Discrete Dynamical Systems

Tools & Theory
emphasizing

Epistemology, Knowledge, & Perception
Tom Malloy

Department of Psychology University of Utah


PAGE CONTENTS

Recent Papers

Overarching Framework

The Map is Not the Territory

Differences that Make a Difference. Gregory Bateson (2000, 2002 , & [with M. C. Bateson] 1987 ) laid a foundation for the nature of learning and for epistemology in general that unites mind and nature as a necessary unity, a unity in which the processes of knowing and the processes of evolution share fundamental principles (2002, p.4).

We are using an NK Boolean System (Kauffman, 1993) to formalize Bateson's (2000, 2002) ecological epistemology within a modern nonlinear dynamic systems approach. This formalization has three fundamental premises.

  • First, the map (what humans and other sentient beings know) is not the territory (that which is known). Moreover, what gets onto maps from territories are differences in the territories.
  • Second, mental process can be abstracted as a flow of differences in a richly connected network. We model this flow with Boolean dynamic systems. Thus James' stream of consciousness becomes a complexly patterned stream of differences hinted at by the simulation shown here. This stream of differences in dynamic systems terms can be construed to flow within the constraints of an adaptive landscape consisting of many basins of attraction, each with an attractor and, usually, many tributaries.
  • Third, higher order knowledge emerges in the process of taking differences in the flow of differences (Bateson, 2000, p. 454ff). In the formal Boolean model this process of finding differences in the flow of differences begins with finding discrete derivatives (TAO's) and continues with finding differences among the derivatives themselves (Meta-TAO's). Considered meta-theoretically, this three-premise perspective is extremely simple compared to the complexity of many cognitive approaches.

Nonlinear Dynamic Systems. Stuart Kauffman (1993, 1995, & 2000), in a line of thought independent of Bateson's, has laid a foundation for the origin of order in biological evolution that establishes self-organization and selection as co-principles "weaving the tapestry of life." One tool in his investigations are Boolean network computer simulations which constitute a useful model for a difference-based approach to epistemology and learning. Boolean networks generate a lanscape of multiple basins of attraction; each basin consists of tributaries whereby the stream of process flows into attractors where it cycles until perturbed. We map these simulated landscapes onto the flow of mental process, onto the stream of consciousness as it were. The mental landscape consists, then, of dynamic patterns related to each other by the structure of the landscape. It is useful to think of mental landscape as an open dissipative system; dynamic patterns flow into and out of the system. These escapements and dissipations from the larger mental context affect the nature of the dynamics of mental process. For example, as an open system eddies (attractor cycles) into which mental process falls are, at a minimu, suseptible to perturbation and tranformation. Some eddies in the flow mental process will be highly stable in the face of perturbation and others not.

Dynamic Knowing. Our general framework is complexity theory, nonlinear dynamic systems (NDS), and the set of theoretical frameworks that are associated with complexity and NDS. Therefore, we view knowleddge as a dynamic process. In the papers, web pages and interactive Java experiments shown below simulations of the NK Boolean systems, invented by Kauffman to study evolution, are developed to study, extend, and make more precise and specific Bateson's epistemology along with his insights into the nature of learning. These simulations open up new phenomena and hypotheses, including:

(a) Emergent levels of cognitive-perceptual categories,
(b)Dynamic form perception,
(c) Abstraction of principles from a single sensory experience without the necessity of experiencing multiple examples from which principles are abstracted
(d) A new way for how mental process (for Bateson, evolution is a mental process) moves in a landscape. This new way of moving in a landscape is one way of specifying what Bateson might have meant by "differences that make a difference."

Top Contents


Top Contents

Top
CONTENTS OF PAGE
Find Resource you want then click GO!

Dynamic Analogue to Figure/Ground

The Direction of Movement and the Pattern You See Depend on How You Focus
(follow DIRECTION and SPEED of arrow)
GO! Overarching Framework

GO!

 Papers and Presentations: 2002, 2003, 2004, 2005, 2006, 2007
GO! E42: Introduction/Tutorial for Discrete Dynamic Systems
GO! Interactive Experiments: Interactivity--The New Language. Simulations are useful in the extreme for understanding nonlinear dynamic systems
GO! Emergent Hierarchies in Perception: Dynamic Constancy--A new principle of perceptual organization and emergent categories
GO! Dynamic Form Perception: Apparent Motion is proposed as a critical process in a new theoretical frame which makes dynamics fundamental to pattern perception. This section includes EXEMPLAR 1, EXEMPLAR 2, and EXEMPLAR 3, all demonstrating the emergence of dynamic form through phase relations in a dynamical system.
GO! Symmetry Groups in Adaptive Landscapes: Knowing begets Knowing: How Derivatives and Meta-Derivatives of Local Dynamics Reveal the Structure of a Landscape
More...
GO! Online Discrete Dynamic Systems Research Lab Publicly available, open source, online research tools for constructing NK Boolean systems
GO! Other Work by Tom Malloy (including papers on Technology Assisted Education)
GO! How to Represent a Dynamic Universe: Theoretical and practical issues both in computer and human representation
GO! Early working draft: Abstracting Principles and Ideas from Experience: The basic Batesonian process of finding differences in differences leads to a hypothesis about how formal principles may be abstracted from a single experience without the necessity of multiple examples from which to abstract those formal principles
GO! Basins, Evolution & Morphogenesis & Knowledge: Under construction
GO!

 Early Working paper: Issues in Methodology Very early thoughts about methodological implications of dynamic systems for classical experimental methodology and some halting steps to an ecology of rigorous qualitative (pattern-based) methods. Under Construction

GO! Related Web Pages of Theoretical Interest
GO!  References and short Bibliography for the working papers on this site

Top Contents

 

Recent Publications, Conference Papers, and Presentations
( get java plugin)
Applets are Interactive Experiences and Experiments

Symposium Papers: Knowing in a World of Broken Symmetries, (2007, July) Society for Chaos Theory in Psychology and the Life Sciences Conference, Orange CA (PDF)

01_The Puzzling Powers of Two: A Brief Introduction to Boolean Systems and Analysis (PDF)
02 Knowing begets knowing: Derivatives and meta-derivatives reveal the topology of basin landscape in Boolean XOR rings (PDF)
03 Sierpinski: The Structure of Boolean Derivatives (PDF)
04 The Knowable Unknowns (PDF)
05 References (PDF)

Presentation Outline for Parts 1 and 2: Knowing in a World of Broken Symmetries HTML
Thomas Malloy, Joel Cooper, Jonathan Butner, Thomas Smith. (2007, July). Knowing in a Word of Broken Symmetries. Society for Chaos Theory in Psyhcology and the Life Sciences Conference, Orange, CA..

Journal Article: Dynamic Constancy in Perceptual Hiearchies (PDF)
Citation: Malloy, T. E. & Jensen, G. C.  (2008).  Dynamic constancy as a basis for perceptual hierarchies.  Nonlinear Dynamics, Psychology, and Life Sciences, 12, 191-203.
Journal Article: Mapping Knowledge to Boolean Dynamic Systems in Bateson's Epistemology (PDF).
Citation: Malloy, T. E., Jensen, G. C., & Song, T. (2005). Mapping knowledge to Boolean dynamic systems in Bateson’s epistemology. Nonlinear Dynamics, Psychology, and Life Sciences, 9 , 37-60.
Journal Article: Steps to an Ecology of Emergence: (PDF)
Citation: Malloy, T. E., Bostic St Clair, C. & Grinder, J. (2005). Steps to an ecology of emergence. Cybernetics & Human Knowing, 12, 102-119.

Malloy, T. E. (2006, August). Prerequisites to a Batesonian Epistemology. Society for Chaos Theory in Psyhcology and the Life Sciences Conference, Baltimore, MD. (PDF)

Malloy, T. E. & Jensen, G. C. (2006, July). Mapping Gregory Bateson's Epistemology to Nonlinear Dynamic Systems Theory: Dynamic Form and Hierarchies of Knowledge. International Society for Systems Sciences 50th Anniversary Conference, Sonoma CA.(HTML)

Malloy, T. E. & Jensen, G. C. (2006, July). Talk Outline for Mapping Bateson's Epistemology to a Boolean Dynamic System . International Society for Systems Sciences 50th Anniversary Conference, Sonoma CA. (HTML)

Malloy, T. E. & Jensen, G. C. (2006, May). The emergence of visual form through phase relations in dynamic systems. Vision Sciences Society 6th Annual Meeting, Sarasota, FL. (PDF)
Malloy, T. E. (2006, February). The Logic of Logic and the Logic of Dreams. Winter Chaos Conference, Pittsburgh, PA.(PDF)

Malloy, T.E. & Jensen, G. C. (2005, August) Evolutionary Process, Epistemological process, and Emergent Hierarchies in Perception. Society for Chaos Theory in Psychology and the Life Sciences 15th Annual International Conference, Denver, CO (PDF)

Outline: CNS Presentation April 8 2005 Seeking a Pattern Language: Perceptual Hierarchies HTML
Outline: CNS Presentation November 2004 Further Steps to an Ecology of Mind: Prerequisites to a Batesonian Epistemology HTML
Malloy, T. E. Outline of New Perceptual Phenomena and Emergence HTML (Very rough draft). Winter Conference 2004).

Outline: Ecology of Emergence Presentation HTML Society for Chaos Theory, Boston 2003

 

Dynamic Form: Zebra-Stripe Camouflage Applet
Conway's Game of Life Applet

Outline: Perceiving Visual Pattern (Society for Chaos Theory, Boston 2003)
  Perceiving Sub-basins Dynamically Applet
  Perceiving Emergent Dynamics Applet
Modeling Discrete Dynamic Systems with Online Java Tools:
An Introduction to E42: HTML: Society for Chaos Theory, Portland, OR, August, 2002

Top Contents

 

Some attempts to provide an
Introduction and Tutorial for N, K Boolean Systems and E42
( get java plugin)
Applets are Interactive Experiences and Experiments

Mapping Knowledge to Boolean Systems in Bateson's Epistemology PDF (more formal)
This includes both E42 and TAO
Discrete Dynamic Systems & Epistemology HTML (more chatty)
4-Node Standard Twinkling Nodes (Applet)
4-Node Standard Historical Trace (Applet)
Genius A more Complex Example of Twinkling Nodes (Applet)
Genius: A more Complex Example of Historical Trace (Applet)
 

TAO: Analyzing and Perceiving Change Over Time (HTML)
This web page provides a detailed description of how E42 finds basins and how it archives and categorizes the basins it finds.
The Flow of TAO Levels out from a Basin
 
Draft: Further Steps to an Ecology of Mind (CNS Presentation, Autumn 2004)

Top Contents

 

Interactive Experiments with Dynamic Systems
All links in this table are Java Applets
( get java plugin)
In a complex dynamic scene with many moving sub-patterns, how do we simultaneously extract multiple different sub-patterns?

 

EXEMPLAR 1: Perceiving Fundamental Frequences of a System through Apparent Motion: Cycles & sub-Cycles Applet This example has Good Supportive Text with Images highlighting cycles and subcycles a dynamic system. Demonstrates how the human perceptual capabilities that result in the illusion of Apparent Motion might could act as a mechanism for extracting the cycles and sub-cycles of a complex dynamic system. (Onlinedata archive)

Perceiving Dynamic Patterns through Apparent Motion: Basins & Sub-basins Applet A second example with good text and 3 experiments
EXEMPLAR 2: Perceiving Emergent Dynamics This applet shows how our apparent motion neurology allows us to perceive general emergent patterns in a complex dynamic scene (when these emergent patterns are technically not a basin or sub-basin of the system). Good supporting text and several experiments.
EXEMPLAR 3: Layered Emergent Dynamics Applet This applet shows complex abstract patterns can flow across each other in different directions and at different rates. It lays a foundation for how the human visual system may extract coherent patterns that can be static or moving.
 
If input from the universe is construed as a dynamic system, how do different modes and strategies for representing this input impact our ability to perceive complex pattern?
Twinkling Nodes & Sound Representations for a dynamic system with long tributaries How do tributaries effect our ability to perceive dynamic pattern?
Historical Trace & (Not functioning yet)

Top Contents

 

Emergent Hierarchies in Perception
( get java plugin)
Journal Article (under editorial review): Dynamic-Constancy-in-Perceptual-Hierarchies_ver-07-03-12.pdf
1) TAO: Analyzing Change over time: 1st Dervivative (Undergraduate Lecture Outline with details) html
2) Recursive TAO: Higher Order Derivatives of Change Over Time (Undergraduate Lecture) html

3) Differences in Differences: The Principle of Dynamic Constancy html
A New Principle of Perceptual Grouping (Draft HTML)

4) Boundary Conditions on the Principle of Dynamic Constancy
 (Draft HTML)

The Flow of TAO Levels out from a Basin Example of dynamically flowing dervatives of change over time for one attractor cycle

 
TAO: Analyzing and Perceiving Change Over Time (HTML)
This web page is more succinct and less detailed than the undergraduate lectures above
 
 

Top Contents

 

Dynamic Perception:
APPARENT MOTION
as a fundamental mechanism of knowledge
( get java plugin)

Representing Dynamic Relations II:
Extracting Patterns in a Dynamic Universe:
Apparent Motion and Pattern Perception (Draft HTML)

 
EXEMPLAR 1: Perceiving Sub-basins Dynamically Applet
EXEMPLAR 2: Derived Forms: Emergent from Phase Relations Applet
EXEMPLAR 3: Layered Emergent Dynamics Applet. This applet shows complex abstract patterns can flow across each other in different directions and at different rates. It lays a foundation for how the human visual system may extract coherent patterns that can be static or moving.

Classic Apparent Motion Applet Review apparent motion phenomena with interactive tools
Random Dot Patterns & Apparent Motion Applet A tool to explore the effect of distance between elements in a random dot pattern on apparent motion
 
Motion Web Pages by Other Labs

http://vision.psy.mq.edu.au/~peterw/demos.html

http://psy.ucsd.edu/~sanstis/motion.html

http://cognitrn.psych.indiana.edu/CogsciSoftware/AppMotion/index.html
Subjective color from apparent motion (Journal of Vision) by Vincent J. Chen and Carol M. Cicerone
Ouchi Apparent Motion Illusion by Peter Kaiser
Motion Perception by George Mather
 
 

Top Contents

Symmetry Groups in Adaptive Landscapes
How Derivatives and Meta-Derivatives of Local Dynamics Reveal the Structure of a Landscape
01_The Puzzling Powers of Two: A Brief Introduction to Boolean Systems and Analysis (PDF)
02 Knowing begets knowing: Derivatives and meta-derivatives reveal the topology of basin landscape in Boolean XOR rings (PDF)
03 Sierpinski: The Structure of Boolean Derivatives (PDF)
04 The Knowable Unknowns (PDF)
05 References (PDF)

 

Representation and Enactment as Fundamental Issues in Knowledge
( get java plugin)

Representing Dynamic Relations I:
Visual and Auditory Representations Draft HTML

The basic cognitive science approach to Representation HTML
David Marr
The kinds and the utility of representational systems HTML
Carmen Bostic St Clair & John Grinder
Enactment: A challenge to representation in knowledge HTML
Francisco Valera, Evan Thompson, & Eleanor Rosch
Interactive Experiences and Experiments demonstrating the impact of various forms of Representation. All are Java Applets
First-Example_L4_N16_Twinkling Nodes Applet
This Java applet demonstrates how system dynamics can be represented visually by twinkling nodes (e.g., Kauffman, 1993). It includes a perturb button and good text

Using Sound & Nodes to Represent Dynamic Pattern Applet
Good instructions and text. Uses a system with short basins (L=4, L=8). Gives direct experience with hearing dynamic patterns. Includes visual representation with twinkling nodes so that a direct comparison of hearing and seeing patterns can be made.

Using a Visual Historical Trace to Represent Dynamic Pattern Applet Same system as the one directly above, but represents system dynamics as a visual historical trace to allow you to compare (based on your experience with the above applet) these three forms of representation (twinkling nodes, sound, trace).

Twinkling Nodes & Sound Representations for a dynamic system with long tributaries How do tributaries effect our ability to perceive dynamic pattern?
Introducing Motion to Representation: Dynamic Pattern Perception

Top Contents

 

Abstracting ideas from Experience
( get java plugin)

Abstraction (Draft HTML)
 

Top Contents

 

Basins, Morphogenesis, and Evolution
( get java plugin)

Basins, Evolution, and Morphogenesis (Under Construction)
 

Top Contents

 

Methodological Issues
( get java plugin)

A Footnote to the Experimental Method Draft PDF (under construction)

 

Top Contents

 

Online Discrete Dynamic Systems Simulation Tools
( get java plugin)
To USE SIMULATION TOOLS in your own research, contact malloy@psych.utah.edu or jensen@psych.utah.edu.

Discrete Dynamic Systems Simulation Tools (access to research software)
New-Media Toolkit Create CD's or Interactive Web Pages
Classic Chaos Theory Tools: The Parabola, Y = aX(1 - X)
Hysteresis

Top Contents

 

Other Work by Tom Malloy

Tom Malloy's Home Page
Malloy, T. E., Jensen, G. C., Regan, A., & Reddick, M. (2002). Open courseware and shared knowledge in higher education. Behavior Research Methods Instruments & Computers, 34, 200-203.
Gordon, E. O. & Malloy, T. E. (2002). Online Homework/Quiz/Exam Applet:
Freely available Java software for evaluating performance online. Behavior Research Methods Instruments & Computers, 34, 241-244.
Malloy, T. E. & Hanley, G. L. (2001). MERLOT: A faculty-focused website of educational resources. Behavior Research Methods Instruments & Computers, 33, 274-276.
Malloy, T. E. & Jensen, G. C. (2001). Utah Virtual Lab: JAVA interactivity for teaching science and statistics online. Behavior Research Methods Instruments & Computers, 33, 282-286
OPEN Learning Management System:
Open-code tools for teaching, learning, and building communities online
Stat Sampler:
Links to interactive, online tools for teaching and learning statistics
Introductory Statistics Course
Ecology Model To find the essays Explore click on the pattern. There is an order to the essays if you can find it.

Personal Ecology To find the essays Explore click on the pattern. There is an order to the essays if you can find it.
Wild Places Well no, this link will take you to the Ecology Model but you can find Wild Places on the side bar.
GroupWare Presentation for Center for Teaching and Learning Exellence

Top Contents

 

 

 

 

 

 

 

 

 

 

 

Top Contents

Related Web Pages of Theoretical Interest
Epistemology Whispering in the Wind: An in-depth discussion of "Neurology and language - those two great sets of transforms that both separate us from, and connect us to, the world around us."
Carmen Bostic St Clair and John Grinder

Society for Chaos Theory in Psychology and the Life Sciences

Emergence and Cellular Automata MIT Media Lab

Santa Fe Institute
Swarm Development Group
Blue Brain Institute Fred Abraham
Ryan Nagy Search Engine Optimization
 
Top Contents

 

 

 

 

 

 

 

 

 

t-ind-test

A-Corr_test