For what it’s worth, Cosma Shalizi’s notebook page on emergence has a very reasonable discussion of emergence, and he actually mentions macro-level properties of gas as a form of “weak” emergence:
The weakest sense [i]s also the most obvious. An emergent property is one which arises from the interaction of “lower-level” entities, none of which show it. No reductionism worth bothering with would be upset by this. The volume of a gas, or its pressure or temperature, even the number of molecules in the gas, are not properties of any individual molecule, though they depend on the properties of those individuals, and are entirely explicable from them; indeed, predictable well in advance.
To define emergence as it is normally used, he adds the criterion that “the new property could not be predicted from a knowledge of the lower-level properties,” which looks to be exactly the definition you’ve chosen here (sans map/territory terminology).
If we taboo “emergence” what do we think is going on with Langton’s Ant?
We have one description of the ant/grid system in Langton’s Ant: namely, the rules which totally govern the behavior of the system. We have another description of the system, however: the recurring “highway” pattern that apparently results from every initial configuration tested. These two descriptions seem to be connected, but we’re not entirely sure how (The only explanation we have is akin to this: Q: Why does every initial configuration eventually result in the highway pattern? A: The rules did it.) That is, we have a gap in our map.
Since the rules, which we understand fairly well, seem on some intuitive sense to be at a “lower level” of description than the pattern we observe, and since the pattern seems to depend on the “low-level” rules in some way we can’t describe, some people call this gap “emergence.”
I recall hearing, although I can’t find a link, that the Langton Ant problem has been solved recently. That is, someone has given a formal proof that every ant results in the highway pattern.
For what it’s worth, Cosma Shalizi’s notebook page on emergence has a very reasonable discussion of emergence, and he actually mentions macro-level properties of gas as a form of “weak” emergence:
To define emergence as it is normally used, he adds the criterion that “the new property could not be predicted from a knowledge of the lower-level properties,” which looks to be exactly the definition you’ve chosen here (sans map/territory terminology).
Let’s talk examples. One of my favorite examples to think about is Langton’s Ant.
If we taboo “emergence” what do we think is going on with Langton’s Ant?
We have one description of the ant/grid system in Langton’s Ant: namely, the rules which totally govern the behavior of the system. We have another description of the system, however: the recurring “highway” pattern that apparently results from every initial configuration tested. These two descriptions seem to be connected, but we’re not entirely sure how (The only explanation we have is akin to this: Q: Why does every initial configuration eventually result in the highway pattern? A: The rules did it.) That is, we have a gap in our map.
Since the rules, which we understand fairly well, seem on some intuitive sense to be at a “lower level” of description than the pattern we observe, and since the pattern seems to depend on the “low-level” rules in some way we can’t describe, some people call this gap “emergence.”
I recall hearing, although I can’t find a link, that the Langton Ant problem has been solved recently. That is, someone has given a formal proof that every ant results in the highway pattern.