What is the book about?
Understanding Complexity introduces to the framework of complex adaptive systems and its core terms and concepts. Which properties makes complex systems complex? Which properties, or rather, which degrees of property manifestation separate them from other types of systems? How can the landscape analogy be helpful to understand complex systems? — and other questions are answered by Scott Page on a low-resolution level not to overwhelm the beginner.
Can I recommend it? Whom is this book for?
Yes, indeed I can, given that you are unfamiliar with complex adaptive systems.
But first, let me tell you what I did not like.
- Sometimes Scott Page overdid on the analogies by not even finishing the first before he goes on to the next. He describes one analogical case, asks how can we understand it, and then uses another analogy. In the end it happened it did not became clear how some of the analogies can be explained in terms of the concept under discussion.
- Some definitions were given by using the term to be explained: e.g. connectedness
However, what I particularly liked was that
- many real-world analogies were used which enhanced understanding a lot and compensated for the abstraction of complex systems.
- he repeated himself. Some terms were explained repeatedly not only in compressed space (directly in sequence) but also in expanded space (across chapters) to reinforce terms and concepts.
- a very sensible chapter division was performed.
That some questions about details were skipped is forgivable considering it is a book for absolute beginners. It was interesting, very comprehensibly written, and exceeded my current level of knowledge so I could learn a lot.
I was even surprised: I expected complexity theory to be less advanced, but it is well known that complex systems were determined to possess a set of clearly defined properties (diversity, adaptiveness, interdependence, connectedness).
What did I learn?
Some facts:
- Tailorism: Named after Frederick Taylor who optimised work processes. Also: Scientific management.
- 1/4th of nodes with n+1 degree if n is the degree
- Power law distributions have lots of nodes with very low degrees, but few nodes with very high degrees (e.g. the world wide web)
- Power law networks are very robust because random node removal is more likely to remove nodes with low degrees (internal)
- Interactions can almost always be described in terms of positive and negative feedbacks
- Diversity promotes phase transitions: Diverse action readiness among the agents, that is diverse thresholds to act, establish a cascade of events
- Lags can cause a system to run in circles instead of stabilising
- Many real-world random events are not truly random: They are the outcomes of complex adaptive systems.
- Complex systems produce novelties.
- System dynamics ignores place and diversity
- The canonical standard-decision making model does not work to figure out what to do in a complex system. It does not take into account the behavior of other interested agents, it translates complexity into uncertainty, it is all exploitation, it focuses on a single outcome and not on system properties. ⇒ takes no account of what the system might be like as a result of one’s action
- Game theory either considers two players or all players, that is low connectedness or high connectedness, because it is easier to predict
- systems are sensitive to its initial conditions + rules
Key terms and concepts
Agent-based models: They are mathematical models that allow us to simulate the trajectories of a system with pre-defined factors.
- For an agent to act, some variable must be above an threshold.
The Exploration-Exploitation distinction: The trade-off between seraching for better solutions and taking advantage of what is known.
- Evolution adjusts the temperature and in turn the flexibility of the agents by changing variation in the species. (Examples of exploration: recombination, mutation; Examples of exploitation: selection)
- in rugged landscapes it is effective to first explore a lot, reduce exploration over time but increase exploitation until the peak is reached
- in dancing landscapes it is necessary to keep exploring to some degree, because one cannot keep exploiting; what was once a good solution has ceased to be one
- If exploration is low because the agents exploit, it pays off to explore better alternative solutions; if exploration is high because hardly any agent exploits, it pays off to exploit oneself
- In other words, exploitation of known solutions makes others adapt by exploring better or alternative solutions. In turn exploration makes others adapt by taking the opportunity to exploit known solutions. This keeps the landscape dancing.
Nonstationary Processes: Processes in which the probability of events changes over time. Stationary processes do not change over time
- Example: A frictionless pendulum will maintain its frequency and amplitude, but if a force is applied like friction with air frequency and amplitude will not remain constant.
Power-Law Network: A network in which the distribution of links fits a model of a type of long-tailed distribution.
Simulated Annealing: A search algorithm in which the probability of making an error decreases over time.
Coupled oscillation: Two agents changing their behavior in regular patterns in dependence on one another. While the pace of the red pendulum increases, the pace of the green pendulum decreases.
Breaking symmetry: Many individuals starting out to perform identical tasks, but then performing idiosyncratic ones.
- Central to emergence
Criticality: Property of a complex system that is prone to produce large events in response to small events by cascading.
- Tipping Point/Critical threshold: The configuration in a complex system in which a sequence of small events (cascade) can push the system into a new macro state.
- Tipping goes only in one direction: Once stability has been reached, it is hard to go back.
Phase Transition: The process in which the system moves from one macro-state to to another.
- Diversity and positive feedbacks promote phase transitions.
Feedback: interactions between instances of the same action
1. Positive feedbacks lead to tipping points/major events (by cascading), if the agents are diverse which makes their critical thresholds diverse
-Example: If everyone had the same threshold of 10, all would leave at the same time, but if one person has a threshold of 0 and another of 1 and 2, etc., then a cascade is initiated causing mass exodus despite the average threshold being, say 50 if the number of people in the room is 100. The threshold does not have to be n+1 assuming all people maintain independent variables being able to cause leaving.
- Example: segregration, despite the agents being tolerant at the micro-level.
- What inititates the cascade is a threshold at the extreme (tail of the distribution).
2. Negative feedbacks lead to stability (with changes but without major events), if the agents are diverse or their thresholds are diverse
- Examples: Lakes and bees are diverse and are able to stabilise the system, but once a certain threshold is reached, whether that is a certain amount of nitrogen in the lake or a certain temperature, the agents cannot compensate anymore for the impact caused by the external event. The lake becomes eutrophic and the bees die.
- The negative feed here is that the more nitrogen is taken up or the more the bees flap their wings, the lower the amount of nitrogen in the lake or the lower the temperature.
Externality: feedback across differnt actions (as opposed to feedback)
Long-Tailed Distribution: A distribution in which most event sizes are small but some are very large. The power law purports that one quantity varies as a power of the other.
What types of systems exist?
Complex systems are only interesting if it’s 4 main features meet a certain configuration which is marked by neither being too simple, nor too complex (chaotic). Then they become a perpetual source of novelty.
- Class 1: Stable, single point equilibria (e.g. ball resting at the bottom of a bowl, farmer’s market)
- Class 2: Periodic orbits; stable predictable patterns (e.g. stoplights, the earth rotating around the sun, prey-predator population sizes)
- Class 3: Chaotic; extremely sensitive to initial conditions (e.g. butterflies causing hurricanes)
- Class 4: Complex; somewhat stable with regular structures, but longer patterns with high information content and still difficult to predict.
What are the properties of complex systems?
1. interdependence:
- low → some change
- high → incomprehensible mangle
- moderate → complexity
- Example: deciding how to dress
2. connectedness
- low or high → quickly achieved equilibrium, because in the first case there is little to adapt to and in the second large convergence on what is most common happens
- moderate → complexity: it takes a long time to stabilise
- Example: The Greeting Game, Paper-Scissors-Rocks, sensitive, toxic, resistant E. Coli
3. diversity
- no diversity → nothing happens
- low to moderate → complexity
- high + much interdependence → incomprehensible mangle or collapse
- high + low interdependence → complexity
- Example: cooking a soup, reactions between chemical elements
4. adaptiveness
- no adaptiveness → complexity possible (Game of Life), but unlikely
- moderate → complexity: following the rules well, but not optimally
- high (following the rules optimally) → equilibrium
- Example: Checkers
What are complex systems?
They are characterised by 4 main features which are moderately pronounced:
- connected: The entities involved are connected with each other.
- interdependent: The connected entities interact with each other and influence each other, locally or globally.
- diverse: They possess entities of different types. (As opposed to variable: a difference in the value of an attribute.)
- adaptive/learning/intelligent: Their entities adapt their behavior to changes of other components in the system.
What is the difference between connectedness and interdependence?
Interdependence requires connectedness, but exerts different effect sizes depending on the degree of connectedness:
- High connectedness + low interdependence = no big effect
- High connectednesss + high interdependence = big effect
- Low connectedness + low interdependence = some effect
- Low connectedness + High interdepedence = moderate effect
What other features do complex systems exhibit?
- Selection: A process through which less fit or lower-performing entities are removed from the population.
- Robustness: The ability of a complex system to maintain functionality given a disturbance.
- Emergence: A higher-level phenomenon that arises from the micro-level interactions. (Weak: explicable; Strong: unexplicable yet, e.g. consciousness)
- Self-Organisation: A form of emergence in which the entities create a pattern or structure from the bottom-up.
- Self-Organised Criticality: A phenomenon in which interaction agents self-organise into states that can produce large events.
In contrast, what are complicated systems?
- connected
- interdependent
- diverse
- but not adaptive, not selective, not producing large events
What is it about the landscape analogy?
The landscape represents a problem or the fixed state of a complex system
- Encoding: The kind of landscape a problem or system produces, depends on the number of variables encoded. The length (and width) encode the variables. They describe the type of solution; the attribute(s) of the solution (e.g. shovel size)
- Height/Elevation represents the value of a potential solution. Local and global peaks represent (sub)optimal solutions.
- If the landscape becomes “bigger”, the number of possible solutions and non-solutions increases, and thus potentially the difficulty to solve the problem
What types of landscapes exist?
- simple landscapes: Neither interactions between actions of a single entity, nor interactions between multiple entities. They possess one global peak. (Example: optimisation of one design feature of one coal shovel.)
- rugged landscapes: Characterised by many possible combinations, and interactions within the actions of a single entity. They possess many local peaks with one (or multiple) global peaks. (Example: optimisation of all design features of one coal shovel; finding the optimal shovel from many good shovels.)
- dancing landscapes: Characterised by *externalities*, that is interactions between mulitple agents. They possess constantly changing local and global peaks. What is a solution today, might not be a solution tomorrow. They lie in the "interesting in-between": between a statistic regularity of high degrees to which the properties are pronounced and stasis of low degrees of property pronunciation. (Example: society)
How do we control complex systems?
- We build in some slack to increase robustness: Since the more a system is optimised, the more critical it becomes.
- We encourage diversity to balance exploration and exploitation, and prevent error.
- We perform safety measures for large events.
- We carefully define goals and incentives to control selection mechanisms:
- Connectedness: We create synergistic links and cut those that limits responsiveness.
What are the causes of diversity?
1. Diversity itself: the more you start with, the more combinations of the attributes of types are possible (positive feedback loop)
2. Weak selective pressure: The less types are removed from the population, the more types survive and reproduce.
3. Dancing landscapes and different landscapes:: An ever changing landscape produces multiple different landscapes that allow different types to solve problems.
What are the differences between evolutionary systems and creative systems?
1. Leap size: Evolution makes no leaps (all structures evolve slowly), while creative systems can jump forth.
2. Interim viability: Evolutionary outputs must be viable each step along the way to survive, while creative systems can produce outputs whose malfunction can be improved.
3. Representation: Evolution is fixed on genes, while creative systems can switch new ways of encoding.