For anyone claiming to write a history of a science of which reasoning forms the very essence, the question of the logic is of paramount importance. For example, a modern western account of any historical period in mathematics would, as a matter of course, show a detailed proof justifying each and every mathematical result discussed. Despite this obvious fact, general histories of Chinese mathematics rarely show concern for this issue. They insist above all on presenting only the mathematical results, the logical underpinnings of which are unclear, and rarely do they provide the reader with any semblance of a proof. While this approach to the history of mathematics is naturally a result of various causes, one which probably plays an essential role is the fact that most Chinese mathematical works themselves contain no logical justifications: according to this worldview, apparently it was enough to state authoritatively that something was true --- it was completely superfluous to demonstrate why it was true.
There is one major exception to this general pattern, namely a set of Chinese argumentative discourses which has been handed down to us from the first millennium A.D. We are referring to the commentaries and sub-commentaries on the Jiuzhang Suanshu [ "The Nine Chapters on the Mathematical Art" ], the key work which inaugurated Chinese mathematics and served as a reference for it over a long period of its history. This fact, which was long unrecognized, means that we are now in a position to know a lot more about the logical construction of mathematics in China than, for example, in Egypt, Mesopotamia, or India.
|What distinguishes the commentaries on the?Jiuzhang Suanshu?from almost all other works of Chinese mathematical history is that the authors of the former|
|Technology Analyst: The programmers at the website Cyberepicuria have recently made a breakthrough, perfecting a special program in which users can enter any foods or any flavors they like, and the website will suggest different foods and food combinations with somewhat different flavors that the users will also like. The website will charge users a modest fee for access. Users of the beta version have reported that, because of the program's suggestions, they have discovered whole new categories of food they have come to enjoy. Because Cyberepicuria is the only website offering this service, anyone who invests in Cyberepicuria right now is likely to double or triple their money in a very short time.|
|Which of the following, if true, most seriously weakens the analyst's argument above?|
|Dark matter and dark energy have little effect on conventional matter over familiar distances. Instead, they make their presence known through their prodigious gravitational effects. In tracking them down, therefore, astronomers have had to study gigantic assemblages of matter, extending across spans of millions and billions of light-years. Perhaps the first to take that sweeping viewpoint was the Swiss-American astronomer Fritz Zwicky. In the 1930`s, Zwicky traced the motions of individual galaxies within great clusters of galaxies and made a remarkable discovery: the individual galaxies are moving too fast to be held together in a cluster by the force of gravity exerted by the starry matter visible within them. From his measurements, Zwicky concluded that the great clusters of galaxies must be held together by the gravitational effect of some unseen mass, which he dubbed"dark matter."|
|It can be inferred from the passage that Zwicky hypothesized the existence of "dark matter" in order to account for|
In?Don Giovanni, what is perhaps Mozart`s best-known opera, there exist two distinct endings, a phenomenon not entirely unknown during the composer`s time, but one that invites the obvious question: Why did Mozart decide to include alternate endings for?Don Giovanni, when he did not do the same with his other famous operas,?Die Zauberfl?te?and?Le Nozze di Figaro. Another question, and one not so obvious, is: Why was Mozart himself uncertain as to which of the two endings to choose, as is evidenced in his correspondence with Lorenzo Da Ponte, the opera`s librettist?
A common answer is to treat both these questions as one: Mozart was uncertain as to which ending to provide, so he wrote both endings. Such a reply ignores an important consideration: Why did Mozart decide to provide these specific endings? Libard provides a reasonable answer: The traditional ending-in the sense that it is the one that was popular during the composer`s day, and continues to be so today-is clearly more palatable for audiences. The hero, Don Giovanni, is chided for his libertine ways and then the cast appears in tutti, bellowing a merry chorus as the curtain falls. The audience is left having a light dose of entertainment, which, after all, was the aim of many of the operas of Mozart`s time. Fine, but then what of the tragic ending? Libard-trading the sensible for the pat-offers little more than that such an ending reflects the political climate of the day.
This alternate ending-Don Giovanni is suddenly cast down to Hell, and instead of being redeemed, the hero emerges from the underworld chastened, and the curtain falls-was interpreted by the critics of the day as heavy-handed didacticism. While such a view is not entirely without merit-Mozart ultimately aimed to impart some lesson for his incorrigible Lothario-it still leaves the questioned unanswered as to why two endings, and what exactly did Mozart aim to communicate that could not be housed in a traditional ending.
One answer offered recently by musicologist Gustavo Lucien is that Mozart balked at including a traditional ending, feeling that it was incongruous with the serious tone of most of the opera. Indeed, Don Giovanni falls more under the rubric of opera serie than opera buffo, the latter typically featuring light endings in which the entire cast sings in an upbeat, major key. Da Ponte, however, insisted that forthwith casting Don Giovanni to Hell, and offering him scant opportunity for redemption, would likely leave the audience feeling ambivalent. Such an ending would also suggest that the librettist had been unable to think of a tidy resolution. Da Ponte, then, was not so much against a tragic ending as he was an abrupt tragic ending. Perhaps, even Mozart was unsure of what to do with Don Giovanni once he was in Hell, and may have even been working out a different ending, using the light ending as a stopgap till he achieved such an aim. In that case the fate of Don Giovanni can best be answered by the fact that Mozart-through debts, ill-health, and the composer`s obligation to compose works for his patrons –was unable to return to a work he had tabled.
|In the context in which it is used"tabled"most nearly means|
The `trophic contamination hypothesis` posits that shorebirds accumulate industrial and urban pollution at stopover sites, toxins that are subsequently released in sudden high doses as fat is burned during migratory flights, disrupting the bird`s ability to make migratory decisions. For example, large contaminant doses might hamper refueling by reducing the satiation signal in shorebirds so that they do not accumulate sufficient fat for migration. A recent study found that, out of those shorebirds that were unable to migrate, some weighed as much as 20% less than the average migrating bird of their species. Whether such findings are a result of shorebirds suffering from trophic contamination, or whether such birds simply cut their migrations short by landing in a foreign ecosystem is unlikely to be resolved until further studies are conducted.?
One promising line of research involves organochlorines, toxins deposited on mudflats in the 1970s and 1980s, now buried by sediments but finally close enough to the surface to be of issue to foraging shorebirds. Organochlorines should be more accessible to long-billed shorebirds that probe deeply for prey than to short-billed species that forage at or near the surface. We predict that an increased number of long-billed shorebirds will either be unable to migrate or will be found along an aberrant flight path.
|According to the passage, the author implies that foreign ecosystems have which potential effect on shorebirds?|
|Vladimir Nabokov, the scientist and the author have been treated as discrete manifestations of a prodigious and probing mind, until now. In her recent biography on Nabokov, Temoshotka makes the bold assertion that these two apparently disparate realms of Nabokov`s polymorphous genius were not so unrelated after all. While Temoshotka cannot be faulted for the boldness of her thesis-Nabokov`s hobby as a lepidopterist (a butterfly collector) and his experience as a novelist informed each other-she fails to make a convincing case. Surely, with enough ingenuity, one can find parallels, as Temoshotka does, between the creative products of Nabokov the naturalist and Nabokov the writer: the intricate butterfly wings that he pored over in his laboratory and the intricate prose that he crafted with sedulous care. But to say the prose of?Lolita?and?Speak Memory?would not have coalesced into their current incarnations had Nabokov`s hobby been, say, lawn tennis is simply reaching too far.|
|The primary purpose of the passage is to|
|A construction project has been tasked with building a four-lane road from a remote mountain fortress to a major expressway lying at the base of the mountain. The slope leading to the mountain fortress is so precipitous that the only conceivable way to carry out the project is by building the road downhill, since construction equipment is able to move down, but not up, the steep terrain. The foreman has devised the following solution: dismantle each construction vehicle and tie a part upon the back of a donkey, an animal capable of making the steep ascent. The foreman has at his disposal more than 100 donkeys, each of which is capable of making multiple trips up the mountain.|
|In order for the foreman`s plan to be successful, which of the following pieces of information is most important?|
|A company that invests the necessary infrastructure in a large untapped diamond mine can reap as much as 700% profit in the first year.?Some of the largest untapped diamond mines in the world are in the nation of Shagoca.?Therefore, the American company that brokers a deal in the capital Conkin that allows it to put the necessary infrastructure in place at those mines stands to reap tremendous profits.|
|Which of the following, if true, most helps to explain why American companies are not eager to invest in infrastructure necessary for diamond mining in Shagoca?|
|The Green Peas Grocery Store in the remote wealthy enclave of Luxville charges more than the Green Peas Grocery Store in Oak City charges for the same items. Clearly, on any given item, the Green Peas grocery franchise is taking advantage of its location in Luxville to reap higher profits on that item.|
|In evaluating the argument, it would be most useful to compare|
|Scientists have created double-blind studies so that neither the subjects of the experiment nor scientists know whether a patient is receiving an actual drug or a placebo, which is nothing more than a sugar pill. Essentially, if one knows that one is receiving an actual pill, such knowledge can affect the outcome of a study. A recent study on the effectiveness of the Selective Serotonin Reuptake Inhibitor (SSRI) Freloxamine on depression found that those subjects administered the drug were 15% more likely to have a decrease in symptoms than the control group, which was comprised of those who received a placebo. Since neither group knew which they were receiving, the placebo or the SSRI inhibitor, the observed drop in depression can only be attributed to Freloxamine.|
|Which of the following, if true, best calls into question the conclusion of the argument?|