Time and Simulation

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Time and Simulation

• 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.
• Dynamical simulation may be a less difficult way
  to investigate the formation of complex entities
  in multiple time dimensions with multiple space
  dimensions.
• 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 themselves according to
  heterochronically complex, interwoven
  morphodynamical rules. Entities are really
  ordered synced processes existing in
  time-ecologies.
• There are Five time-space dimensions causally
  nested in everyday life notemoral, biotemporal,
  eotemporal, prototemporal, and atemporal.
• A time-ecology can be for example, encompass a
  specific policy sector regulated via its own
  extended geophysical, social, and mental spaces
  all of which are instantiated in multiple
  time-space dimensions. A time-ecology involves
  multiple levels and complex past-present-future
  feedbacks.
• Describing and Understanding
• For a simulation we are looking at a space-time
  topology problem involving mapping of differing
  space-time event streams that continuously form a
  time-ecology of developing agents and landscapes
  according to complex systems dynamics
• Experimenting
• Translating and combining these five temporal
  dimensions, including temporal orientation and
  perspective, into a realistic simulation has not
  been done to my knowledge

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Characteristics of Time

• The time of a time-ecology is
• background independent and local
• Time is local resulting from continuously
  changing local topologies as delimited by five
  temporal levels of nested causalities in space
  including that forming/enacted by the entity
• Temporal background independence produces local
  outcomes that emerge from changes in the
  relational streams of 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)
• These flows are continuously structurating forms
  be they called "agent" or "landscape" or
  network. Remember, everything is 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
  budgets
• Time budgets in turn regulate the heterochrony of
  event flows in a time-ecology or 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 topological 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, and orientability, all of which
  express the depth or thickness of time-space
  dimension as a local organization that can be
  moved, even acted through.
• Thus, 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 the point
  in a flow of the space-time topological
  dimensions.
• In all cases it is the particular deformation of
  the dimensional topology of the space that
  determines how objects are instantiated.
• 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.

TIME STRUCTURES
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Five Temporalities and Associated Causalities

• Nootemporal a noetic (symbolic) intentionality.
• Propagates via networks but does not propagate
  uniformly and does feedback from the future into
  the past and visa versa
• Noetic time chunking Past-future-present-future-f
  uture-past-present.
• Causality is omnidirectional with neither the
  past nor the future being fully determined.
• Biotemporal The inner developmental and growth
  organization of life.
• Patterned living things go through developmental
  life cycles with beginnings, middles, and ends.
• Biotemporality is strictly local, is bounded in
  space-time (birth-death) and propagates through
  short range networks (sexuality, simple division,
  etc),
• Distinguishes past and future relative to
  developmental and growth processes.
• Human agents have characteristic temporal noetic
  intentionality that accompany each stage.
• 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.
  This time is physicist's t.
• Eotemporality is the block universe of large
  scale matter
• It is characterized the simultaneous existence of
  all presents in the block-universe (no flow) with
  time-reversal symetry.
• Eotemporal time obeys the inverse square law
  propagating uniformly, and has No feedback from
  the future into the past making causality
  unidirectional or (Gödel flows from the future
  into the past making any direction in time
  impossible) SEE NEXT SLIDE
• Causality is deterministic.

TIME STRUCTURES
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Eotemporality The Block Universe

• Affords equal (ontological) status to all points
  in space-time, thus regarding temporality as an
  illusory human construct with no reference to
  reality as understood by modern physics.
• Nothing singles out a privileged special moment
  as the present or any process that would
  systematically turn future events into the
  present, then past, events. In short, ... time
  does not pass or flow.
• Think of the universe as a large block of events.
  The events we would like to call future, past,
  and present all exist "timelessly" in the block
  universe, with certain geometric topological?
  relationships between them.
• Simultaneity is relative to a frame of motion.
• Paul Davies, "That Mysterious Flow

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Determinism in the Eotemporal Block Universe
The relationship described in above holds between
any time slices of the universe, and thus, given
the laws, the present implies the future and also
the past. We are free to take the present as
fundamental in the relationship of determination
as much as we are free to take any other time
slice as fundamental. In fact, no time slice, no
state of the universe at a time, is
fundamental. According to this view there is
a disconnect between the block universe that we
exist in and causal laws which give direction to
physical processes.
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Eotemporal 2nd Law is Double NOT Single Headed

• Various Physical Laws are time asymmetric in
  defining arrows of causality like the second
  law of thermodynamics. Entropy increasing
  apparently gives time an arrow.
• But, the Second Law is derivative of the
  statistical application of Newtons laws of
  motion. Since Newtons laws of motion have no
  built-in temporal orientation, then systems may
  evolve towards greater entropy in either the
  future or the past. (Greene, p160) Thus there is
  an overwhelming probability that a system had
  greater entropy in both the future and the past.
  Gravity provides the arrow.

Entropy
Entropy
Present
Present
Time
Time
Usual Mistaken
Correct
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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 a dimension of a local
topology.
Time is Event Propagation in Space is Past-Present Future Relationship Is Causality is
Nootemporal Local Chunking Networks via Local or Extended Hubs and Nodes Omni-directional (continuous redefining) Complex Beauty Valuing Visual Verbal
Biotemporal Bounded Developmental/Growth/ Death Local Reproductive Networks Unidirectional Morpho- dynamics Unidirectional Interactive/ Evolutionary
Eootemporal Block-universe and time-asymetric due to perturbation Inverse Square Law and diffusion Meaningless Deterministic
TIME STRUCTURES
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Time Characteristics (Continued)

• Different topological geometries can be
  distinguished 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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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)

• Thus the local form of temporality at anyone
  point is restricted by equations defining the
  overall topological structure of the
  agent/landscapes respective five dimensional
  space-times, and, by their rates 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. Remember,
  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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TIME STRUCTURES
Source Victoria Koehler-Jones, 1999.
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TIME STRUCTURES
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Application

• Public Policy Making and Implementation

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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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Thoughts on Autonomous Agent Temporal Design
Issues
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Elementary One-Dimensional Cellular Automata and
2 Worlds
Ci-r(t-1) Ci-1(t-1) Ci (t-1) Ci1(t-1) Cir(t-1)
Ci(t)
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 on a Matrix 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 which should play a significant
  role does not demonstrate both forward and
  backward causal symmetry
• Future is highly problematic because it does not
  approach at all in nootemporal time, but emerges
  from agent/landscape interaction (computer
  machine time)
• 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