A few comments and clarificatory remarks about the distinctions between *Graphs* (as a mathematical concept and as a database design approach).

A *Graph* (as studied by mathematicians) defines:

- A
**Set**of**Vertices**(*Nodes*) - A
**Set**of**Edges**that hold or obtain between**Vertices**

**Edges** can be **Directed** or **Undirected**.

Note that

Categoriesare notGraphsin the sense above. (See also: https://math.stackexchange.com/a/1239207 and https://mathoverflow.net/a/384839.)

**Graph** databases are a kind of NoSQL (*Non-Relational*) database that's probably easiest to comprehend by contrasting against other common database patterns:

**Document Databases**- specifically refer to a kind of*NoSQL*database whereby data is stored in**Collections**of**Documents**with (potentially deeply) nested**Embedded Documents**and/or by "pointing" to other**Documents**(via**DBRefs**or**DocumentReferences**- note that**DocumentReferences**are essentially what are called**No-Constraint (Weak) Foreign Key Associations**).**Relational Databases**- specifically refer to a kind of*Relational Database*which supports some*Structured Query Language*dialect whereby data is stored in**Tables**by**Row**and**Column**with associations between data points being specified by**Foreign Key**relationships (that are defined on**Tables**and which support**JOIN**operations).

**Graph Databases**, by contrast, query by a "set" of interconnected data points (inspired by the mathematical notion above). From the Meta official blogs and documentation:

- "Every data item, such as a user, check-in, or comment, is represented by a typed object containing a dictionary of named fields."
- "It represented data items as nodes (objects), and relationships between them as edges (associations).
**Typed Objects**(*Graph-Theoretic Vertices*) are connected by explicit associations (*Graph-Theoretic Edges*) bidirectional, symmetric, etc.) to other such**Typed Objects**.

Despite those specific differences, I think

Functional ProgrammingandGraph Databasesare most in the spirit of and aligned with the philosophical notions I've introduced.

Some intuitions about **Object-Hood** that have been defended throughout philosophical history:

- They have boundaries. (Think
**Encapsulation**in Computer Science and Programming.) - They are (usually) spatial or at least located in some background space or universe. (Whether in Cyberspace, Heap Space, or Physical Space.)
- They
*self-subsist*(do not flicker in and out of existence - they*persist*,*endure*,*perdure*- one of the wonders about modern particles and Quantum Foam is that they defy this intuition). - When overlapping, they retain their individual essence or identity (they neither merge nor blend, they are merely arranged in some kind of spatial arrangement, e.g.).
- They can be
*grouped*or*clustered*together (*to form*or be*contained*within a**Container**which may itself be an**Object**as**Sets**are currently seen as). - They are the
*referents*of*singular terms*- what*names*refer to. - They obey Leibniz's
*Principle of the Identity of Idiscenernibles*(which Quantum Particles appear to defy). - They are
*discrete*.

A **Relational Bundle** (what I've since dubbed a **Connector**) is a Non-Objectual Entity:

- (
**RR**)*Legs*may take*relations*. - (
**LL**)*Legs*may take other*legs*. - (
**RS**)*Legs*may take*relational structures*. - (
**BTR**)*Legs*do not take anything other than*relations*, other*legs*, or*relational structures*.

(*The original formulation.*)

The choice of nomenclature is explained further here being inspired by the topological notion called a "pair of pants", key chains, and other trope-theoretic notions like

compresence.

A slightly different formulation:

`◠`

has one or many`│`

`|`

take`|`

`|`

take`◠`

This can be compressed further (as I've demonstrated):

`▢`

has one or many`▢`

`▢`

take`▢`

Note that `▢`

, `◠`

, and `│`

needn't obey **Uniform Substitution** and/or **Variable Binding** (found in Lambda Calculus) - a key feature of the described approach is the denial of these common linguistic properties.

Take your pick from the variety of formulations thus far!

The perspective here is that *connections*, *associations*, and *relationships* are first-class citizens not secondary entities that link **Objects** (as an afterthought).

Note that

Relational Bundle Diagramsso defined can express Graph Theory.Relational bundlesare strictly moreabstractorgeneralthanGraphs. I've even supplied a tentative alternative formulation of theOrdinalswithout recourse toSets.

What might a "purely relational" database look like?

No

**Objects**(**Sets**or otherwise) within its more fundamental ontological dependencies (let's just call those what they are.)- Which might form a model of Hyper Computation - e.g. -
`N+1`

information units might be packed into`N`

units inherently due the non-atomic nature of interwoven**Relations**. - The successor entities would lack certain intuitive features described above.
- Note that every Computer Science paradigm today is
*objectual*somewhere in its conceptual dependency tree. - Arguably, much more performant at handling deeply interconnected data (discrete or otherwise).

- Which might form a model of Hyper Computation - e.g. -
Something like light-wave propagation in Photonic Computing. (Exhibiting intrinsically connected wave-like behavior rather than discrete

**Objects**bound by some kind of**Relation**.)Consider something like the following

*path*-based data structure.Static

**Objects**(or other entities) are "strung together" (query, associations) into a single relational entity (the depicted "golden braid"):We observe that intutions surrounding data representation (

**Rows**,**Columns**, etc.) can be seen as dual manifestations of the same:And, that one of the two manifestations lends itself nicely to

*Relational Bundle Theory*above.

- Path Deformation
- On Connection Theory
- On Connection Theory #2
- Ontological Gaps
- Sign, Identity, Relations
- Fun Math Stuff and the Philosopher's Stone
- Fun Math Stuff and the Philosopher's Stone #2
- Fun Math Stuff and the Philosopher's Stone #3
- Relational Bundle Theory and Graphs

##### post: 2/21/2023