The Applications of Systems Science

Understanding How the World Works and How You Work In It

Week 3 – Principles of Organization, Networks, & Complexity

• Boundaries

• Components can be subsystems

• Structural and functional hierarchies

• Interconnections between components at any level

• Connections are forces and flows

• A general measure of complexity is the hierarchical tree depth

Motivating Questions

• What does it mean to say that “everything is connected to everything else?” – Direct connections vs. indirect connections

– Things affect one another

• What do we mean when we say that something is complex? – Lots of different kinds of things connected

– The component things are themselves composed of smaller (and connected) things

General Organization

Environment

System of interest

boundary

inputs outputs

sources

sinks

New environment

Original system of interest

former sources and sinks now included in a larger system of

interest

New sources and sinks

New boundary

New system of interest

Generic System of Interest

Expanded System of Interest

Boundaries

concrete, regular, tight boundary

concrete, irregular, porous boundary

fuzzy, irregular, porous boundary

strong couplings

couplings

boundary components

internal component(s)

weak couplings between boundary components and external entities

etc.

“conceptual” boundary

Example of boundary mechanics

Examples of physical boundary types

Example of a boundary of choice

Systems Composed of Subsystems

Whole System of Interest

Components are

subsystems

Components

Level of the Whole System of Interest

One level down (smaller)

One level further down

Meta-Level

Component “Personalities” and Interactions - Connections

B

D E

Z

A

C

A A

D

C Z

E

B

D B

C

A

1

4

2 3 5

6

Different components with different personalities and connection potentials

Examples of Interactions and Matching

Networks of Interactions - Relations

Sparse interactions Dense interactions

Interactions: Forces & Flows

• Systems interface with their environments through interactions with other systems/entities

• Flows: Energy, materials, messages

• Forces: The usual suspects (gravity, electromagnetic)

Process/System

Sources Sinks

Energy

Messages

Low Entropy Materials

High Entropy Materials (waste)

Products

Messages

Inputs Outputs

Force Interactions

Waste Heat

Abstract Network Representation

inputs outputs

decomposed node

Graph theory mathematics can be used to answer structural and functional questions about this network (a directed graph)

Interesting Properties of Evolving Networks

Hubs: Small World Phenomena

Cliques: Auto-organizing Phenomena

Structural & Functional Hierarchies

subsystems

inputs outputs

larger system

coupling strengths high

coupling strengths medium

coupling strengths with other systems

low to high

System

Subsystems & interconnections

Components & interconnections

Complexity

Relational complexity

Compositional complexity

Simplicity

Structural complexity

A B

C D

A Hierarchy of Composition

stable combinations and free atoms

strong/stable interactions

transient combinations of stable components

whole system-of-interest level

relatively stable complex component level

free atoms level – maximum entropy

Hierarchic System

L-0

L-1

L-2

L-3

L-4

weak/transient interactions

increasingly complex combinations and free atoms

Levels of Organization

Chemical Atomic Level (L-0) Carbon, Hydrogen, Nitrogen, Oxygen,

Phosphorus, Sulfur (CHNOPS) – plus trace elements

Chemical Molecular Level (L-1)

Amino acids, Fatty acids, Nucleic acids, Carbohydrates – sundry other low weight molecules

Structural Molecular Level (L-2)

Proteins, RNAs, DNAs, Fats, Polysaccharides, etc.

Functional Unit Level (L-3)

Ribosomes, Mitochondria, Chromosomes, Golgi apparatus, etc.

System Level (L-4)

Cell

Increasing combinations

Increasing consolidation

Seminar Questions - Organization • How can we characterize the relations

between hierarchical organization, network structures, and component interactions?

• What are the characteristics of the “boundary” of a corporation?

• What are some examples of stuffs that “flow” between systems in the real world?

• What exactly do we mean by the depth of a hierarchy of organization and why is it a reasonable index of complexity?