| Over the years, our students have pointed out films they thought exhibited chaos,
or more precisely, sensitivity to initial conditions. These include |
| Sliding Doors |
| Unexpectedly fired Helen (Gwynth Paltrow) leaves her former work early and takes
the train home. In one scenario, she just barely gets through the sliding doors of the
train, arrives home early, and finds her husband Gerry (John Lynch) in bed with his
mistress Lydia (Jeanne Tripplehorn). Acrimonious events follow. In another scenario,
Helen does not get through the sliding doors, must take the next train, arrives
home after Lydia has departed, doesn't leave Gerry, etc. The film interweaves these two
storylines, handily cutting Helen's hair in one to help differentiation of the lines. |
| This is a classical example of the butterfly effect, paralleling
Captain Madden's missing the train by a few seconds in Borges' The
garden of forking paths. |
| This film ilustrates a more complete rendering of chaos, with common themes and character
traits appearing in both, metaphorically illustrating the presence of unstable order in
chaotic systems. |
| |
| Run Lola Run |
| Nothing I could write would improve on quoting from Roger Ebert's review. |
"And the story of Lola's 20-minute run is told three times, each time with small
differences that affect the outcome and the fate of the characters.
"Film is ideal for showing alternate and parallel time lines. It's literal; we see
Lola running, and so we accept her reality, even though the streets she runs through and the
people she meets are altered in each story. The message is that the smallest events can have
enormous consequences. A butterfly flaps its wings in Malaysia, causing a hurricane in
Trinidad. You know the drill." |
|
| |
| Chaos Theory |
| Frank (Ryan Reynolds), a time management expert, is tricked by his wife Susan (Emily Mortimer)
into leaving the house 10 minutes late one morning. Throughout the day, this escalates until Frank
arrives late for a time management lecture (!). Upset, on the way home he helps a pregnant woman get
to the hospital and fills out paperwork leading the hospital staff to think he is the father. Susan
answers a phone call from the hospital and deduces Frank has been having an affair. She throws
him out and limits his access to their daughter. To prove he was not the father of the baby of the
woman he took to the hospital, Frank undergoes a medical test. Turns out Frank can prove non-paternity
in a way he didn't expect: he is
incapable of fathering children. So his marriage did involve an infidelity, but by Susan, not
by Frank. Several more things happen, but the general path of the narrative should be clear
by now. These are large consequences of starting a day 10 minutes late. |
| Is this an example of chaos, or even of the butterfly effect? Maybe, though in the day of
a time management expert, wouldn't actions to be arranged with a minimum of waiting time? Should we
expect Frank to arrive at the ferry so early that he could absorb being 10 minutes late and not miss
the boat? For such a person, a 10 minute delay hardly appears to constitute a small change in the
initial conditions of the day. |
| The film seems to be more of an example of self-organized
criticality, a sandpile
poined on the brink of avalanche: one extra grain dislodges two, which start four rolling down the
side, and so on. |
| |
| The Butterfly effect |
| Again, quoting Roger Ebert's review, |
| "Chaos theory teaches us that small events can have enormous consequences. An opening title
informs us that butterfly flapping its wings in Asia could result in a hurricane halfway around the
world. Yes, although given the number of butterflies and the determination with which they flap
their little wings, isn't it extraordinary how rarely that happens? 'The Butterfly Effect' applies
this theory to the lives of four children whose early lives are marred by tragedy. When one of them
finds that he can go back in time and make changes, he tries to improve the present by altering the past.
"The only problem is, he then returns to a present that is different than the one he departed from -
because his actions have changed everything that happened since." |
|
| Any potential interest in the varied unfolding of events is, in my opinion, completely swamped
by this little issue of traveling back in time simply by reading old notebooks. How does THAT work?
I'm much more intrigued by THAT. Then, too, were only small changes made in the past? And in what
sense small? But compared with time travel, these questions drift up like warmth through a poorly
insulated roof during a harsh New England winter. |
| |
| The Stoneraft |
| Reference to chaos is more subtle in George Sluizer's film based on the wonderful novel by
Nobel laureate Jose Saramago. The Iberian peninsula breaks off from the rest of Europe and
drifts off toward the Azores. No explanation is offered. The story unfolds through the actions
and interactions of five people and a dog (an inhabitant of many of Saramago's novels). Each of
the five have had an odd experience: being followed by a flock of birds, skipping a heavy
stone like a flat rock across the water, feeling terrestrial tremors unfelt by others,
tracing in the dirt a line that cannot be erased, trying to unravel a sock that appears to be
made of an infinite length of yard (reminding us of the infinite supply of pages in Borges'
"The book of sand"). Government agents think some of these people may be the cause of the
literal separation of Spain and Portugal from the rest of the EU, or perhaps they are the way to
save the peninsula turned island. Yet again quoting Roger Ebert's review, |
| "Much of the story is told at the pace of a leisurely day in the country, as the five characters
and the dog muse about the curious turn of events. Is it possible that the small actions of these people
could have set into motion the partitioning of subcontinents? After all, doesn't chaos theory teach us
that the beating of a butterfly's wings in Asia could theoretically begin a chain of events leading to
a hurricane in ... the Azores, wasn't it?" |
|
| Here the mysteries upon mysteries are so much more central to the story, in fact, to Saramago's
whole cosmology, that they don't distract us from trying to identify familiar causal themes. This world
is at once familiar and so fundamentally foreign that it invites us to seek threads of chaotic behavior.
Halfway through the book, I had an image of Saramago, the beloved professor saying, "Now students, today
we discuss sensitivity to initial conditions." If anything, the film makes this image even more immediate. |
| |
| Of course, we are happy to hear of other examples. |