2. Learn an urgent lesson from a chaotic g tree! fi Carlos E. Puente University of California, Davis THE KEY ROLE OF SCIENCE IN THE NEW EVANGELIZATION Ateneo Ponti cio Regina Apostolorum fi Rome, May 2013
Feb 23, 2016
2. Learn an urgent lesson from a chaotic fig tree!
Carlos E. PuenteUniversity of California, Davis
THE KEY ROLE OF SCIENCE IN THE NEW EVANGELIZATION
Ateneo Pontificio Regina ApostolorumRome, May 2013
ThesisWe humans, with a soul,
may learn from recent advancements
regarding natural complexity
in order to find the peace of Christ
and share the good news in a novel way…
e fig tree and Holy Scripture
Adam and Eve covered with fig leaves (Gn 3:7)
a symbol of Israel together with the vine (Hos
2:14)
King Hezekiah healed by prophet Isaiah (Is
38:21)
e fig tree and Holy Scripture
Adam and Eve covered with fig leaves (Gn 3:7)
a symbol of Israel together with the vine (Hos
2:14)
King Hezekiah healed by prophet Isaiah (Is
38:21)
Nathanael is seen under the fig tree (Jn 1:47–51)
the parable of the barren fig tree (Lk 13:6–9)
Jesus curses a fruitless fig tree (Mt 21:18–22, Mk
11:12–23)
the lesson from a fig tree (Mk 13:28–31, Lk
21:29–33)
e logistic map
... a population of “rabbits” as a function of time
𝑋𝑘+1=𝛼 𝑋𝑘 (1−𝑋𝑘 ) ,𝛼∈ [0,4 ]
e logistic map
... a population of “rabbits” as a function of time
𝑋𝑘+1=𝛼 𝑋𝑘 (1−𝑋𝑘 ) ,𝛼∈ [0,4 ]
e logistic map
... a population of “rabbits” as a function of time
𝑋𝑘+1=𝛼 𝑋𝑘 (1−𝑋𝑘 ) ,𝛼∈ [0,4 ]
𝛼=2.8
e logistic map
... a population of “rabbits” as a function of time
𝑋𝑘+1=𝛼 𝑋𝑘 (1−𝑋𝑘 ) ,𝛼∈ [0,4 ]
𝛼=2.8
different cases depending on the parameter :
The logistic dynamics
𝑋∞=0
0<𝛼≤1
𝑌=𝑋
The logistic dynamics𝑌=𝑋
𝑋∞=0
0<𝛼≤1 1<𝛼≤3
The logistic dynamics
𝑋∞=0
period 2
0<𝛼≤1
𝑌=𝑋
1<𝛼≤3
The logistic dynamics
1<𝛼≤3
period 4
𝑌=𝑋
𝑋∞=0
period 2
0<𝛼≤1
The logistic dynamics
1<𝛼≤3
period 4
𝑋∞=0
period 2
0<𝛼≤1
period
aperiodic
aperiodic
𝑌=𝑋(𝛼>𝛼∞≈3.5699)
The logistic dynamics
𝑌=𝑋
period 5aperiodic
period 3
(𝛼>𝛼∞≈3.5699)
aperiodic
The logistic dynamics
e diagram of bifurcations
e diagram of bifurcations
the tree contains periodic behavior, for any natural number
e diagram of bifurcations
e diagram of bifurcations
after the dusty strange attractors are common
e diagram of bifurcations
after the dusty strange attractors are commonin the white bands there are the “buds” of the tree
Intermediate bud of period 3
Intermediate bud of period 3
… exquisite self-similarity ad infinitum
Thorns galorethe chaotic tree contains many
multifractal thornsthey combine imbalances and holes, as
in :
Thorns galorethe chaotic tree contains many
multifractal thornsthey combine imbalances and holes, as
in :
they happen at ends of white bands of buds for all periods
Universality on the fig treebifurcations happen in an orderly fashion:
(Feigenbaum, 1978)
0…openings
…durations
Universality on other chaotic treesstraight root, “tender branch,” branches, and dust
(“fig leaves”)
𝑓 ( 𝑋 )=𝛼 𝑋 (1−𝑋 )3𝑓 ( 𝑋 )=𝛼 𝑋 (1− 𝑋 3 )
Universality on other chaotic treesstraight root, “tender branch,” branches, and dust
(“fig leaves”)
𝑓 ( 𝑋 )=𝛼 𝑋 (1−𝑋 )3𝑓 ( 𝑋 )=𝛼 𝑋 (1− 𝑋 3 )
relevant in biology, ecology, chemistry, physics, economics…
Universality on other chaotic treesstraight root, “tender branch,” branches, and dust
(“fig leaves”)
𝑓 ( 𝑋 )=𝛼 𝑋 (1−𝑋 )3𝑓 ( 𝑋 )=𝛼 𝑋 (1− 𝑋 3 )
relevant in biology, ecology, chemistry, physics, economics…the dynamics of convection are reproduced if is heat
(Libchaber, 1979)
In the summit of chaosall appears to wander in a compact strange
attractor when :
In the summit of chaos
however, unstable extensions of the tree need to be excluded:
all appears to wander in a compact strange attractor when :
Oscillations on the summitpre-images of eventual repetitions every three generations
are not part of the attractor:
Oscillations on the summitpre-images of eventual repetitions every three generations
are not part of the attractor:
similar trees for every period need to be excluded …
Oscillations on the summitpre-images of eventual repetitions every three generations
are not part of the attractor:
similar trees for every period need to be excluded …the strange attractor is therefore dust
An escape to the originthere are also few points that improbably return to the root
pre-images of zero rest despite high heat:
An escape to the originthere are also few points that improbably return to the root
pre-images of zero rest despite high heat:
points associated with the middle paint an inverted square root!
An escape to the originthere are also few points that improbably return to the root
pre-images of zero rest despite high heat:
points associated with the middle paint an inverted square root!
the ideas remind us of the concept of purgatory
Plain common senseit is much better not to miss the point!
in order to avoid chaos and its infernal turbulence:
Plain common senseit is much better not to miss the point!
in order to avoid chaos and its infernal turbulence:
come down the tree lowering your heat to find the root
Plain common senseit is much better not to miss the point!
in order to avoid chaos and its infernal turbulence:
come down the tree lowering your heat to find the rootabandon yourself to the threshold, , to reach the Origin
Plain common senseit is much better not to miss the point!
in order to avoid chaos and its infernal turbulence:
come down the tree lowering your heat to find the rootabandon yourself to the threshold, , to reach the Originmove away from nonlinearities () to escape thorns and
dust
A scientific prophetic tree?
A scientific prophetic tree?
an allegorical fig tree without fruit, consistently cursed
A scientific prophetic tree?
an allegorical fig tree without fruit, consistently cursedthis tree and other trees have tender branches and
many buds
A scientific prophetic tree?
an allegorical fig tree without fruit, consistently cursedthis tree and other trees have tender branches and
many budsthe ax is at the root of the trees, Nathanael is at the
rootwe may curse the fig tree as He rebuked the wind
Our optionsorder
simplicityserenitypeace
disordercomplexityturbulence
chaos
Our optionsorder
simplicityserenitypeace
decreasingGod’s way
below Y = Xabandonment
disordercomplexityturbulence
chaosincreasingour way
above Y = Xselfishness
Our optionsorder
simplicityserenitypeace
decreasingGod’s way
below Y = Xabandonment
obedienceblessingrestingHeaven
disordercomplexityturbulence
chaosincreasingour way
above Y = Xselfishness
rebelliousnesscurse
wanderinghell
Feigenbaum’s parabel
Foliage of disordertrapped in empty
dust,jumps astir forever
enduring subtle thrust.
Crossing of the outset
leaving faithful rootlooming tender
offsetfailing to yield fruit
Cascade of bifurcations,
increasing heat within,
inescapable succession
of branches bent by wind.
Sprouting of dynamics
attracted to the strange,
o infinity remindingat the origin: the
flame.
Could it be, oh my friends
that science offers a rhyme?
For a rotten tree foretells
the very advent of time.
Could it be, oh how plain,
that nature extends a call?
For old parable proclaims
the crux in growing small.
In the midst of chaos
there is a small gate
leading to fine rest.
In the midst of chaos
there are loyal paths
inviting to a dance.
On top of the fig tree
there is a key pointthat runs to the
core.
On top of the fig tree
there is a clear lightthat averts a fright.
In the midst of chaos
there is leaping game
discerning the way.
In the midst of chaos
there is a fine wellwatering the brain.
On top of the fig tree
there is a clean frame
that cancels the blame.
On top of the fig tree
there is mighty helpthat shelters from
hell.
Other coincidencesthe four states on the parable of the sower: fruit in the rootY = X is “our shelter from the wind”
Other coincidencesthe four states on the parable of the sower: fruit in the rootY = X is “our shelter from the wind”
“abandon yourself, pick up your + and follow me”“whoever loses his life for my sake will save it”
“if a grain of wheat dies, it produces much fruit”
Other coincidencesthe four states on the parable of the sower: fruit in the rootY = X is “our shelter from the wind”
“abandon yourself, pick up your + and follow me”“whoever loses his life for my sake will save it”
“if a grain of wheat dies, it produces much fruit”in the summit of chaos: wheat vs. chaff, sheep vs. goats“though 1,000 fall at your side, 10,000 at your right…”
“can you bury the haughty in the dust together?”
Other coincidencesthe four states on the parable of the sower: fruit in the rootY = X is “our shelter from the wind”
“abandon yourself, pick up your + and follow me”“whoever loses his life for my sake will save it”
“if a grain of wheat dies, it produces much fruit”in the summit of chaos: wheat vs. chaff, sheep vs. goats“though 1,000 fall at your side, 10,000 at your right…”
“can you bury the haughty in the dust together?”“people do not pick figs from thornbushes”
the power of sainthood is visualized geometrically:the escape point from chaos is the Ω point
Le plus improbable
In the most hellish beat
a silly and vain defeat
also a spectacle disjoint
an epsilon from the point
chaudement guérissable
oh purgation ineffable
oh victoire admirableoh miracle vénérable
In the symbolic tree
thorns, dust in a spree
but in humble zero set
line cancels all debt
In the unbent choice
always a clear voice
an appointed up lift
deterministic a gift
In the highest ugly heat
almost never a repeat
sad travel with no rest
ever close to the best
sûrement misérableoh détour incroyabledynamique indésirable
étrange état exécrable
également déplorablepériodicité
interminableobstination réprochableoh hasard inévitable
In the real driving seat
surely a fantastic feat
a way to erected root
faithful relief and fruit
égoïsme détectableoh fractal pitoyableoh origine inégalableoh paradis inalterable
oh l'amour véritableoh poème formidablemiséricorde verifiableoh le plus
improbable
Voice by Sandrine Matiasek
Animations by Mahesh L. Maskey