Modern science, exclusive of geometry, is a comparatively recent creation and can be said to have originated with Galileo and Newton. Galileo was the first scientist to recognize clearly that the only way to further our understanding of the physical world was to resort to experiment. However obvious Galileo’s contention may appear in the light of our present knowledge, it remains a fact that the Greeks, in spite of their proficiency in geometry, never seem to have realized the importance of experiment. To a certain extent this may be attributed to the crudeness of their instruments of measurement. Still an excuse of this sort can scarcely be put forward when the elementary nature of Galileo’s experiments and observations is recalled. Watching a lamp oscillate in the cathedral of Pisa, dropping bodies from the leaning tower of Pisa, rolling balls down inclined planes, noticing the magnifying effect of water in a spherical glass vase, such was the nature of Galileo’s experiments and observations. As can be seen, they might just as well have been performed by the Greeks. At any rate, it was thanks to such experiments that Galileo discovered the fundamental law of dynamics, according to which the acceleration imparted to a body is proportional to the force acting upon it.
The next advance was due to Newton, the greatest scientist of all time if account be taken of his joint contributions to mathematics and physics. As a physicist, he was of course an ardent adherent of the empirical method, but his greatest title to fame lies in another direction. Prior to Newton, mathematics, chiefly in the form of geometry, had been studied as a fine art without any view to its physical applications other than in very trivial cases. But with Newton all the resources of mathematics were turned to advantage in the solution of physical problems. Thenceforth mathematics appeared as an instrument of discovery, the most powerful one known to man, multiplying the power of thought just as in the mechanical domain the lever multiplied our physical action. It is this application of mathematics to the solution of physical problems, this combination of two separate fields of investigation, which constitutes the essential characteristic of the Newtonian method. Thus problems of physics were metamorphosed into problems of mathematics.
But in Newton’s day the mathematical instrument was still in a very backward state of development. In this field again Newton showed the mark of genius by inventing the integral calculus. As a result of this remarkable discovery, problems, which would have baffled Archimedes, were solved with ease. We know that in Newton’s hands this new departure in scientific method led to the discovery of the law of gravitation. But here again the real significance of Newton’s achievement lay not so much in the exact quantitative formulation of the law of attraction, as in his having established the presence of law and order at least in one important realm of nature, namely, in the motions of heavenly bodies. Nature thus exhibited rationality and was not mere blind chaos and uncertainty. To be sure, Newton’s investigations had been concerned with but a small group of natural phenomena, but it appeared unlikely that this mathematical law and order should turn out to be restricted to certain special phenomena; and the feeling was general that all the physical processes of nature would prove to be unfolding themselves according to rigorous mathematical laws.
When Einstein, in 1905, published his celebrated paper on the electrodynamics of moving bodies, he remarked that the difficulties, which surrounded the equations of electrodynamics, together with the negative experiments of Michelson and others, would be obviated if we extended the validity of the Newtonian principle of the relativity of Galilean motion, which applies solely to mechanical phenomena, so as to include all manner of phenomena: electrodynamics, optical etc. When extended in this way the Newtonian principle of relativity became Einstein’s special principle of relativity. Its significance lay in its assertion that absolute Galilean motion or absolute velocity must ever escape all experimental detection. Henceforth absolute velocity should be conceived of as physically meaningless, not only in the particular realm of mechanics, as in Newton’s day, but in the entire realm of physical phenomena. Einstein’s special principle, by adding increased emphasis to this relativity of velocity, making absolute velocity metaphysically meaningless, created a still more profound distinction between velocity and accelerated or rotational motion. This latter type of motion remained absolute and real as before. It is most important to understand this point and to realize that Einstein’s special principle is merely an extension of the validity of the classical Newtonian principle to all classes of phenomena.
According to the author, why did the Greeks NOT conduct experiments to understand the physical world?
Show Hint
Then see what the author says about the instrument excuse in the very next lines.
- Apparently they did not think it necessary to experiment.
- They focused exclusively on geometry.
- Their instruments of measurement were very crude.
- The Greeks considered the application of geometry to the physical world more important.
The Correct Option is A
Solution and Explanation
The question asks for the reason the author gives for the Greeks NOT doing experiments. The capital letters on NOT tell us to look for the author's own explanation, not just any reason that sounds sensible. So we must find the place in the passage where the author talks about the Greeks and experiments. This is in the first paragraph.
Step 2: Read what the author says about the Greeks:
The author writes that Galileo "was the first scientist to recognize clearly" that experiment is the only way to understand the physical world. Then comes the key sentence: "the Greeks, in spite of their proficiency in geometry, never seem to have realized the importance of experiment."
So the plain reading is that the Greeks did not experiment because they did not see why it mattered. The word "realized" points to an idea in their minds, not to a lack of tools or a different interest.
Step 3: Check the "crude instruments" excuse:
The author next says the missing experiments "may be attributed to the crudeness of their instruments of measurement" only "to a certain extent". Then he cancels it: "Still an excuse of this sort can scarcely be put forward." The reason is that Galileo's tests were very simple (a swinging lamp, falling bodies, balls on slopes), and "they might just as well have been performed by the Greeks." So the author rejects the instrument excuse.
Step 4: Check option (1):
It says the Greeks did not think it necessary to experiment. This matches "never seem to have realized the importance of experiment". The word "Apparently" fits the passage too, because the author says "seem to". So (1) is the best choice.
Step 5: Check option (2):
The passage says the Greeks were good at geometry. It never says they were busy with geometry alone or that geometry kept them from experiments. The word "exclusively" has no support, so (2) is wrong.
Step 6: Check option (3):
This is the excuse the author himself throws out, as shown in Step 3. It is a trap for readers who stop reading after the first half of the sentence. So (3) is wrong.
Step 7: Check option (4):
The passage says that before Newton, mathematics, mainly geometry, was studied "as a fine art without any view to its physical applications". So the Greeks did not rank geometry applied to the physical world as more important. (4) says the opposite, so it is wrong.
Final Answer:
The author blames the Greeks' failure to see the value of experiment, which is option (1). \[ \boxed{1} \]
The statement “Nature thus exhibited rationality and was not mere blind chaos and uncertainty” suggests that
Show Hint
Ask what kind of order Newton found in the heavens.
- problems that had baffled scientists like Archimedes were not really problems.
- only a small group of natural phenomena was chaotic.
- physical phenomena conformed to mathematical laws.
- natural phenomena were evolving towards a less chaotic future.
The Correct Option is C
Solution and Explanation
We are given one sentence from the third paragraph and asked what it suggests. This is an inference question, so the answer should be an idea that follows closely from the sentence and its surroundings, not a new idea brought from outside.
Step 2: Read the sentence in its setting:
The paragraph says Newton invented integral calculus and found the law of gravitation. Then it says the real importance of his work lay in "having established the presence of law and order at least in one important realm of nature, namely, in the motions of heavenly bodies." The next sentence is the one in the question: "Nature thus exhibited rationality and was not mere blind chaos and uncertainty."
The word "thus" shows that this line is a conclusion drawn from the law and order found in the heavens. A little later the paragraph adds that people felt "all the physical processes of nature would prove to be unfolding themselves according to rigorous mathematical laws."
Step 3: Say the meaning in simple words:
Nature is not random. It follows rules, and those rules can be written as mathematical laws. That is what "rationality" means here.
Step 4: Check option (1):
The passage says Newton's calculus solved problems "which would have baffled Archimedes". It does not say those problems were not real problems. This option twists a different sentence, so it is wrong.
Step 5: Check option (2):
The author says Newton studied only "a small group of natural phenomena". He does not say only a small group was chaotic. In fact he says the order was unlikely to be restricted to special phenomena. So (2) is wrong.
Step 6: Check option (3):
Physical phenomena obeying mathematical laws is exactly the idea in Step 3. So (3) is correct.
Step 7: Check option (4):
The sentence is about how nature already was, not about nature moving towards a future state. Nothing in the passage talks about evolution or a less chaotic future. So (4) is wrong.
Final Answer:
The sentence suggests that physical phenomena follow mathematical laws, which is option (3). \[ \boxed{3} \]
Newton may be considered one of the greatest scientists of all time because he
Show Hint
The words "joint contributions" tell you what two things are being put together.
- discovered the law of gravitation.
- married physics with mathematics.
- invented integral calculus.
- started the use of the empirical method in science.
The Correct Option is B
Solution and Explanation
We need the reason the author gives for calling Newton one of the greatest scientists. The reason will be stated near the words "greatest scientist of all time" in the second paragraph.
Step 2: Find the exact sentence:
The passage says Newton was "the greatest scientist of all time if account be taken of his joint contributions to mathematics and physics." The key words are "joint contributions". The author then says that Newton's "greatest title to fame lies in another direction", meaning something other than the empirical method.
That other direction is explained next: before Newton, mathematics was a fine art with almost no physical use, but "with Newton all the resources of mathematics were turned to advantage in the solution of physical problems." The author calls this "the essential characteristic of the Newtonian method".
Step 3: Say it in simple words:
Newton joined mathematics to physics. "Married" is a picture word for "joined together", so this is option (2).
Step 4: Check option (1):
Newton did discover the law of gravitation, and the passage mentions it. But the author says the real importance of that work was not the exact formula. It was the proof that nature has law and order. So this is not the reason given for his being the greatest. (1) is wrong.
Step 5: Check option (3):
The passage praises the invention of integral calculus as a mark of genius. But it presents calculus as the tool needed to make the physics and mathematics combination work, since "the mathematical instrument was still in a very backward state". The "because" in the question points to the joining of the two fields. So (3) is a part, not the main reason.
Step 6: Check option (4):
The passage calls him "an ardent adherent of the empirical method", so he followed it. Galileo is the one called the first to see clearly that experiment was the way. Also, the author says Newton's fame lies in "another direction". So (4) is wrong.
Final Answer:
Newton is rated the greatest because he combined mathematics with physics, which is option (2). \[ \boxed{2} \]
Which of the following statements about modern science best captures the theme of the passage?
Show Hint
The answer that holds for all the paragraphs is the theme.
- Modern science rests firmly on the platform built by the Greeks.
- We need to go back to the method of enquiry used by the Greeks to better understand the laws of dynamics.
- Disciplines like Mathematics and Physics function best when integrated into one.
- New knowledge about natural phenomena builds on existing knowledge.
The Correct Option is D
Solution and Explanation
The question asks for the theme, which is the single idea that covers the whole passage. A correct theme must fit all four paragraphs. A choice that fits only one paragraph, or that adds an idea from outside, is wrong.
Step 2: Trace the passage paragraph by paragraph:
Paragraph 1: Galileo starts modern science by insisting on experiment, and finds the law of dynamics.
Paragraph 2: Newton comes "next" and uses mathematics for physical problems.
Paragraph 3: Newton's calculus and gravitation show law and order in nature.
Paragraph 4: Einstein extends "the validity of the Newtonian principle" to all phenomena.
The pattern is a chain. Each scientist takes what the earlier one built and moves it forward. The words "next advance", "extended" and "merely an extension" show this.
Step 3: Check option (1):
The passage says the Greeks never grasped the value of experiment, and that modern science "can be said to have originated with Galileo and Newton". So modern science does not rest on the Greeks. (1) is wrong.
Step 4: Check option (2):
The Greeks are shown as failing to see the use of experiment. The author never suggests going back to their way. (2) is wrong.
Step 5: Check option (3):
Joining mathematics and physics is the main point of paragraph 2 and the start of paragraph 3. But paragraphs 1 and 4 are about experiment and relativity, and they are not about joining subjects. So (3) covers only a part of the passage. It is too narrow to be the theme.
Step 6: Check option (4):
New knowledge building on existing knowledge fits the whole chain from Galileo to Newton to Einstein. This is the theme.
Final Answer:
The idea that runs through the passage is that new knowledge builds on what is already known, which is option (4). \[ \boxed{4} \]
The significant implication of Einstein’s special principle of relativity is that
Show Hint
Think about what that tells you about the power of experiments.
- absolute velocity was meaningless in the realm of mechanics.
- Newton’s principle of relativity needs to be modified.
- there are limits to which experimentation can be used to understand some physical phenomena.
- it is meaningless to try to understand the distinction between velocity and accelerated or rotational motion.
The Correct Option is C
Solution and Explanation
The stem asks for the "significant implication" of Einstein's special principle of relativity. An implication is something that follows from the principle. So first we need to know what the principle says, using the last paragraph.
Step 2: What the principle says:
The paragraph says the principle holds that "absolute Galilean motion or absolute velocity must ever escape all experimental detection." So no experiment of any kind can ever show absolute velocity. Therefore absolute velocity is "physically meaningless" in "the entire realm of physical phenomena", and not only in mechanics.
It also says this "created a still more profound distinction between velocity and accelerated or rotational motion", because the latter "remained absolute and real as before".
Step 3: Draw the implication:
If some quantity can never be found by any experiment, then experiment has a limit. There are physical things that we cannot understand by experimenting. That is what option (3) says.
Step 4: Check option (1):
In mechanics absolute velocity was already meaningless in Newton's day ("as in Newton's day"). The new point of Einstein is that it is meaningless in all of physics. So (1) is not the significant implication, and it also describes an old position. It is wrong.
Step 5: Check option (2):
The passage says Newton's principle was extended, not corrected. The last line calls Einstein's principle "merely an extension". So no change to Newton's principle is needed. (2) is wrong.
Step 6: Check option (4):
The passage says the opposite. The principle created a "more profound distinction" between velocity and accelerated or rotational motion, and the author says "it is most important to understand this point". So it is not meaningless to study the distinction. (4) is wrong.
Final Answer:
The principle implies that experiment cannot detect absolute velocity, so there are limits to experimentation, which is option (3). \[ \boxed{3} \]
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