If experiments generate structured variation,
then modelling cannot remain what it was.
It cannot remain:
the description of objects with intrinsic properties
Because the stability we are tracking is no longer located in the object alone.
It is distributed across:
- system
- apparatus
- configuration
- constraint
What needs to be modelled is not a thing.
It is a relation that stabilises under specific conditions.
The inherited model
Standard modelling begins from a familiar assumption:
- there are objects
- objects have properties
- properties can be measured
- laws describe how those properties relate
This works extraordinarily well—provided that:
properties can be treated as independent of the conditions under which they are measured
Under that assumption, modelling can proceed by:
- isolating variables
- defining equations
- solving for values
The object anchors the model.
What changes under visible conditions
Once conditions are treated as part of the phenomenon, this anchor shifts.
Because now:
- properties depend on configuration
- measurements depend on interaction
- values stabilise only within regimes
The question becomes:
what exactly is the model about?
If it is still about “the object,” it must now include:
- all the conditions that make its properties appear stable
At that point, the object is no longer primary.
What is primary is:
the structure of relations that produce object-like stability
The shift: from entity to relation
The modelling pivot is this:
instead of modelling what something is, we model how stability arises across configurations
This does not eliminate objects.
It repositions them.
Objects become:
compressed descriptions of stable relational patterns
They are not abandoned.
They are derived.
What a relational model tracks
A relational model does not begin with a fixed entity.
It begins with:
- a space of configurations
- a set of constraints
- a family of interactions
It then tracks:
- how outcomes vary across that space
- where stability emerges
- how different regimes connect
The central question is:
what remains stable under which transformations?
Revisiting constants
Under object-based modelling, a constant is:
a fixed property of a system
Under relational modelling, a constant becomes:
an invariant within a class of transformations across configurations
This is more precise.
Because it specifies:
- the domain in which stability holds
- the transformations under which it persists
- the conditions under which it breaks
A constant is no longer assumed.
It is located within a structure.
A gravitational example
Instead of modelling gravity as:
a force with a universal constant G
we model:
how different experimental configurations produce G-like stable relations
The model then includes:
- configuration parameters
- interaction structures
- transformation rules between regimes
The output is not a single value.
It is:
a map of how gravitational interaction stabilises across conditions
Equations do not disappear
This shift does not eliminate mathematics.
It changes what equations do.
Instead of expressing:
relations between intrinsic properties
they express:
relations between configurations and outcomes
Equations become:
- mappings
- transformation rules
- stability conditions
They describe not just what holds, but where and how it holds.
From solution to structure
In traditional modelling, we solve equations to obtain:
- a value
- a trajectory
- a prediction
In relational modelling, the goal shifts.
We seek:
- families of solutions
- structures of variation
- patterns across regimes
A single solution is no longer sufficient.
What matters is:
how solutions organise across changing conditions
Why this is not abstraction for its own sake
This is not a philosophical overlay.
It is driven by practical necessity.
When:
- measurements diverge systematically
- configurations matter
- invariance is local rather than global
object-based models struggle to account for the full structure of results.
Relational models:
incorporate that structure directly
They do not treat variation as residual.
They treat it as primary data.
What becomes visible
Relational modelling makes visible:
- regime boundaries
- transition points
- sensitivity to constraints
- equivalence across different configurations
These are not secondary features.
They are:
the structure within which object-like stability appears
The cost
This approach is more demanding.
Because:
- models are higher-dimensional
- results are less easily summarised
- interpretation requires tracking relations, not just values
There is no single number to report.
There is a structured field to describe.
The gain
The gain is significant.
We obtain:
- deeper explanatory coherence
- the ability to unify seemingly divergent results
- a framework for incorporating misalignment
- a way to extend models across regimes without forcing collapse
Most importantly:
we model what is actually happening in practice, rather than what we assume must be happening
Closing
Objects have been the anchors of scientific modelling.
But under visible conditions, they are no longer the starting point.
They are:
stabilised outcomes of relational structures
To model effectively is therefore not to describe objects in isolation.
It is to:
map the relations through which those objects become stable, comparable, and measurable
The final step is to ask what this does to one of science’s most central commitments:
if models describe structured relations rather than fixed properties, what does it mean to predict?
No comments:
Post a Comment