Around 1960, mathematician Edward Lorenz found unexpected behavior in
apparently simple equations representing atmospheric air flows.
Whenever he ran his model with the same inputs, different outputs
resulted - although the model lacked any random elements. Lorenz
realized that the tiny rounding errors in his analog computer
mushroomed over time, leading to erratic results. His findings marked
a seminal moment in the development of chaos theory, which despite its
name, has little to do with randomness.
TO understand how unpredictability can arise from deterministic
equations, which do not involve chance outcomes, consider the
non-chaotic system of two poppy seeds placed in a round bowl. As the
seeds roll to the bowl's center, a position known as a point
attractor, the distance between the seeds shrinks. If instead, the
bowl is flipped over, two seeds placed on top will roll away from each
other. Such a system, while still technically chaotic, enlarges
initial differences in position.
Chaotic systems, such as a machine mixing bread dough, are
characterized by both attraction and repulsion. As the dough is
stretched, folded and pressed back together, any poppy seeds sprinkled
in are intermixed seemingly at random. But this randomness is
illusory. In fact, the poppy seeds are captured by "strange
attactors," staggeringly complex pathways whose tangles appear
accidental but are in fact determined by the system's fundamental
equations.
During the dough-kneading process, two poppy seeds positioned next to
each other eventually go their separate ways. Any early divergence or
measurement error is repeatedly amplified by the mixing until the
position of any seed becomes effectively unpredictable. It is this
"sensitive dependence on initial conditions" and not true randomness
that generates unpredictability in chaotic systems, of which one
example may be the Earth's weather. According to the popular
interpretation of the "Butterfly effect", a butterfly flapping its
wings caused hurricanes. A better understanding is that the butterfly
causes uncertainty about the precise state of the air. This
microscopic uncertainty grows until it encompasses even hurricanes.
Few meteorologists believe that we will ever ben able to predict rain
or shine for a particular day years in the future.
1. The main purpose of this passage is to
(A) Explain complicated aspects of certain physical systems
(B) trace the historical development of scientific theory
(C) distinguish a mathematical patter from its opposition
(D) describe the spread of a technical model from one field of study to others
(E) contrast possible causes of weather phenomena
2. In the example discussed in the passage, what is true about poppy seeds in bread dough, once the dough has been thoroughly mixed?
(A) They have been individually stretched and folded over, like miniature versions of the entire dough
(B) They are scattered in random clumps throughout the dough
(C) They are accidentally caught in tangled objects called strange attractors
(D) They are bound to regularly dispersed patterns of point attractors
(E) They are positions dictated by the underlying equations that govern the mixing process
3. According to the passage, the rounding errors in Lorenz's model
(A) Indicated that the model was programmed in a fundamentally faulty way
(B) were deliberately included to represent tiny fluctuations in atmospheric air currents
(C) were imperceptibly small at first, but tended to grow
(D) were at least partially expected, given the complexity of the actual atmosphere
(E) shrank to insignificant levels during each trial of the model
4. The passage mentions each of the following as an example of potential example of chaotic or non-chaotic system Except
(A) a dough-mixing machine
(B) atmospheric weather patters
(C) poppy seeds place on top of an upside-down bowl
(D) poppy seeds placed in a right-side up bowl
(E) fluctuating butterfly flight patterns
5. It can be inferred from the passage that which of the following pairs of items would most likely follow typical pathways within a chaotic system?
(A) two particles ejected in random directions from the same decaying atomic nucleus
(B) two stickers affixed to balloon that expands and contracts over and over again
(C) two avalanches sliding down opposite sides of the same mountain
(D) two baseballs placed into an active tumble dryer
(E) two coins flipped into a large bowl
apparently simple equations representing atmospheric air flows.
Whenever he ran his model with the same inputs, different outputs
resulted - although the model lacked any random elements. Lorenz
realized that the tiny rounding errors in his analog computer
mushroomed over time, leading to erratic results. His findings marked
a seminal moment in the development of chaos theory, which despite its
name, has little to do with randomness.
TO understand how unpredictability can arise from deterministic
equations, which do not involve chance outcomes, consider the
non-chaotic system of two poppy seeds placed in a round bowl. As the
seeds roll to the bowl's center, a position known as a point
attractor, the distance between the seeds shrinks. If instead, the
bowl is flipped over, two seeds placed on top will roll away from each
other. Such a system, while still technically chaotic, enlarges
initial differences in position.
Chaotic systems, such as a machine mixing bread dough, are
characterized by both attraction and repulsion. As the dough is
stretched, folded and pressed back together, any poppy seeds sprinkled
in are intermixed seemingly at random. But this randomness is
illusory. In fact, the poppy seeds are captured by "strange
attactors," staggeringly complex pathways whose tangles appear
accidental but are in fact determined by the system's fundamental
equations.
During the dough-kneading process, two poppy seeds positioned next to
each other eventually go their separate ways. Any early divergence or
measurement error is repeatedly amplified by the mixing until the
position of any seed becomes effectively unpredictable. It is this
"sensitive dependence on initial conditions" and not true randomness
that generates unpredictability in chaotic systems, of which one
example may be the Earth's weather. According to the popular
interpretation of the "Butterfly effect", a butterfly flapping its
wings caused hurricanes. A better understanding is that the butterfly
causes uncertainty about the precise state of the air. This
microscopic uncertainty grows until it encompasses even hurricanes.
Few meteorologists believe that we will ever ben able to predict rain
or shine for a particular day years in the future.
1. The main purpose of this passage is to
(A) Explain complicated aspects of certain physical systems
(B) trace the historical development of scientific theory
(C) distinguish a mathematical patter from its opposition
(D) describe the spread of a technical model from one field of study to others
(E) contrast possible causes of weather phenomena
2. In the example discussed in the passage, what is true about poppy seeds in bread dough, once the dough has been thoroughly mixed?
(A) They have been individually stretched and folded over, like miniature versions of the entire dough
(B) They are scattered in random clumps throughout the dough
(C) They are accidentally caught in tangled objects called strange attractors
(D) They are bound to regularly dispersed patterns of point attractors
(E) They are positions dictated by the underlying equations that govern the mixing process
3. According to the passage, the rounding errors in Lorenz's model
(A) Indicated that the model was programmed in a fundamentally faulty way
(B) were deliberately included to represent tiny fluctuations in atmospheric air currents
(C) were imperceptibly small at first, but tended to grow
(D) were at least partially expected, given the complexity of the actual atmosphere
(E) shrank to insignificant levels during each trial of the model
4. The passage mentions each of the following as an example of potential example of chaotic or non-chaotic system Except
(A) a dough-mixing machine
(B) atmospheric weather patters
(C) poppy seeds place on top of an upside-down bowl
(D) poppy seeds placed in a right-side up bowl
(E) fluctuating butterfly flight patterns
5. It can be inferred from the passage that which of the following pairs of items would most likely follow typical pathways within a chaotic system?
(A) two particles ejected in random directions from the same decaying atomic nucleus
(B) two stickers affixed to balloon that expands and contracts over and over again
(C) two avalanches sliding down opposite sides of the same mountain
(D) two baseballs placed into an active tumble dryer
(E) two coins flipped into a large bowl
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