Chaos, Complexity & Christianity

1. Chaos, Complexity & Christianity Carlos E. Puente University of California, Davis Université Interdisciplinaire de Paris Avril 11, 2012

2. esis We humans, with a soul, may learn from recent advancements regarding natural complexity in order to find peace…

3. Outline The hypotenuse: the pathway to peaceFaith lessons from chaotic fig trees

4. Pythagorean eorem c b a

5. A Game for Kids

6. A Game for Kids 70% 30%

7. A Game for Kids 70% 30%

8. A Game for Kids 70% 30% …

9. A Game for Kids 1 1 1 1 2 1 1 3 3 1 … game defines a multiplicative cascade

10. e Cascade, Twelve Levels Later intertwined thorns via layers having distinct densities ultimate support on each of the layers is dust game generates a multifractal

11. Another Game for Kids

12. Another Game for Kids

13. Another Game for Kids

14. Another Game for Kids cascadeyields equal disjoint thorns over dust varying the holesize gives topologically the layers on first game Moral: the two games are intimately related

15. Accumulated Masses of Clay ...simply from the dynamics of the games notchesabove: etc. plateausbelow: etc.

16. Accumulated Masses of Clay cumulative sets have no derivatives and are locally flat they have maximal lengths: also maximal combining the games and adding randomness

17. A Veritable Deception

18. A Veritable Deception

19. A Veritable Deception a devil’s staircase…

20. Fully-Developed Turbulence (Meneveau and Sreenivasan, 1987) eddies layers in one-dimensional turbulence as in first cascade dissipation:atmospheric, boundary layer, wake of a cylinder… universal

21. Our Turbulent Times inequities competition disparities discriminations forced equality fear selfishpostures and actions of the world under poverty kids diea day for lack of water violenceand terror…

22. An Optimal System? 5, 10, 20 and 40% largest thorns have 57, 70, 84 and 95% of the mass

23. An Optimal System? 5, 10, 20 and 40% largest thorns have 57, 70, 84 and 95% of the mass this is quite close to the United States: 59, 71, 84 and 95% Moral: as both cascades dissipatethe energy, if we ride them, they lead us to bite the dust

24. Common-Sense Code for Peace run cascade in reverse to achieve equilibrium live at low Reynolds numbers to avoid violence cut mountains and fill valleysto restore unity

25. Common-Sense Code for Peace run cascade in reverse to achieve equilibrium live at low Reynolds numbers to avoid violence cut mountains and fill valleysto restore unity

26. e Unique Geometric Solution 50-50 no holes a straight and solid condition without thornsor dust the hypotenuse is the path of peace! Moral: humbly rectify and loveeveryone to find truth

27. A Veritable Invitation

28. A Veritable Invitation to the Origin…

29. Equilibrium is an Improbable Point it is hypocriticalto judge if we are “far away” from the point a convex surface is found for a finitenumber of levels: balanceis found easily aided by gravity in truth there is darknessbetween 6and 9…

30. Our Options equilibrium calmness rectitude fifty-fifty shortest reconciliation integration, wholeness unity positive, to the future turbulence violence wickedness inequity longest separation division, emptiness dust negative, to the past

31. Pathways Two options before us two pathways ahead, the one is the longest the other straight. We journey directly or go by the legs, we follow intently or end up in pain. By walking the flatness or hiking the spikes, we travel in lightness or take serious frights. e incentive is unity and the call proportion, the key is forgiveness and the goal true notion. In wandering wickedness there is never fruit, but in ample humbleness one encounters the root.

32. e Fig Tree & e Bible Adam and Eve covered with fig leaves (Gn 3:7) A symbol of Israel together with the vine (Hos 2:14) King Hezekiah healed by prophet Isaiah (Is 38:21) Nathanael is seen under the fig tree (Jn 1:47–51) The parable of the barren fig tree (Lk 13:6–9) Jesus curses a fruitless fig tree (Mt 21:18–22, Mk 11:12–23) The lesson from a fig tree (Mk 13:28–31, Lk 21:29–33)

33. e Logistic Map ...a population of “rabbits” as a function of time different cases depending on the parameter :

34. e Logistic Map ...a population of “rabbits” as a function of time different cases depending on the parameter :

35. e Logistic Map ...a population of “rabbits” as a function of time different cases depending on the parameter :

36. From the Origin to Bifurcations

37. From the Origin to Bifurcations

38. From the Origin to Bifurcations period 2

39. From the Origin to Bifurcations period 4 period 2

40. Periodicities and Chaos Intertwined aperiodic aperiodic

41. Periodicities and Chaos Intertwined aperiodic period 5 aperiodic period 3

42. e Diagram of Bifurcations the tree contains periodic behavior, for any natural number

43. Dust Galore & Self-Similarity after the dusty strange attractors are common in the periodic “buds” there are small copies of the tree:

44. Intermediate Bud of Period 3 and similar for all intermediate buds of period 9 and all others

45. orns Galore the chaotic tree contains many multifractalthorns they combine imbalances and holes, as in : they happen at ends of white bands of buds for all periods

46. Universality on the Fig Tree (Feigenbaum, 1978) bifurcations happen in an orderly fashion: openings durations

47. Universality on Other Chaotic Trees straight root, “tender branch,” branches, and dust (“fig leaves”) relevant in biology, ecology, chemistry, physics, economics… the dynamics of convection are reproduced if 𝛼 is heat

48. In the Summit of Chaos all appears to wander in a dusty “strange attractor” when :

49. In the Summit of Chaos all appears to wander in a dusty “strange attractor” when : however, unstable extensions of the tree need to be excluded:

50. Oscillations on the Summit pre-images of eventual repetitions every three generations are not in attractor similar trees for other points need to be excluded, and for every period the ultimate attractor is therefore dust