# SIG-FPT 2026-10-02 — Session Notes

Participants:
  - Patrick Nast | UTC-7
  - Robby Rao | UTC - 7
  - Venkatesh Rao | UTC-8
  - Shingai Thornton | UTC-04:00
  - Giovanni Merlino | UTC+2
  - Ergod | UTC+1

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## 📖 The Reading

The session centered on Shingai Thornton's talk/write-up for the Protocol Institute's "atomic protocol"/SIG-FPT challenge, in which he attempts to find a common formal core across three mathematical definitions of "system" from the systems-theory tradition:
- **George Klir** (transcribed "Clear"/"clears") — a set-theoretic definition (things + relations)
- **Mario Bunge** (transcribed "Boonghe"/"Boomhai"/"Mario Boomhai")
- **George Mobus** (the "MOBUS"/"Mobis" formalism)

The common formulation discussed was roughly `S = (T, R)` (a tuple of things/participants and relations), with a protocol framed as a set of participants plus rules constraining them.

## 🧭 Overview

After a round of feedback, Shingai described his academic context (PhD in Systems Science at Binghamton, advised by Cliff Joslyn) and his goal of building rigorous, diagrammatic modeling tools accessible to non-mathematicians. The bulk of the session was a probing Q&A: Patrick questioned whether a protocol is really a "system" or just the *rules/relations*, and whether "dependency" is a richer (directed) notion than a bare relation; Ergod pushed on where *dynamics* and *emergence* live in these static formalisms. The group closed with planning for next sessions, converging on category theory as the likely tool for the compositional ambitions.

## 💡 Key Points & Themes

- **The synthesis approach.** Shingai took several systems-theory definitions and tried to extract a common core. The one invariant he found across Klir, Bunge, and Mobus is some notion of **dependency** — things related such that they depend on each other. Ergod characterized this as a "synthesis relationship," looking for a common denominator.
- **Protocol = rules, not the whole system.** Patrick argued a protocol is better understood as the *rules* (closer to relations/edges) that mediate a system, not the system itself. Shingai agreed, noting Mobus is explicit that "a protocol is a set of rules... for how things cross boundaries," and that his own `S = (T, R)` framing was an artifact of how he and Claude attacked the challenge.
- **Constructivism vs. realism.** Shingai described Klir as an adamant *constructivist* — systems don't exist "out there"; humans impose systemness by choosing things and relations. Shingai leans *realist*: systems have independent existence, and he finds "things + relations" unnatural as a complete account.
- **Relation vs. dependency (directedness).** Patrick pressed: isn't a plain relation an undirected tuple/edge, whereas dependency implies a *directed* arrow ("a depends on b")? Why isn't Klir's minimal, undirected version the more fundamental one? Shingai clarified Klir makes *no* assertion about direction — arbitrary relations, no directed graphs, no baked-in dependency. Bunge and Mobus, by contrast, do assert flows and directed graphs in their core math.
- **Where dynamics live.** Ergod distinguished three "powers" of a model: *descriptive*, *computational*, and *prescriptive* (e.g., prescriptive = telling you things about protocol design). He argued `S = (T, R)` only gives a static snapshot. Shingai agreed dynamics are *added later* in Klir (via a "mechanism" component, history, and a time interval Δt), whereas he personally believes dynamics should be *baked in* — which is why he's biased toward the more complex Mobus/Bunge definitions.
- **Dependency doesn't explain *why*.** Ergod drew on his own experience building a code-base dependency graph (to compute "blast radius" of a change): a dependency graph shows *how far* a change can propagate but "doesn't tell you why anything changes." He wants models that let dynamics flow and let structure (e.g., a protocol, a technology) *emerge*, rather than models where the sought-for thing is smuggled in as a seed ("when they find it, it was already there").
- **Emergence across the three frameworks.** Shingai reported: Klir — no rigorous treatment of emergence that he's seen; Mobus — discusses it philosophically but not rigorously; **Bunge** — sits in the middle and gives a *rigorous set-theoretic definition of emergence*, which earned Cliff Joslyn's approval. Shingai wants to incorporate this and offered to share a PDF.
- **Recursive nesting / hyper-objects.** Ergod asked about treating clusters of systems as a single higher-level system (a "hyper-object"). Shingai described Mobus's methodology: start from a system of interest, identify its environment/super-system, then recursively decompose into subsystems. He noted Cliff pushes back that Mobus's "bottom" isn't truly mathematical — it bottoms out in a *process ontology* (primitives like transferring, splitting, combining) rather than a formalism.
- **A recurring arrival at category theory.** Patrick observed the group keeps landing on category theory when trying to formalize compositional/multi-scale structure (he cited compositional game theory). Shingai and Patrick agreed Cliff is nudging Shingai toward *categorical systems theory* as the place where cross-scale, compositional reasoning gets "unlocked" — at the cost of actually learning category theory.

## 🔀 Questions & Disagreements

- **Is a protocol a system or just its rules?** Patrick vs. the `S = (T, R)` framing; Shingai largely conceded Patrick's point.
- **Relation vs. dependency:** Patrick asked whether dependency (directed) is strictly more structured than a bare relation, and if so why Klir's minimal version isn't the most fundamental. Shingai acknowledged this might be "getting at something fundamental" that would require revisiting the Lean proofs and the core claims of the talk. Left open.
- **Should dynamics be baked into the definition or added afterward?** Shingai favors baking in; Klir adds them later. Framed as a genuine philosophical/modeling choice, not resolved.
- **Emergence vs. injection:** Ergod's worry that frameworks "bake in the definition of the very thing they are trying to find." Open question of how much of what Shingai examined is genuinely emergent vs. presupposed.
- **Constructivist vs. realist grounding** of systems — a standing difference between Shingai (realist) and Klir (and implicitly Cliff's preference for Klir).
- Note: audio/mic problems (Giovanni, Shingai dropping out) interrupted several exchanges, so some back-and-forth was fragmentary.

## 🔗 References Mentioned

- **George Klir** ("Clear") — set-theoretic systems definition; founded the Systems Science program at Binghamton.
- **Mario Bunge** ("Boonghe") — rigorous set-theoretic definition of emergence.
- **George Mobus** — the "MOBUS" formalism; process ontology; recursive system/super-system/subsystem methodology.
- **Cliff Joslyn** — Shingai's PhD advisor; scientist/knowledge engineer at Pacific Northwest National Laboratory; studied under Klir.
- **Binghamton University** — online Systems Science PhD program.
- **Claude** (AI) — used by Shingai to help attack the challenge.
- **Lean** — theorem prover used to formalize the talk's claims.
- **Jules Hedges — compositional game theory** (cited by Patrick as an analogous category-theory application).
- **Edward Lee's book on embedded / cyber-physical systems** (Giovanni's recommendation; from his IoT course / prior Protocol School talk) — representing a *different* lineage of systems theory and tooling (e.g., model checking, older than Lean).
- Concepts raised across sessions: process theory, polynomial functors, Petri nets, stigmergy ("stigmergy work").
- Giovanni mentioned a **new PhD student** starting work on **formal verification for swarms of agents**, flagging possible crossover.

## ✅ Action Items & Next Time

- **Shingai** to share a PDF of Bunge's rigorous definition of emergence after the call; will remain on Discord and is open to follow-up calls.
- **Giovanni** to post a link to Lee's embedded/cyber-physical-systems book; Shingai to look into it.
- **Venkatesh** proposed the schedule:
  - **Oct 16** — debrief + road-mapping (after a funding conversation with a potential sponsor) on where to take the stigmergy work.
  - **Oct 30** — a dedicated session on **Lean**.
  - Afterward, possibly run **two parallel tracks**: (1) stigmergy / "atomic protocol" deep dive, and (2) the broad general formal-theory / theory-rising effort — contingent on critical mass (Shingai, Ergod, plus Quentin and Petra, who have theoretical interest, potentially returning).
- Standing interest in forming a group to **learn category theory together**.
- Next call in two weeks.

## ⭐ Memorable Quotes

- **Ergod:** "The thing that I always notice about dependency is that it doesn't tell you why anything changes."
- **Shingai:** "George Clear's definition of system is probably, like, my least favorite of the three... whereas I would say it's probably Cliff's favorite."
- **Patrick:** "Feel like we end up here, like, once every six months... well, you probably need to use category theory at the expense of having to learn category theory."