e delightful and comforting joy of the holy trinity
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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 - PowerPoint PPT PresentationTRANSCRIPT
e delightful and comforting joy of the Holy Trinity
THE GEOMETRY OF EVANGELII GAUDIUM
Ateneo Pontificio Regina ApostolorumRome, March 2014
Carlos E. PuenteUniversity of California, Davis
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 down the quantity
Mountain-like profiles(Barnsley, 1988)
now join from left to right and go up and down the 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 thorns over dust
a universal process that ends in dissipation
Turbulence and multifractals(Meneveau and Sreenivasan, 1987)
⋮
the spiky set is the histogram of points obtained while iterating:
using a 70-30 biased coin step by step
Turbulence and multifractals(Meneveau and Sreenivasan, 1987)
⋮
the spiky set is the histogram of points obtained while iterating:
using a 70-30 biased coin step by step
wires and textures are related: histograms over y? hydrology?
A geometric approach to complexity(Puente, 1992, 1994)
A geometric approach to complexity(Puente, 1992, 1994)
is “illumination” on a wire and 𝑑𝑦 is derived
projection
A geometric approach to complexity(Puente, 1992, 1994)
is “illumination” on a wire and 𝑑𝑦 is derived
projection
is also a transformation of turbulence
A geometric approach to complexity(Puente, 1992, 1994)
is “illumination” on a wire and 𝑑𝑦 is derived
projection
is also a transformation of 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)
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 conduction related
toLOVE
The limit in the case + –(Puente et al., 1996)
is a Gaussian curve for any non-discrete
a surprising bridge from dissipation to conduction related
toLOVE
case - - yields oscillations between two bells
Gaussians everywhere!(Puente and Klebanoff, 1994)
Gaussians everywhere!(Puente and Klebanoff, 1994)
elliptical bells also happen and oscillations among bells
Gaussians everywhere!(Puente and Klebanoff, 1994)
elliptical bells also happen and oscillations among bells
portions of the wire also define bells, ad infinitum
Gaussians everywhere!(Puente and Klebanoff, 1994)
elliptical bells also happen and oscillations among bells
portions of the wire also define bells, ad infinitum
proof of higher-dimensional Gaussian remains elusive
Treasures inside the bell(Puente, 2003)
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 + +
The limit in the case + +
a delightful bell concentrated at infinity
The limit in the case + +
a delightful bell concentrated at infinity
the maximally positive wire filters any disorder and reflects
true LOVE
The limit in the case + +
a delightful bell concentrated at infinity
the maximally positive wire 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 Spirit that comes from them
On the life of Jesus Christ and beyond
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
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
More on the Holy Spirit
an “angel-winged” transformation containing infinite unity
More on the Holy Spirit
an “angel-winged” transformation containing infinite unity
as the Holy Spirit is reflected in the loving spiral of number
More on the Holy Spirit
an “angel-winged” transformation containing infinite unity
as the Holy Spirit is reflected in the loving spiral of number
it is also seen in the irrational number , for the calculus of love
yields
Yet more on the Holy Spirit
also from Jesus’ parable of the vine and the branches:
I. Jesus is the vine, the essence, or number 1
Yet more on the Holy Spirit
also from Jesus’ parable of the vine and the branches:
I. Jesus is the vine, the essence, or number 1II. we are the branches, who pick up the cross and follow,
Yet more on the Holy Spirit
also from Jesus’ parable of the vine and the branches:
I. Jesus is the vine, the essence, or number 1II. we are the branches, who pick up the cross and follow,
III. if we stay with Him and Him in us,
Yet more on the Holy Spirit
also from Jesus’ parable of the vine and the branches:
I. Jesus is the vine, the essence, or number 1II. we are the branches, who pick up the cross and follow,
III. if we stay with Him and Him in us,
IV. we may ask God and get power,
Yet more on the Holy Spirit
also from Jesus’ parable of the vine and the branches:
I. Jesus is the vine, the essence, or number 1II. we are the branches, who pick up the cross and follow,
III. if we stay with Him and Him in us,
IV. we may ask God and get power,
V. Therefore, in the pruning of sanctification: = e , the Holy Spirit
The Eucharistic Doxology
Through Christ, , with Him, , and in Him, ,
O God, almighty Father, , in the unity of the Holy Spirit, ,
all glory and honor is yours, for ever and ever, AMEN.
Trinitarian numbers
always found on each block: 0, 1 and ∞
Trinitarian numbers
always found on each block: 0, 1 and ∞
the Father in , the Son in , and the Holy Spirit in
Trinitarian numbers
always found on each block: 0, 1 and ∞
the Father in , the Son in , and the Holy Spirit in
the “irrationals” in the formula of the bell invite us to
freedom!
𝑓 (𝑥 )= 1
√2𝜋𝑒−𝑥
2 /2
Our options
conduction
infiniteness
plenitude
trust
dissipation
finiteness
solitude
disbelief
Our options
conduction
infiniteness
plenitude
trust
faith
freedom
one day at a
time
harmony
dissipation
finiteness
solitude
disbelief
doubts
slavery
anxiety
intermittency
Our options
conduction
infiniteness
plenitude
trust
faith
freedom
one day at a
time
harmony
light
heavenly
always +
Love
dissipation
finiteness
solitude
disbelief
doubts
slavery
anxiety
intermittency
darkness
earthly
a bit −
else
e amazing bell
e bell peals silent, o o
reflecting its peace,and inside it gatherslovely masterpiece.
Symmetric pure beauty, o o
o mighty delight,this limit in fullnessstores life’s designs.
Such vessel contains, o o
alephs of all tastes,diatoms and crystals
including DNA.
But there is a case, o o
reason to this call:the forward
selectionthat raises it all.
ere is clear choicethat rotates the 8,by loving sincerely
we surely converge.
Notice, this is cogent:the bell's central
theme,by living in freedom
one fulfills the dream.
There is transformation
that kindles the heart,by loving in plenitude
we become smart.
For love mends the spiky
and takes to the clouds,
by living the presentone joins blessed
crowd.
O see, this is truthful:the plus all the way,by loving the enemywe learn how to play.
Dimensional growth,oh essence of life,
by living in harmonyone nails normal plan.
O notice the symbols,oh irrational might,by loving simplicitywe experience the
light.
O listen, you colleague,
let's go out the cave,by living in unity
we shall all prevail.
O notice, my friend,the plea from a bell,by loving and lovingjoy will have no end.
e antidoteFrom x into yas unnatural
flow,mapping
immensityleaving dust
below.
From x into yinspiring all
awe,o plus of libertyforever aglow.
From x into yonly a tiny
piece,wired to totality
o normal release.
From x into yo infinite fleece,
by packing vitality
no thorns but peace.
From x into ysingular the
dough,symphony of
unitybreeding single
row.
From x into yby breaking a
spell,amazing simplicity
o refuge from hell.
From x into yfrom holy plateau,perennial immunity
o spirit on the go.
From x into ytriune is the
cell,omnipotent
divinityo sacred God's
bell.
Y = X
Y = Xis justice that illuminates,
is balance that fascinates:
Y = X.
Y = Xis the practical alliance,
is the precious reliance:Y = X.
Y = Xis true word that
matures,is a spiral that endures:
Y = X.
Y = Xis the spotless resting
place,is the state of mighty
grace:Y = X.
Y = Xis smoothness that
esteems,is a lovely dove that
gleams:Y = X.
Y = Xis the short and precious root,
is the weaving of the truth:Y = X.
Y = Xis a future that
forgives,is crowned science that
is:Y = X.
Y = Xis the ever tender
tune,is the impartial tribune:
Y = X.
Y = Xis all innocence that
heeds,is a garden with no
weeds:Y = X.
Y = Xis the simple clear sign,is the majestic design:
Y = X.
Y = Xis brotherhood that
heals,is diversity that
shields:Y = X.
Y = Xis the real chaste
embrace,is the goodness of a
yes:Y = X.
Y = Xis a smile that edifies,is a spin that rectifies:
Y = X.
Y = Xis all gentleness in us,is the everlasting plus:
Y = X.
Y = Xis inspiration that calls,is growing to be small:
Y = X.
Y = Xis the forgotten
territory,is the improbable
story:Y = X.
Y = Xis revelation that nests,
is surrendering the rest:
Y = X.
Y = Xis the dustless short
incline,is the faithful narrow
line:Y = X.
Y = Xis renouncing all
spears,is experiencing no
fears:Y = X.
Y = Xis the perennial
giveaway,is pure life with no
decay:Y = X.
Y = Xis the only perfect
remedy,is loving, even the
enemy:Y = X.
Y = Xis revelation that nests,
is surrendering the rest:
Y = X.
Y = Xis the dustless short
incline,is the faithful narrow
line:Y = X.
Y = Xis renouncing all
spears,is experiencing no
fears:Y = X.
Y = Xis the perennial
giveaway,is pure life with no
decay:Y = X.
Y = Xis the only perfect
remedy,is loving, even the
enemy:Y = X.