# In social complex systems, the whole can be more or less than (the sum of) the parts

## TL;DR

This paper uses a statistical physics model to explore how interactions among complex agents can lead to both standardization and collective order, reconciling sociological and physical perspectives on system behavior.

## Contribution

It introduces a mean-field model demonstrating how agent interactions can reduce individual complexity and induce collective order, bridging sociological and physical views.

## Key findings

- Interactions cause agents to standardize in the same internal state.
- Standardization can lead to global order under certain conditions.
- Both complexity reduction and collective organization are interconnected phenomena.

## Abstract

We discuss in a statistical physics framework the idea that ``the whole is less than the parts'', as sometimes advocated by sociologists in view of the intrinsic complexity of humans, and try to reconcile this idea with the statistical physicists wisdom according to which ``the whole is more than the sum of its parts'' due to collective phenomena. We consider a simple mean-field model of interacting agents having an intrinsic complexity modeled by a large number of internal configurations. We show by analytically solving the model that interactions between agents lead, in some parameter range, to a `standardization' of agents in the sense that all agents collapse in the same internal state, thereby drastically suppressing their complexity. Slightly generalizing the model, we find that agents standardization may lead to a global order if appropriate interactions are included. Hence, in this simple model, both agents standardization and collective organization may be viewed as two sides of the same coin.