According to the new framework, complex systems emerge by organizing themselves into hierarchies of levels that operate independently of lower-level details. The researchers suggest that emergence should be thought of as a kind of “software of the natural world.” Just as laptop software runs without tracking all the microscopic details about the electronics in a computer circuit, emergence is governed by macroscopic rules that appear self-contained, without paying attention to what the components are doing.
The researchers used a mathematical formalism called computational dynamics to identify criteria for determining whether a system has this kind of hierarchical structure. They tested these criteria on several model systems known to exhibit novel types of phenomena, including neural networks and Game of Life-style cellular automata. In fact, the degrees of freedom, or independent variables, that capture the behavior of these systems at microscopic and macroscopic scales are exactly the relationships that the theory predicts.
Of course, new matter or energy that does not exist microscopically does not appear at the macroscopic level in emerging systems. Rather, emerging phenomena, from the Great Red Spot to conscious thought, require a new language to describe the system. “What these authors have done is try to formalize that,” he said. Chris Adami“I’m all for this idea of making things mathematical,” said the complexity researcher at Michigan State University.
The need for finishing
Rosas has approached the subject of injury from several directions. His father was a famous conductor in Chile, and Rosas first studied and performed music there. “I grew up in the concert hall,” he says. He then turned to philosophy, then a degree in pure mathematics, and suffered from “an excess of abstraction” that he “cured” with a doctorate in electrical engineering.
A few years ago, Rosas began thinking about the thorny question of whether the brain is a computer. Think about what happens on your laptop: software that produces predictable, repeatable outputs for a given set of inputs. But when you look at the actual physics of the system, the electrons don’t all follow the same trajectories every time. “It’s a mess,” Rosas says. “It’s never going to be exactly the same.”
Software seems to be “closed” in the sense that it does not depend on the detailed physics of microelectronic hardware. The brain behaves somewhat similarly: our behavior is consistent, even though neural activity is not the same in every situation.
Rosas and colleagues actually found that there are three different types of closures involved in a new system. If you invested a lot of time and energy into gathering information about all the microstates of the system (electronic energy, etc.), would the output of your laptop be more predictable? Generally not. This is the case when: Information closure: As Rosas said, “Any detail below the macro doesn’t help you predict the macro.”
What if we want to control the system, not just predict it? Would low-level information help? Again, generally not. Interventions at the macro level, such as changing software code by typing on a keyboard, are not made more reliable by attempting to change individual electron trajectories. If low-level information does not add additional control over the macro outcome, the macro level Causally closed: It is only creating its own future.
