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# Around 1960, mathematician Edward Lorenz found unexpected behavior in

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Around 1960, mathematician Edward Lorenz found unexpected behavior in  [#permalink]

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Updated on: 22 Aug 2019, 22:36
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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

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Originally posted by vomhorizon on 18 Nov 2012, 03:20.
Last edited by SajjadAhmad on 22 Aug 2019, 22:36, edited 1 time in total.
Updated - Complete topic (259).
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Re: Around 1960, mathematician Edward Lorenz found unexpected behavior in  [#permalink]

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26 Jan 2013, 14:42
1
A E C E D

Question 2 - the third paragraph discusses how poppy seeds are niter mixed seemingly at random, but the positions of the seeds are not random. They a actually determined by the system's fundamental equations.

Question 5 - this question asks to infer which system would be the most chaotic and resemble the typical pathways. Only answer D mentions a system by which the system's fundamental equations are pre-determined and thus two baseballs placed into a tumble dryer reflect this.

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Re: Around 1960, mathematician Edward Lorenz found unexpected behavior in  [#permalink]

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12 Mar 2013, 06:16
3
1. A
2. E
3. C
4. E
5. D
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Re: Around 1960, mathematician Edward Lorenz found unexpected behavior in  [#permalink]

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21 Jun 2013, 10:47
Hmm, despite correctly answering this question, I have a concern:

Question 3:
I agree that C is the "best" answer, but I use the word "best" with reservation.
The passage states that "Whenever he reran his model with the same inputs, different outputs resulted"
This implies that even at the beginning, he could see the impact of these rounding errors.
Thus, how can we say that these errors started off as being "imperceptibly small"?

- Do people agree on this or am I incorrect?
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Re: Around 1960, mathematician Edward Lorenz found unexpected behavior in  [#permalink]

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22 Jun 2013, 13:25
mattce wrote:
Hmm, despite correctly answering this question, I have a concern:

Question 3:
I agree that C is the "best" answer, but I use the word "best" with reservation.
The passage states that "Whenever he reran his model with the same inputs, different outputs resulted"
This implies that even at the beginning, he could see the impact of these rounding errors.
Thus, how can we say that these errors started off as being "imperceptibly small"?

- Do people agree on this or am I incorrect?

Hi,

Here is a piece of my mind. Lets re-read this line from the passage again with a certain degree of criticality:
" Lorenz realized that the tiny rounding errors in his analog computer mushroomed over time, leading to erratic results."
The word "realized" clearly indicates that over the period of time iterating through his experiments he realized the imperceptible or "difficult to perceive" errors are indeed making a difference to the final result.

Hence the correct answer speaks out among the rest. Hope that helps

Btw a good passage. A difficult read but comparatively easier questions. All correct within 9mins & xx secs
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Re: Around 1960, mathematician Edward Lorenz found unexpected behavior in  [#permalink]

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26 Oct 2013, 05:00
took me 10 mins for this RC dont know good or bad.Got 4 questions right had no clue about the 5th one ...

1.A
2.E
3.C
4.E
5.C

Can any one please explain the 5th one ....

Regards,
abhinav
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Re: Around 1960, mathematician Edward Lorenz found unexpected behavior in  [#permalink]

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26 Oct 2013, 11:05
Here is the explanation for the 5th question. Hope this helps.

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? - On a bigger picture this question is asking which system is similar to the systems described in the passge. There are two systems described in the passage to explain chaotic system 1. poppy seeds in bowl/ dough 2. butterfly effect on weather (very vaguely)

(A) two particles ejected in random directions from the same decaying atomic nucleus - Nothing is mentioned about decaying atomic nucleus. This is not remotely closer to either of the two systems described in the passage
(B) two stickers affixed to balloon that expands and contracts over and over again - Nothing is mentioned about balloon expanding and contracting. This is not remotely closer to either of the two systems described in the passage
(C) two avalanches sliding down opposite sides of the same mountain - This may be remotely related to weather. keep it.
(D) two baseballs placed into an active tumble dryer - Very similar to the poppy seeds in bowl. This is it!
(E) two coins flipped into a large bowl - Nothing is mentioned about flipping coins. This is not remotely closer to either of the two systems described in the passage

abhinav11 wrote:
took me 10 mins for this RC dont know good or bad.Got 4 questions right had no clue about the 5th one ...

1.A
2.E
3.C
4.E
5.C

Can any one please explain the 5th one ....

Regards,
abhinav
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Re: Around 1960, mathematician Edward Lorenz found unexpected behavior in  [#permalink]

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14 Nov 2013, 08:32
vomhorizon wrote:
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

OA's to follow..

I am having trouble with q 4.
I don't understand how E is the answer.
" 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."
It's written that the butterfly effect is "in chaotic systems".... So why is E the answer?
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Re: Around 1960, mathematician Edward Lorenz found unexpected behavior in  [#permalink]

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05 Aug 2015, 05:07
Hi guys,

Please care to explain the second question.

Here is my query.
The question is about the poppy seeds.
The answer option E talks about the positions of poppy seeds.Poppy seeds can be in certain positions governed by system's fundamental equations not the positionsthemselves.
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Re: Around 1960, mathematician Edward Lorenz found unexpected behavior in  [#permalink]

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25 May 2018, 21:49
1
This is a passage from MGMAT RC book. Level -700 .
For the question 4, I could not get anything which mentioned about the 'Right side bowl...' plz explain the answer why is it E ?
Give explanation for question 5 also.
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Re: Around 1960, mathematician Edward Lorenz found unexpected behavior in  [#permalink]

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17 Nov 2019, 07:14
got all right except for 5th , someone please explain ..5th
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Re: Around 1960, mathematician Edward Lorenz found unexpected behavior in  [#permalink]

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17 Nov 2019, 19:11
summary:
Para 1. introduces a concept to set the context
Para 2. Para 3 and para 4 are supporting examples.

1. The main purpose of this passage is to

(A) Explain complicated aspects of certain physical systems - yes, as per para summaries
(B) trace the historical development of scientific theory - no, other than 1st para, no timelines are mentioned it is not about history
(C) distinguish a mathematical patter from its opposition - partially true but not the main summary. it is part of the concept
(D) describe the spread of a technical model from one field of study to others - author does cover various examples to explain the theory but the very purpose is not to define the spread of the theory but to explain
(E) contrast possible causes of weather phenomena - no! only mentioned in last para

2. In the example discussed in the passage, what is true about poppy seeds in bread dough, once the dough has been thoroughly mixed?
Refer para 4 "It is this "sensitive dependence on initial conditions"

(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
Para 1. "Lorenz realized that the tiny rounding errors in his analog computer mushroomed over time, leading to erratic results."

(C) were imperceptibly small at first, but tended to grow

4. The passage mentions each of the following as an example of potential example of chaotic or non-chaotic system Except
Para 4. "Butterfly effect", is discussed but not flight patterns

(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?
Para 4. 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.

(A) two particles ejected in random directions from the same decaying atomic nucleus. - Word same shows source is same. so no
(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 - placed but sensitive to early placement
(E) two coins flipped into a large bowl - different context.
Re: Around 1960, mathematician Edward Lorenz found unexpected behavior in   [#permalink] 17 Nov 2019, 19:11
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