According to the new framework, a complex system shows its emergence by organizing itself into a hierarchy of levels that function independently of the details of lower levels. The researchers suggest that we think of emergence as a kind of “software in the natural world.” Just as the software on a laptop works without having to keep track of all the microscale information about the electrons in computer circuits, emergent phenomena are governed by macroscale rules that appear independent of what the parts that compose them do.
Using a mathematical formalism called computational mechanics, the researchers identified criteria for determining which systems have this kind of hierarchical structure. They tested these criteria on several model systems known to exhibit emergent-type phenomena, including neural networks and Game of Life-style cellular automata. Indeed, the degrees of freedom, or independent variables, that capture the behavior of these systems at microscopic and macroscopic scales have precisely the relationship that the theory predicts.
Of course, no new matter or energy appears at the macroscopic level in emergent systems that does not exist at the microscopic level. Rather, emergent phenomena, from the Great Red Spots to conscious thoughts, demand a new language to describe the system. “What these authors have done is try to formalize that,” he said. Chris Adamicomplex systems researcher at Michigan State University. “I fully applaud this idea of doing things mathematically.”
A need for closure
Rosas approached the topic of emergence from multiple perspectives. His father was a famous conductor in Chile, where Rosas first studied and played music. “I grew up in concert halls,” he said. He then moved on to philosophy, followed by a degree in pure mathematics, which gave him “an overdose of abstractions” that he “cured” with a doctorate in electrical engineering.
A few years ago, Rosas began thinking about the controversial question of whether the brain is a computer. Consider what happens in a laptop. The software generates predictable, repeatable results for a given set of input data. But if you look at the actual physics of the system, the electrons won’t follow identical paths every time. “It’s chaos,” Rosas says. “It will never be exactly the same.”
Software appears to be “closed,” in the sense that it does not depend on the detailed physics of microelectronic hardware. The brain behaves in a similar way: there is a consistency in our behaviors, even though neural activity is never identical under any circumstances.
Rosas and his colleagues realized that there are in fact three different types of closure involved in emergent systems. Would the output of your laptop be more predictable if you invested a lot of time and energy in collecting information about all the microstates (electronic energies, etc.) of the system? In general, no. This corresponds to the case of news closureAs Rosas said, “All the details below the macro are not useful for predicting the macro.”
What if we want to not only predict but also control the system? Does lower-level information help in this case? Again, usually not: interventions we make at the macro level, such as changing software code by typing on the keyboard, do not become more reliable by trying to alter the individual electron trajectories. If lower-level information does not add any additional control over macro outcomes, the macro level is closed causallyHe alone is the cause of his own future.
