"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.”

Which of the following would strengthen the ending of 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.”

The purpose of this passage is __________.

Adapted from “Darwin’s Predecessors” by J. Arthur Thomson in Evolution in Modern Thought (1917 ed.)

In seeking to discover Darwin's relation to his predecessors, it is useful to distinguish the various services which he rendered to the theory of organic evolution.

As everyone knows, the general idea of the doctrine of descent is that the plants and animals of the present day are the lineal descendants of ancestors on the whole somewhat simpler, that these again are descended from yet simpler forms, and so on backwards towards the literal "Protozoa" and "Protophyta" about which we unfortunately know nothing. Now no one supposes that Darwin originated this idea, which in rudiment at least is as old as Aristotle. What Darwin did was to make it current intellectual coin. He gave it a form that commended itself to the scientific and public intelligence of the day, and he won widespread conviction by showing with consummate skill that it was an effective formula to work with, a key which no lock refused. In a scholarly, critical, and preeminently fair-minded way, admitting difficulties and removing them, foreseeing objections and forestalling them, he showed that the doctrine of descent supplied a modal interpretation of how our present-day fauna and flora have come to be.

In the second place, Darwin applied the evolution-idea to particular problems, such as the descent of man, and showed what a powerful tool it is, introducing order into masses of uncorrelated facts, interpreting enigmas both of structure and function, both bodily and mental, and, best of all, stimulating and guiding further investigation. But here again it cannot be claimed that Darwin was original. The problem of the descent or ascent of man, and other particular cases of evolution, had attracted not a few naturalists before Darwin's day, though no one [except Herbert Spencer in the psychological domain (1855)] had come near him in precision and thoroughness of inquiry.

In the third place, Darwin contributed largely to a knowledge of the factors in the evolution-process, especially by his analysis of what occurs in the case of domestic animals and cultivated plants, and by his elaboration of the theory of natural selection, which Alfred Russel Wallace independently stated at the same time, and of which there had been a few previous suggestions of a more or less vague description. It was here that Darwin's originality was greatest, for he revealed to naturalists the many different forms—often very subtle—which natural selection takes, and with the insight of a disciplined scientific imagination he realized what a mighty engine of progress it has been and is.

What is the overall purpose of this passage?

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 best states the main idea of this passage?

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.

Which of the following best states the main idea of this passage?

Adapted from "How the Soil is Made" by Charles Darwin in Wonders of Earth, Sea, and Sky (1902, ed. Edward Singleton Holden)

Worms have played a more important part in the history of the world than most persons would at first suppose. In almost all humid countries they are extraordinarily numerous, and for their size possess great muscular power. In many parts of England a weight of more than ten tons (10,516 kilograms) of dry earth annually passes through their bodies and is brought to the surface on each acre of land, so that the whole superficial bed of vegetable mould passes through their bodies in the course of every few years. From the collapsing of the old burrows, the mold is in constant though slow movement, and the particles composing it are thus rubbed together. Thus the particles of earth, forming the superficial mold, are subjected to conditions eminently favorable for their decomposition and disintegration. This keeps the surface of the earth perfectly suited to the growth of an abundant array of fruits and vegetables.

Worms are poorly provided with sense-organs, for they cannot be said to see, although they can just distinguish between light and darkness; they are completely deaf, and have only a feeble power of smell; the sense of touch alone is well developed. They can, therefore, learn little about the outside world, and it is surprising that they should exhibit some skill in lining their burrows with their castings and with leaves, and in the case of some species in piling up their castings into tower-like constructions. But it is far more surprising that they should apparently exhibit some degree of intelligence instead of a mere blind, instinctive impulse, in their manner of plugging up the mouths of their burrows. They act in nearly the same manner as would a man, who had to close a cylindrical tube with different kinds of leaves, petioles, triangles of paper, etc., for they commonly seize such objects by their pointed ends. But with thin objects a certain number are drawn in by their broader ends. They do not act in the same unvarying manner in all cases, as do most of the lower animals.

Worms are characterized as all of the following in this passage EXCEPT __________.

Adapted from "Bats" by W. S. Dallas in A Book of Natural History (1902, ed. David Starr Jordan)

Like the owls, with which they share the dominion of the evening air, the bats have a perfectly noiseless flight; their activity is chiefly during the twilight, although some species are later, and in fact seem to keep up throughout the whole night. As they rest during the day, concealed usually in the most inaccessible places they can find, and are seen only upon the wing, their power of flight is their most striking peculiarity in the popular mind, and it is perhaps no great wonder that by many people, both in ancient and modern times, they have been regarded as birds. Nevertheless, their hairy bodies and leathery wings are so unlike anything that we ordinarily understand as pertaining to a bird, that opinion was apparently always divided, as to the true nature of these creatures—“a mouse with wings,” as Goldsmith called it once, according to James Boswell, is certainly a curious animal, and very difficult to classify so long as the would-be systematist has no particularly definite ideas to guide him. The likeness of the bat to a winged mouse has made itself felt in the name given to the creature in many languages, such as the “chauvesouris” of the French and the “flitter-mouse” of some parts of England, the latter being reproduced almost literally in German, Dutch, and Swedish, while the Danes called the bat a “flogenmues,” which has about the same meaning.

Throughout this passage the author primarily highlights the __________ nature of bats.

Adapted from "The Man-Like Apes" by T. H. Huxley in A Book of Natural History (1902, ed. David Starr Jordan)

The orangutan is found only in Sumatra and Borneo, and is common in either of these islands—in both of which it occurs always in low, flat plains, never in the mountains. It loves the densest and most sombre of the forests, which extend from the seashore inland, and thus is found only in the eastern half of Sumatra, where alone such forests occur, though, occasionally, it strays over to the western side. On the other hand, it is generally distributed through Borneo, except in the mountains, or where the population is dense. In favorable places the hunter may, by good fortune, see three or four in a day.

Except in the pairing time, the old males usually live by themselves. The old females and the immature males, on the other hand, are often met with in twos and threes, and the former occasionally have young with them, though the pregnant females usually separate themselves, and sometimes remain apart after they have given birth to their offspring. The young orangs seem to remain unusually long under their mother’s protection, probably in consequence of their slow growth. While climbing, the mother always carries her young against her bosom, the young holding on by the mother’s hair. At what time of life the orangutan becomes capable of propagation, and how long the females go with young is unknown, but it is probable that they are not adult until they arrive at ten or fifteen years of age. A female which lived for five years at Batavia had not attained one-third the height of the wild females. It is probable that, after reaching adult years, they go on growing, though slowly, and that they live to forty or fifty years. The Dyaks tell of old orangs that have not only lost all their teeth, but which find it so troublesome to climb that they maintain themselves on windfalls and juicy herbage.

The primary purpose of this passage is to __________.

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.

Which of the following best expresses the main idea of the passage?

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.

The purpose of the passage’s third paragraph is __________.