"Abstraction in the Sciences" by Matthew Minerd (2014)

Thinking “abstractly” is not a term that means quite the same thing in all of the sciences. Although we rarely think about this, it plays a key role in almost all of our day-to-day thought. Consider a zoologist working in a lab with many animals. When she is studying any individual tiger, she is not completely worried about the particular tiger—at least not primarily. Instead, she is trying to figure out certain characteristics of tigers in general. By meticulous testing, the zoologist carefully works out the physiology of tigers and considers what are absolutely necessary elements of their physical makeup. Even when she places a tiger in different habitats, her sight is aimed at the general condition of tigers and their needs in general.

However, things become even stranger when you start to consider how we think about mathematical objects. Consider the case of geometric figures. A triangle appears to be rather simple for most of us to think about. You can draw a triangle on a piece of paper, each side having a certain thickness and length. However when you think about this in geometry class, the triangle’s edges have no real thickness. Neither a point nor a line has a thickness for the mathematician. Such a thickness only exists on our paper, which represents the point or line. Consider also a line drawn on a piece of graph paper. Technically, there are an infinite number of points in the line. Indeed, even between 4.5 and 4.6, there are an infinite number of numbers—for example 4.55 is between them, then 4.555 between 4.55 and 4.6, and 4.5555 between 4.555 and 4.6, et cetera. In all of these cases, the mathematical reality takes on a very peculiar character when you consider it in the abstract. However, the concrete triangle remains very tangible and ordinary. Likewise, 4.6 and 4.5 inches still have 0.1 inches between them. Nevertheless, in the abstract, mathematical realities are quite strange, even stranger then the idea of “a tiger in general.”

What are the two things being contrasted in the first paragraph?

Adapted from “Humming-Birds: As Illustrating the Luxuriance of Tropical Nature” in Tropical Nature, and Other Essays by Alfred Russel Wallace (1878)

The food of hummingbirds has been a matter of much controversy. All the early writers down to Buffon believed that they lived solely on the nectar of flowers, but since that time, every close observer of their habits maintains that they feed largely, and in some cases wholly, on insects. Azara observed them on the La Plata in winter taking insects out of the webs of spiders at a time and place where there were no flowers. Bullock, in Mexico, declares that he saw them catch small butterflies, and that he found many kinds of insects in their stomachs. Waterton made a similar statement. Hundreds and perhaps thousands of specimens have since been dissected by collecting naturalists, and in almost every instance their stomachs have been found full of insects, sometimes, but not generally, mixed with a proportion of honey. Many of them in fact may be seen catching gnats and other small insects just like fly-catchers, sitting on a dead twig over water, darting off for a time in the air, and then returning to the twig. Others come out just at dusk, and remain on the wing, now stationary, now darting about with the greatest rapidity, imitating in a limited space the evolutions of the goatsuckers, and evidently for the same end and purpose. Mr. Gosse also remarks, ” All the hummingbirds have more or less the habit, when in flight, of pausing in the air and throwing the body and tail into rapid and odd contortions. This is most observable in the Polytmus, from the effect that such motions have on the long feathers of the tail. That the object of these quick turns is the capture of insects, I am sure, having watched one thus engaged pretty close to me.”

How does the quotation from Mr. Gosse relate to the evidence provided by other scientists earlier in the passage?

Adapted from “Humming-Birds: As Illustrating the Luxuriance of Tropical Nature” in Tropical Nature, and Other Essays by Alfred Russel Wallace (1878)

The food of hummingbirds has been a matter of much controversy. All the early writers down to Buffon believed that they lived solely on the nectar of flowers, but since that time, every close observer of their habits maintains that they feed largely, and in some cases wholly, on insects. Azara observed them on the La Plata in winter taking insects out of the webs of spiders at a time and place where there were no flowers. Bullock, in Mexico, declares that he saw them catch small butterflies, and that he found many kinds of insects in their stomachs. Waterton made a similar statement. Hundreds and perhaps thousands of specimens have since been dissected by collecting naturalists, and in almost every instance their stomachs have been found full of insects, sometimes, but not generally, mixed with a proportion of honey. Many of them in fact may be seen catching gnats and other small insects just like fly-catchers, sitting on a dead twig over water, darting off for a time in the air, and then returning to the twig. Others come out just at dusk, and remain on the wing, now stationary, now darting about with the greatest rapidity, imitating in a limited space the evolutions of the goatsuckers, and evidently for the same end and purpose. Mr. Gosse also remarks, ” All the hummingbirds have more or less the habit, when in flight, of pausing in the air and throwing the body and tail into rapid and odd contortions. This is most observable in the Polytmus, from the effect that such motions have on the long feathers of the tail. That the object of these quick turns is the capture of insects, I am sure, having watched one thus engaged pretty close to me.”

Which of the following does the author contrast in this passage?

Adapted from “Introduced Species That Have Become Pests” in Our Vanishing Wild Life, Its Extermination and Protection by William Temple Hornaday (1913)

The man who successfully transplants or "introduces" into a new habitat any persistent species of living thing assumes a very grave responsibility. Every introduced species is doubtful gravel until panned out. The enormous losses that have been inflicted upon the world through the perpetuation of follies with wild vertebrates and insects would, if added together, be enough to purchase a principality. The most aggravating feature of these follies in transplantation is that never yet have they been made severely punishable. We are just as careless and easygoing on this point as we were about the government of the Yellowstone Park in the days when Howell and other poachers destroyed our first national bison herd, and when caught red-handed—as Howell was, skinning seven Park bison cows—could not be punished for it, because there was no penalty prescribed by any law. Today, there is a way in which any revengeful person could inflict enormous damage on the entire South, at no cost to himself, involve those states in enormous losses and the expenditure of vast sums of money, yet go absolutely unpunished!

The gypsy moth is a case in point. This winged calamity was imported at Maiden, Massachusetts, near Boston, by a French entomologist, Mr. Leopold Trouvelot, in 1868 or 69. History records the fact that the man of science did not purposely set free the pest. He was endeavoring with live specimens to find a moth that would produce a cocoon of commercial value to America, and a sudden gust of wind blew out of his study, through an open window, his living and breeding specimens of the gypsy moth. The moth itself is not bad to look at, but its larvae is a great, overgrown brute with an appetite like a hog. Immediately Mr. Trouvelot sought to recover his specimens, and when he failed to find them all, like a man of real honor, he notified the State authorities of the accident. Every effort was made to recover all the specimens, but enough escaped to produce progeny that soon became a scourge to the trees of Massachusetts. The method of the big, nasty-looking mottled-brown caterpillar was very simple. It devoured the entire foliage of every tree that grew in its sphere of influence.

The gypsy moth spread with alarming rapidity and persistence. In course of time, the state authorities of Massachusetts were forced to begin a relentless war upon it, by poisonous sprays and by fire. It was awful! Up to this date (1912) the New England states and the United States Government service have expended in fighting this pest about $7,680,000!

The spread of this pest has been retarded, but the gypsy moth never will be wholly stamped out. Today it exists in Rhode Island, Connecticut, and New Hampshire, and it is due to reach New York at an early date. It is steadily spreading in three directions from Boston, its original point of departure, and when it strikes the State of New York, we, too, will begin to pay dearly for the Trouvelot experiment.

Howell’s story is different from that of Mr. Trouvelot’s in that __________.

Adapted from “Feathers of Sea Birds and Wild Fowl for Bedding” from The Utility of Birds by Edward Forbush (ed. 1922)

In the colder countries of the world, the feathers and down of waterfowl have been in great demand for centuries as filling for beds and pillows. Such feathers are perfect non-conductors of heat, and beds, pillows, or coverlets filled with them represent the acme of comfort and durability. The early settlers of New England saved for such purposes the feathers and down from the thousands of wild-fowl which they killed, but as the population increased in numbers, the quantity thus furnished was insufficient, and the people sought a larger supply in the vast colonies of ducks and geese along the Labrador coast. 

The manner in which the feathers and down were obtained, unlike the method practiced in Iceland, did not tend to conserve and protect the source of supply. In Iceland, the people have continued to receive for many years a considerable income by collecting eider down, but there they do not “kill the goose that lays the golden eggs.” Ducks line their nests with down plucked from their own breasts and that of the eider is particularly valuable for bedding. In Iceland, these birds are so carefully protected that they have become as tame and unsuspicious as domestic fowls In North America. Where they are constantly hunted they often conceal their nests in the midst of weeds or bushes, but in Iceland, they make their nests and deposit their eggs in holes dug for them in the sod. A supply of the ducks is maintained so that the people derive from them an annual income.

In North America, quite a different policy was pursued. The demand for feathers became so great in the New England colonies about the middle of the eighteenth century that vessels were fitted out there for the coast of Labrador for the express purpose of securing the feathers and down of wild fowl. Eider down having become valuable and these ducks being in the habit of congregating by thousands on barren islands of the Labrador coast, the birds became the victims of the ships’ crews. As the ducks molt all their primary feathers at once in July or August and are then quite incapable of flight and the young birds are unable to fly until well grown, the hunters were able to surround the helpless birds, drive them together, and kill them with clubs. Otis says that millions of wildfowl were thus destroyed and that in a few years their haunts were so broken up by this wholesale slaughter and their numbers were so diminished that feather voyages became unprofitable and were given up. 

This practice, followed by the almost continual egging, clubbing, shooting, etc. by Labrador fishermen, may have been a chief factor in the extinction of the Labrador duck, that species of supposed restricted breeding range. No doubt had the eider duck been restricted in its breeding range to the islands of Labrador, it also would have been exterminated long ago.

Which of the following does the passage directly compare?

"Comparing Technologies: A Difficult Endeavor" by Matthew Minerd (2014)

Comparisons of technology are often difficult to make, not only because of the rapid pace of improvements but also because of the many new applications that are available as time progresses. If we were to consider the contemporary graphing calculator and the calculation capacities of computing machines from fifty years ago, there would be astounding improvements between these two devices. However, the improvements are not reduced merely to speed improvements. A graphing calculator also has numerous output capacities that far exceed those available much older computers, none of which had the ability to represent their output in any manner even closely resembling that of contemporary devices. Merely consider the display capacities of such a device. These enable users to input many new kinds of information, enabling design engineers to design new hardware functions to match the new means of collecting user input.

The situation is even more obvious when one considers the numerous functions performed by a modern “smartphone.” These devices are equipped with a panoply of features.  With all of these new functions come many new types of computational capabilities as well. In order to process images quickly, specialized hardware must be designed and software written for it in order to ensure that there are few issues with the phone’s operation. Indeed, the whole “real time” nature of telecommunications has exerted numerous pressures on the designers of computing devices. Layers of complexity, at all levels of production and development, are required to ensure that the phone can function in a synchronous manner. Gone are the days of asynchronous processing, when the computer user entered data into a mainframe, only to wait for a period of time before the processing results were provided. Today, even the smallest of digital devices must provide seamless service for users. The effects of this requirement are almost beyond number.

Which of the following best describes the contrast between newer and older calculating devices?

Adapted from “Birds in Retreat” in “Animal Defences—Active Defence” in Volume Four of The Natural History of Animals: The Animal Life of the World in Its Various Aspects and Relations by James Richard Ainsworth Davis (1903)

Among the large running birds are forms, like the African ostrich, in which the absence of powers of flight is largely compensated by the specialization of the legs for the purpose of rapid movement on the ground. For straightforward retreat in open country nothing could be more effective; but another kind of adaptation is required in birds like rails, which are deficient in powers of flight, and yet are able to run through thickly-growing vegetation with such rapidity as to commonly elude their enemies. This is rendered possible by the shape of their bodies, which are relatively narrow and flattened from side to side, so as to easily slip between the stems of grasses, rushes, and similar plants. Anyone who has pursued our native land-rail or corn-crake with intent to capture will have noted how extremely difficult it is even to get within sight of a bird of this sort. 

Certain birds, unfortunately for themselves, have lost the power of flight without correspondingly increased powers of running, and have paid the penalty of extinction. Such an arrangement, as might be anticipated, was the result of evolution in islands devoid of any predatory ground-animals, and a classic example of it is afforded by the dodo and its allies, birds related to the pigeons. The dodo itself was a large and clumsy-looking species that at one time abounded in the island of Mauritius, which, like oceanic islands generally, possessed no native mammals, while its indigenous reptiles were only represented by lizards. The ubiquitous sailor, however, and the animals (especially swine) which he introduced, brought about the extinction of this helpless bird in less than a century after its first discovery in 1598. Its memory is now only kept green by a few contemporary drawings and descriptions, certain museum remains, and the proverb "as extinct as a dodo.” A similar fate must overtake any organism suddenly exposed to new and unfavorable conditions, if devoid of sufficient plasticity to rapidly accommodate itself to the altered environment.

One of the main differences between an ostrich and a rail, according to the passage, is __________.

Adapted from “Birds in Retreat” in “Animal Defences—Active Defence” in Volume Four of The Natural History of Animals: The Animal Life of the World in Its Various Aspects and Relations by James Richard Ainsworth Davis (1903)

Among the large running birds are forms, like the African ostrich, in which the absence of powers of flight is largely compensated by the specialization of the legs for the purpose of rapid movement on the ground. For straightforward retreat in open country nothing could be more effective; but another kind of adaptation is required in birds like rails, which are deficient in powers of flight, and yet are able to run through thickly-growing vegetation with such rapidity as to commonly elude their enemies. This is rendered possible by the shape of their bodies, which are relatively narrow and flattened from side to side, so as to easily slip between the stems of grasses, rushes, and similar plants. Anyone who has pursued our native land-rail or corn-crake with intent to capture will have noted how extremely difficult it is even to get within sight of a bird of this sort. 

Certain birds, unfortunately for themselves, have lost the power of flight without correspondingly increased powers of running, and have paid the penalty of extinction. Such an arrangement, as might be anticipated, was the result of evolution in islands devoid of any predatory ground-animals, and a classic example of it is afforded by the dodo and its allies, birds related to the pigeons. The dodo itself was a large and clumsy-looking species that at one time abounded in the island of Mauritius, which, like oceanic islands generally, possessed no native mammals, while its indigenous reptiles were only represented by lizards. The ubiquitous sailor, however, and the animals (especially swine) which he introduced, brought about the extinction of this helpless bird in less than a century after its first discovery in 1598. Its memory is now only kept green by a few contemporary drawings and descriptions, certain museum remains, and the proverb "as extinct as a dodo.” A similar fate must overtake any organism suddenly exposed to new and unfavorable conditions, if devoid of sufficient plasticity to rapidly accommodate itself to the altered environment.

How does the second paragraph relate to the first paragraph?

Adapted from “Comets” by Camille Flammarion in Wonders of Earth, Sea, and Sky (1902, ed. Edward Singleton Holden)

The history of a comet would be an instructive episode of the great history of the heavens. In it could be brought together the description of the progressive movement of human thought, as well as the astronomical theory of these extraordinary bodies. Let us take, for example, one of the most memorable and best-known comets, and give an outline of its successive passages near the Earth. Like the planetary worlds, comets belong to the solar system, and are subject to the rule of the Star King. It is the universal law of gravitation which guides their path; solar attraction governs them, as it governs the movement of the planets and the small satellites. The chief point of difference between them and the planets is that their orbits are very elongated, and instead of being nearly circular, they take the elliptical form. In consequence of the nature of these orbits, the same comet may approach very near the sun, and afterwards travel from it to immense distances.

Thus, the period of the Comet of 1680 has been estimated at three thousand years. It approaches the sun, so as to be nearer to it than our moon is to us, whilst it recedes to a distance 853 times greater than the distance of the Earth from the sun. On the 17th of December, 1680, it was at its perihelion—that is, at its greatest proximity to the sun; it is now continuing its path beyond the Neptunian orbit. Its velocity varies according to its distance from the solar body. At its perihelion it travels thousands of leagues per minute; at its aphelion it does not pass over more than a few yards.  

Its proximity to the Sun in its passage near that body caused Newton to think that it received a heat twenty-eight thousand times greater than that we experience at the summer solstice, and that this heat being two thousand times greater than that of red-hot iron, an iron globe of the same dimensions would be fifty thousand years entirely losing its heat. Newton added that in the end, comets will approach so near the sun that they will not be able to escape the preponderance of its attraction, and that they will fall one after the other into this brilliant body, thus keeping up the heat which it perpetually pours out into space. Such is the deplorable end assigned to comets by the author of the Principia, an end which makes De la Brétonne say to Rétif: "An immense comet, already larger than Jupiter, was again increased in its path by being blended with six other dying comets. Thus displaced from its ordinary route by these slight shocks, it did not pursue its true elliptical orbit; so that the unfortunate thing was precipitated into the devouring centre of the Sun." "It is said," added he, "that the poor comet, thus burned alive, sent forth dreadful cries!"

According to the author, what is the primary difference between comets and planets?

Adapted from Volume Four of The Natural History of Animals: The Animal Life of the World in Its Various Aspects and Relations by James Richard Ainsworth Davis (1903)

The examples of protective resemblance so far quoted are mostly permanent adaptations to one particular sort of surrounding. There are, however, numerous animals which possess the power of adjusting their color more or less rapidly so as to harmonize with a changing environment.

Some of the best known of these cases are found among those mammals and birds that inhabit countries more or less covered with snow during a part of the year. A good instance is afforded by the Irish or variable hare, which is chiefly found in Ireland and Scotland. In summer, this looks very much like an ordinary hare, though rather grayer in tint and smaller in size, but in winter it becomes white with the exception of the black tips to the ears. Investigations that have been made on the closely allied American hare seem to show that the phenomenon is due to the growth of new hairs of white hue. 

The common stoat is subject to similar color change in the northern parts of its range. In summer it is of a bright reddish brown color with the exception of the under parts, which are yellowish white, and the end of the tail, which is black. But in winter, the entire coat, save only the tip of the tail, becomes white, and in that condition the animal is known as an ermine. A similar example is afforded by the weasel. The seasonal change in the vegetarian Irish hare is purely of protective character, but in such an actively carnivorous creature as a stoat or weasel, it is aggressive as well, rendering the animal inconspicuous to its prey.

For what reason does the author describe the Irish hare as “vegetarian” in the underlined sentence?