🧭 Lead and Follow — From Myth to 'Yes! This is Easy' Reality

🎩 The Traditional View

For decades, partner dance has taught Lead/Follow as a kind of mysterious "Leader" does something and "Follower" does their best to respond to it.

“One person gives the signal, and the other responds to it.”

all wrapped in:

• Gender roles
• Vague metaphors like “intention,” “tone,” or “connection”
• A strange mix of physical cues and social storytelling

It worked — mostly — because dancers developed intuition and touch over years of frustration and practice.

The 25% Problem

More accurately you only have a 25% chance of it working. Takes this fun example where for every step in any direction:

It's ok, we've all been there.

But... wouldn't it be nice if there was something that's provable, easy to understand and works? (With no fluff and bs)

🔍 The Problem

This model assumes:

• That a clear signal is always sent,
• That the Follower can interpret and execute it correctly,
• That deviations are due to “bad following” or “weak leading”,
• Everyone gets frustrated and are told to 'just practice'.

Read about the Sheer Improbability of Synchronization

✅ How Lead and Follow Really Works

Thanks to math and physics we now know:

Lead/Follow is not a transmission-reception model.
It is a recursive, probabilistic, energy-aware negotiation of energy exchange and motion.

TL;DR: We’ve done the overthinking so you don’t have to.

This is the reality of 'Lead and Follow'

Leader instigates an action and then synchronizes with whatever the Follower does.

It's really easy. It eliminates push and pull. It's proven by math and physics.

It fixes the Sheer Improbability of Synchronization problem too!

Simple Proof: This applies to just about any Dance Position (DP) but we'll assume that Leader and Follower are in Closed Position.

The simple truth is that the Follower can't (and should NOT) predict what the Leader is going to do. It's a lot of work and aside from anything else Follower is supposed to be enjoying themselves.

The Leader simply doesn't know where the Follower will go because Follower doesn't know themselves.

But the Follower does tell the Leader where they are when they do it. In our single step example the Leader continues to move until they can feel Follower is no longer moving back (because they stop moving!) and at that point Leader puts weight on their moving foot.

Leader never, ever, ever puts weight on their foot before the Follower has put weight on theirs.

That of course is extended to:

Leader always synchronizes with what the Follower has just done

What other option does Leader have?

• Complain that their partner isn't following (good luck)
• Tell their partner they did something wrong (good luck with that)
• Pick Follower up and plop them down in the "correct position"

Timing Details:

• Leaders Timing Model
• Followers Timing Model

Something this radical, this simple and this easy should have proof!

• [(Im)Probability of Synchronization]/inside-the-steps/probability/probability/improbability-of-synchronization/default.md) The chances of you synchronizing with your partner explained.

• Schrödinger’s Follower:
  The Follower exists in a 'superposition' of possible responses until their motion is observed.

Followers Movement Is In Control:
The Leader doesn’t lead — they use the new reality of where the Follower is for their next action.

• Least Action Principle:
  The Follower’s response follows Maupertuis’ principle — they take their most energetically efficient (i.e. preferred) path, which might even be the one Leader was hoping for.

• Matching Energy:
  Matching Leaders and Followers energy is nearly impossible. Instead, Leader adapts to where the Follower actually is rather than where Leader thought they should go.

To quote the Wisdom of the Great Philosopher Jagger who teaches that "You can't always get what you want, But if you try sometime you'll find, You get what you need "

📚 Citations & Influences

A curated list of foundational thinkers whose principles underlie the Unified Partner Motion Model in DanceBot.

🧠 Classical Mechanics & Motion

⚖️ Sir Isaac Newton

• Philosophiæ Naturalis Principia Mathematica (1687)
• Core: Laws of motion, inertia, force = mass × acceleration
• Influence: Motion intention, directional force clarity, inertia management

🧠 Leonhard Euler

• Mechanica (1736)
• Core: Equations of motion, rotational dynamics, rigid body mechanics
• Influence: Frame stability, rotational balance, angular momentum control

🧠 Pierre-Louis Maupertuis

• Accord de différentes lois de la nature qui avaient jusqu'ici paru incompatibles (1744)
• Core: Principle of Least Action
• Influence: The Follower’s motion collapse into energy-minimizing trajectories

🧠 Joseph-Louis Lagrange

• Mécanique Analytique (1788)
• Core: Lagrangian mechanics, generalized coordinates, reformulation of Newton’s laws
• Influence: The mathematical framework for least action in partner motion, used to model Follower collapse trajectories and joint motion under constraint

🌌 Quantum & Probabilistic Thinking

🧠 Erwin Schrödinger

• Schrödinger's Cat thought experiment (1935)
• Core: Superposition and collapse
• Influence: “Schrödinger’s Follower” - motion doesn’t exist until observed

🧠 Richard Feynman

• Feynman Lectures on Physics (1964)
• Core: Path integrals, probabilistic motion, energy transfer models
• Influence: Dance as a series of energy negotiations, not fixed commands

🔁 Control Theory & Systems Modeling

🧠 James Clerk Maxwell

• On Governors (1868)
• Core: Feedback and control loops
• Influence: Early precursor to PID-style feedback in connection

🧠 Hendrik Lorentz & Henri Poincaré

• Core: Dynamical systems, perturbation theory
• Influence: Non-linear partner interaction, sensitivity to timing and small force errors

⚙️ Engineering Analogues

🧠 Norbert Wiener

• Cybernetics (1948)
• Core: Feedback, systems regulation, input/output logic
• Influence: Frame as a dynamic, mutually updating signal interface

🧠 Claude Shannon

• A Mathematical Theory of Communication (1948)
• Core: Signal/noise, transmission theory
• Influence: Teaching translation - leading isn’t “broadcasting,” it’s low-latency signal encoding