Deep section · R — Relation

Relation (R): webs of "in-between"

If Δ secures the idea that there are differences at all, R is about what happens when those differences cannot help but stand in patterns. Relations are the "in-betweens" that turn scattered differences into structure.

1. From pairs to patterns

With a single difference, there is not much more to say. With two or more, questions arise immediately:

• Is this difference larger or smaller than that one?
• Does one difference depend on another?
• Are they compatible, or do they interfere?

These questions presuppose ways of comparing, ordering, and connecting. Those ways of "standing with respect to" are relations.

2. Relations are not optional extras

IO treats relations as primitive in a structural sense. We do not start from self-contained objects and then imagine relational ties being added later as "links" between them. Instead:

As soon as you have multiple differences, you already have a web of possible relations.

Whether we describe that web in terms of distances, causal connections, similarity measures, or something else is a modelling choice. The underlying idea is that the world is patterned, not a loose heap of unrelated bits.

3. Examples of relational structure

Everyday cases make this easy to see:

• In geometry, points stand in relations of distance, angle, adjacency, and containment.
• In time, events stand in relations of before/after, simultaneity, and possible influence.
• In social systems, agents stand in relations like friend, stranger, ally, or rival.

Physics, biology, psychology, and sociology can all be seen as different ways of charting relational structure at different scales and with different emphases.

4. Why R leads naturally toward information

Once some relations become stable and repeatable, they can be used to draw inferences: if A stands in relation R to B, then C is more likely than D. At that point, relational structure starts to carry information.

That is why the IO chain moves from Δ → R → I. We do not add "information" as an independent ingredient; it emerges from how relations constrain what is possible.