Professor, Director of the Collective Computation Group, Santa Fe Institute

In physics a fine-grained description of a system is a detailed description of its microscopic behavior. A coarse-grained description is one in which some of this fine detail has been smoothed over. 

Coarse-graining is at the core of the second law of thermodynamics, which states that the entropy of the universe is increasing. As entropy, or randomness, increases there is a loss of structure. This simply means that some of the information we originally had about the system has become no longer useful for making predictions about the behavior of a system as a whole. To make this more concrete, think about temperature. 

Temperature is the average speed of particles in a system. Temperature is a coarse-grained representation of all of the particles’ behavior–the particles in aggregate. When we know the temperature we can use it to predict the system’s future state better than we could if we actually measured the speed of individual particles. This is why coarse-graining is so important–it is incredibly useful. It gives us what is called an effective theory. An effective theory allows us to model the behavior of a system without specifying all of the underlying causes that lead to system state changes. 

It is important to recognize that a critical property of a coarse-grained description is that it is “true” to the system, meaning that it is a reduction or simplification of the actual microscopic details. When we give a coarse-grained description we do not introduce any outside information. We do not add anything that isn’t already in the details. This “lossy but true” property is one factor that distinguishes coarse-graining from other types of abstraction. 

A second property of coarse-graining is that it involves integrating over component behavior. An average is a simple example but more complicated computations are also possible. 

Normally when we talk of coarse-graining, we mean coarse-grainings that we as scientists impose on the system to find compact descriptions of system behavior sufficient for good prediction. In other words, coarse-graining helps the scientist identify the relevant regularities for explaining system behavior. 

However, we can also ask how adaptive systems identify (in evolutionary, developmental, or learning time) regularities and build effective theories to guide decision making and behavior. Coarse-graining is one kind of inference mechanism that adaptive systems can use to build effective theories. To distinguish coarse-graining in nature from coarse-graining by scientists, we refer to coarse-graining in nature as endogenous coarse-graining. 

Because adaptive systems are imperfect information processors, coarse-graining in nature is unlikely to be a perfect or “true” simplification of the microscopic details as it is the physics sense. It is also worth noting that coarse-graining in nature is complicated by the fact that in adaptive systems it is often a collective process performed by a large number of semi-independent components. One of many interesting questions is whether the subjectivity and error inherent in biological information processing can be overcome through collective coarse-graining.  

In my view two key questions for 21st-century biology are how nature coarse-grains and how the capacity for coarse-graining influences the quality of the effective theories that adaptive systems build to make predictions. Answering these questions might help us gain traction on some traditionally quite slippery philosophical questions. Among these, is downward causation “real” and are biological systems law-like?