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 e delightful and comforting joy of the Holy Trinity

THE GEOMETRY OF EVANGELII GAUDIUM.  e delightful and comforting joy of the Holy Trinity. Carlos E. Puente University of California, Davis. Ateneo Pontificio Regina Apostolorum Rome, March 2014. Thesis We humans, with a soul, may learn from recent advancements

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 e delightful and comforting joy of the Holy Trinity

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  1. THE GEOMETRY OF EVANGELII GAUDIUM e delightful and comforting joy of the Holy Trinity 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. Mountain-like profiles(Barnsley, 1988) seeking extensions to mountain surfaces to study evolution of rivers …

  4. Mountain-like profiles(Barnsley, 1988) first join the left, middle, and right points from the middle of the two segments go up and down a quantity z

  5. Mountain-like profiles(Barnsley, 1988) now join from left to right and go up and downthe quantity

  6. Mountain-like profiles(Barnsley, 1988) now join from left to right and go up and downthe quantity … the mountain arises adding more points up and down in powers of z

  7. Other interesting profiles(Barnsley, 1988) case + - is the mountain case - - alternates ups and downs case + + gets new points always going up

  8. Other interesting profiles(Barnsley, 1988) case + - is the mountain case - - alternates ups and downs case + + gets new points always going up as z increases, the fractal wires become infinite and fill more space

  9. Other interesting profiles(Barnsley, 1988) wires may also be found iterating two linear maps:

  10. Other interesting profiles(Barnsley, 1988) wires may also be found iterating two linear maps: the signs correspond to those of and,with magnitudes equal to z

  11. Turbulence and multifractals (Meneveau and Sreenivasan, 1987) • a cascade of eddies generating intermittent violence • progressive fragmentation leading to thornsover dust • a universal process that ends in dissipation

  12. Turbulence and multifractals (Meneveau and Sreenivasan, 1987) the spiky setis the histogram of points obtained while iterating: using a 70-30 biasedcoin step by step

  13. Turbulence and multifractals (Meneveau and Sreenivasan, 1987) the spiky setis the histogram of points obtained while iterating: using a 70-30 biasedcoin step by step wires and textures are related: histograms over y? hydrology?

  14. A geometric approach to complexity(Puente, 1992, 1994)

  15. A geometric approach to complexity(Puente, 1992, 1994) is “illumination” on a wire and 𝑑𝑦is derived projection

  16. A geometric approach to complexity(Puente, 1992, 1994) is “illumination” on a wire and 𝑑𝑦is derived projection is also a transformationof turbulence

  17. A geometric approach to complexity(Puente, 1992, 1994) is “illumination” on a wire and 𝑑𝑦is derived projection is also a transformationof turbulence “shadow” appears random but is entirely deterministic

  18. Projections galore varying interpolating points with statistics as in natural data sets

  19. A detailed storm in Boston(Puente and Obregón, 1996) a model projection (center) of a real data set (right) model also preserves statistical and chaotic features of data

  20. Extensions to higher dimensions(Puente, 1994) a pollution pattern based on a wire in four dimensions similarly for rainfall patterns and others…

  21. The limit in the case + –(Puente et al., 1996)

  22. The limit in the case + –(Puente et al., 1996) is a Gaussian curve for any non-discrete

  23. The limit in the case + –(Puente et al., 1996) is a Gaussian curve for any non-discrete a surprising bridge from dissipation to conductionrelated toLOVE

  24. The limit in the case + –(Puente et al., 1996) is a Gaussian curve for any non-discrete a surprising bridge from dissipation to conductionrelated toLOVE case - - yields oscillations between two bells

  25. Gaussians everywhere!(Puente and Klebanoff, 1994)

  26. Gaussians everywhere!(Puente and Klebanoff, 1994) elliptical bells also happenand oscillationsamong bells

  27. Gaussians everywhere!(Puente and Klebanoff, 1994) elliptical bells also happenand oscillationsamong bells portions of the wire also define bells, ad infinitum

  28. Gaussians everywhere!(Puente and Klebanoff, 1994) elliptical bells also happenand oscillationsamong bells portions of the wire also define bells, ad infinitum proof of higher-dimensional Gaussian remains elusive

  29. Treasures inside the bell(Puente, 2003)

  30. Treasures inside the bell(Puente, 2003) superposition of many lovely patterns give perfect circles

  31. Treasures inside the bell(Puente, 2003) superposition of many lovely patterns give perfect circles in the space-filling limit there is hidden order in chance

  32. Designs inside the bell(Puente, 2003) suitable iterations of simple maps yield arbitrary ice crystals the rosette of DNA is coded via the binary expansion of π

  33. The limit in the case + +

  34. The limit in the case + + a delightful bell concentrated at infinity

  35. The limit in the case + + • a delightful bell concentrated at infinity • the maximally positivewire filters any disorder and reflects true LOVE

  36. The limit in the case + + • a delightful bell concentrated at infinity • the maximally positivewire filters any disorder and reflects true LOVE • Where, O death, is your victory? Where, O death, is your sting?

  37. The limit in the case + + dx may be any process yielding a power-law,

  38. The limit in the case + + dx may be any process yielding a power-law, distributions of natural and man-made complexity: “heavy tails” as in earthquakes, wars, and wealth inequalities

  39. e majestic trilogy the Father mighty in heaven the Son always perfect and positive and the Holy Spiritthat comes from them

  40. On the life of Jesus Christ and beyond

  41. On the life of Jesus Christ and beyond His birth and miracles, the Eucharist in “a piece of the wire”

  42. On the life of Jesus Christ and beyond His birth and miracles, the Eucharist in “a piece of the wire” unity with the Father, baptism, transfiguration, resurrection, and Ascension

  43. On the life of Jesus Christ and beyond His birth and miracles, the Eucharist in “a piece of the wire” unity with the Father, baptism, transfiguration, resurrection, and Ascension Assumption of Mary and rapture of the Church, St. Augustine

  44. Other matters of faith

  45. Other matters of faith “look not on our sins, but on the faith of your Church”

  46. Other matters of faith “look not on our sins, but on the faith of your Church” “love covers a multitude of sins,” “the flesh produces death, but the Spirit life”

  47. Other matters of faith “look not on our sins, but on the faith of your Church” “love covers a multitude of sins,” “the flesh produces death, but the Spirit life” “the law is only a shadow,” “everlasting sin against the Holy Spirit”

  48. More on the Holy Spirit

  49. More on the Holy Spirit an “angel-winged” transformationcontaining infinite unity

  50. More on the Holy Spirit an “angel-winged” transformationcontaining infinite unity as the Holy Spirit is reflected in the loving spiral of number

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