from a chaotic fi g tree Carlos E Puente University of California Davis THE KEY ROLE OF SCIENCE IN THE NEW EVANGELIZATION Ateneo Pontificio Regina Apostolorum Rome May 2013 Thesis ID: 183954
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Slide1
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 Apostolorum
Rome, May 2013Slide2
ThesisWe humans, with a soul,may learn from recent advancementsregarding natural complexity
in order to find the peace of Christand share the good news in a novel way…Slide3
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
)Slide4
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
)
t
he
parable of the barren fig
tree
(Lk
13:6–9
)
Jesus
curses a fruitless fig
tree
(Mt
21:18–22
, Mk
11:12–23
)
t
he
lesson from a fig
tree
(Mk
13:28–31
, Lk
21:29–33
)Slide5
e logistic map... a population
of “rabbits” as a function of time
Slide6
e logistic map... a population of “rabbits” as a function of
time
Slide7
e logistic map... a population of “rabbits” as a function of
time
Slide8
e logistic map... a population of “rabbits” as a function of
time
different
cases depending on the parameter
:
Slide9
The logistic dynamics
Slide10
The logistic dynamics
Slide11
The logistic dynamics
period 2
Slide12
The logistic dynamics
period 4
period 2
Slide13
The logistic dynamics
period 4
period 2
period
Slide14
aperiodic
aperiodic
The logistic dynamicsSlide15
period 5
aperiodic
period 3
aperiodic
The logistic dynamicsSlide16
e diagram of bifurcationsSlide17
e diagram of bifurcations
the
tree contains periodic behavior, for any natural numberSlide18
e diagram of bifurcationsSlide19
e diagram of bifurcations
after
the dusty
strange attractors are
common
Slide20
e diagram of bifurcations
after
the
dusty
strange attractors are common
in the
white bands there are the
“buds”
of
the
tree Slide21
Intermediate bud of period 3Slide22
Intermediate bud of period 3
… exquisite self-similarity
ad infinitumSlide23
Thorns galore
the chaotic tree contains many
multifractal thornsthey combine imbalances and holes, as in
:
Slide24
Thorns galore
the chaotic tree contains many
multifractal thornsthey combine imbalances and holes, as in
:
they happen at ends of
white bands
of buds for all
periodsSlide25
Universality on the fig treebifurcations happen in an orderly fashion:
(Feigenbaum, 1978)
0…
openings
…
durations
Slide26
Universality on other chaotic trees
straight root, “tender branch,” branches, and dust (“fig leaves”)
Slide27
Universality on other chaotic trees
straight root, “tender branch,” branches, and dust (“fig leaves”)
relevant in biology, ecology, chemistry, physics, economics
…Slide28
Universality on other chaotic trees
straight root, “tender branch,” branches, and dust (“fig leaves”)
relevant in biology, ecology, chemistry, physics, economics…
the dynamics of
convection
are reproduced if
is
heat
(Libchaber, 1979
)
Slide29
In the summit of chaos
all appears to wander in a compact strange attractor when
:
Slide30
In the summit of chaoshowever, unstable extensions of the tree need to be excluded:
all appears to wander in a compact
strange attractor
when
:
Slide31
Oscillations on the summit
pre-images
of eventual
repetitions every
three
generations
are
not
part of the attractor:Slide32
Oscillations on the summit
pre-images of eventual repetitions every three generations
are not part of the attractor:
similar trees for
every
period
need
to be
excluded …Slide33
Oscillations on the summit
pre-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
dustSlide34
An escape to the origin
there
are also few points that improbably return to the
root
pre-images of zero
rest despite
high
heat
:Slide35
An escape to the origin
there
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!Slide36
An escape to the origin
there
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
purgatorySlide37
Plain common sense
it is
much better not to miss the point
!
in order to
avoid
chaos
and its
infernal
turbulence:Slide38
Plain common sense
it 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 rootSlide39
Plain common sense
it 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
abandon yourself to the
threshold
,
, to reach the
Origin
Slide40
Plain common sense
it 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
abandon yourself to the
threshold
,
, to reach the
Origin
move
away from nonlinearities (
) to escape
thorns
and
dust
Slide41
A scientific prophetic tree?Slide42
A scientific prophetic tree?
an allegorical
fig tree
without fruit, consistently
cursedSlide43
A scientific prophetic tree?
an allegorical
fig tree
without fruit, consistently
cursed
this tree and other
trees
have tender branches and many
budsSlide44
A scientific prophetic tree?
an allegorical
fig tree
without fruit, consistently
cursed
this tree and other
trees
have tender branches and many buds
the ax is at the
root
of the trees, Nathanael is at the
rootwe may curse the fig tree as He
rebuked the windSlide45
Our optionsordersimplicity
serenitypeace
disordercomplexityturbulence
chaosSlide46
Our optionsorder
simplicityserenitypeace
decreasingGod’s waybelow Y = X
abandonment
disorder
complexity
turbulence
chaos
increasing
our way
above Y = X
selfishnessSlide47
Our optionsorder
simplicityserenitypeace
decreasingGod’s way
below Y = X
abandonment
obedience
blessing
resting
Heaven
disorder
complexity
turbulence
chaos
increasing
our way
above Y = X
selfishness
rebelliousness
curse
wandering
hellSlide48
Feigenbaum’s parabelSlide49
Foliage of disordertrapped in empty dust,jumps astir forever
enduring subtle thrust.Crossing of the outset
leaving faithful rootlooming tender offset
failing 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
reminding
at 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.Slide50
In the midst of chaosthere 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
point
that runs to the core
.
On
top of the fig
tree
there is a clear
light
that averts a fright
.
In the midst of chaos
there is leaping game
discerning the way.
In the midst of chaos
there is a fine well
watering 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 help
that shelters from hell.Slide51
Other coincidencesthe four states on the parable of the sower: fruit
in the rootY = X is “our shelter from the
wind”Slide52
Other coincidencesthe four states on the parable of the sower:
fruit in the root
Y = 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
”Slide53
Other coincidencesthe four states on the parable of the sower:
fruit in the root
Y = 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?”Slide54
Other coincidencesthe four states on the parable of the sower:
fruit in the root
Y = 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
pointSlide55
Le plus improbableSlide56
In the most hellish beata silly and vain defeatalso a spectacle disjointan epsilon from the point
chaudement guérissable
oh purgation ineffableoh victoire admirable
oh
miracle
vénérable
In the symbolic
tree
thorns
, dust in a
spree
but in humble zero setline cancels all debtIn 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
misérable
oh
détour
incroyable
dynamique
indésirable
étrange
état
exécrable
également
déplorable
périodicité
interminable
obstination
réprochable
oh
hasard
inévitable
In
the real driving
seat
surely
a fantastic
feat
a
way to erected
root
faithful
relief and
fruit
égoïsme
détectable
oh
fractal
pitoyable
oh
origine
inégalable
oh
paradis
inalterable
oh
l'amour
véritable
oh
poème
formidable
miséricorde
verifiable
oh
le plus
improbable
V
oice by Sandrine
MatiasekSlide57
Animations by Mahesh L. Maskey