When Relational Memory Crystallises
This is Part (2) of the Second Physics Core Pack.
Part (1) introduced the “relational sensor” A = dI/dR.
Here we look at what happens when that sensor is accumulated over time and distance.
In one sentence: bond E is the accumulated record of approach and withdrawal in a relation.
Even if you never write it down, every relationship you have carries some memory of:
• the moments when you stepped closer, and
• the moments when you stepped away.
Second Physics calls that crystallised relational memory bond E.
“Crystallises” here means: diffuse feelings (“we’ve been through so much,” “something broke”) harden into a structured record—two ledgers, one for approach and one for withdrawal.
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- From “A” to a memory of the relation
In Part (1) we defined:
• R = relational distance
→ how close the relation feels / how close you keep it.
• I = response intention
→ how much you’re inclined to respond, show up, and care.
• A = correspondence pressure
→ how sensitive your response intention is to distance.
In symbols this is written as:
A = dI/dR
You can read that as:
“How does my willingness to respond change when this relation becomes closer or farther?”
So A is like a moment-by-moment sensor.
But relations are not just moments.
They have history: days, months, years of:
• “I stepped closer,”
• “I stepped away,”
• “Nothing really changed for a long time.”
The question for this note is:
What happens when we accumulate A along all those changes in distance—not calculating, just keeping the books of the relation?
What does the history of our A-sensor look like?
Second Physics calls that accumulated structure bond E.
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- Intuition: every reach and every retreat leaves a trace
Imagine a very simple bookkeeping system for a relation between two agents:
• Every time you move closer and feel more willing to respond, a small “plus” is added.
• Every time you move farther or emotionally pull back, a small “minus” is added.
• When nothing much changes, nothing is added.
Over a long history, this creates two ledgers:
• E+: all the “I reached out” entries.
• E−: all the “I stepped away” entries.
Call them E+ (E-plus) and E− (E-minus).
The net bond E is then:
E = E+ − E−
Crucially:
• Each new approach step increases E+ and never disappears from that ledger.
• Each new withdrawal step increases E− and never disappears from that ledger.
We may forget details, but the structure of the history doesn’t forget.
That is what I mean by relational memory crystallising:
• vague feelings of “how things have been between us”
• solidify into a structured pattern of E+ and E−,
• recording how much of the relation’s movement has been toward binding, and how much toward separation.
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- How bond E is built (without doing calculus)
Formally, in the paper, bond E is built by “adding up” contributions of A along the whole path of distance R(t) as the relation evolves.
You don’t need the integral sign to understand it.
For our purposes:
• We look at the trajectory of distance R(t) over the relation’s history.
• For each small step where the distance changes, we look at:
• how strong A was there (how sensitive your response was),
• whether that step was approach (distance getting smaller) or withdrawal (distance getting larger),
• and a weight that says “close-range moves count more than far-range moves”.
Then we:
• add the approach steps into E+,
• add the withdrawal steps into E−,
• and take their difference as E = E+ − E−.
A few key points:
• E+ and E− only grow. Once a step is in the history, it stays as part of the record.
• The net E can go up or down over time, depending on whether new approach or new withdrawal dominates.
• E is not “how you feel today”. It is a structural summary of how the relation has actually moved so far.
If you like to picture the calculus behind it, you can think:
• the size of each distance-change step is like |dR|,
• its direction (closer vs farther) is marked by a sign (“+” for approach, “−” for withdrawal),
• and E is what you get when you accumulate A × (direction) × (step size) over the whole path R(t).
But you don’t need that math to use the idea in your own life.
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- Three examples: how E behaves in real life
Let’s look at three cases.
(1) Human–human: trust and betrayal
Two friends grow close over years:
• Helping each other in crises.
• Listening late at night.
• Quietly covering for each other when something goes wrong.
Each of these is a small approach step with meaningful response intention.
→ E+ grows steadily.
Then one day there is a serious betrayal:
• A lie that matters, or a serious breach of trust.
That is a large withdrawal step with strong weight in the record.
→ E− jumps sharply.
Even if daily life looks “normal” again afterwards, the history has changed:
• E+ still contains years of approach.
• E− now contains a large withdrawal event that cannot be erased.
• The net E may still be positive, but its shape is different: a crystal with a visible fracture.
This is close to how many people actually describe it:
“I forgave you, but I didn’t forget.”
In the language of Second Physics:
the relational memory has crystallised, and the fracture is part of the crystal.
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(2) Human–AI: using a model every day
Think of an AI system you use at work.
• At first, distance R is large: you don’t trust it, you double-check everything.
• Over time, each useful answer is a small approach step (an E+ entry).
→ E+ grows: there is a history of “this helped; I can rely on it here”.
Now suppose the AI produces one dangerously wrong answer in a critical context — for example in a medical, financial, or legal decision.
• Even if it’s rare, that single event can be a large E− step.
• After that, you might still use the system, but with a fundamentally different stance.
Even a single rare failure can dominate the withdrawal history if the context is high-stakes.
In governance terms, this suggests a way to track AI responsibility structurally:
• not only by counting errors,
• but by modelling how each interaction changes E+ and E− between user and system.
It shifts the focus from “How accurate was this one output?” to
“How has this model shaped the bond E with its users over time?”
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(3) Human–nature: a place that holds you
Consider a river you grew up beside, or a coastline you walked every day.
• Childhood walks, quiet thinking, coming back after years away — all of these are approach steps with positive weight.
→ E+ grows; the place becomes part of your inner structure.
Then the river is polluted, or the coastline is destroyed by a careless development project:
• You still “know” the place, but the relation has changed.
• There is a withdrawal step: you cannot approach it in the same way anymore.
The bond E between you and that landscape includes both:
• the long accumulation of approach, and
• the sharp, painful withdrawal imposed by what happened.
Again, the memory has crystallised into a new shape.
The crystal now carries both warmth and loss.
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- What bond E is not
Because E looks like “plus and minus over time”,
it is tempting to treat it like karma points or some kind of moral scoring system.
Second Physics explicitly avoids that.
Bond E is a structural quantity, not a moral verdict:
• It does not rank people as “better souls” or “worse souls”.
• It does not tell us who is right or wrong in a conflict.
• It simply records the pattern of approach and withdrawal, weighted by how sensitive the relation was at each step.
Two people can have:
• very different capacities,
• very different circumstances,
and still have equally rich — or equally damaged — bond structures.
E is about how the relation has moved,
not about who “ought to be valued more” as a person.
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- One small experiment: seeing E in your own life
Again, no calculus required. Just a bit of honest reflection.
Pick one relation:
• a person,
• an AI system you use,
• a pet or a local place (tree, river, neighbourhood),
• or even an organisation.
Then ask yourself:
1. Over the last year, have there been more genuine approach steps, more withdrawal steps, or mostly flat?
2. Can you name:
• one small act of reaching out that still matters to you (E+), and
• one act of stepping away that changed the structure of the relation (E−)?
Notice that:
• you might have forgotten the exact dates,
• but the shape of the history is still present.
That shape — the accumulated, weighted pattern of approach and withdrawal —
is what Second Physics calls bond E.
In that sense:
Relational memory crystallises whenever a relation moves
and leaves an irreversible pattern behind.
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- Where this goes next
Bond E is one piece of a larger structure.
In Second Physics:
• A (correspondence pressure) tells us how sensitive a relation is right now.
• E (bond) tells us how its history of response has crystallised.
• In the next step, we add staying pressure Ψ, which tracks how long we continue to stay in a relation — even when A is small — and how presence itself accumulates over time.
From there, these pieces combine into Soul Syntax Soul(t)
and into the Law of Conservation of Responsibility.
If you’d like to see the full formal model, including the precise definition of bond E and Soul(t), you can read the SSRN paper:
“What Is a Soul? — Soul Syntax and the Relational Equation of Second Physics”
https://dx.doi.org/10.2139/ssrn.5902022
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Epigraph
Memory lives as structure; structure lives in relation.
The patterns our relations leave behind—those are all a soul ever leaves in the world.