"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 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?

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 aspect(s) of the king penguin and the emperor penguin does the passage contrast?

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 does the author compare to “like a cat after a mouse"?

Adapted from "Life Growth - Frogs" by Margaret Warner Morley in A Book of Natural History (1902, ed. David Starr Jordan)

Our common frogs, like many of the fishes, do not trouble themselves about the fate of their eggs after they are carefully laid in a safe place. They trust Mother Nature to see the little tadpoles safely through the perils of childhood, to help them avoid being eaten or starving, and cut, not their teeth, but their arms and legs.

In Venezuela, however, there dwells a frog with well developed maternal instinct. The mothers have pockets on their backs, not for their own convenience, but as cradles for their babies. The fathers put the fertilized eggs into the pockets of the mothers, and there they remain, well guarded, until the young are able to care for themselves.

How does the frog found in Venezuela differ from frogs generally found elsewhere?

Adapted from "The Wild Llama" by Charles Darwin in A Book of Natural History (1902, ed. David Starr Jordan)

The wild llama is the characteristic quadruped of the plains of Patagonia; it is the South American representative of the camel in the East. It is an elegant animal in a state of nature, with a long slender neck and fine legs. It is very common over the whole of the temperate parts of the continent, as far south as the islands near Cape Horn. It generally lives in small herds of from half a dozen to thirty in each, but on the banks of the St. Cruz we saw one herd which must have contained at least five hundred.

They are generally wild and extremely wary. Mr. Stokes told me that he one day saw through a glass a herd of these animals which evidently had been frightened and were running away at full speed, although they were so far away that he could not distinguish them with his naked eye. The sportsman frequently receives the first notice of their presence by hearing from a long distance their peculiar shrill, neighing note of alarm. If he then looks attentively, he will probably see the herd standing in a line on the side of some distant hill. On approaching nearer, a few more squeals are given, and off they set at an apparently slow, but really quick canter, along some narrow beaten track to a neighboring hill. If, however, by chance, he abruptly meets a single animal, or several together, they will generally stand motionless and intently gaze at him, then perhaps move on a few yards, turn round, and look again. What is the cause of this difference in their shyness? Do they mistake a man in the distance for their chief enemy, the puma? Or does curiosity overcome their timidity?

Why does the author equate llamas with camels in the passage's first sentence?