What is the partonomy of the Universe and what does repetition have to do with it? Addressing that question is the goal of this book. We can try answering the first part of the question with the notion of a physical set, but we immediately run into the problem that physical sets do not seem equipped to tackle power strips or trees, or much of anything that isn’t nanoscopic or astronomical. We solicit sem-linking, expanding the notion of the physical set and banishing that problem, but two more problems arise which are more subtle and basically mirror images of each other.

The physical, more specifically electromagnetic, set corresponding to atomic helium is {e1, e2, nuc_He}. The nuclear primitives of the atom have been reprimitivized and the new primitive has been denoted by nuc_He. Reprimitivization is just a special case of sem-linking, so we can also say that the primitives have been sem-linked and the product of the sem-linking has been denoted by nuc_He. nuc_He is a nuclear set, but what is that set explicitly? In the last chapter, I noted that the nucleus of helium-4 was {{q_u1, q_u2, q_d1}, {q_u1, q_u2, q_d1}, {q_u1, q_d1, q_d2}, {q_u1, q_d1, q_d2}}. Helium-4 is just one of the varieties, also known as isotopes, of helium, however; another, much less common, isotope is helium-3, whose nucleus is {{q_u1, q_u2, q_d1}, {q_u1, q_u2, q_d1}, {q_u1, q_d1, q_d2}}. To say both nuc_He = {{q_u1, q_u2, q_d1}, {q_u1, q_u2, q_d1}, {q_u1, q_d1, q_d2}, {q_u1, q_d1, q_d2}} and nuc_He = {{q_u1, q_u2, q_d1}, {q_u1, q_u2, q_d1}, {q_u1, q_d1, q_d2}} is a flagrant mathematical falsehood; sets with a different number of elements cannot be equal. But we need this falsehood, just like we needed the fraudulence of reprimitivization, or else we wouldn’t be able to speak intelligently about chemical elements. So we see that the first of the two problems is that entities with different partonomies should sometimes be reckoned as being equivalent.

But what does repetition have to do with the first problem? Why is it that to speak intelligently about nuclei, sem-linked clusters of quark triplets, we use words that reflect the number of protons, positively charged quark triplets, instead of say the number of neutrons or the total number of nucleons? The concept of “isotope” should be familiar to many of my readers, but less so perhaps are the concepts of “isotone” and “isobar.” If {n, n, p, p} and {n, p, p} are isotopes, then {n, n, p, p} and {n, n, p} are isotones and {n, n, p} and {n, p, p} are isobars.¹ The names of chemical elements track isotopes and not isotones or isobars because it is the electromagnetic charge of nuclei that determines their interactions after reprimitivization, which in turn determines the repetitivities of the electromagnetic sets they participate in. Atoms that bond to other atoms almost never have nuclei with 2, 10, 18, 36, 54, or 86 protons, for instance, but there is no such rigid pattern with the number of neutrons.  If the number of neutrons or nuclei determined the patterns, then the nomenclature would correspond to isotones or isobars instead of isotopes.²

The second problem is the mirror opposite: sometimes, entities with the same partonomy should not be reckoned as being equivalent. The different elements of a partonomy may be situated at different distances from each other, or be rotated, or otherwise be arranged in such a way that their partonomic breakdown remains exactly the same but their character is different. For instance, the partonomies of a flag at full mast and a flag at half mast are the same, as are the partonomies of “d” and “p,” a straight and a curved rod, chair and boat cyclohexane, the skeletons of a bat wing and of a human arm. Equivalent partonomies do not necessitate any equivalent character, even though they often coincide. In effect, there are repetitivities that have no partonomic significance, but instead differentiate among entities with the same partonomies.

Since physical position is so important for determining the identity and character of what repeats, I’ll enlist the word “pose” to describe this notion of physical set relationships dependent upon physical position. That addresses the second problem; to address the first problem simultaneously, I’ll generalize pose to also account for blindness to changes in partonomic structure that preserve important aspects of repetition, as with isotopes above. Now let me coin the word “symposition.” Actually, I flatter myself; those letters have been positioned together before, although crucially, Google reveals that the letters of “a symposition is” have not. Repairing the oversight, a symposition is a collection of entities defined by their characteristic relational poses. A symposition, importantly, can ignore variation in non-characteristic poses predicated on changes in the partonomic hierarchy, unlike a physical set, and also unlike a physical set may care very much about poses that do not change the partonomic hierarchy. I will use braces {} around one term henceforward to identify sympositions, unless I want to identify a set, in which case that will be clear. A symposition’s entities can also be called its symponents, which are also sympositions in their own right unless they are physical primitives. Sympositions, like physical primitives and physical sets, can interact. The concepts of pose and interaction are analogous, the first one highlighting more static relationships within a symposition and the latter more dynamic ones between sympositions, but it should be clear that there is no fundamental divide between the two notions.

At the scale of atoms, the interactions between sympositions are still neatly described by the Standard Model. However, as sympositions climb ever more levels, it becomes unmanageable to the point of absurdity to use the Standard Model to specify their interactions. In that case, we can say the Standard Model or its fundamental forces have been masked. The three bonding forces, however, are not masked in the same way. The strong force is masked exactly once into the residual strong force that bonds nucleons. The gravitational force is never masked because it is monovalently attractive and doesn’t have different charges like the strong force, such that all gravitational interactions involve just orbits. Consequently almost all the masking in the Universe is masked electromagnetism, which is not surprising since it is the only divalent bonding force, and indeed it is the force that supports power strips and trees.

In a partonomy, one can move both horizontally from one symponent to the next of a given symposition, or one can move vertically from a symposition to its symponents on a lower level or to the symposition it is a symponent of on a higher level. This vertical and horizontal space around a symposition in a partonomy is the symposition’s partonomic neighborhood. The partonomic neighbors of the Earth, for instance, are horizontally the other planets and vertically its own geologic layers and the Solar System as a whole. In many cases the horizontal spread of a partonomic neighborhood will be very similar to a spatial neighborhood, but only insofar as spatial relationships are a proxy for pose. Two partonomic neighborhoods that would otherwise be isolated can sometimes be connected by a symposition that allows the sympositions in both neighborhoods to interact. Such a symposition is a partonomic duct. Microscopes and telephones are examples of partonomic ducts, the former vertically and the latter horizontally. Partonomic ducts effectively expand a symposition’s partonomic neighborhood and allow it to interact with more sympositions.

So we have a Dusty Universe filled with physical primitives, and these primitives get sem-linked into sympositions on account of their pose. In turn, collections of sympositions can themselves be sem-linked into larger sympositions, again on account of their pose. Thus we can fashion for the Universe a set whose primitives are the physical primitives and whose elements are those sympositions which cannot be sem-linked further. I call such a symposition incorporating all sympositions the Logos,³ and we can observe that as the Universe has developed after the Big Bang, the Logos has inexorably shrank in the number of elements at the top and gotten correspondingly hierarchically deeper, even while retaining approximately the same number of physical primitives. The Logos can also be conceptualized as everything in the Universe that is not inherent in the Dust itself but rather in its arrangement. Finally, instead of asking “What is the partonomy of the Universe?” we can ask “What is the Logos, and how did it grow upon the Dust?”

Footnotes

1. Where “n” denotes a neutron and “p” a proton. The contradistinction of “isotope” and “isotone” should be obvious.

2. It’s worth pointing out that the repetitive patterns appealed to for naming nuclei are outside of them and not within them. This will be revisited later.

3. It is unfortunate that “logos” has such a close association with the “ethos, logos, pathos” trifecta of rhetoric, as the term has a very rich philosophical and religious history that has nothing to do with the art of giving speeches. Philo of Alexandria, a Hellenized Jew, described the Logos in De Profugis as “the bond of everything, holding all things together and binding all the parts, and prevents them from being dissolved and separate.” I believe his definition of the term matches mine very well. Further, the ending “-logy” derives from “logos,” and it is convenient that many of the -logies explore different parts of the Logos, such as cosmology and the cosmologos. But perhaps that is facile; less so is a contrasting of “analogy” and “homology,” which I will explore later.