What is a Complex System?

Summary

This module delves into the concept of complex systems, acknowledging the lack of a formal definition and offering a working one. It defines a system as a set of elements with connections, leading to emergent organization. Complexity arises from many distributed parts with local interactions and self-organization, creating hierarchical structures. Key properties include interdependence, non-linearity, high connectivity, and autonomy, which together drive the emergence of new patterns and the adaptability of complex systems.

Takeaways

• 🔍 A complex system is a special class of system without a formal definition, characterized by multiple perspectives and opinions.
• 🧩 A system consists of elements and relations, where unordered systems lack specific structure or order, while ordered systems can function as a whole.
• 🌟 Emergence is a key concept in complex systems, where a global pattern of organization arises from the interaction of parts, leading to a coherent whole.
• 🌐 Complex systems are hierarchical, with elements nested within subsystems that form larger systems, creating a multi-dimensional structure.
• 🔄 Non-linearity is a pervasive theme in complex systems, where the interaction of parts can lead to exponential growth or decay, and sensitivity to initial conditions.
• 🔗 Connectivity is a defining feature of complex systems, with dense interconnectivity shaping the system's structure and behavior.
• 🌐 The concept of space is redefined in complex systems through the topology created by connectivity, focusing on network positions and degrees of connectivity.
• 🦜 Autonomy and adaptation allow elements within complex systems to self-organize and evolve, leading to diverse and heterogeneous responses to phenomena.
• 🌿 Evolution plays a role in complex systems, where elements are subject to selection pressures, leading to adaptation and increased complexity.
• 🔑 The four primary parameters of complexity include the number of elements, non-linearity, connectivity, and autonomy/adaptation, shaping the macro-scale evolution of systems.

Q & A

What is the working definition of a complex system as presented in the script?

A complex system is a special class of system consisting of many parts that are distributed with local interactions and self-organization, giving rise to new emergent levels on different scales. It has a hierarchical structure with elements nested inside subsystems, which in turn form part of larger systems.

How does the script differentiate between an ordered and unordered system?

An unordered system is a set of things without a specific structure or order, described by listing its elements and their properties. In contrast, an ordered system has parts that are arranged in a specific way, functioning together as a whole and exhibiting a global pattern of organization.

What is meant by the term 'emergence' in the context of complex systems?

Emergence refers to the phenomenon where a whole new level of the system develops, which then starts to interact with other systems in its environment, leading to the development of new patterns of organization and another level of organization.

Why is the number of parts and their distribution considered a primary source of complexity in a system?

The number of parts and their distribution contribute to complexity because complex systems consist of many different parts that are distributed out without centralized control, leading to the formation of organization through local interactions and self-organization.

How does interdependence and non-linearity contribute to the complexity of a system?

Interdependence and non-linearity contribute to complexity because the combined effect of parts can be greater or less than the sum of their individual properties due to their interconnected nature, leading to exponential growth or decay and sensitivity to initial conditions.

What is the significance of connectivity in complex systems?

Connectivity is significant as it defines the system's nature and structure. At a critical level of connectivity, the system becomes a network of connections, and the focus shifts to how things flow within this network, redefining space in terms of network topology.

How does autonomy and adaptation contribute to the complexity of a system?

Autonomy and adaptation contribute to complexity by allowing elements within the system to synchronize their states locally or cooperate, leading to the emergence of patterns of organization from the bottom up without centralized coordination.

What is the role of feedback loops in complex systems?

Feedback loops play a crucial role in complex systems by creating non-linear interactions over time, which can lead to exponential relations between input and output, and potentially trigger phase transitions or rapid changes in the system.

How does the script explain the concept of hierarchy in complex systems?

The script explains that complex systems have a hierarchical structure where elements are nested inside subsystems, which in turn form part of larger systems. This multi-dimensional property means they are composed of many elements on many different scales, with all levels affecting each other.

What is the butterfly effect, and how does it relate to complex systems?

The butterfly effect is a concept in chaos theory that suggests small changes in initial conditions can lead to significant and unpredictable outcomes in complex systems. It illustrates the sensitivity to initial conditions, where minor variations can trigger large systemic effects.

How does the script define a system?

A system is defined as a set of parts called elements and a set of connections between these parts called relations. The elements can be ordered or unordered, and the relations determine how the parts interact and contribute to the overall functionality of the system.

Outlines

00:00

🔍 Introduction to Complex Systems

This paragraph introduces the concept of complex systems, noting the absence of a formal definition and the existence of multiple perspectives. It describes a system as a collection of elements with connections called relations. The paragraph differentiates between ordered and unordered systems, using examples like a pile of stones and a car to illustrate the concept of emergence, where the whole exhibits properties beyond the sum of its parts. The discussion then moves to the self-organization of parts into a coherent whole, leading to new levels of organization. The paragraph emphasizes the hierarchical structure of complex systems, where elements are nested within subsystems, contributing to a multi-dimensional and interconnected nature. It introduces the idea that complex systems consist of many parts with local interactions and self-organization, leading to emergent levels on different scales.

05:01

🌀 Key Properties of Complex Systems

The second paragraph delves into the properties that define complex systems, starting with the idea that they consist of many parts without centralized control. It discusses the phenomenon of emergence, where local interactions lead to new levels of organization. The paragraph then addresses interdependence and non-linearity, explaining how the combined effect of parts can be greater or less than the sum of their individual properties due to their interconnected nature. Examples such as sound waves and division of labor are used to illustrate non-linearity. The concept of phase transitions and sensitivity to initial conditions, central to chaos theory, are introduced with the butterfly effect as an example. The paragraph also covers the importance of connectivity in complex systems, highlighting how increased connectivity transforms systems into networks and redefines space in terms of network topology. Lastly, it touches on autonomy and adaptation, explaining how elements within complex systems can synchronize or cooperate, leading to diverse responses and the capacity for evolution and adaptation without centralized coordination.

10:02

🌐 Summary of Complex Systems Characteristics

The final paragraph summarizes the key characteristics of complex systems that have been discussed. It reiterates that complex systems are a special class of systems defined by a set of elements and their relations. The paragraph emphasizes the importance of the number of elements and the hierarchy within the system, non-linearity and its implications for system behavior, and the role of connectivity in shaping system structure. It concludes by discussing autonomy and adaptation as critical factors that enable self-organization and evolution on a macro scale, shaping complex systems through processes akin to natural selection.

Keywords

💡Complex System

A complex system, as discussed in the video, is a special class of system that lacks a formal definition but is characterized by a set of elements and relations between them. It is a concept that is central to the video's theme as it sets the stage for understanding the various properties and behaviors of such systems. The video uses examples like a car's parts working together to form a functional vehicle and the organization of cells and organs in a body to illustrate how complex systems emerge from the interaction of their parts.

💡Elements

Elements in the context of complex systems refer to the individual parts or components that make up the system. They are the basic units that, when connected through relations, contribute to the overall functionality of the system. The video explains that these elements can be ordered or unordered, and it is through their specific arrangement and interaction that complex systems exhibit emergent properties, such as the cells in our body forming a complex organism.

💡Relations

Relations in complex systems denote the connections between elements. These are what give structure and order to the system, allowing the elements to interact in a meaningful way. The video emphasizes that it is through these relations that a system can function as a coherent whole, rather than just a collection of isolated parts. An example given is the specific arrangement of parts in a car that enables it to operate as a transportation vehicle.

💡Emergence

Emergence is a key concept in complex systems, referring to the phenomenon where a new level of organization or pattern arises from the interaction of the system's elements. This emergent behavior is not simply the sum of the individual parts but represents a higher level of organization. The video uses the example of a car's functionality emerging from the specific arrangement of its parts and the global system of an organism emerging from the organization of cells and organs.

💡Hierarchy

Hierarchy in complex systems refers to the multi-level structure where elements are nested within subsystems, which in turn are part of larger systems. This concept is integral to the video's message as it illustrates the layered nature of complex systems, such as how individuals form social groups, which form broader societies, and so on. The video highlights that these systems are not flat but have a hierarchical structure that contributes to their complexity.

💡Interdependence

Interdependence in complex systems means that the elements are highly interconnected and rely on each other for the system's overall functioning. This interdependence leads to non-linearity, a key characteristic of complex systems. The video explains that the interdependence creates a situation where the whole is more than the sum of its parts, as seen in the division of labor in human communities or the cancellation of sound waves through interference.

💡Non-linearity

Non-linearity is a fundamental concept in the discussion of complex systems, indicating that the behavior of the system is not directly proportional to the inputs or changes in its elements. The video describes non-linearity as a pervasive theme, where the combined effect of elements can be greater or less than the sum of their individual properties due to their interdependent nature. This can lead to exponential growth or decay, known as phase transitions.

💡Connectivity

Connectivity in complex systems refers to the density and structure of the interconnections between elements. The video emphasizes that as connectivity increases, the system's nature is more defined by its network of connections rather than the properties of individual components. High levels of connectivity can lead to the system being perceived as a network, where the position and degree of connectivity within the network structure become crucial.

💡Autonomy

Autonomy in the context of complex systems means that the elements have a degree of independence and can operate according to their own rules or instructions without centralized control. The video discusses how autonomy allows for self-organization and adaptation, leading to the emergence of patterns and organization from the bottom up. Examples include flocking birds, the internet, and economies, where elements coordinate locally to create macro-level patterns.

💡Adaptation

Adaptation in complex systems is the capacity of elements to adjust to their local environment, which contributes to the system's ability to evolve and change over time. The video explains that with autonomy and adaptation, complex systems can respond diversely to phenomena, leading to heterogeneity and high levels of diversity. Adaptation is a key driver of evolution in complex systems, as seen in ecosystems, markets, and democracies, where elements are subject to selection pressures.

Highlights

Complex systems have no formal definition and are subject to various perspectives and opinions.

A system is defined as a set of parts (elements) and connections (relations) between these parts.

Unordered systems lack specific structure or order, such as a pile of stones.

Ordered systems function together as a whole, leading to the emergence of a global pattern of organization.

Complex systems are characterized by the emergence of new levels of organization through self-organization.

Complex systems consist of many parts distributed without centralized control.

The phenomenon of emergence leads to new levels of organization interacting with the environment.

Complex systems exhibit a hierarchical structure with elements nested within subsystems.

Interdependence and non-linearity are key features of complex systems.

Non-linearity can result in exponential growth or decay due to feedback loops.

Sensitivity to initial conditions, as seen in chaos theory, is a central concept in complex systems.

Connectivity is a defining feature of complex systems, often appearing as networks.

Autonomy and adaptation allow elements within complex systems to self-organize and evolve.

Complex systems are often heterogeneous with high levels of diversity.

Elements within complex adaptive systems are subject to evolutionary forces of selection.

The macro scale system adapts to its environment through decentralized coordination and evolution.

Transcripts

in this module we will be trying to

define what exactly a complex system is

before we start we should note that

there is no formal definition for what a

complex system is and thus there remains

many different perspectives and opinions

on the subject what we present here is

just a working definition

firstly a complex system is a special

class of system a system is simply a set

of parts called elements and a set of

connections between these parts called

relations these parts can be ordered or

unordered an unordered system is simply

a set of things because there is no

specific structure or order we can

describe a set simply by listing all of

its elements and their properties so a

pile of stones on the ground is an

example of an unordered set as there is

no pattern or order to the system we can

only describe it by describing the

properties of each element in isolation

and then adding them all up with the

whole set being nothing more than the

sum of its individual parts

if in contrast through the relations

these parts are ordered in a specific

way then they can function together as

an entirety and out of these parts

working together we get the emergence of

a global pattern of organization that is

capable of functioning as a coherent

whole for example if all the parts in

our car are arranged in a specific way

then we will have the global

functionality of a vehicle of

transportation or out of the specific

arrangement of billions of cells and the

different specialized organs that make

up our body we get the emergence of a

global system that enables us to operate

as an entire organism so that is the

basic model of the system it consists of

elements and relations when those

elements work together we get the

emergence of a new level of organization

now let's start adding complexity to

this probably the only property that

will be in all definitions of a complex

system is that they consist of many

parts many parts that are distributed

out without centralized control

organization is formed out of the local

interactions between the parts through a

process of self-organization that gives

rise to the emergence of new levels of

organization with the phenomenon of

emergence that we were previously

discussing a whole new level to the

system has developed which then starts

to interact with other systems in its

environment the result being that new

patterns of organization developed and

once again we get the emergence of

another level of organization and so on

people form part of social groups that

form part of broader society which in

turn forms part of humanity the point to

take away here is that these systems

have a hierarchical structure this is a

pervasive phenomenon in our world

elements are nested inside of subsystems

which in turn form part of larger

systems and so on all complex systems

have this multi-dimensional property to

them they are composed of many elements

on many different scales with all of

these levels affecting each other a

business is part of a local economy

which is part of a national economy

which in turn is part of a global

economy each is interconnected and

interdependent with the others we cannot

fully isolate one component or reduce

the whole thing to one level and this is

a primary source of complexity so this

is our first property to a complex

system many different parts that are

distributed out with local interactions

and self-organization giving rise to new

emergent levels on different scales

next interdependence and non-linearity

the parts to a complex system are highly

interdependent in this interdependence

creates non-linearity almost all well

formulated definitions for complex

systems involve the term non-linearity

it is a continuously recurring and

pervasive theme non-linearity arises

from the fact that when we put two or

more things together the result may not

necessarily be a simple addition of each

elements properties in isolation in

contrary we may get a combined effect

that is greater or less than the simple

sum of each part because of their

interdependent nature examples of this

might be two sound waves that are

perfectly out of sync cancelling each

other out through noise interference or

the division of labor as can be seen in

many human and insect communities

resulting in synergies which means the

output will be far greater than what

individuals could accomplish in

isolation

due to what are called feedback loops

nonlinear systems may grow or decay at

an exponential rate these periods of

rapid change are defined as phase

transitions

thus complex systems are known to be

able to shift or flip into whole new

regimes within very brief periods of

time some small change in input value to

the system can through feedback loops

trigger a large systemic effect this is

called sensitivity to initial conditions

and it is the central idea within chaos

theory examples of this butterfly effect

can be seen in financial crises and the

collapse of ecosystems such as coral

reefs

next connectivity many definitions for

complex systems involve dense or high

levels of interconnectivity between

components as we turn up the degree of

connectivity it becomes the nature and

structure of these connections that

define the system as opposed to the

properties of its components how are

things connected and what is connected

to what become the main questions at

some critical level of connectivity the

system stops being a set of parts and

becomes a network of connections and it

is now all about how things flow in this

network networks are the Trudy Amma tree

of complex systems in this connectivity

reshapes our traditional 3-dimensional

Euclidean conception of space in complex

systems like the global air

transportation system or the financial

system or the Internet space is

redefined in terms of topology created

by connectivity what matters is your

position in the network structure and

your degree of connectivity connectivity

again leads us into the world of

complexity as the number of relations

between elements can grow in an

exponential fashion if we take just a

handful of elements they can become

connected and possibly thousands or even

millions of different ways

lastly autonomy and adaptation whether

we are talking about a flock of birds

the internet or our global economy there

is no top-down centralized mechanism for

coordinating the whole system within

complex systems elements have a degree

of autonomy often through their capacity

to adapt to their local environment

according to their own set of

instructions without centralized

coordination and with a degree of

autonomy elements can synchronize their

states locally or cooperate resulting in

the emergence of patterns of

organization from the bottom up with

autonomy and adaptation also comes the

capacity for a variety of different

responses for any given phenomenon

meaning complex systems are often

heterogeneous with high levels of

diversity ecosystems and multicultural

societies are good examples of this

without centralized coordination complex

systems develop on the macroscale

through a process of evolution elements

within complex adaptive systems are

subject to the evolutionary force of

selection where those that are best

suited to that environment are selected

and replicated while others are not

products are subjected to selection

within a market environment in

democracies politicians are subject to

selection by voters and creatures and

ecosystems are subjected to natural

selection through competition in such a

way the whole macro scale system manages

to adapt to its environment without

centralized coordination and develop to

exhibit higher levels of both

differentiation and integration the

greater the autonomy and capacity for

adaptation that elements have the more

complex the system we are dealing with

in summary we have been trying to lay

down a basic working definition for a

complex system while remembering that

there is no formal consensus on the

subject we firstly talked about how a

complex system is a special class of

system we defined a system as a set of

elements and the relations between them

we saw how when these parts are arranged

in a specific order for them to function

as an entirety we get what is called the

process of emergence whereby a new level

of organization emerges we then began to

add complexity to our model of a system

by defining it as a product of four

primary parameters firstly talking about

the number of elements and different

levels to the hierarchy within our

system we then discussed non-linearity

as another dimension to complexity were

non-additive interactions and feedback

loops over time can give us exponential

relations between the input and output

to a system and lead to phase

transitions we also talked about

connectivity as another driver of

complexity as heightened connectivity

within complex systems means they often

appear to us as networks

lastly we discussed how autonomy and

adaptation enables self-organization in

the process of evolution that shapes

complex systems on the macro scale