It is notorious that breakthroughs in science often come in tandem: Th

Question

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.    1 
 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

2 
 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

3 
 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

4 
 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

5 
 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

6 
 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

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

Kaplan GRE Verbal Workout 2007

Devayusssh · Answer

Please have the answers uploaded .

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Ruchi007 · Answer

Sajjad1994  Please provide an explanation to #5.

Sajjad1994 · Answer

Official Explanation

5. The author suggests that cases of simultaneous discovery

Explanation

This choice paraphrases the first sentence of the last paragraph.

Choice (A)  goes too far. The author does stress the preliminary work done by others, but doesn’t suggest that the discovery of the calculus (or similar discoveries) was not a breakthrough.

Choice (B)  is contradicted in the first paragraph.

Choice (C)  is not implied—we don’t know what influences Leibniz, Newton, Darwin, et al., may have been aware of. Newton is the only example given of delayed publication, making  choice (E)  unlikely.

Answer: D

Dhruv1212 · Answer

Can Someone please explain answer 6

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Sajjad1994 · Answer

Official Explanation

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

Difficulty Level:   700

Explanation

This is a logic question—what is the author trying to do by drawing this connection? Copernicus and Kepler are mentioned in the fourth sentence of the last paragraph, in the context of the series of scientific and mathematical advances that  “prepared the ground”  for Newton and Leibniz. So the point is that science builds on earlier work; it is evolutionary even when making great advances.

The  “great man”  view in  choice (A)  probably refers to the misconception that breakthroughs are  “solitary acts of genius” (first sentence of paragraph 4) ; this is not the author’s view.

Choice (B)  is a big overstatement; the passage says that simultaneous discoveries occur often, not all the time.

Choice (C)  overstates the case. The author doesn’t think independent discovery is a myth at all. Newton and Leibniz are examples of independent discovery. Neither one, of course, was wholly “independent” of previous developments, but their discoveries were made on their own.

Choice (E)  never happens. Physicists, or at least astronomers, are mentioned, as are mathematicians, but they are not compared.

Answer: D

It is notorious that breakthroughs in science often come in tandem: Th

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It is notorious that breakthroughs in science often come in tandem: Th

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615 to 715 in 15 Days (Ria's Strategies)

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