Answers and Explanations—6.3 Difference and Analytical Engines

P1	Paragraph 1	Comments
S1	The shift in processing power and information storage from human beings to computers over the past several decades represents the most significant change in productivity since the Industrial Revolution.	Shift from humans to computers = biggest change in work since Industrial Revolution.
2	Despite all of the obvious technological improvements in production, manufacturing technique, materials, and engineering, no other innovation can rival computers in terms of their overall impact on the economy.
3	The most basic dichotomy in information processing today lies between computers on the one hand and human beings on the other.

	The word “dichotomy” in the passage is closest in meaning to	VOCABULARY. “Dichotomy” = contrast, opposition, or separation between two different things.
✗	A comparison	“Comparison” emphasizes similarity, not difference.
✓	B contrast	Correct. “The most basic dichotomy in information processing today lies between computers on the one hand and human beings on the other” = the most basic contrast, opposition, or separation in information processing lies between computers and humans.
✗	C contradiction	In a few circumstances, “dichotomy” might go so far as to mean “contradiction” (= logical inconsistency between two things). But here, the dichotomy between humans and computers is not one of literal, logical contradiction. Rather, it is a contrast or opposition.
✗	D confluence	“Confluence” = the flowing together of two things.

	Which of the sentences below best expresses the essential information in the highlighted sentence in paragraph 1? Incorrect choices change the meaning in important ways or leave out essential information.	Simplify Sentence. The first part of S2 acknowledges the technological advances in production, manufacturing technique, materials, and engineering that have occurred. The second part of S2 states that they cannot compare to computers in terms of their overall economic impact.
✗	A Despite technological improvements in computers, innovations in such areas as production and manufacturing rival them with regard to their economic impact.	This version claims that the other listed items can rival computers in terms of economic impact. The original sentence claims the opposite.
✓	B The economic impact of computers is unmatched by that of any technological innovation in other areas such as manufacturing and production.	Correct. This choice says essentially the same thing as S2, but changes the order of ideas and simplifies the language.
✗	C In spite of developments in production, manufacturing technique, materials, and engineering, none of these are as economically innovative as computers.	The comparison in the original sentence is about overall impact on the economy. But in this version, the comparison is about the degree of “economic innovation,” which means something different.
✗	D Despite technological improvements in their production, computers cannot match other inventions in terms of their overall impact on the economy.	In the original sentence, computers surpass other inventions with regard to economic impact. Moreover, this version relates the “Despite” part to computers (“their production”), whereas in the original sentence, the contrasted technological improvements were about the other inventions.

P2	Paragraph 2	Comments
S1	Interestingly, if a person today were asked, “When was the first computer program ever written?”, he or she would probably miss the mark by over a century.	First computer program was written over a century before you might expect.
2	Many might think of the Electronic Numerical Integrator and Computer (ENIAC).	Various early computers.
3	Completed in 1946 at the University of Pennsylvania, ENIAC was the first completely electronic general-use computer.
4	Others may think of the Universal Automatic Computer (UNIVAC), the first commercially used electronic computer, built in 1951 by the inventors of ENIAC.
5	Or perhaps one would think of the electromechanical machines that preceded ENIAC, such as those that controlled telephone exchanges in the first half of the twentieth century.
6	In fact, the first completed computer program dates back to 1843.	But actual first program was written in 1843.
7	It was written by Ada Lovelace (1815–1852), a mathematician and colleague of Charles Babbage (1791–1871), inventor of the “difference engine” and, later, the “analytical engine.”	Ada Lovelace. Charles Babbage, who invented the difference & analytical engines.

	According to paragraph 2, which of the following statements about the first computer program is true?	Fact. S3–5 discuss the first electronic computers ever built. S6–7 point out that the first completed computer program predates those electronic computers by over 100 years.
✓	A It was written in the nineteenth century.	Correct. S6–7: “the first completed computer program dates back to 1843. It was written by Ada Lovelace (1815–1852).” These dates were in the nineteenth century.
✗	B It was written by Charles Babbage.	S7 states that Ada Lovelace was a colleague of Charles Babbage (and the rest of the passage is devoted to discussing Babbage’s inventions). But S6–7 clearly state that it was Lovelace who wrote the first computer program.
✗	C It was written for ENIAC at the University of Pennsylvania.	S3 states that ENIAC was the first completely electronic general-use computer, but S6–7 later clarify that the first completed computer program came over 100 years before that.
✗	D It was written for a completely electronic general-use computer.	S3: “ENIAC was the first completely electronic general-use computer.” The first computer program was written over 100 years earlier.

	According to paragraph 2, all of the following statements about UNIVAC are true EXCEPT:	Negative Fact. S4 discusses the background of UNIVAC. Three answer choices will be referenced in the paragraph. One answer choice will not be.
✗	A It was built by the creators of ENIAC.	S4: “Others may think of the Universal Automatic Computer (UNIVAC)… built in 1951 by the inventors of ENIAC.”
✗	B It was the first electronic computer used commercially.	S4: “Others may think of the Universal Automatic Computer (UNIVAC), the first commercially used electronic computer.”
✓	C It was an electromechanical machine that preceded ENIAC.	Correct. S4 states that UNIVAC was built in 1951, while S3 states ENIAC was built in 1946. Furthermore, nothing in the paragraph indicates that it was “electromechanical,” rather than fully electronic.
✗	D It was created after machines to control telephone exchanges were developed.	S4 states that UNIVAC was built in 1951, while S3 states ENIAC was built in 1946. S5 mentions “electromechanical machines that preceded ENIAC, such as those that controlled telephone exchanges.” Therefore, these machines were developed before UNIVAC was invented.

P3	Paragraph 3	Comments
S1	Babbage was an English mathematician, inventor, and engineer.
2	He is regarded by many as the father of modern-day computing.	Babbage = father of modern computing.
3	He began work designing the first version of his difference engine in 1822.	1822: started working on difference engine.
4	This mechanical engine was to compute the value of polynomial functions using a mathematical process known as “finite differences.”	Mechanical engine to compute math values.
5	Using this method, the difference engine would only be capable of adding and subtracting.
6	Unfortunately, Babbage ran into difficulties both with funding his project and with the builder of the initial prototype of his design, and the project was abandoned partway through.	But he ran into difficulties.
7	Eventually, Babbage shifted to designing what he called the “analytical engine,” which drew on his designs for the difference engine but was intended as a more general computing machine.	Shifted to more general “analytical engine.”

	The word “abandoned” in the passage is closest in meaning to	VOCABULARY. “Abandon” = leave behind, give up, walk away from permanently.
✗	A corrected	The project wasn’t corrected (fixed) but rather abandoned (given up).
✗	B continued	Opposite. To continue is to keep going, while abandon means to quit.
✗	C shackled	Not quite. “Shackle” = constrain, restrict, restrain. This is not the same as “abandon.”
✓	D scrapped	Correct. “The project was abandoned partway through” = the project was scrapped or given up partway through.

	In paragraph 3, why does the author provide the information regarding funding for the initial prototype of the difference engine?	Purpose. S6: “Unfortunately, Babbage ran into difficulties both with funding his project and with the builder of the initial prototype of his design, and the project was abandoned partway through.” The author is strongly implying that difficulties with funding (as well as with the builder) led to Babbage’s abandonment of the difference engine and his shift in focus to the analytical engine.
✗	A To assert that the difference engine would have been completed with better funding	S6 indicates that Babbage had difficulties with funding. But nothing in the passage suggests that he could have completed the work with better funding. S6 also notes that Babbage also had separate difficulties with the builder of the prototype.
✗	B To acknowledge the resources that made completing the prototype of the difference engine possible	The prototype of the difference engine was never completed.
✓	C To explain, at least in part, why the prototype of the difference engine was abandoned	Correct. S6 directly implies that difficulties with funding led to, or at least contributed to, the fact that Babbage abandoned development of the difference engine.
✗	D To highlight a factor that would be useful as focus shifted to the analytical engine	Perhaps Babbage recognized that he would need better funding sources for his next project. But the passage never makes this claim.

P4	Paragraph 4	Comments
S1	The analytical engine featured a new concept called “punched cards,” which would contain coded information that the engine would accept as inputs.	“Punched card” inputs.
2	The machine would then produce outputs in the form of a drawn curve, printed output, or additional punched cards to be used later.	Various outputs.
3	The machine would have a unit designed to perform computation and another unit to store information.	Computation and storage.
4	Though the design of these units was mechanical rather than electronic, they are directly analogous to the processor and memory found in computers today.	Mechanical, but analogous to electronic components of today’s computers.

	The phrase “analogous to” in the passage is closest in meaning to	VOCABULARY. “Analogous” = similar, parallel, comparable.
✗	A coupled with	Not quite. “Coupled” = attached, joined. The use of this word would imply physical attachment in this case.
✓	B comparable to	Correct. “They are directly analogous to the processor and memory” = they are directly comparable to these parts.
✗	C opposed to	In some ways the opposite. “Antithetical” = opposing, contradictory.
✗	D descended from	These mechanical elements may have been ancestors of components of modern computers. But “ancestral” and “analogous” are not synonyms.

	According to paragraph 4, all of the following are design features of the analytical engine EXCEPT:	Negative Fact. The entire paragraph is devoted to describing the design of the analytical engine. Three answer choices will be contained in the paragraph. One answer choice will not be.
✗	A It would produce punched cards as output.	S2: “The machine would then produce outputs in the form of… additional punched cards to be used later.”
✗	B It would receive instructions via punched cards.	S1: “The analytical engine featured… ‘punched cards,’ which would contain coded information that the engine would accept as inputs.”
✗	C It would store information and perform calculations.	S3: “The machine would have a unit designed to perform computation and another unit to store information.”
✓	D It would contain a basic electronic processor.	CORRECT. S4: “the design of these units was mechanical rather than electronic.”

P5	Paragraph 5	Comments
S1	Lovelace’s computer program, designed for use on the analytical engine once it was built, was modest by modern standards.	Lovelace’s program for the engine: modest to our eyes.
2	It simply entailed a written, step-by-step description of how a machine might compute a mathematical series known as the Bernoulli numbers.	Step-by-step description of how to compute certain numbers.
3	However, as simple as it was, it had all of the traits of a modern-day computer algorithm: a set of instructions to be followed by a computer, operating upon a set of inputs, in order to arrive at a desired set of outputs.	Simple. But all the traits of a modern algorithm.

	According to paragraph 5, Lovelace’s computer program	Fact. S1 states that Lovelace’s program was “modest by modern standards.” S2 describes its simple purpose. S3 indicates, however, that “it had all of the traits of a modern-day computer algorithm.”
✗	A appeared ill-suited to compute a mathematical series	S2 states that it was a step-by-step description of how to compute a mathematical series. The paragraph never claims that Lovelace’s program was ill-suited to carry out this task.
✗	B was eventually used on modern computers	The passage does not state that Lovelace’s program was ever used on a modern computer.
✗	C was employed to discover the Bernoulli numbers	Lovelace’s program was designed to work on the analytical engine once it was built. But with the use of “would” throughout, the paragraph implies that it never was built. Furthermore, the Bernoulli numbers seem to have already been known before she wrote the program. Nothing indicates that her program enabled their discovery.
✓	D had the core features of modern algorithms	Correct. S3: “it had all of the traits of a modern-day computer algorithm.”

P6	Paragraph 6	Comments
S1	Like the original difference engine, Babbage’s analytical engine was never completely built.	Analytical engine was never completed.
2	The combination of financial resources and available technology to implement Babbage’s blueprint was simply insufficient during his lifetime.
3	In fact, Babbage worked for decades to simplify his design so that building it would be feasible; he was only able to finish building a small portion of it before his death in 1871.	He built just a small part before he died.
4	Babbage’s son, Henry, continued to work on building the analytical engine, and was able to produce some of the desired outputs from the machine.	Son kept working on. Produced some outputs.
5	However, Henry never came close to realizing his father’s complete vision.	But never realized the vision.

	The phrase “feasible” in the passage is closest in meaning to	VOCABULARY. “Feasible” = possible, practical.
✗	A comprehensible	Not quite. Comprehension of the plans would have been necessary for them to be carried out. But comprehension would not have been sufficient. In general, “comprehensible” and “feasible” are not synonyms.
✗	B postponable	Unrelated. To “postpone” is to put off or delay.
✓	C achievable	Correct. “Babbage worked for decades to simplify his design so that building it would be feasible” = he worked to simplify his design so that building it would be achievable or possible.
✗	D impossible	Opposite.

	Paragraph 6 mentions which of the following as a difficulty facing the construction of Babbage’s analytical engine?	Fact. S2 outlines difficulties that Babbage faced in this task.
✓	A Adequate technology was not available.	Correct. S2: “The combination of financial resources and available technology to implement Babbage’s blueprint was simply insufficient during his lifetime.”
✗	B Babbage’s son did not fully understand the design.	Nothing in the paragraph indicates that Henry had difficulty understanding his father’s design. In fact, Henry was able to complete portions of it that his father never did.
✗	C Babbage’s son produced some intended outputs from the machine.	S4 states that Henry was able to do this, but this fact did not impede construction of the analytical engine.
✗	D Babbage died prematurely in 1871.	Nothing in the paragraph suggests that Babbage’s death was “premature,” or that a few additional years of life would necessarily have enabled Babbage to complete construction of the analytical engine. Indeed, Babbage “was only able to finish building a small portion of it before his death.”

P7	Paragraph 7	Comments
S1	It was not until 1991, in Australia, that a complete version of Babbage’s difference engine was produced.	1991: an actual version of the difference engine was built.
2	The completed “Difference Engine No. 2” implemented Babbage’s designs, correcting for some errors (which may have been intentional), and was constructed using only methods that might have been available in the nineteenth century.	Corrected some errors, used only 19th-century methods.
3	The finished machine works exactly as Babbage would have hoped.	It worked!
4	To this day, though, no analytical engine that matches Babbage’s later designs has ever been fully built.	No analytical engine has been fully built.

	According to paragraph 7, which of the following is true of the completed “Difference Engine No. 2”?	Fact. S1–3 discuss the completed version of this difference engine in Australia in 1991.
✗	A It corrected intentional design flaws.	S2 states that the design flaws may have been intentional. But they were not necessarily intentional.
✓	B It was built in a fashion that would have been possible in the 1800s.	Correct. S2 states that the machine “was constructed using only methods that might have been available in the nineteenth century.”
✗	C It did not perform as Babbage would have wanted.	S3: “The finished machine works exactly as Babbage would have hoped.”
✗	D It followed the completion of a version of Babbage’s analytical engine.	S4: “To this day, though, no analytical engine that matches Babbage’s later designs has ever been fully built.”

P3	Paragraph 3	Comments
S1–2	Babbage was an English mathematician, inventor, and engineer. He is regarded by many as the father of modern-day computing.
3–4	A He began work designing the first version of his difference engine in 1822. This mechanical engine was to compute the value of polynomial functions using a mathematical process known as “finite differences.”	Placement of the new sentence here does not provide a previous noun (in S2) for “This prototype engine” to refer to.
5–6	B Using this method, the difference engine would only be capable of adding and subtracting. Unfortunately, Babbage ran into difficulties both with funding his project and with the builder of the initial prototype of his design, and the project was abandoned partway through.	Placing the new sentence here does give “This prototype engine” a good reference point in S4. But this placement improperly disrupts the direct connection between S4 (which describes a “mathematical process”) and S5 (“Using this method”).
7	C Eventually, Babbage shifted to designing what he called the “analytical engine,” which drew on his designs for the difference engine but was intended as a more general computing machine.	Correct. The modifier “This prototype engine” refers to the abandoned machine discussed above. The rest of the paragraph follows the fact that the difference engine prototype was not built.
End	D	Placing the new sentence here implies that “Difference Engine No. 1” was the name of the “analytical engine.” However, these two kinds of engines are distinguished carefully in the passage.

	This prototype engine, known as “Difference Engine No. 1,” would never be fully constructed. Where would the sentence best fit?	Insert Text. The previous sentence needs to refer to an engine, so that “This prototype engine” makes sense. Given the content of the new sentence, this engine ought to be a difference engine that Babbage was trying to build. Wherever the new sentence is placed, it should not interrupt the logical flow of existing sentences.
✗	A Choice A
✗	B Choice B
✓	C Choice C	Correct.
✗	D Choice D

	Whole Passage	Comments
P1	The shift in processing power and information storage from human beings to computers over the past several decades represents the most significant change in productivity since the Industrial Revolution…	Shift from humans to computers = biggest change in work since Industrial Revolution.
P2	Interestingly, if a person today were asked, “When was the first computer program ever written?”, he or she would probably miss the mark by over a century…	First computer program was written over a century before you might expect. Various early computers. But actual first program was written in 1843. Ada Lovelace. Charles Babbage, who invented the difference & analytical engines.
P3	Babbage was an English mathematician, inventor, and engineer…	Babbage = father of modern computing. 1822: started working on difference engine. Mechanical engine to compute math values. But he ran into difficulties. Shifted to more general “analytical engine.”
P4	The analytical engine featured a new concept called “punched cards,” which would contain coded information that the engine would accept as inputs…	“Punched card” inputs. Various outputs. Computation and storage. Mechanical, but analogous to electronic components of today’s computers.
P5	Lovelace’s computer program, designed for use on the analytical engine once it was built, was modest by modern standards…	Lovelace’s program for the engine: modest to our eyes. Step-by-step description of how to compute certain numbers. Simple. But all the traits of a modern algorithm.
P6	Like the original difference engine, Babbage’s analytical engine was never completely built…	Analytical engine was never completed. He built just a small part before he died. Son kept working on. Produced some outputs. But never realized the vision.
P7	It was not until 1991, in Australia, that a complete version of Babbage’s difference engine was produced…	1991: an actual version of the difference engine was built. Corrected some errors, used only 19th-century methods. It worked! No analytical engine has been fully built.

	Although the nineteenth-century inventions of Charles Babbage were not completed in his lifetime, they foreshadow the modern computer.	Summary. Correct answers must be clearly expressed in the passage. They must also be among the major points of the passage. They should tie as directly as possible to the summary given.
✓	a The first known computer program was written by Ada Lovelace to be used on Babbage’s analytical engine.	Correct. P2 and P4 discuss the historical significance of Lovelace’s program in the context of Babbage’s inventions and the development of modern computer programming.
✗	b Babbage is acknowledged as the inventor of ENIAC and UNIVAC, the first fully electronic computing machines.	P2 states that ENIAC and UNIVAC were completed nearly a century after Babbage’s death (1871, from P6). Babbage’s influence on those projects was probably significant. But the passage never states that Babbage is acknowledged as the inventor of these computing machines.
✓	c The recent completion of one of Babbage’s designs showed that his machines could work as “computation engines,” as intended.	Correct. This is a significant event in P7, especially in light of the difficulties Babbage had in building his machines during his lifetime (and the difficulties others had after his death). His designs didn’t just signal to later inventors the features that computers should have. His designs actually contained mechanical models of those features, models that would work as expected if built.
✓	d Babbage’s mechanical machines provided models for many features of modern electronic computing.	Correct. Various “computer” features (such as printed output, storing information, and performing mathematical computations) are outlined in P4.
✗	e Henry Babbage, Charles’s son, was never able to turn his father’s vision into reality.	This detail is mentioned in P6. However, it is relatively minor in the scheme of this passage.
✗	f Modern computing power is unlikely to be the most important economic innovation in history.	P1 makes an opposing point, although not in as stark and extreme a fashion.