A creative apologetics about our eternal destiny based on chaos theory

1. THE GEOMETRY OF EVANGELII GAUDIUM A creative apologetics about our eternal destiny based on chaos theory Carlos E. Puente University of California, Davis Ateneo Pontificio Regina Apostolorum Rome, March 2014

2. Thesis We humans, with a soul, may learn from recent advancements regarding the geometry of natural complexity in order to fill our hearts with the joy of the Gospel and take the mission to share the good news in a renewed fashion…

3. e fig tree and Holy Scripture Adam and Eve covered with fig leaves (Gn 3:7) asymbol of Israel together with the vine (Hos 2:14) King Hezekiah healed by prophet Isaiah (Is 38:21)

4. e fig tree and Holy Scripture Adam and Eve covered with fig leaves (Gn 3:7) asymbol 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)

5. e logistic map ... a population of “rabbits” as a function of time

6. e logistic map ... a population of “rabbits” as a function of time

7. e logistic map ... a population of “rabbits” as a function of time

8. e logistic map ... a population of “rabbits” as a function of time different cases depending on the parameter :

9. The logistic dynamics

10. The logistic dynamics

11. The logistic dynamics period 2

12. The logistic dynamics period 4 period 2

13. The logistic dynamics period 4 period 2 period

14. The logistic dynamics aperiodic strange aperiodic chaos

15. The logistic dynamics aperiodic period 5 aperiodic period 3

16. e diagram of bifurcations

17. e diagram of bifurcations the tree contains periodic behavior, for any natural number

18. e diagram of bifurcations

19. e diagram of bifurcations after the dusty strange attractors are common

20. e diagram of bifurcations after the dusty strange attractors are common in the white bands there are the “buds”of the tree

21. Intermediate bud of period 3

22. Intermediate bud of period 3 … exquisite self-similarityad infinitum

23. Thorns galore the chaotic tree contains many multifractalthorns they combine imbalances and holes, as in :

24. Thorns 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

25. Universality on the fig tree (Feigenbaum, 1978) bifurcations happen in an orderly fashion: openings durations

26. Universality on other chaotic trees straight root, “tender branch,” branches, and dust (“fig leaves”)

27. Universality on other chaotic trees straight root, “tender branch,” branches, and dust (“fig leaves”) relevant in biology, ecology, chemistry, physics, economics…

28. 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 is heat (Libchaber, 1979)

29. In the summit of chaos all appears to wander in a compact strange attractor when :

30. In the summit of chaos all appears to wander in a compact strange attractor when : however, unstable extensions of the tree need to be excluded:

31. Oscillations on the summit pre-images of eventual repetitions every three generations are not part of the attractor:

32. Oscillations on the summit pre-images of eventual repetitions every three generations are not part of the attractor: similar trees for every period need to be excluded …

33. Oscillations on the summit pre-images of eventual repetitions every three generations are not part of the attractor: similar trees for every period need to be excluded … the strange attractor is therefore dust

34. An escape to the origin there are also few points that improbably return to the root pre-images of zero rest despite high heat:

35. An escape to the origin there are also few points that improbably return to the root pre-images of zero rest despite high heat: points associated with the middle paint an inverted square root!

36. An escape to the origin there are also few points that improbably return to the root pre-images of zero rest despite high heat: points associated with the middlepaint an inverted square root! the ideas remind us of the concept of purgatory

37. Plain common sense it is much better not to miss thepoint! in order to avoid chaos and its infernal turbulence:

38. Plain common sense it is much better not to miss thepoint! in order to avoid chaos and its infernal turbulence: come down the tree lowering your heat to find the root

39. Plain common sense it is much better not to miss thepoint! in order to avoid chaos and its infernal turbulence: come down the tree lowering your heat to find the root abandon yourself to the threshold, , to reach the Origin

40. Plain common sense it is much better not to miss thepoint! in order to avoid chaos and its infernal turbulence: come down the tree lowering your heat to find the root abandon yourself to the threshold, , to reach the Origin move away from nonlinearities () to escape thorns and dust

41. A scientific prophetic tree?

42. A scientific prophetic tree? • an allegorical fig tree without fruit, consistently cursed

43. A scientific prophetic tree? • an allegorical fig tree without fruit, consistently cursed • this tree and other trees have tender branches and many buds

44. A scientific prophetic tree? • an allegorical fig tree without fruit, consistently cursed • this tree and other trees have tender branches and many buds • the ax is at the root of the trees, Nathanael is at the root • we may curse the fig tree as He rebuked the wind

45. Our options order simplicity serenity peace disorder complexity turbulence chaos

46. Our options order simplicity serenity peace decreasing God’s way below abandonment disorder complexity turbulence chaos increasing our way above selfishness

47. Our options order simplicity serenity peace decreasing God’s way below abandonment obedience blessing resting Heaven disorder complexity turbulence chaos increasing our way above selfishness rebelliousness curse wandering hell

48. Feigenbaum’s parabel Foliage of disorder trapped in empty dust, jumps astir forever enduring subtle thrust. Crossing of the outset leaving faithful root looming tender offset failing to yield fruit Cascade of bifurcations, increasing heat within, inescapable succession of branches bent by wind. Sprouting of dynamics attracted to the strange, o infinity reminding at the origin: the flame. Could it be, oh my friends that science offers a rhyme? For a rotten tree foretells the very advent of time. Could it be, oh how plain, that nature extends a call? For old parable proclaims the crux in growing small.

49. In the midst of chaos there is a small gate leading to fine rest. In the midst of chaos there are loyal paths inviting to a dance. On top of the fig tree there is a key point that runs to the core. On top of the fig tree there is a clear light that averts a fright. In the midst of chaos there is leaping game discerning the way. In the midst of chaos there is a fine well watering the brain. On top of the fig tree there is a clean frame that cancels the blame. On top of the fig tree there is mighty help that shelters from hell.

50. Other coincidences • the four states on the parable of the sower: fruit in the root • Y = X is “our shelter from the wind”