e delightful and comforting joy of the holy trinity the geometry of evangelii gaudium ateneo...

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.