So far, the notion of symposition that I have constructed suggests that the “collection of entities” is always a collection of symponents that are lower in the partonomy and thus closer to the Dust than the symposition itself. Sympositions that behave in this way are intrinsic sympositions with intrinsic symponents, and the relationships among them are intrinsic poses. But what if one of the entities in the repetitive collection, one of the symponents, is higher or lateral in the partonomy than the symposition that is specified?

To illustrate, let’s try to come up with an intrinsic distillation that specifies stars and one that specifies moons. For something to be a star, it is sufficient for its symponents to interact in such a way that they have collapsed and rounded themselves under their own gravity and have thereafter begun nuclear fusion. Now for a moon, we might want to say that it needs to be rounded, or perhaps not performing nuclear fusion, but any specification we come up with suffers from a particularly thorny fact: if all we do is set the moon in motion around a star, it stops being a moon! In other words, a moon is a moon not because of the relationships of the symponents within it, but rather on the relationships between it and the symposition it is a symponent of and its other symponents. If an individual is a moon, then another individual is a planet and not a star. We can define “part” explicitly as an intrinsic symponent, so then the symponents of a star are just its parts, whereas the symponents of a moon are not just its parts. Not all symponents are parts. Furthermore, we can denote intrinsic sympositions as “compositions,” and my reason for coining a new word becomes clear.¹ Symponents that are not parts are extrinsic symponents, and they belong to extrinsic sympositions. Furthermore, we can see that a symposition’s intrinsic poses are just its symponents’ extrinsic poses.

If all of the parts of a distillation are very highly modular, then it could be said to be part-independent. The identity of a part-independent distillation would depend entirely on its extrinsic symponents. {possession}_d is an example of such a symposition, as is {satellite}_d in its scientific meaning as any celestial body orbiting a planet or minor planet. A possession and a satellite can have any structure; all they need is to be associated in a specific way with a possessor and a planet or minor planet, respectively, which are outside of the possession or satellite themselves. The symposition that is highly modular in both intrinsic and extrinsic symponents is, uniquely and quite deliciously, {symposition}_d. Part-independent sympositions must still have parts, however, because if they didn’t have parts, they wouldn’t have primitives and thus they wouldn’t even be present in the Logos. Since primitives are subject to the forces of the Standard Model, there is always at least some structure in a symposition at the lowest nuclear and chemical levels, which form the material it is made of and which we can call the substrate.

A symposition with very many symponents at some level, but especially at the top, has less structure than it could otherwise have. Contrast snowflakes with water. The partonomy of a tiny pile of snowflakes splits at the top into just several dozen or hundred snowflakes and then into the dendrites and finally into water molecules and primitives. After they melt into a droplet, however, the top level splits directly into many more than several trillion water molecules. If you could watch the evolution of the partonomy as the snowflakes melt, you’d see a wholesale disintegration of the levels above the substrate supporting the dendrites of the snowflakes. I refer to the missing levels in a symposition that has little structure as a partonomic gap. Partonomic gaps are particularly interesting in the context of distillation. Since sympositions above extreme gaps may not be able to distinguish among the individuals below the gap, their distillations may be better expressed not as discrete trees linking symponents above the gap to those below, but as quasi-continuous radiations.²

Many sympositions have a partonomic gap somewhere between the Dust at the bottom and the symponents near the top. We can define several classes of sympositions based on the relationship between the top levels and the substrate. A substrate-independent symposition has a substrate that is very highly modular, and a substrate-dependent symposition has a substrate that is minimally or not at all modular. {planet}_d is substrate-independent because it can be made out of gas, or rock, or liquid, with no requirements as to elemental composition or anything else. Still, the substrate can’t quite be anything, because if it’s pressurized and hot enough to perform nuclear fusion, then it’s a {star}_d. {neutron star}_d is substrate-dependent because the bottom levels must be nucleon degenerate. {diamond ring}_d is substrate-dependent because it has a symponent that must have carbon atoms in a diamond cubic crystal structure. {dining table}_d is substrate-independent and part-dependent.

If there are no partonomic gaps in the symposition, then the symposition must have a dedicated structure all throughout from Dusty floor to ceiling. Such a symposition could be called substrate-connected. Molecules are very close to the primitives and are effectively substrate themselves, so they are substrate-connected but trivially so. Generally, most macroscopic sympositions are not substrate-connected, but living beings and increasingly digital technologies form very conspicuous exceptions.

Substrates, parts, and extrinsic symponents are useful for describing many sympositions, but they are a simplification. Let’s temporarily define a partonomic gap more specifically as separating two levels whenever the sympositions at the upper level collect more than 150 symponents each from the lower level. Then for an entity with 1 mole of atoms, it must have at least 10 levels above the level of atoms for it not to have a partonomic gap.³ We can easily imagine sympositions that have multiple partonomic gaps, perhaps two, such that the symposition is substrate dependent, with a partonomic gap over the substrate, with several levels of structure over the partonomic gap, and then another partonomic gap, and then finally the symposition itself, but then perhaps extrinsic symponents that themselves may or may not have partonomic gaps, etc. Something that could qualify as that is a {national railroad system}_d, which has a partonomic gap between the various substrates of the rails, crossties, etc and a few foot long stretch of railroad, another partonomic gap between that stretch and the hundreds of miles of a single railroad, and then perhaps another partonomic gap between a single railroad and the system of hundreds of railroads. The level at the few foot long stretch is not the substrate, and though I could define a term for it, I don’t think it would be particularly useful. Overall, the vertical density of levels can be extensively quantified for many different sympositions, but the simple picture of substrates, parts, and extrinsic symponents captures much of the variation in the Logos.

Footnotes

1. And since “com-” and “-position” are both internal to the same language, Latin, whereas “sym-” is from another language, Greek, we have pun on their semantic vs. etymological differences.

2. Actually continuous radiations could be provided by String Theory.

3. 1 mole of atoms is Avogadro’s number of them which is 6.022 × 10²³. 150¹⁰ < Avogadro’s number < 150¹¹