- Things can be hidden in space, and they can be hidden in time…But the way in which complex phenomena are hidden, beyond masking space and time, is through non-linearity, randomness, collective dynamics, hierarchy, and emergence – a deck of attributes that have proved ill suited to our intuitive and augmented abilities to grasp and to comprehend.
- Linearity should not be an issue. Economic systems are obviously nonlinear, as are many, if not most, systems of current interest in physics. A more controversial question concerns the direction of feedback. Whereas a strictly linear system can have only negative feedback if divergence is to be avoided, positive feedback can occur in nonlinear systems of a saturation mechanism operates. Such systems tend to have multiple equilibria or resting points and great sensitivity to initial conditions. Traditionalists find it hard to relinquish uniqueness and global stability, but physicists are easily convinced and find positive feedback natural.
- In 1966, Robert Paine introduced the concept of “keystone species,” top predators such as starfish and sea otters, whose removal can lead to cascading effects in system properties. Since then, the concept has been extended to species other than top predators. Some, for instance, consider the distemper virus that kills lions in Africa to be a keystone species. Levin cites “a quarter century of research on keystone species – predators, competitors, mutualists, pathogens, among others – demonstrates a diversity of situations in which individual species play critical roles, at least in determining community structure.
- The authors wish to thank our co-organizer, Jennifer Dunne, for reminding us that the laws of life are hierarchical and must look upward to ecology as well as downward to physics and chemistry.
- Ludwig Boltzmann, in about 1884, coined the term ergodic for situations with identical time averages and ensemble averages. Not every situation is like this, however; there exist “nonergodic” situations as well, and these are often as counterintuitive as the ergodic situations seem trivial. So, do we have to be more careful when we talk about expected returns and average performances? There are two averages, not one – two ways of characterizing an investment, two quantities with different meanings…Herein lies the danger: if we don’t actually play many identical games at once, then such an average only has practical relevance if it is identical to the quantity we’re interested in, often the time average. There may be many possible paths from here into the future, but only one will be realized. In our game, you are risking your entire wealth, which obviously cannot be done many times simultaneously, so the ensemble average is not really the relevant quantity. Technically, it stems from a thought experiment involving other universes
- What is good for groups is not always good for the individuals comprising them. For example, both multicellular organisms and social insect colonies are functionally specialized and hierarchically organized collectives that are highly successful in maintaining and transmitting accumulated knowledge, in the form of genetic instructions, to the next generation; but they also have little regard for the fates of most cells or insects. This same pattern is apparent, in an attenuated way, in human societies. For example, economist George Steckel and anthropologist Jerome Rose (2002) examined health indicators for Prehispanic New World societies and found that the median health of individuals declined as societies grew more complex. This suggests social complexity emerges from mechanisms that promote coordinated behavior even if it is not in the best interest of each individual. In the case of multi-celled organisms and insect colonies, the solution was to make the coordinating individuals (cells, insects) genetics clones or siblings. That way, genes that promote cooperation could spread even if the most cooperative individuals left no offspring.
- Instead of assuming agents were perfectly rational, we allowed there were limits to how smart they were. Instead of assuming the economy displayed diminishing returns (negative feedback), we allowed that it might contain increasing returns (positive feedback). Instead of assuming the economy was a mechanistic system operating at equilibrium, we saw it as an ecology – of actions, strategies, and beliefs competing for survival – perpetually changing as new behaviors were discovered.
- Thermodynamics is the study of the macroscopic behavior of systems exchanging work and heat with connected systems or their environment. The four laws of thermodynamics all operate on average quantities defined at equilibrium – temperature, pressure, entropy, volume, and energy. These macroscopic variables exist in fundamental relationships with each other, as expressed, for example, in the ideal gas law. Thermodynamics is an extremely powerful framework as it provides experimentalists with explicit, principle recommendations about what variables should be measured and how they are expected to change relative to each other, but it is not a dynamical theory and offers no explanations for the mechanistic origins of the macroscopic variables it privileges.
- This introduces two important concepts: first, the idea of scaling, which refers to how measurable properties of a system change with its size; second, the concept of economies of scale. The latter means that, as cities grow, they need less of something per person: roads, sewers, or gas stations, for example
- The study of complex systems, like all of science, is a search for order. Traditionally, science seeks order by understanding the simplest parts of a system. How does a single gas particle behave given a certain temperature? Which gene in our DNA determines eye color? Scientists then try to develop theories that explain more general observations based on their detailed understanding of the individual parts.
- We know from the application of the scientific method – that is, from observation, then explanation, then prediction, and finally verification – that gravity causes the apple to move toward the ground at a specific and constant rate of acceleration
What I got out of it
- A series of articles on complexity that helps give a broad overview of the field and how far it has come in the last several decades. The physical book also has some fun and interesting ways to help categorize and organize the chapters and knowledge
