HIDDEN ORDER

Chapter 1: Basic Elements

Complex Adaptive Systems (cas)

• Aggregates of independent agents• Agents behavior governed by a collection

of rules• Persistence and coherence in the face of

change– Dependent on extensive interaction,

aggregation of diverse elements, and adaptation and learning

• i.e. economy, ecosystem, CNS

Objectives

• Purpose of the book is to formulate a solid theory about complex adaptive systems– Separate fundamental characteristics from

idiosyncrasies – Difficult to do because of nonlinearities– Compensate with cross-disciplinary

comparisons

Seven Basics

• Four properties and three mechanisms shared by all cas

• Not the only shared characteristics.

• The rest can be built from a combination of these seven

Aggregation (Property)

• 2 senses• 1st Sense: Constructing Models• 2nd Sense: What cas do

– Emergence of complexity from a network of simpler agents.

– Aggregates can act as agents in higher-level structures (meta-agents)

– i.e. Cells Tissues Organs Organ Systems Organism

Tagging (Mechanism)

• A mechanism that facilitates aggregation by bringing like things together– i.e. a flag used to rally a group of people,

pheromones and visual patterns that lead to selective mating

• Allow observation of properties hidden by symmetry.– i.e. painting a stripe on a cue ball to see

changes in the axis of rotation

Nonlinearity (Property)

• A function is linear its value can be calculated by adding the values of its parts.– i.e. A=B+C

• Nonlinearlity of Pool Ball Example– (B+W)(t+1)=(B+W)+c(B)(W)– (G+W)(t+1)=(G+W)+c’(G)(W)– Can we simplify the model by aggregating B and G into a single

category S? (S=B+G)– No. There is no coefficient that works for all combinations of B

and G. – If the function was linear, then we could take the average of c

and c’

Flow (Property)

• [node, connector, resource]• [phones, phone lines, conversations]• Multiplier Effect

– Occurs after additional resource is added at a node– Initial effect is multiplied as the resource is passed

through the network

• Recycling Effect– Result of cycles in a network– Recycling with the same input produces a greater

output at each node

Diversity (Property)

• Not random.

• System will adapt to fill holes.– New agent typically occupies same niche as

previous agent and provides most of the missing connections

– Leads to convergence in biology• i.e. squid vs. mammalian eye

– Founder Effect

Diversity (Property)

• Pattern of diversity in cas is dynamic.

• Diversity is a product of adaptation. Each new adaptation creates possibilities of new interactions and new niches

Internal Models (mechanism)

• Allows for anticipation

• Two types– Tactit: prescribes an action under an implicit

prediction of a desired future state• i.e. a bacteria swimming up a nutrient gradient

– Overt: used as a basis for explicit explorations of alternatives (lookahead)

• i.e. exploring possible scenarios before moving a chess piece

Building Blocks

• How are internal models built from constantly changing environments?– Situations are distilled into useful and relevant

building blocks– A flat tire while driving a red Saab on the

expressway?– Decompose into rules about cars, tires, and

expressways

Hidden Order Chapter 2

Adaptive Agents

By John Holland

Requirements of Adaptive Agents

1. Performance System - a universal way to represent the capabilities of different agents using messages and conditional rules

2. Rule Discovery - making changes to an agent’s capabilities by means of a credit score

Making Use of Binary

• A detector receives a message when conditions are met, the result of which triggers an action and completes the rule

• Messages - strings of 1’s and 0’s of length (L)

• Conditions - strings 1’s, 0’s and #’s (signifying no specificity), also of length L

Messages from Two Sources

1) Detector Originated - derived from and given meaning by the environment

2) Rule Originated - produced by other rules, given meaning only when they activate effectors

Credit Scores

• Rules have strength that is like having cash on hand, and can be viewed as being producers, middlemen, or consumers that buy, sell, and trade messages

• The ultimate consumer is the rule that is active when the agent receives a reward from the environment

• All rules down the line are credited and automatically strengthened

Building Blocks

• Rules can be divided into building blocks called schemata.

• Successful rules have schemata that in general serve as better building blocks than random binary strings

• Successful schemata are singled out by replacing other parts of the sequence with the * symbol

Crossing Over

• Binary sequences are crossed over using the genetic algorithm

• Short schemata are conserved through probability

• Longer schemata are preserved because they are composed of shorter successful schemata that appear in a large portion of the gene pool

Mutation

• Successful rules can become fixed in a population before other more successful rules can be discovered

• Random mutations disrupt fixation during crossing over, restoring adaptation

The Prisoner’s Dilemma

• A game where two players simultaneously decide to defect (D), or cooperate (C)

• Tit-for-tat is a favorable strategy that produces a relatively large number of points

• Agents that begin with schemata for tit-for-tat discover better strategies by deciding on whether an opponent is bluffing or not