Mathematics and models are central to physics, offering precise language to describe, predict, and explain phenomena. Traditionally, models are seen as representations of an objective external reality composed of discrete entities.
From a relational ontology, models and mathematics are better understood as instruments for navigating the field of relational potential, capturing patterns of systemic constraints and actualisations rather than fixed objects.
1. Traditional Views of Models and Mathematics
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Models represent objects and their interactions,
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Mathematics encodes universal, observer-independent laws,
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Reality is assumed to be external and fixed.
2. Relational Perspective on Modelling
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Models are constructs reflecting relational patterns within a system,
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Mathematics maps systemic constraints and potential transitions,
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No single “correct” model exists—models are perspectival tools adapted to contexts.
3. Implications for Physics
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Models must accommodate dynamism, emergence, and systemic coherence,
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Mathematical formalisms can be seen as describing topologies of relational space and time,
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Scientific progress involves expanding and refining relational models rather than uncovering ultimate entities.
4. Toward a Pragmatic Pluralism
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Multiple models can coexist, each highlighting aspects of relational structure,
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The value of models lies in their efficacy for understanding and intervention,
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This supports a pluralistic yet coherent approach to physical theory.
Closing
Models and mathematics do not reveal a static reality but provide flexible, evolving maps of relational processes—essential tools in the ongoing project of reimagining physics.
Next, we will examine how this relational approach influences the concept of emergence in physics.
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