e Faith of a Hydrologist

Carlos E. PuenteUniversity of California, Davis

Ateneo Pontificio Regina ApostolorumRoma, Aprile 17, 2012

esis

We humans, with a soul,

may learn from recent advancements

regarding natural complexity

in order to find peace…

different shapes depend on signs of and

(Barnsley, 1988)Simple Maps and Fractal Wires

(0,0) (1,0)

(1/2, 1)

⋮

𝑤1 (𝑥 )=𝑥2,𝑤2 (𝑥 )= 𝑥

2+12

70% 30%

gives a multifractal using a biased coin

(Meneveau and Sreenivasan, 1987)Cascades, Turbulence and Multifractals

is “illumination” on a wire and 𝑑𝑦 is derived projection

is also a “transformation” of turbulence

“shadow” appears random but is entirely

deterministic

(Puente, 1992, 1994)A Platonic Approach to Complexity

Projections Galore

varying interpolating points

with statistics as in natural hydrologic sets

a model projection (center) of a real data set (right)

model also preserves statistical and chaotic features of

data

(Puente and Obregón, 1996)A Detailed Storm in Boston

a pollution pattern based on a wire in four

dimensions

similarly for rainfall patterns and others…

(Puente, 1994, 2004)Extensions to Higher Dimensions

is a Gaussian curve for any non-discrete

a surprising bridge from dissipation to conduction and

love

– – case yields oscillations between two bells

(Puente et al., 1996)Exploring the Limit: e + – Case

circular bells are the most common, but ellipticals do

happen

there are also cases producing oscillations among bells

proof of higher-dimensional Gaussian remains elusive

(Puente and Klebanoff, 1994)Mighty Gaussians Everywhere!

superposition of many lovely patterns give perfect

circles

in the space-filling limit there is hidden order in chance

(Puente, 2003)Treasures Inside the Bell

suitable iterations of simple maps yield arbitrary ice

crystals

the rosette of DNA is coded via the binary expansion of

π

(Puente, 2003)Designs Inside the Bell

A Truly Special + + Case

a delightful-sounding bell concentrated at infinity

the wire that is maximally positive filters any disorder:

Where, O death, is your victory? Where, O death, is

your sting?

e Majestic Trilogy

the Father mighty in heaven

the Son always perfect and positive

and the Holy Spirit that comes from them… St.

Augustine

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

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 of good things to come”

On the Unity of the Holy Spirit

“angel-winged” transformation via midpoint additions of infinite

unity

the Holy Spirit is also seen in the number and the irrational number

, and the calculus of love is integration without differentiation:

also, from Jesus’ parable of the vine and the branches:

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

these irrational numbers are part of the formula for the bell—

integral to freedom

𝑓 (𝑥 )= 1

√2𝜋𝑒−𝑥

2 /2

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,reflecting its peace,

and inside it gathers

lovely masterpiece.

Symmetric pure beauty,

o mighty delight,this limit in fullness

stores life’s designs.

Such vessel contains,

alephs of all tastes,diatoms and

crystalsincluding DNA.

But there is a case,reason to this call:

the forward selection

that raises it all.

ere is clear choicethat rotates the 8,by loving sincerely

we surely converge.