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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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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 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…
Mountain-like profiles(Barnsley, 1988) seeking extensions to mountain surfaces to study evolution of rivers …
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
Mountain-like profiles(Barnsley, 1988) now join from left to right and go up and downthe quantity
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
Other interesting profiles(Barnsley, 1988) case + - is the mountain case - - alternates ups and downs case + + gets new points always going up
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
Other interesting profiles(Barnsley, 1988) wires may also be found iterating two linear maps:
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
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
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
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?
A geometric approach to complexity(Puente, 1992, 1994) is “illumination” on a wire and 𝑑𝑦is derived projection
A geometric approach to complexity(Puente, 1992, 1994) is “illumination” on a wire and 𝑑𝑦is derived projection is also a transformationof turbulence
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
Projections galore varying interpolating points with statistics as in natural data sets
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
Extensions to higher dimensions(Puente, 1994) a pollution pattern based on a wire in four dimensions similarly for rainfall patterns and others…
The limit in the case + –(Puente et al., 1996) is a Gaussian curve for any non-discrete
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
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
Gaussians everywhere!(Puente and Klebanoff, 1994) elliptical bells also happenand oscillationsamong bells
Gaussians everywhere!(Puente and Klebanoff, 1994) elliptical bells also happenand oscillationsamong bells portions of the wire also define bells, ad infinitum
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
Treasures inside the bell(Puente, 2003) superposition of many lovely patterns give perfect circles
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
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
The limit in the case + + a delightful bell concentrated at infinity
The limit in the case + + • a delightful bell concentrated at infinity • the maximally positivewire filters any disorder and reflects true LOVE
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?
The limit in the case + + dx may be any process yielding a power-law,
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
e majestic trilogy the Father mighty in heaven the Son always perfect and positive and the Holy Spiritthat comes from them
On the life of Jesus Christ and beyond His birth and miracles, the Eucharist in “a piece of the wire”
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
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
Other matters of faith “look not on our sins, but on the faith of your Church”
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”
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”
More on the Holy Spirit an “angel-winged” transformationcontaining infinite unity
More on the Holy Spirit an “angel-winged” transformationcontaining infinite unity as the Holy Spirit is reflected in the loving spiral of number