Chapter 1: Everything in the World around you can be split into smaller and smaller pieces until you reach the smallest particles studied by physicists, and we can call all of these the Dust. Most of the things made from the Dust are repeats to some degree, including both smaller things and also the bigger things that those make up. Motivation: to highlight the ubiquity of divisibility and repetition and their relationships with the smallest physical objects.
Chapter 2: There is a sequence of divisibility scales, a sequence of cosmic events, and a sequence of stellar masses that are special, and they are related to each other and to the fundamental physical interactions or forces of the Dust. The sequences are arranged by the strengths of the fundamental interactions, with the strong nuclear force on one side, gravity on the other, and electromagnetism in between. Motivation: to ground my ideas about divisibility and repetition on physics and physical forces.
Chapter 3: The sequences of divisibility scales invites the possibility that many more scales or levels can be found between electromagnetism and gravity, ignoring the space between the strong force and electromagnetism because it is exhausted by the residual strong force. The entities on vertically neighboring levels are connected by divisibility/parthood relationships, and the hierarchical structure documenting these relationships between levels is called a partonomy. Motivation: to borrow structural notions inherent in physics into domains not obviously physical.
Chapter 4: The identification of parthood relationships, however, is fundamentally arbitrary and must be done by reference to the repetition of entities with similar partonomies on similar levels. An entity that is cross-referenced like that we can call a symposition. The symposition whose partonomy is also the partonomy of the Universe we can call the Logos. Motivation: to highlight the reliance of the identification of repetition on the identification of divisibility.
Chapter 5: We can identify three notions subsumed into the concept of a symposition. The individual is a symposition upon a specific subset of the Dust; the population is a specific group of individuals, itself upon its own specific subset of the Dust; and the distillation is the integration of the repetitions expressed by a specific population into a ghostly individual nowhere present upon a specific subset of the Dust. Motivation: to clarify the differences among the three types of sympositions by their unique relationships with repetition and divisibility.
Chapter 6: A distillation can have structure at many different levels, depending on what repeats in the population being distilled. It can have structure at the substrate, which is the bottom levels where parthood is determined by the strong nuclear and the electromagnetic forces; it can have structure above the distillation itself or below it but in other distilled individuals; it can have structure at the highest divisible parts; or it can have structure below those parts to somewhere above the substrate. Motivation: to highlight the fact that a symposition’s external context is identified in the same way as its internal parts and that its statistical structure can occur even above or outside of it.
Chapter 7: The enumeration of parts or symponents and their relationships for any symposition provides the list of dimensions for a multidimensional parameter space in which the symposition will inhabit a specific point detailing its characteristics. Because of repetition, many different individuals can be be localized in the same parameter space, and the shape of their distribution in it is called a histogram. The presence of symponents as dimensions implies a hierarchy of parameter spaces that frame the Logos. Motivation: to ground the notions of sympositions and the Logos in mathematics.
Chapter 8: A taxonomy, like a partonomy, is a hierarchical structure organized by type-of relationships, instead of part-of relationships. These relationship connect subpopulations to populations and stricter distillations to laxer distillations. This is strictly the case only for linnaean taxonomies. Their opposite, cartesian taxonomies, describe series of subpopulations whose dimensions expand like a multidimensional matrix instead of a hierarchical tree. Motivation: to clarify the types of mathematical objects applicable to taxonomies.
Chapter 9: Over parameter spaces at length scales at which the fundamental forces operate, we can straightforwardly construct potential energy landscapes according to the equations of physics that show how the Dust will move. We can thus understand the story of Chapter 2 as resulting from particles and their sympositions traversing the potential energy landscapes in the levels in the Logos. As the Logos has cooled after the Big Bang, the number of dimensions and levels has expanded between electromagnetism and gravity, being filled with more and more sympositions. Motivation: to conceptually unite the activity of physical forces with the high-dimensional nature of sympositions in the Logos.
Chapter 10: The symponents of a symposition can be discovered spatiotemporally as well as just spatially, again depending on the characteristics of repetition in the relevant population. The details of this imply that partonomies, like taxonomies, are not always hierarchical. The Logos is thus an entity spanning all of spacetime, not just space. Motivation: to clarify the partonomic similarities and differences between time and space and to show the further similarities between taxonomies and partonomies.
Chapter 11: There are two accounts for the repetition of sympositions across spacetime, differentiated by their disposition towards time. A symposition is episodically well-existent if it comes into the World, and it is dynamically well-existent if stays around in the World for a while when it gets here. Sometimes, there is repetition inside of an individual’s dynamic well-existence, and we can call the internal symposition that repeats a sem-loop. Motivation: to introduce the two forms of well-existence and explain their relationship with time.