A system has higher or lower complexity

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A note for Lesson no. 2, "Your Brain Is a Network," in Seven and a Half Lessons About the Brain by Lisa Feldman Barrett.
Some context from page 41 is:

A system has higher or lower complexity depending on how much information it can manage by reconfiguring itself.

The appendix adds:

The brains of other animals, such as monkeys and worms, also have complexity.

A complex system is made up of a large number of elements that interact with one another. In a system with N elements, there are N! (N factorial) possible patterns of those elements — each additional element multiplies the number of possible patterns. This mathematical observation is the scientific origin of the phrase, "the whole is more than the sum of the parts."[1]

Some of a brain's complexity comes from the fact that it's made of many, many neurons that can create gazillions of different patterns of activity. In addition, neurons can communicate with one another in two ways: Neurons can communicate with one another via discrete bursts of electrical activity along axons, followed by brief transfers of chemicals in synapses; this is called digital communication. But neurons can also communicate in a continuous and graded way, which is called analog communication. Scientists suspect that the interaction of analog and digital communication between neurons provide a brain with a profound degree of complexity.[2]

Any brain is a complex system, but some animal brains are more complex than others. It is interesting that more complex brains have evolved many times, independently, in different animals, including in insects.[3] Larger brains tend to be more complex, and brain size is associated with all sorts of abilities: copying (learning), creativity (innovation), and flexibility.[4] For example, birds and primates with larger brains innovate more than those with smaller brains.[4] One thing that adds to the complexity of a brain is the number of neurons that are multi-functional, also called domain-general or mixed selectivity (e.g., [5][6][7][8]). With more complexity, a brain can create a large repertoire of patterns that allow a rich capacity to model and respond to the various conditions in the body and in the world. Brains with higher complexity are likely to remember better and to generate more creative responses to new challenges, and therefore are likely to be more adaptable. To quote Sporns, "Complexity, and with it the capacity to respond and act differently under different circumstances, is the brain's answer to the persistent challenges of a variable and only partially predictable environment" (p. 303).[9] Complex systems also have more degeneracy,[10] and therefore a brain of high complexity may be more resilient to injury. A complex brain is also more expensive (metabolically speaking).

In general, and all things being equal, larger animals tend to have larger, more complex brains (both structurally and in how they function), but such animals also tend to have larger, more complex niches. A brain that encounters more complex situations will be wired to produce more complex dynamics.[9] Animals with relatively larger (and likely more complex) brains are more likely to survive, and their species evolves more quickly. For example, innovative birds are less likely to migrate and more likely to innovate during harsh winters, more likely to survive and establish themselves in a new location, and more likely to evolve into new species.[4]

To learn more about complexity in the human brain, here are some references:


  1. Simon, Herbert A. 1962. “The Architecture of Complexity.” Proceedings of the American Philosophical Society 106 (6): 467–482, p. 468.
  2. Cicurel, Ronald, and Miguel A. L. Nicolelis. 2015. The Relativistic Brain: How It Works And Why It Cannot Be Simulated By A Turing Machine. CreateSpace Independent Publishing Platform.
  3. Roth, Gerhard. 2015. "Convergent Evolution of Complex Brains and High Intelligence." Philosophical Transactions of the Royal Society B 370 (1684): 20150049.
  4. 4.0 4.1 4.2 Laland, Kevin N. 2017. Darwin’s Unfinished Symphony: How Culture Made the Human Mind. Princeton, NJ: Princeton University Press.. See also the references therein.
  5. Fusi, Stefano, Earl K. Miller, and Mattia Rigotti. 2016. "Why Neurons Mix: High Dimensionality for Higher Cognition." Current Opinion in Neurobiology 37: 66-74.
  6. Rigotti, Mattia, Omri Barak, Melissa R. Warden, Xiao-Jing Wang, Nathaniel D. Daw, Earl K. Miller, and Stefano Fusi. 2013. "The Importance of Mixed Selectivity in Complex Cognitive Tasks." Nature 497 (7451): 585-590.
  7. Brincat, Scott L., Markus Siegel, Constantin von Nicolai, and Earl K. Miller. 2018. "Gradual Progression From Sensory To Task-related Processing in Cerebral Cortex." Proceedings of the National Academy of Sciences 115 (30): E7202-E7211.
  8. Siegel, Markus, Timothy J. Buschman, and Earl K. Miller. 2015. "Cortical Information Flow During Flexible Sensorimotor Decisions." Science 348 (6241): 1352-1355.
  9. 9.0 9.1 9.2 Sporns, Olaf. 2011. Networks of the Brain. Cambridge, MA: MIT Press.
  10. Edelman, Gerald M., and Joseph A. Gally. 2001. “Degeneracy and Complexity in Biological Systems.” Proceedings of the National Academy of Sciences 98 (24): 13763–13768.
  11. Bullmore, Ed, and Olaf Sporns. 2012. “The Economy of Brain Network Organization.” Nature Reviews Neuroscience 13 (5): 336–349.