According to the new framework, complex systems exhibit emergence by organizing themselves into hierarchical structures, where each level functions independently of the details of lower levels. The researchers propose thinking of emergence as a kind of “nature’s software.” Just as the software in your laptop works without keeping track of all the micro-level information about the electrons in your computer’s circuits, emergent phenomena are governed by macro-level rules that appear self-contained, without concern for how their components work.
The researchers used a mathematical formalism called computational mechanics to identify criteria for determining which systems have such hierarchical structure. They tested these criteria on several model systems known to exhibit emergent phenomena, including neural networks and Game of Life-style cellular automata. In fact, the degrees of freedom, or independent variables, that capture the micro- and macro-scale behavior of these systems are exactly the same relationships that the theory predicts.
Of course, new matter or energy doesn’t appear in an emergent system at the macro level that doesn’t exist at the micro level. Rather, emergent phenomena, from the Great Red Spot to conscious thought, require new language to describe the system. “What these authors have done is tried to formalize it,” says Chris Adami, a complex-systems researcher at Michigan State University. “I totally support this idea of making things mathematical.”
The need for resolution
Rosas approached the topic of emergence from different directions. His father was a famous Chilean conductor, where Rosas first studied and performed music. “I grew up in concert halls,” he says. He then turned to philosophy, followed by a degree in pure mathematics. He suffered from an “overdose of abstract ideas,” but a PhD in electrical engineering “cured” him.
A few years ago, Rosas started thinking about the difficult question of whether the brain is a computer. Think about what goes on inside your laptop: Software produces predictable, repeatable outputs for a given set of inputs. But if you look at the actual physics of the system, the electrons don’t follow the same trajectory every time. “It’s messy,” Rosas says. “It’s never going to be exactly the same.”
Software appears to be “closed” in the sense that it is independent of the detailed physical properties of the microelectronic hardware. The brain works in a similar way: our neural activity is never identical across circumstances, but our behavior is consistent.
Rosas and colleagues thought that emergent systems actually involve three different types of closure: If you spent a lot of time and effort gathering information about all the microstates in the system (such as the energy of the electrons), would the output of your laptop become more predictable? In general, no. This is because Information closure“All the sub-macro details are not useful for predicting the macro,” Rosas said.
If you want to control a system, not just predict it, is low-level information useful there? This usually doesn’t help either. Interventions you make at the macro level, like changing software code by typing on a keyboard, are no more reliable than trying to change the orbitals of individual electrons. If low-level information doesn’t give you more control over the macro outcome, then the macro level is Causally closed: It creates its own future.
