Introduction to Complex Systems

Complex systems display emergent properties that arise from interactions. These properties do not exist in any of the components in isolation and cannot easily be derived from reductive analysis of the system.

No items found.

Review Questions

For each of the following examples, describe whether it can be best understood within the reductionist paradigm or the complex systems paradigm, and explain why.

  • A bottle of water
  • A single living cell in an organism
  • A toaster

A bottle of water: reductionist paradigm. There are too many particles for us to track them all, but the water’s properties, such as temperature and pressure, can be understood with statistics.

A single living cell in an organism: complex systems paradigm. There are many interrelated processes going on within a cell. It exhibits emergent patterns, but the components do not all behave like a perfectly predictable mechanism.

A toaster: reductionist paradigm. A toaster has relatively few components and they are rigidly configured such that pushing the lever down should reliably trigger a series of events that switches it on to toast the bread.

View Answer
Hide Answer

A city’s inhabitants form a complex social system. We can generally predict with high levels of confidence and reliability how busy the roads and public transport systems will be at certain times of day. How does this kind of predictability differ from what we can predict about a simple system?


Certain patterns of regularity often emerge in complex systems, so we may be able to predict certain aspects of their behaviors, particularly if they are familiar systems that we have a lot of historical data on. However, we cannot usually predict the behaviors of complex systems in more detail, such as which specific cars will be travelling along which roads at a precise time. This is in contrast with simple, mechanistic systems, for which we can usually predict at a higher level of detail what each component will do at a given time in response to an input. It can also be more difficult to predict the long-run trajectory of complex systems, for example what the transport system and roads will look like in 100 years, because complex systems can evolve more freely into a wider range of states. Mechanistic systems on the other hand tend not to evolve independently in this way.

View Answer
Hide Answer

For each of the following phenomena, identify which hallmark(s) of complexity it demonstrates and explain your answer.

  1. A flock of starlings forming large-scale structured patterns in the air.
  2. A train track is blocked by fallen trees after an intense storm and needs to be cleared. A replacement bus service is offered until the trains are able to run again.
  3. In many sports teams, different players are assigned different roles. However, there are usually multiple players responsible for each task, such as defending and attacking. Additionally, there are reserve players, who can be brought on if a player gets injured, for example.
  4. A phenomenon called Metcalfe’s law, which was originally derived from the study of computer networks, proposes that a network’s power is proportional to the square of the number of participants (such as individual computers or people) within it.
  5. Economic bubbles in financial systems often occur when a particular asset’s value begins to rise, incentivizing more investors to buy it, believing that its value will continue to increase. However, its price cannot continue to rise forever, and, at some point, such bubbles usually “burst” relatively suddenly, creating shocks within the economy.

1. Emergence

2. Adaptive behavior

3. Distributed functionality

4. Scalable structure and power laws

5. Feedback loops and nonlinearity, self-organized criticality

View Answer
Hide Answer