A complicated system exhibits emergence, according to the up-to-date framework, organizing itself into a hierarchy of levels, each of which operates independently of the details of the lower levels. The researchers suggest that we think of emergence as a kind of “software in the natural world.” Just as the software on your laptop runs without having to keep track of all the micro-level information about the electrons in a computer circuit, emergent phenomena are governed by macro-level rules that seem to be self-sufficient, no matter what the parts 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 phenomena, including neural networks and Game of Life-style cellular automata. Indeed, the degrees of freedom, or independent variables, that reflect the behavior of these systems at microscopic and macroscopic scales are related in exactly the way the theory predicts.
Of course, no up-to-date matter or energy appears at the macroscopic level in emergent systems that are not microscopically present. Rather, emergent phenomena, from Great Red Spots to conscious thought, require up-to-date language to describe the system. “What these authors have done is to try to formalize this,” he said. Chris Adamiresearcher in complicated systems at Michigan State University. “I totally support this idea of making things mathematical.”
Need for closure
Rosas approached the topic of emergence from many angles. His father was a renowned conductor in Chile, where Rosas first studied and played music. “I grew up in concert halls,” he said. Then he switched to philosophy, then to pure mathematics, which gave him an “abstract overdose” that he “cured” with a doctorate in electrical engineering.
A few years ago, Rosas started thinking about the thorny question of whether the brain is a computer. Consider what’s going on inside your laptop. The software generates 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 identical trajectories every time. “It’s a mess,” Rosas said. “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 similarly: our behaviors are consistent even though the neural activity is never identical under any given set of circumstances.
Rosas and colleagues concluded that there are actually three different types of closures in emergent systems. Would the output from your laptop be more predictable if you invested a lot of time and energy in collecting information about all the microstates—electron energies, etc.—in the system? Generally, no. This corresponds to a case of information closure:As Rosas stated, “All the details below the macro are not helpful in predicting the macro.”
What if you want to not only predict but also control the system—does lower-level information aid with that? Again, usually not: the interventions we make at the macro level, such as changing software code by typing, do not become more reliable when we try to change the trajectories of individual electrons. If lower-level information does not add further control over macro outcomes, the macro level is Causally closed:He himself is the cause of his own future.