Time and Simulation

1. 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.netWWW.Timestructures.com

2. 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

3. 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-timetopologyproblem 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 The Basic Problem

4. 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

5. 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-ecologyor 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 localproximity 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. Characteristics of Time (Continued) TIME STRUCTURES

6. 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. • Kaluza’s dimensions? Topologically, three are extended and one is tightly curled up much like Riemann’s wrinkles. TIME STRUCTURES

7. Five Temporalities and Associated Causalities • Nootemporal: a noetic (symbolic) intentionality. • Propagatesvia 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), • Distinguishespast 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. 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

8. 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“

9. 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.

10. 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 Time Usual & Mistaken Correct

11. 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 STRUCTURES

12. 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 Characteristics (Continued) TIME STRUCTURES

13. 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

14. 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

15. TIME STRUCTURES Source: Victoria Koehler-Jones, 1999.

16. TIME STRUCTURES

17. Application: Public Policy Making and Implementation

18. Public Policy Time-Ecology Extended From The Past Into The Future TIME STRUCTURES

19. Replace Table 1, p. 47 TIME STRUCTURES

20. Replace Table 1, p. 48 TIME STRUCTURES

21. Thoughts on Autonomous Agent Temporal Design Issues

22. Space Elementary One-Dimensional Cellular Automata and 2 Worlds Time -1 Space -1 Time 2 Space2 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

23. 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: Wolfram:http://www.wolframscience.com/nksonline/page-171

24. 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

25. 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

26. Close 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 History: Body/Soul; Linear movement creates Sin-gravity; Time ends; sin and Grace; physical space time extended Movement. Sin = Gravity of Soul Space Grace = Space/Time Antidote Sin/Grace = Local Warp Hell: no future; less and less movement (colder) caused by increased Gravity of sin; eternity. Nootemporal: Locally Warped Dante Space-Time Space/Time is organized according to Closeness To God Far From God TIME STRUCTURES

27. Eootemporal Dimension: Physical Laws Nootemporal: Dante Dimension Rules for Placement and Proximity Space-Time Topology An Example of a Partial Local Topology: The Dante and Eootemporal Intersect Movement of the intersect TIME STRUCTURES

28. Living Dimensions Crossing Through TIME STRUCTURES

29. “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

30. 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 Uneven Time Chunks Future Approach B 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

31. 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