1. FROM MODERN SCIENCE TO GOD’S MERCY A merciful lesson from a chaotic fig tree Carlos E. Puente University of California, Davis

2. Thesis We humans, with a soul, may learn from recent advancements regarding the geometry of natural complexity in order to fully grasp the boundless nature of God’s mercy and take on 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) a symbol 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) 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)

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

9. The logistic dynamics

16. e diagram of bifurcations

17. the tree contains periodic behavior, for any natural number

18. e diagram of bifurcations

21. Intermediate bud of period 3

22. … exquisite self-similarity ad infinitum

23. Thorns galore

24. they happen at ends of white bands of buds for all periods

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

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”)

29. In the summit of chaos

30. 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 middle paint an inverted square root! the ideas remind us of the concept of purgatory

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

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

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

41. A merciful scientific prophetic tree?

42. an allegorical fig tree without fruit, consistently cursed

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

44. A merciful 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

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 o ff set 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 o ff ers 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”

51. Other coincidences the four states on the parable of the sower: fruit in the root Y = X is “our shelter from the wind” “abandon yourself, pick up your + and follow me” “whoever loses his life for my sake will save it” “if a grain of wheat dies, it produces much fruit”

52. Other coincidences the four states on the parable of the sower: fruit in the root Y = X is “our shelter from the wind” “abandon yourself, pick up your + and follow me” “whoever loses his life for my sake will save it” “if a grain of wheat dies, it produces much fruit” in the summit of chaos: wheat vs. chaff, sheep vs. goats “though 1,000 fall at your side, 10,000 at your right…” “can you bury the haughty in the dust together?”

53. Other coincidences the four states on the parable of the sower: fruit in the root Y = X is “our shelter from the wind” “abandon yourself, pick up your + and follow me” “whoever loses his life for my sake will save it” “if a grain of wheat dies, it produces much fruit” in the summit of chaos: wheat vs. chaff, sheep vs. goats “though 1,000 fall at your side, 10,000 at your right…” “can you bury the haughty in the dust together?” “people do not pick figs from thornbushes” the power of sainthood is visualized geometrically: the escape point from chaos is the Ω point

54. Le plus improbable In the most hellish beat a silly and vain defeat also a spectacle disjoint an epsilon from the point chaudement guérissable oh purgation ineffable oh victoire admirable oh miracle vénérable In the symbolic tree thorns, dust in a spree but in humble zero set line cancels all debt In the unbent choice always a clear voice an appointed up lift deterministic a gift In the highest ugly heat almost never a repeat sad travel with no rest ever close to the best sûrement misérable oh détour incroyable dynamique indésirable étrange état exécrable également déplorable périodicité interminable obstination reprochable oh hasard inévitable In the real driving seat surely a fantastic feat a way to erected root faithful relief and fruit égoïsme détectable oh fractal pitoyable oh origine inégalable oh paradis inaltérable oh l'amour véritable oh poème formidable miséricorde verifiable oh le plus improbable

55. A unique merciful way