M02 — From billiard balls to dynamics
Time: ~45–60 min · Depends on: M01 · Unlocks: M03
The idea in one minute
Instead of one-shot impacts, think of systems moving on a landscape of possibilities. Over time they tend toward certain patterns (attractors). Living systems often stay organized far from equilibrium by flowing energy through constrained structures. That dynamical vocabulary is the bridge Juarrero needs for action and later for constraints.
Why this matters
If intention is not a pellet that fires once, what is it? DiA’s answer will be: something more like a pattern that continuously shapes trajectories — an attractor on a landscape. You need the landscape idea first.
Core teaching
1. Possibility space (phase space)
Imagine every relevant state a system could be in as a point in a huge space. A phase space (or possibility space) is that abstract map of “where the system can be.”
Constraints (next module) will sculpt this space. For now: behavior is a path through possibilities, not only a chain of discrete collisions.
2. Attractors = tendencies, not one-shot events
An attractor is a pattern the system tends to settle into or orbit:
- Resting at a posture
- A repeating cycle (heartbeat-like rhythms, habits)
- More complex recurrent patterns
Important: attractors describe tendencies over time, not single impacts. Depth ≈ how hard to knock out of the pattern; breadth ≈ how much variation still counts as “the same” pattern.
3. Far from equilibrium
A crystal at rest is ordered in a dead way. A living cell, a convection pattern, a laser, a conversation — these stay ordered while energy and matter flow through them. Far-from-equilibrium order is maintained by flow under constraints, not by freezing into a static block.
Classic classroom image: Bénard cells — heat a fluid layer and ordered convection cells appear. Order from throughput + constraints, not from a tiny manager particle pushing each molecule into a hexagon.
4. Intention as landscape (preview)
DiA will treat an intention less like a force-pulse and more like a constraint landscape that organizes motor and behavioral trajectories so they realize meaningful content. Full story in M03 + claim C006; for now, keep: dynamics > one collision.
Must-get summary
- Behavior = trajectory in a space of possibilities
- Attractors = long-run tendencies / patterns
- Living order often = far-from-equilibrium, flowing, constrained
- This vocabulary replaces “one hit then done” for complex systems
Key terms
Claims this module prepares
- C006 — Intentions as dynamical attractors (full lock-in after M03/M07 light touch)
Check questions
- In plain language, what is an attractor?
- How does a “trajectory” differ from “event A then event B”?
- Why does far-from-equilibrium matter for life-like order?
If you’re stuck
Picture a marble on a hilly landscape. Hills and valleys shape where it rolls without a cue stick hitting it at every moment. That’s the intuition.
Go deeper (optional)
- REPORT §§2.6, 5.1–5.2
- Illustrated HTML report: attractor landscape / Bénard images
- Book: DiA dynamical chapters (later)