Sorting Out the SpaceTime of Agent Simulations

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Sorting Out the Space-Time of Agent Simulations

• By Gus Koehler
• Time Structures and
• The University of
• Southern California

Prepared for presentation at FRIAM, Applied
Complexity Group, Santa Fe, New Mexico, April
22, 2005 Contact 1-916-564-8683
rhythm3_at_earthlink.net WWW.Timestructures.com
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Physicists unreflectively Assert That

• If string theory is correct, we must entrain
  the possibility that space-time has more than
  four dimensions. The number of time dimensions
  must be kept equal to one it seems very
  difficult if not altogether impossible, to
  construct a consistent theory with more than one
  time dimension. The extra dimensions must
  therefore be spatial.
• Just because something is difficult does not
  mean it is not worth attempting.
• Simulation may be a way to investigate multiple
  time dimensions involving multiple space
  dimensions leading to mathematical insights.
• Barton Zwiebach (2004). A First Course in String
  Theory. Cambridge, UK Cambridge University
  Press, p.28.

TIME STRUCTURES

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The Basic Problem

• Assumptions
• Biological, physical, and social entities
  continually form themeselves according to
  heterchronic complex, interwoven morphodynamical
  rules. Entities are really ordered processes.
• There are Five time-space dimensions causally
  nested in everyday life
• A time-ecology for example can be a Specific
  policy sector regulated via its own extended
  geophysical, social, and mental spaces
  instantiated in multiple time-space dimensions.
  It involves multiple levels and complex
  past-present-future feedbacks.
• Describing and Understanding
• Is a space-time topology problem involving
  mapping differing space-time event streams that
  continuously form time-ecology developing agents
  and landscapes according to complex systems
  dynamics
• Experimenting
• Translation and combination of five temporal
  dimensions, including temporal orientation and
  perspective, into a simulation has not been done
  to my knowledge

TIME STRUCTURES
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Characteristics of Time

• Time-ecology time is background independent and
  local
• Time is local, resulting from continuously
  changing local topologies as delimited by five
  temporal levels of nested causality
• Temporal background independence produces local
  outcomes that emerge from changes in relational
  streams of often propagating events
• Each local event stream has varying temporal
  progressions and perceptions (capacity to move in
  and to receive varying kinds of information,
  energy or resources)
• This flow is continuously structurating forms be
  they called "agent" or "landscape" or network,
  instantiated in a time-ecology
• This is not existence within time existence is
  time.
• (Goodhew and Loy, 2002).

TIME STRUCTURES
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Characteristics of Time (Continued)

• Social Decision windows present opportunities to
  take action to change the temporal and
  socio-economic growth and development of a
  time-ecologys time budgets
• Time budgets in turn regulate the heterochrony of
  event flows in a time-ecology or the space-time
  of some complex system (called chronocomplexity)
• Space-time is inseparably entwined with the
  topology of the space-time dimensions of a local
  point in a dynamical flow
• Topology includes both mathematical and
  phenomenological places
• The space-time topology structure of a universe
  is the structure of the arena in which the
  processes that comprise the history of that
  universe occur. This involves place (space), in
  the sense of to place or topos
• The topology of space-time involves local
  proximity and envelopment as continuity,
  connectivity, orientability all expressing the
  time-space dimension of depth or thickness as a
  local organization that can be moved, even acted
  through.
• Anticipating our discussion, local space-time
  topology permits variations in placement and
  envelopment practices regulating heterochronic
  flows of energy, information, and resources
  according to chronocomplex laws as they converge
  into propagating flow patterns (velocity cones)
  across a time-ecology. Such local space-time
  topological patterns are symmetry conserving as a
  pattern moves forward or backward in a time.
  Evolution may selectively change a time-ecology
  and break such symmetries.

TIME STRUCTURES
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Characteristics of Time (Continued)

• Proximity, envelopment, posture and placement
  define how process is instantiated at a point in
  a flow of space-time topological dimensions.
• Ex. A paper with a two dimensional point can
  be crumpled. 2D movement over crumple experiences
  a force making it impossible to move in a
  straight line under specific local conditions
• Ex. Riemann gravity was caused by the
  crumpling of the three-dimensional universe into
  an unseen fourth dimension.
• Ex. Kaluza, an additional fifth spatial
  dimension unified Relativity and
  Electromagnetic Theory.
• Kaluzas dimensions? Topologically, three are
  extended and one is tightly curled up much like
  Riemanns wrinkles.
• In all cases it is the particular deformation of
  the dimensional topology of the space that
  determines how objects are instantiated.

TIME STRUCTURES
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Five Temporalities and Associated Causalities

• Nootemporala noetic (symbolic) intentionality.
• Noetic time chunking Past-future-present-future-f
  uture-past-present.
• Propagates via networks but does not propagate
  uniformly and does feedback from the future into
  the past and visa versa
• Causality is unidirectional with neither the past
  nor the future being fully determined.
• Biotemporal The inner developmental and growth
  organization of life.
• Distinguishes past and future relative to
  developmental and growth processes.
• Patterned living things go through developmental
  life cycles with beginnings, middles, and ends.
• Human agents have characteristic temporal noetic
  intentionality that accompany each stage.
• Biotemporality is strictly local, is bounded in
  space-time (birth-death) and propagates through
  short range networks (sexuality, simple division,
  etc),
• Causality is unidirectional but is open to
  natural selection as a process for selecting
  heterochronic wild rhythms giving birth to
  novelty.
• Eotemporal The universe of large scale matter.
  Its time is physicist's t.
• It is characterized by a continuous and nowless
  flow of time .
• Causality is deterministic.
• Eootemporality is the universe of large scale
  matter
• It is characterized by a continuous, stable, and
  now-less flow of time with no directions in
  time.
• Eootemporal time obeys the inverse square law
  propagating uniformly, and has
• No feedback from the future into the past making
  causality unidirectional

TIME STRUCTURES
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Time Characteristics (Continued)

• Thus the local topological temporal form at a
  point is restricted by the equations defining
  the overall topological structure of the
  agent/landscapes respective five dimensional
  space-times, and, as suggested below, their rate
  of rotation. (Calabi-Yau spaces for example)
• Topological spatial dimensions can be large and
  extended or small and curled up. We dont know
  how to visualize time dimensions yet. But, as
  noted, each of our five temporalities extend
  themselves differently.
• Varying space dimensions (four or more) have been
  explored using projections and shadows (Banchoff,
  1996). How to visualize temporal dimensions?

TIME STRUCTURES
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Greenes Diagram of Six Dimension Calabi-Yau
spaces For String Theory (one time dimension)
Source Greene, 1999, p. 207. From a discussion
of Calabi-Yau spaces see http//electron.fullerto
n.edu/heidi/5
TIME STRUCTURES
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Time Characteristics (Continued)

• Can distinguish between different topological
  geometries by what is allowed in rotational
  transformations at a point in the time-ecology.
• Ex. different particles emerge from the way
  various dimensions of space are rotated about a
  point. Rotating a photon out of 4 D space into 8
  D space creates a photino in 8 D space.
• The important point is that the qualities of the
  formed event are different (Stewart, 2001).
• the above example suggests that rotation through
  five time dimensions produces varying topological
  qualities in placement and proximity.

TIME STRUCTURES
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Three Principal Temporalities and Associated
Causalities
Five forms of causality and different ways of
extension in space supports my assertion that
each temporality is dimension of a local
topology.
TIME STRUCTURES
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TIME STRUCTURES
Source Victoria Koehler-Jones, 1999.
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Regional Economy
Legislative/ Administrative Processes
Economic Development Programs for Business
TIME STRUCTURES
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Public Policy Time-Ecology Extended From The Past
Into The Future
TIME STRUCTURES
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Replace Table 1, p. 47
TIME STRUCTURES
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Replace Table 1, p. 48
TIME STRUCTURES
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TIME STRUCTURES
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Elementary One-Dimensional Cellular Automata and
2 Worlds
Time -1
Space -1
Time 2
Space 2
Instantiated Point
Torus W CA move off of side or Bottom and return
on Other side or top. Folding the edges
Together creates a Torus but in 2D.
Ci (t-1)
F-World CA return from edge.
From Gary Flake (1998). The Computational
Beauty of Nature. Boston Bradford Book, p.
232-233. and http//atlas.wolfram.com/01/01/
TIME STRUCTURES
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Two Dimensional Cellular Automata and Displayed
as Three dimensional Object
T8
T4
T5
T6
T7
T3
T1
T2
T1
Space at T1
Space at T1
T1
Tn
TIME STRUCTURES
Source Wolframhttp//www.wolframscience.com/nkso
nline/page-171
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Current CA Temporal Barriers

• Two Dimensional topology with one dimension of
  background dependent time, not five in background
  independent time
• Placement, proximity, and performance rules are
  imposed from another dimension that does not
  change with the simulations dimensions
• No memory, no past or other time relationship in
  the simulations dimension except that imposed
  from outside
• There is nothing special about a cells discrete
  spatial landscape position
• Emergent patterns are a series of past screen
  shots assembled outside of simulations time.
  They are not all simultaneously present in the
  present. Clearly biotemporality can not be
  depicted in such space-time
• Nootemporal time does not demonstrate both
  forward and backward causality
• Future is highly problematic because it does not
  approach at all in nootemporal time, but emerges
  from agent/landscape interaction.
• There are multiple local presents across a
  time-ecology constantly structurating multiple
  developmental patterns, not one

.
TIME STRUCTURES
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Inter-dimensional Penetration and Causality The
Foundation of Time-Based Cellular Automata
2D CA grid on edge at T2,S2
Looking down on CA 2D grid at T2,S2
TIME STRUCTURES
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Nootemporal Locally Warped Dante Space-Time
Space/Time is organized according to Closeness
To God
Far From God
TIME STRUCTURES
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An Example of a Partial Local Topology The Dante
and Eootemporal Intersect
Movement of the intersect
TIME STRUCTURES
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Living Dimensions Crossing Through
TIME STRUCTURES
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Puzzle Piece
Two Agents as continuous Event Streams
Pipe
Point 3
Nootemporal Foresight Horizon
Various Causal Processes According to
temporality
Movement Into Past
Political Jurisdiction
Point 2
Future Developmental Stage
Biotemporal
Eootemporal
Diagram Local Topology Of Three Simulation
Points
Point 1
Landscape With no Agent
TIME STRUCTURES
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Past Fading A
Agent A Heterochrony of Nested Temporalities
Future Approach A
Local Landscape (Spatial-Temporal)
Pipes with Velocity Cones
Agent B Heterochrony of Nested Temporalities
Future Approach B
Uneven Time Chunks





Future Approach B

Past fading B
Policy Window
Various Long- and Short-Term Cycles at Various
Scales
Simulation of Two Agents on Their Landscapes
Through Time
TIME STRUCTURES
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Requirements for Temporal Agent Based Simulation
Time is Background independent Five dimensional
agent and landscape topology causally nested in
local space-time Velocity cones characterize
information, resources, and energy (propagation)
exchanges Heterochronic structuration of agent
and landscape Event flows of entrained noetic
temporal chunking, allomteric biotemporality, and
Eootemporality
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Gravitational Oscillations Caused by Two Black
Holes http//sprott.physics.wisc.edu/pickover/dpsi
ral.jpg
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http//sprott.physics.wisc.edu/pickover/JCthugha10
.html