Is the property objective or subjective? The coarse grained property is objective—e.g. the largest connected component in percolation. The meta-property that a coarse-grained property is emergent is as objective as the entropy of a configuration. It is model dependent, but in most cases we can’t come up with a model that makes it go away.
To the extent “emergentness” is subjective, it is because it is relative to a model. So in some cases it could possibly be the result of ignorance of a better model. But we can’t claim “emergentness” due to ignorance of any workable model, we can only say “I don’t know”.
Conjecturing that a property is emergent is a guide to inquiry. It is saying “Let’s look for a model of this property that’s robust under perturbation of the elements of the ensemble, but where the value of the property changes dramatically due to small changes in the average value of some properties of the elements. The model will be based on some highly simplified view of how the elements interact.”
Some observations about models of emergent properties:
We don’t have a very good “toolbox” for building them yet. We’re getting better, but have a long way to go before we know how to proceed when we conjecture that a property is emergent.
We are even weaker in the design of emergent systems. That is why even very simple designs with emergent properties, like flocking, seem so striking. This is a serious disability because we depend on systems with major emergent properties, such as markets, and we don’t know how to manage them very effectively.
Often when people claim properties are “mysterious”, we could dispell these claims if we could respond with an intuitive account of how those properties emerge. Lacking such an account, we are often vulnerable to mystification.
Thanks, Eliezer. Regarding your questions:
Is the property objective or subjective? The coarse grained property is objective—e.g. the largest connected component in percolation. The meta-property that a coarse-grained property is emergent is as objective as the entropy of a configuration. It is model dependent, but in most cases we can’t come up with a model that makes it go away.
To the extent “emergentness” is subjective, it is because it is relative to a model. So in some cases it could possibly be the result of ignorance of a better model. But we can’t claim “emergentness” due to ignorance of any workable model, we can only say “I don’t know”.
Conjecturing that a property is emergent is a guide to inquiry. It is saying “Let’s look for a model of this property that’s robust under perturbation of the elements of the ensemble, but where the value of the property changes dramatically due to small changes in the average value of some properties of the elements. The model will be based on some highly simplified view of how the elements interact.”
Some observations about models of emergent properties:
We don’t have a very good “toolbox” for building them yet. We’re getting better, but have a long way to go before we know how to proceed when we conjecture that a property is emergent.
We are even weaker in the design of emergent systems. That is why even very simple designs with emergent properties, like flocking, seem so striking. This is a serious disability because we depend on systems with major emergent properties, such as markets, and we don’t know how to manage them very effectively.
Often when people claim properties are “mysterious”, we could dispell these claims if we could respond with an intuitive account of how those properties emerge. Lacking such an account, we are often vulnerable to mystification.