"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 is meant by the underlined selection, "Her sight is aimed at"?

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 phrase “harmonize with,” underlined in the first paragraph, most closely means __________.

Adapted from "Sea-slugs and Cuttlefish" by Charles Darwin in A Book of Natural History (1902, ed. David Starr Jordan)

I was much interested, on several occasions, by watching the habits of a cuttlefish. Although common in the pools of water left by the retiring tide, these animals were not easily caught. By means of their long arms and suckers, they could drag their bodies into very narrow crevices; and when thus fixed, it required great force to remove them. At other times they darted, with the rapidity of an arrow, from one side of the pool to the other, at the same instant discoloring the water with a dark chestnut-brown ink. These animals also escape detection by a very extraordinary, chameleon-like power of changing their color. They appear to vary their tints according to the nature of the ground over which they pass: when in deep water, their general shade was brownish-purple, but when placed on the land, or in shallow water, this dark tint changed into one of a yellowish green.

This cuttlefish displayed its chameleon-like power both during the act of swimming and whilst remaining stationary at the bottom. I was amused by the various arts to escape detection used by one individual, which seemed fully aware that I was watching it. Remaining for a time motionless, it would then stealthily advance an inch or two, like a cat after a mouse; sometimes changing its color, it proceeded, till having gained a deeper part, it darted away, leaving a dusky train of ink to hide the hole into which it had crawled.

What is the “chameleon-like” power of the cuttlefish that the author describes?

Adapted from Chatterbox Stories of Natural History by R. Worthington (1880)

The guinea pig is a native of South America, and is remarkable for the beauty and variety of its colors and the neatness of its appearance. These little pets are very careful in keeping themselves and their offspring neat and tidy, and may be frequently seen smoothing and dressing their fur, somewhat in the manner of a cat. After having smoothed and dressed each other's fur, both turn their attention to their young, from whose coats they remove the smallest speck of dirt, at the same time trying to keep their hair smooth and unruffled. The guinea pig feeds on bread, grain, fruit, vegetables, tea leaves, and especially garden parsley, to which it is very partial. It generally gives birth to seven and eight young at a time, and they very soon are able to take care of themselves.

Which part of a guinea pig is compared to a cat in the passage?

Adapted from Chatterbox Stories of Natural History by R. Worthington (1880)

The guinea pig is a native of South America, and is remarkable for the beauty and variety of its colors and the neatness of its appearance. These little pets are very careful in keeping themselves and their offspring neat and tidy, and may be frequently seen smoothing and dressing their fur, somewhat in the manner of a cat. After having smoothed and dressed each other's fur, both turn their attention to their young, from whose coats they remove the smallest speck of dirt, at the same time trying to keep their hair smooth and unruffled. The guinea pig feeds on bread, grain, fruit, vegetables, tea leaves, and especially garden parsley, to which it is very partial. It generally gives birth to seven and eight young at a time, and they very soon are able to take care of themselves.

According to the passage, which of these is a guinea pig’s favorite food?

Adapted from Chatterbox Stories of Natural History by R. Worthington (1880)

I would now like to talk briefly about the beaver. This industrious animal is generally found in Canada and the northern portions of the United States, where it makes its home on the banks of the rivers and lakes. Here they assemble in hundreds to assist each other in the construction of their dams, and in the building of their houses, which are put together with a considerable amount of engineering skill. The materials used in building the dams are wood, stones, and mud, which they collect themselves for that purpose, and after finishing the dam, or winter storehouse, they collect their stores for the winter's use, and then make a connection with their houses in the banks. Their skins are valuable in making fine hats, and their flesh is much relished by the hunters. The beaver is an interesting animal in many respects, and the expression “busy as a beaver” is borne out by its habits.

Which of these aspects of beavers does the author not talk about in this passage?

Adapted from Cassell’s Natural History by Francis Martin Duncan (1913)

The penguins are a group of birds inhabiting the southern ocean, for the most part passing their lives in the icy waters of the Antarctic seas. Like the ratitae, penguins have lost the power of flight, but the wings are modified into swimming organs and the birds lead an aquatic existence and are scarcely seen on land except in the breeding season. They are curious-looking creatures that appear to have no legs, as the limbs are encased in the skin of the body and the large flat feet are set so far back that the birds waddle along on land in an upright position in a very ridiculous manner, carrying their long narrow flippers held out as if they were arms. When swimming, penguins use their wings as paddles while the feet are used for steering.

Penguins are usually gregarious—in the sea, they swim together in schools, and on land, assemble in great numbers in their rookeries. They are very methodical in their ways, and on leaving the water, the birds always follow well-defined tracks leading to the rookeries, marching with much solemnity one behind the other in soldierly order. 

The largest species of penguins are the king penguin and the emperor penguin, the former being found in Kerguelen Land, the Falklands, and other southern islands, and the latter in Victoria Land and on the pack ice of the Antarctic seas. As they are unaccustomed from the isolation of their haunts to being hunted and persecuted by man, emperor penguins are remarkably fearless, and Antarctic explorers invading their territory have found themselves objects of curiosity rather than fear to the strange birds who followed them about as if they were much astonished at their appearance. 

The emperor penguin lays but a single egg and breeds during the intense cold and darkness of the Antarctic winter. To prevent contact with the frozen snow, the bird places its egg upon its flat webbed feet and crouches down upon it so that it is well covered with the feathers. In spite of this precaution, many eggs do not hatch and the mortality amongst the young chicks is very great.

What does the text mean by the underlined clause “the mortality amongst the young chicks is very great”?

Adapted from "Some Strange Nurseries" by Grant Allen in A Book of Natural History (1902, ed. David Starr Jordan)

Many different types of animals employ one of two strategies in raising their young. Certain animals, called “r-strategists,” turn out thousands of eggs with reckless profusion, but they let them look after themselves, or be devoured by enemies, as chance will have it. Other animals, called “K-strategists,” take greater pain in the rearing and upbringing of the young. Large broods indicate an “r” life strategy; small broods imply a “K” life strategy and more care in the nurture and education of the offspring. R-strategists produce eggs wholesale, on the off chance that some two or three among them may perhaps survive an infant mortality of ninety-nine per cent, so as to replace their parents. K-strategists produce half a dozen young, or less, but bring a large proportion of these on an average up to years of discretion.

Which of the following is suggested by the passage's wording?

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.

What aspect of worms does the author of this passage seem to find most “surprising"?

Adapted from A Catechism of Familiar Things: Their History and the Events Which Led to Their Discovery by the Benziger Brothers (1881)

Iron is one of the most useful and abundant metals, being found in all mineral earths, stones, plants, and animal fluids. Iron is found in great masses, in various states, in the bowels of the earth; it is usually, however, compounded with stone, from which it is separated by the action of fire. In some parts of the world, whole mountains are formed of iron; among these may be mentioned the Pilot Knob and the Iron Mountain, in Missouri, being unsurpassed by anything of the kind found elsewhere.

It is hard, fusible, not very malleable, but extremely ductile, and very tenacious; it is of a greyish color, and nearly eight times heavier than water. Without iron, society could make no progress in the cultivation of the ground, in mechanical arts or trades, in architecture or navigation; it is therefore of the greatest use to man.

“Pilot Knob” is an example of __________.