Around 1960, mathematician Edward Lorenz found unexpected behavior in

Question

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 
 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 
 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 
 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 
 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 
 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

roman325 · Answer

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.

Hope this is helpful!

Pranjal3107 · Answer

For Q4, how do you distinguish b/w option D and E ? The butterfly effect explanation is in some ways related to the theory behind chaotic systems. Whereas in D,
 poppy seeds placed in a right-side up bowl. Right side up bowl confused me. 
Can someone please explain ?

richirish · Answer

Let me try and help.

From the Passage -  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.

Now a butterfly flapping its wing is not equal to the "flight path" of the butterfly, the question is deliberately using closely related words handpicked from the passage to use your short term memory against you, but if you slow it down and really read through the options and refer back to the passage, this difference will become clear to you.

Hope it helps

bM22 · Answer

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

Explanation: Chaotic systems are characterized by both attraction and repulsion. We need to find pairs of items would most likely follow typical pathways within a chaotic system analogous to the poppy seeds sprinkled in a machine mixing bread dough, as can be inferred from the 3rd and 4th para of the passage. Now, the most similar is option D.

Thanks.

guddo · Answer

1. The main purpose of this passage is to

The passage explains how chaotic systems can be deterministic and yet unpredictable. It uses Lorenz’s weather model, poppy seeds in a bowl, and bread dough mixing to explain sensitive dependence on initial conditions.  So the passage mainly explains a difficult feature of certain physical systems : how unpredictability can arise without true randomness.

(A) Explain complicated aspects of certain physical systems

This is correct. The passage explains chaos, strange attractors, deterministic equations, and why systems such as weather can become effectively unpredictable.

(B) trace the historical development of scientific theory

This is too broad. Lorenz is mentioned at the beginning, but the passage does not mainly trace the history of chaos theory.

(C) distinguish a mathematical pattern from its opposition

This is vague and inaccurate. The passage distinguishes chaos from randomness, but that is part of a broader explanation, not the main purpose.

(D) describe the spread of a technical model from one field of study to others

This is not supported. The passage does not discuss how a model spread across fields.

(E) contrast possible causes of weather phenomena

This is too narrow. Weather is only one example of a chaotic system.

Answer: (A)

Around 1960, mathematician Edward Lorenz found unexpected behavior in

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Around 1960, mathematician Edward Lorenz found unexpected behavior in

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