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12 Jul 2023, 07:30
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Question 1
B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
15%
(low)
Question Stats:
85% (02:51) correct
15%
(02:30) wrong
based on 88
sessions
History
Date
Time
Result
Not Attempted Yet
Question 2
B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
5%
(low)
Question Stats:
85% (00:37) correct 15%
(01:04) wrong
based on 94
sessions
History
Date
Time
Result
Not Attempted Yet
Question 3
A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
15%
(low)
Question Stats:
77% (00:34) correct 23%
(01:08) wrong
based on 93
sessions
History
Date
Time
Result
Not Attempted Yet
Question 4
D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
5%
(low)
Question Stats:
92% (00:38) correct 8%
(00:36) wrong
based on 86
sessions
History
Date
Time
Result
Not Attempted Yet
Question 5
D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
58% (00:47) correct 42%
(00:59) wrong
based on 83
sessions
History
Date
Time
Result
Not Attempted Yet
Question 6
D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
65%
(hard)
Question Stats:
42% (00:58) correct 58%
(00:56) wrong
based on 77
sessions
History
Date
Time
Result
Not Attempted Yet
It is notorious that breakthroughs in science often come in tandem: The same, or almost the same, theoretical advance is made simultaneously by two or more investigators. Watson and Crick “raced” Linus Pauling to verify the helical structure of DNA; Darwin and Alfred Wallace announced the essentials of evolutionary theory simultaneously in 1858. Why should this occur? Why—to take another example—should Newton and Leibniz have worked out the differential calculus independently and in isolation from one another, when they were not even working on the same sorts of problems?
Newton’s work on the calculus stemmed from his interest in the physical problem of the measurement of continuously changing quantities. Take, for example, the problem of determining the velocity of a freely falling body at a given instant. The body is constantly accelerating due to gravity. An approximate velocity at any time may be found by measuring the distance traveled over a very brief time interval, such as a hundredth of a second; if one reduces the time interval measured until it approaches zero, the approximate velocity over the interval approaches the actual velocity at any instant as a limit. Newton’s genius was to grasp how to calculate such a change over an infinitesimal time period through a mathematical operation known as differentiation.
For various reasons, Newton delayed publishing a clear account of his calculus for nearly forty years. In the meantime, Leibniz approached the calculus from a completely different standpoint, that of the formal geometric problem of determining the tangent to a curve (later, for the integral calculus, the area under a curve). This geometric problem was mathematically equivalent to Newton’s consideration of bodies in motion, however, since the changing position of such a body over time can be plotted graphically as a curve in which the tangent to the curve at any point represents the velocity of the body at a given instant. Thus, Leibniz’s formal geometric approach duplicated Newton’s results.
This phenomenon of simultaneous discovery is surprising only to a public that views such breakthroughs as solitary acts of genius. In reality, Newton and Leibniz’s ground had been thoroughly prepared in advance. In the century before Newton’s birth, Europe had seen an explosion of scientific inquiry. Copernicus, Kepler, and others had formulated the laws of planetary motion and celestial mechanics. More specifically, when he began his mathematical work, Newton was already familiar with Descarte’s coordinate geometry, the mathematics of infinitesimal intervals recently developed by John Wallis, and the method of finding tangents through differentiation worked out by Isaac Barrow. Thus, both the scientific problems and the conceptual tools that stimulated and facilitated Newton’s astonishingly rapid development of the differential calculus were already the common property of science. Given Newton’s delay in publishing his work, an independent discovery of the calculus by some other genius became not only possible but likely.
Newton’s work on the calculus stemmed from his interest in the physical problem of the measurement of continuously changing quantities. Take, for example, the problem of determining the velocity of a freely falling body at a given instant. The body is constantly accelerating due to gravity. An approximate velocity at any time may be found by measuring the distance traveled over a very brief time interval, such as a hundredth of a second; if one reduces the time interval measured until it approaches zero, the approximate velocity over the interval approaches the actual velocity at any instant as a limit. Newton’s genius was to grasp how to calculate such a change over an infinitesimal time period through a mathematical operation known as differentiation.
For various reasons, Newton delayed publishing a clear account of his calculus for nearly forty years. In the meantime, Leibniz approached the calculus from a completely different standpoint, that of the formal geometric problem of determining the tangent to a curve (later, for the integral calculus, the area under a curve). This geometric problem was mathematically equivalent to Newton’s consideration of bodies in motion, however, since the changing position of such a body over time can be plotted graphically as a curve in which the tangent to the curve at any point represents the velocity of the body at a given instant. Thus, Leibniz’s formal geometric approach duplicated Newton’s results.
This phenomenon of simultaneous discovery is surprising only to a public that views such breakthroughs as solitary acts of genius. In reality, Newton and Leibniz’s ground had been thoroughly prepared in advance. In the century before Newton’s birth, Europe had seen an explosion of scientific inquiry. Copernicus, Kepler, and others had formulated the laws of planetary motion and celestial mechanics. More specifically, when he began his mathematical work, Newton was already familiar with Descarte’s coordinate geometry, the mathematics of infinitesimal intervals recently developed by John Wallis, and the method of finding tangents through differentiation worked out by Isaac Barrow. Thus, both the scientific problems and the conceptual tools that stimulated and facilitated Newton’s astonishingly rapid development of the differential calculus were already the common property of science. Given Newton’s delay in publishing his work, an independent discovery of the calculus by some other genius became not only possible but likely.
1. The primary purpose of this passage is to
A. present mathematical discoveries
B. clarify a recurring phenomenon in scientific history
C. solve a long-standing puzzle in intellectual history
D. describe a period of rapid scientific change
E. recollect a scandalous incident
A. present mathematical discoveries
B. clarify a recurring phenomenon in scientific history
C. solve a long-standing puzzle in intellectual history
D. describe a period of rapid scientific change
E. recollect a scandalous incident
2. According to the author, Newton devised the differential calculus in an attempt to understand
A. why falling bodies accelerate
B. how to measure continuously varying quantities
C. how to measure the area under a curve
D. the relationship between average and actual speeds
E. how to find tangents by differentiation
A. why falling bodies accelerate
B. how to measure continuously varying quantities
C. how to measure the area under a curve
D. the relationship between average and actual speeds
E. how to find tangents by differentiation
3. It can be inferred that the author regards the development of the calculus as
A. an outgrowth of previous intellectual developments
B. a unique act of genius
C. an achievement whose significance has been overestimated
D. an unusual case of near-simultaneous discovery
E. a breakthrough that solved a classic scientific problem
A. an outgrowth of previous intellectual developments
B. a unique act of genius
C. an achievement whose significance has been overestimated
D. an unusual case of near-simultaneous discovery
E. a breakthrough that solved a classic scientific problem
4. The passage implies that Newton and Leibniz arrived at similar results because
A. they used similar approaches
B. they knew of each other’s work
C. no one had previously considered the problem of continuous motion
D. the problems they considered were mathematically equivalent
E. they were competing to win recognition for the discovery of the calculus
A. they used similar approaches
B. they knew of each other’s work
C. no one had previously considered the problem of continuous motion
D. the problems they considered were mathematically equivalent
E. they were competing to win recognition for the discovery of the calculus
5. The author suggests that cases of simultaneous discovery
A. cannot really be called break throughs, since the important work has been done by others
B. are extremely rare in science
C. are made by individuals unaware of the historical influences on their thought
D. seem remarkable to a public influenced by an inaccurate notion of genius
E. usually occur when one discoverer delays publication of his results
A. cannot really be called break throughs, since the important work has been done by others
B. are extremely rare in science
C. are made by individuals unaware of the historical influences on their thought
D. seem remarkable to a public influenced by an inaccurate notion of genius
E. usually occur when one discoverer delays publication of his results
6. In the final paragraph the author draws connections between the work of Leibniz and Newton and the work of Copernicus and Kepler primarily in order to
A. provide support for the “great man” view of scientific history
B. argue that the work of most scientific geniuses reveals unusually coincidental patterns of discovery
C. expose the myth of independent scientific discovery
D. describe the evolutionary nature of scientific achievement
E. compare the work of physicists to that of mathematicians
A. provide support for the “great man” view of scientific history
B. argue that the work of most scientific geniuses reveals unusually coincidental patterns of discovery
C. expose the myth of independent scientific discovery
D. describe the evolutionary nature of scientific achievement
E. compare the work of physicists to that of mathematicians
RC Butler 2023 - Practice Two RC Passages Everyday.
Passage # 232 Date: 12-Jul-2023
This question is part of RC Butler 2023. Click here for Details
Passage # 232 Date: 12-Jul-2023
This question is part of RC Butler 2023. Click here for Details
Kaplan GRE Verbal Workout 2007
13 Jul 2023, 09:50
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