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@earthlink.net WWW.Timestructures.com
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
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 timespace 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
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
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
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 threedimensional universe into an unseen fourth dimension.”
• Ex. Kaluza, an additional fifth spatial dimension unified Relativity and
Electromagnetic Theory.
•Kaluza’s dimensions? Topologically, three are extended and one is
tightly curled up much like Riemann’s wrinkles.
TIME STRUCTURES
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-future-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 timereversal 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.
Not Concerned here with:
•
Prototemporal: is the time of elementary objects such as quarks, photons, etc. Causality is probabilistic and stochastic
•
Atemporal: the mode of time characteristic of a black hole. There is no mode of causation
TIME STRUCTURES
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“
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.
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
Newton’s laws of motion. Since Newton’s 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
Correct
Time
Usual & Mistaken
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
Past-Present
Propagation in Future
Space is:
Relationship
Is:
Causality is:
Nootemporal
Local Chunking
Networks via
Local or
Extended
Hubs and
Nodes
Omnidirectional
(continuous
redefining)
Complex
Beauty
Valuing
Visual
Verbal
Biotemporal
Bounded
Developmental/
Growth/
Death
Local
Reproductive
Networks
Unidirectional
Morphodynamics
Unidirectional
Interactive/
Evolutionary
Eootemporal
Block-universe
and timeasymetric
due to
perturbation
Inverse
Square
Law and
diffusion
Meaningless
Deterministic
TIME STRUCTURES
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
Greene’s 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.fullerton.edu/~heidi/5
TIME STRUCTURES
Time Characteristics (Continued)
• Thus the local form of temporality at anyone “point” is
restricted by equations defining the overall topological
structure of the agent/landscape’s 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 don’t 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
Nootemporal Temporal Orientation and Perspective
Vary by Individual and by Organization
Differing pasts:
Experiences
Expectations
Rate of movement
into the present
Rate of vanishing
into the past
Near or far
Density
Market and Industry
Government
Disaster Response
Warfare
Housing and Community
Environment/Nat. Resources
Health, Welfare & Safety
Differing Futures:
Expectations
Control
Depth
Differing Presents:
Narrow or wide
Rate of
movement
into the past
Rate of movement
into the future
Density
Rate of movement
into future
How the past is
brought forward
Density
TIME STRUCTURES
Source: Victoria Koehler-Jones, 1999.
TIME STRUCTURES
Application:
Public Policy Making and
Implementation
.
Public Policy Time-Ecology Extended From The Past
Into The Future
Heterocrony
Flow: Natural Environment
Unfolding: Rhizome, Hierarchical, etc. & Mixed Foresight
H.
Flow: Industry
Unfolding: Rhizome & Complex Foresight
H.
Flow: Legislative/Regulative
Unfolding: Tree & Clear Foresight
H.
Flow: Community
Unfolding: Rhizome, Hierarchical, etc., & Mixed Foresight
H.
Rhizome
Interface:
Networks And
Formats
Dynamic
topology and
geometry (site
of
heterochrony)
at the interface
as they
grow/mature
into each other
Tree
TIME STRUCTURES
Preliminary Identification of a Government/Industry Cluster Clock-Time
Replace Table 1, p. 47
Event Layers
(Colors in last slide are keyed to diagrams below)
Organization or Process
Scale: Length of
Manner of Spatial Extension
Cycle
Level One (100+ yrs)
1. Government Administrative
Institution life-cycle 27-100 yrs (Kaufman (1976)
Jurisdiction
2. Large firm life-cycle
50-100+ yrs (Atlantic Monthly)
Domestic/global
Level Two (10-80 yrs)
3. National GDP expand/contract 59-80 yrs (Pagan (1997)
Jurisdiction
4. Kondratieff long wave cycles
40-65 yrs (De Greene, 1988).
Economy
5. Major Party realignment
40 yrs (Key, )
Political boundaries
6. Congressional institutional
organizational life-cycle
20-40 yrs (Rieselback,1986)
Institution
7. Industry cluster formation/death
10-50 yrs (Saxinean, Rees and Stafford, 1986)
Network
8. Regional Infrastructure
(roads, ports, etc.)
25-30 yrs
Network
9. Policy cycles
12-27 yrs (Schlesinger, 1986; and Klingberg, 1983). Varies by policy Area Jurisdiction
10. District reapportionment
10 yrs
Jurisdiction
Level Three (1-9 yrs)
11. Business cycle
1-9 yrs (Temin, 1998)
Economy
12. Business network formation
life-cycle
virtual and various
Domestic/global
13. Small and medium sized
firm life-cycle
5 yrs to form; (Young, ?) 5 yrs to die (D=Aveni, 1989). Domestic
14. Governors and Members
professional life-cycle
4-6 yrs
Indiv./population
TIME STRUCTURES
15. State regional economies
5-7 yrs
16. Business Cycle (expand/cont) 5-7 yrs (Kimberly, Robert Miles, 1980)
Economy
Replace Table 1, p. 48
27. Product innovation
S curve cycles
6 mon. per season (Modis, 1998) . Firm
Level Five (Hours to 6 months)
28. Programatic interventions
(funds and services)
29. Demand for data bites and
internet core
(100% increase)
30. Media content cycles
monthly
Jurisdiction
2 months (McQuillan, 1999)
(story coverage time)
Economy
Circulation
Level Six (Minutes to seconds) (Lemke, 2000)
31. Interpersonal dialogue
32. Utterance (word or phrase)
33. Vocal sound
seconds/minustes
second (1-10)
10^-1 Sec.
Person
Person
Level Seven (Less than a second) (Lemke, 2000)
34. Neuronal patterns
10^-2 Sec.
35. Neural firings (nural processes) 10^-3 Sec.
36. Membrane process (Ligand binding)
10^-4 Sec.
37. Chemical synthesis (Neurotransmitters) 10^-5 Sec.
Brain
Source: Gus Koehler, “A Framework for Visualizing the Chronocomplexity of Politically
Regulated Time-Ecologies,” Prepared for Presentation at International Society for the Study of
Time, 2001 Conference, Gorgonza, Italy, July 8-22, 2001.
This material is based upon work supported by the U.S. National Science Foundation under Grant No.
0083934. Any opinions, findings, and conclusions or recommendations expressed in this material are those
of the author and do not necessarily reflect the views of the National Science Foundation. Coinvestigating
institutions each with complementary research to this effort include, of which this document is Part I:
Arizona State University, University of Southern California, Institute for Law and Systems Research, and
Time Structures.
TIME STRUCTURES
Thoughts on Autonomous Agent
Temporal Design Issues
Elementary One-Dimensional Cellular Automata and 2 Worlds
Time -1
Ci-r(t-1)
…
Ci-1(t-1)
Ci (t-1)
Ci+1(t-1)
…
Ci+r(t-1)
Space -1
Ci(t)
Time 2
Space 2
Space
Instantiated Point
Ci (t-1)
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.
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
Two Dimensional Cellular Automata on a Matrix and Displayed as
Three dimensional Object
T1
T3
T2
T4
T5
T6
T7
T8
T1
Space at T1
Space at T1
T1
Tn
Source: Wolfram:http://www.wolframscience.com/nksonline/page-171
TIME STRUCTURES
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 simulation’s dimension except that
imposed from outside
•
There is nothing special about a cell’s discrete spatial landscape position
•
Emergent patterns are a series of past screen shots assembled outside of simulation’s
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
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
Nootemporal: Locally Warped Dante Space-Time
Close to GOD
Space/Time is organized
according to Closeness
To God
Heaven: eternity, no history, no future
Fixed forever with no movement; eternity
Purgatory: necessity
Of upward narrowing
movement in time; distance =
Relative suffering- space
Sin = Gravity of
Soul Space
Grace = Space/Time
Antidote
History: Body/Soul; Linear movement creates Sin-gravity;
Time ends; sin and Grace; physical space time extended
Movement.
Hell: no future; less and less movement
(colder) caused by increased Gravity of sin; eternity.
Sin/Grace = Local
Warp
Far From God
TIME STRUCTURES
An Example of a Partial Local Topology: The Dante and
Eootemporal Intersect
Eootemporal Dimension: Physical Laws
Nootemporal:
Dante Dimension
Rules for Placement and
Proximity
Space-Time Topology
Movement of the intersect
TIME STRUCTURES
Living Dimensions Crossing
Through
TIME STRUCTURES
“Puzzle Piece”
Two Agents as continuous
Event Streams
Pipe
Point 3
Various
Causal Processes
According
to temporality
Nootemporal
Foresight Horizon
Movement
Into Past
Point 2
Future
Developmental
Stage
Biotemporal
Political
Jurisdiction
Eootemporal
Point 1
Landscape
With no Agent
TIME STRUCTURES
Diagram: Local
Topology
Of Three Simulation
Points
Past Fading A
Future Approach A
Agent A: Heterochrony
of Nested
Temporalities
Local Landscape
(Spatial-Temporal)
Pipes with Velocity
Cones
Future Approach B
Agent B: Heterochrony
of Nested
Temporalities
Uneven Time Chunks
Future Approach B
Past fading B
Policy
Window
Simulation of Two Agents on Their
Landscapes Through Time
Various Long- and Short-Term
Cycles at Various Scales
TIME STRUCTURES
Requirements for Temporal Agent Based Simulation
Time is Background independent
Five dimensional agent and landscape
topology causally nested in local spacetime
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