mathematical zero, it will be desirable to utilize some different terminology to avoid confusion. We will therefore refer to this deviation as a displacement of the space-time ratio from the normal unit value. When the speed, s/t, is 1/n we will say that there is a displacement in time (or "time displacement") of n-1 units. Conversely, when the speed is n/1, and n units of space are associated with each unit of time, we will say that there is a displacement in space (or "space displacement") of n-1 units. In this connection it should be noted that in the region of displacements in time (speed = 1/n) a higher displacement value (a greater deviation from the unit speed that constitutes the natural datum) corresponds to a lower speed as customarily measured.

1. In the context of a stationary, three-dimensional reference system, coincident translational motion in more than one dimension is impossible, as each omtion alters locations in a different manner, and such motion would result in the same absolute locaiton occupying two or more different positions in the reference system. Rotational motion, on the other hand, does not alter the location in a reference system of this kind, and coincident rotational motion an all three dimensions is therefore possible.
2. It is not possible, however, for a one-dimensional object, such as a photon, to have rotational motions of the same kind in all three dimensions. Rotation of the photon cannot take place independently around the line of vibration as an axis. Such a rotation would be indistinguishable from no rotation at all. The photon may, however, rotate around its midpoint. One such rotation generates a two-dimensional figure, a disk. Rotation of the disk around a diameter generates a three-dimensional figure, a sphere. Since no fourth dimension is available, this process cannot be continued farther. The basic rotation of the photon is thus two-dimensional.
3. With this two-dimensional rotation in existence, the photon may rotate around the third axis in the opposite scalar direction. This is a rotation of the sphere generated by the basic rotation. Since the two-dimensional rotation is distributed over all three dimensions, the additional rotation in the third dimension is not required for stability of the structure, and the total rotation of the atom therefore consists of a two-dimensional rotation of each photon, with or without an oppositely directed one-dimensional rotation. For convenience, we will refer to the one-dimensional rotation as electric rotation, and the two-dimensional rotation as magnetic rotation. At the present stage of development, there are no electric or magnetic forces in the structures under consideration, but the identification of "electric" with "one-dimensional" and "magnetic" with "two-dimensional" will be of advantage when electric and magnetic phenomena are introduced later in the development.
4. The speed of the electric rotation is independent of that of the magnetic rotation, except to the extent that probability considerations favor the magnetic rotation, and the speeds in the two magnetic dimensions are partially independent, inasmuch as this rotation may be distributed spheroidally rather than spherically. Consequently, there are a number of different combinations of rotational speeds, which give rise to corresponding differences in physical behavior: differences in the properties of the various rotational combinations, we may say. The theoretical universe thus contains many different kinds of atoms with different properties. These can be identified as the chemical elements, each element corresponding to a specific combination of rotations.
5. The number of such combinations that can actually exist in limited by the probability principles, the validity of which, in application to the theoretical universe, is specified in the postulates. The most significant limitation results from the principle that small numbers of units are more probable than large numbers.
6. Geometrical considerations indicate that two photons can rotate around the same central point without interference if the rotational speeds are the same, thus forming a double unit. For a given number of units of effective motion, such combinations result in lower displacement values, and the probability principles therefore give them precedence over single units with higher displacement values. All rotating units with sufficient net total displacements to enable forming double units therefore do so.
7. The electric rotations of the two photons of a double unit can, and therefore do, take place in different dimensions. Each such rotation involves only one photon. Similar independence of the magnetic rotations is not possible because each is distributed over all available dimensions. Each magnetic rotation therefore involves movement of both photons. As a result, a unit of magnetic rotation in an atom is equivalent to 2n² units of electric rotation, where n is the effective magnetic displacement.
8. In the normal outward progression each unit of motion, s/t = 1/1, is succeeded by a similar 1/1 unit, yet another, and so on, the total up to tany specific point being n units. In a combination structure, involving a series of displacements, the sequence is 1/1, 1/2, 1/3,... 1/n, or the reciprocals of these values, 1/1, 2/1, 3/1... n/1. Here, n is the last unit, not the total, and in order to arrive at a total a summation of the individual values is required. To obtain the total electric equivalent of a magnetic displacement, we must similarly sum up the individual 2n² terms.
9. Since the simple motions that have been considered thus far are inherently scalar, addition of another displacement of the same kind of an existing displacement would simply alter the scalar magnitude, without changing the nature of the motion. In order that there may be motion of the original motion—rotation of a photon, for example—it is necessary for the added displacement to be of an opposing nature. We have previously noted that the basic two-dimensional rotation of the photon can be rotated in the opposite scalar direction, but this is possible only because the magnitude of the one-dimensional rotation is less than that of the two-dimensional rotation, and the net rotational displacement of the combination is still negative, as it must be to oppose the positive vibrational motion. This possibility is not open in the case of the original rotation of the photon, but the necessary dissimilarity between the vibration and the rotation can be attained by means of the divergence of displacements in space from displacements in time. A photon with a vibrational displacement in time can acquire a rotational displacement in space, and vice versa.
10. For the present we will be dealing only with those atoms whose vibrational displacement is in space and whose net rotational displacement is in time. The terms "matter", without any qualification, will hereafter refer to aggregates of atoms of this nature. Where it is desired to differentiate specifically between this and the inverse type of matter, in which the displacement of the vibration is in time and the net displacement of the rotation is in space, we will use the term "ordinary matter".
11. While we will include all rotational combinations with net rotational displacement in time under the classification "matter", we will hereby restrict the term "atom" so that it applies only to those combinations which include two rotating systems.
12. Since the magnetic rotational displacement is numerically smaller than the equivalent electric displacement, it is correspondingly more probably, and the magnetic rotation consequently takes precedence over the electric rotation wherever both would otherwise be possible. It will therefore be appropriate to begin our identification of the specific rotational combinations by considering those which have no effective electric rotation.
13. If a unit of space displacement is added to a motion with n units of time displacement, the new unit and one of the time displacement units constitute a full unit of motion (displacement zero) and since every such unit is independent, according to the postulates, this new unit separates from the remainder, leaving a residue of n-1 units of time displacement. Adding space displacement is therefore the equivalent of subtracting time displacement, and vice versa.
14. A structure in which the rotation is limited to one unit of magnetic displacement may be represented by the symbol 0-0-0, where the first two numbers represent the displacements in the magnetic dimensions and the third represents the electric displacement. In accordance with the principle expressed in item 13, the one unit of rotational time displacement merely neutralizes the one unit of vibrational space displacement, and brings the new total to zero. The 0-0-0 structure is therefore the rotational equivalent of nothing at all: the rotational base, we will call it.
15. By the operation of probability, added units of magnetic displacement go alternately to the two magnetic dimensions. A second such unit therefore brings the structure up to ½-½-0. As has been stated, we are restricting the term "atom" to those combinations with two rotating systems, which requires effective rotational displacements in both magnetic dimensions. The ½-½-0 combination does not qualify as an atom under this definition. The question as to just what it actually is will be considered in Section F.
16. The next combination, 2-1-0, is the first of the purely magnetic rotational combinations that qualifies as an element. As has been noted, each magnetic displacement unit is equivalent to 2n² electric displacement units, and the total displacement of this atom above the rotational base, in electric equivalent, is 4 units.
17. Inasmuch as the electric displacement unit is the smallest rotational unit that exists, and therefore the smallest amount by which one rotational combination can differ from another, the possible combinations form a series in which the total equivalent electric displacement of each successive member is one unit greater than that of its predecessor. We will identify the position in this sequence as the atomic number of the element, and because the first two units of displacement have been excluded from the atomic classification, this atomic number can be described as the net total equivalent electric displacement, less two units. On this basis, the atomic number of the 2-1-0 combination is 2, and we will identify this structure as the element Helium.
18. The 2-1-0 combination is one unit above the rotational base in each magnetic dimension. Addition of another magnetic unit therefore requires 2 x 2², or 8, equivalent units. The result is 2-2-0, atomic number 10, which we identify as the element Neon. Another magnetic addition produces 3-2-0, atomic number 18, the element Argon. Similar additions complete the series of inert gases, a group of elements whose distinctive properties results from the fact that these are the only chemical elements without effective rotation in the electric dimension.

Atomic Number
Element
Displacements
2
Helium
2-1-0
10
Neon
2-2-0
18
Argon
3-2-0
36
Krypton
3-3-0
54
Xenon
4-3-0
86
4-4-0

The reason why the series terminates at 4-4-0 rather than continuing on to higher values will emerge later in the development.

19. In view of the greater probability of the magnetic displacement, the role of the electric displacement is confined to filling in the gaps between the combinations listed in the foregoing table. For example, helium is followed by these four elements:

Atomic Number
Element
Displacements
3
Lithium
2-1-1
4
Beryllium
2-1-2
5
Boron
2-1-3
6
Carbon
2-1-4

20. The next combination in this sequence would be 2-1-5, but another factor enters into the situation at this point because electric rotation can take place with displacement in space as well as with displacement in time. As previously noted, the rotational displacement of the atom as a whole--that is, the net total displacement--must be in time in order to constitute rotation of the photon. But as long as the larger component of this total, the magnetic displacement, is in time, the smaller component can be in space. In this case, the addition of space displacement reduces the net total time displacement. The 7-unit net effective time displacement that corresponds to the structure 2-1-5 can therefore be attained in an alternate manner by adding 3 units of displacement in space to the 2-2-0 combination. To distinguish space displacements from time displacements, we will enclose the space values in parentheses. On this basis, the alternate 7-unit structure is 2-2-(3), and by reason of the greater probability of the smaller electric displacement, this structure exists in preference to 2-1-5.
21. The other members of the second half of the group of elements between helium and neon are subject to the same considerations, and this sequence is as follows:

Atomic Number
Element
Displacements
6
Carbon
2-2-(4)
7
Nitrogen
2-2-(3)
8
Oxygen
2-2-(2)
9
Fluorine
2-2-(1)

The probabilities of the two possible structures are nearly equal for carbon, midway between the two inert gases, inasmuch as the electric displacement is 4 in both cases. This element can therefore take either structure, and it is shown in both tabulations.

22. Each of the other gaps between inert gas elements is similarly filled by a series of combinations in which there is an increasing electric displacement in time up to the midpoint of the series, followed by a decreasing electric displacement in space in conjunction with the next higher magnetic displacement. Availablity of electric displacement in space, as a component of the rotational combinations, also permits the existence of an element below helium. This is hydrogen, atomic number 1, which has rotational displacements if 2-1-(1).
23. All of the foregoing conclusions with respect to the effect of probability are based on a consideration of the characteristics of the elements as they exist in isolation. When they are interacting with other elements, as in chemical compounds, additional probability factors may be involved, and the net effect of all of the probability factors mauy be involved, and the net effect of all of the probability factors may favor some combination other than that which would exist if no external forces may be to favor 2-1-5 rather than 2-2-(3), or 2-2-(5) rather than 2-1-3.