Adapted from The Evolutionist at Large by Grant Allen (1881)

I am engaged in watching a brigade of ants out on foraging duty, and intent on securing for the nest three whole segments of a deceased earthworm. They look for all the world like those busy companies one sees in the Egyptian wall paintings, dragging home a huge granite colossus by sheer force of bone and sinew. Every muscle in their tiny bodies is strained to the utmost as they pry themselves laboriously against the great boulders that strew the path, and that are known to our Brobdingnagian intelligence as grains of sand. Besides the workers themselves, a whole battalion of stragglers runs to and fro upon the broad line that leads to the headquarters of the community. The province of these stragglers, who seem so busy doing nothing, probably consists in keeping communications open, and encouraging the sturdy pullers by occasional relays of fresh workmen. I often wish that I could for a while get inside those tiny brains, and see, or rather smell, the world as ants do. For there can be little doubt that to these brave little carnivores here the universe is chiefly known as a collective bundle of odors, simultaneous or consecutive. As our world is mainly a world of visible objects, theirs, I believe, is mainly a world of olfactible things.

In the head of every one of these little creatures is something that we may fairly call a brain. Of course most insects have no real brains; the nerve-substance in their heads is a mere collection of ill-arranged ganglia, directly connected with their organs of sense. Whatever man may be, an earwig at least is a conscious, or rather a semi-conscious, automaton. He has just a few knots of nerve cells in his little pate, each of which leads straight from his dim eye or his vague ear or his indefinite organs of taste; and his muscles obey the promptings of external sensations without possibility of hesitation or consideration, as mechanically as the valve of a steam engine obeys the governor balls. The poor soul's intellect is wholly deficient, and the senses alone make up all that there is of him, subjectively considered. But it is not so with the highest insects. They have something that truly answers to the real brain of men, apes, and dogs, to the cerebral hemispheres and the cerebellum that are superadded in us mammals upon the simple sense-centers of lower creatures. Besides the eye, with its optic nerve and optic perceptive organs—besides the ear, with its similar mechanism—we mammalian lords of creation have a higher and more genuine brain, that collects and compares the information given to the senses, and sends down the appropriate messages to the muscles accordingly. Now, bees and flies and ants have got much the same sort of arrangement, on a smaller scale, within their tiny heads. On top of the little knots that do duty as nerve centers for their eyes and mouths, stand two stalked bits of nervous matter, whose duty is analogous to that of our own brains. And that is why these three sorts of insects think and reason so much more intellectually than beetles or butterflies, and why the larger part of them have organized their domestic arrangements on such an excellent cooperative plan.

We know well enough what forms the main material of thought with bees and flies, and that is visible objects. For you must think about something if you think at all; and you can hardly imagine a contemplative blow-fly setting itself down to reflect, like a Hindu devotee, on the syllable Om, or on the oneness of existence. Abstract ideas are not likely to play a large part in apian consciousness. A bee has a very perfect eye, and with this eye it can see not only form, but also color, as Sir John Lubbock's experiments have shown us. The information that it gets through its eye, coupled with other ideas derived from touch, smell, and taste, no doubt makes up the main thinkable and knowable universe as it reveals itself to the apian intelligence. To ourselves and to bees alike the world is, on the whole, a colored picture, with the notions of distance and solidity thrown in by touch and muscular effort; but sight undoubtedly plays the first part in forming our total conception of things generally.

What is the main idea of the first paragraph?

Adapted from The Evolutionist at Large by Grant Allen (1881)

I am engaged in watching a brigade of ants out on foraging duty, and intent on securing for the nest three whole segments of a deceased earthworm. They look for all the world like those busy companies one sees in the Egyptian wall paintings, dragging home a huge granite colossus by sheer force of bone and sinew. Every muscle in their tiny bodies is strained to the utmost as they pry themselves laboriously against the great boulders that strew the path, and that are known to our Brobdingnagian intelligence as grains of sand. Besides the workers themselves, a whole battalion of stragglers runs to and fro upon the broad line that leads to the headquarters of the community. The province of these stragglers, who seem so busy doing nothing, probably consists in keeping communications open, and encouraging the sturdy pullers by occasional relays of fresh workmen. I often wish that I could for a while get inside those tiny brains, and see, or rather smell, the world as ants do. For there can be little doubt that to these brave little carnivores here the universe is chiefly known as a collective bundle of odors, simultaneous or consecutive. As our world is mainly a world of visible objects, theirs, I believe, is mainly a world of olfactible things.

In the head of every one of these little creatures is something that we may fairly call a brain. Of course most insects have no real brains; the nerve-substance in their heads is a mere collection of ill-arranged ganglia, directly connected with their organs of sense. Whatever man may be, an earwig at least is a conscious, or rather a semi-conscious, automaton. He has just a few knots of nerve cells in his little pate, each of which leads straight from his dim eye or his vague ear or his indefinite organs of taste; and his muscles obey the promptings of external sensations without possibility of hesitation or consideration, as mechanically as the valve of a steam engine obeys the governor balls. The poor soul's intellect is wholly deficient, and the senses alone make up all that there is of him, subjectively considered. But it is not so with the highest insects. They have something that truly answers to the real brain of men, apes, and dogs, to the cerebral hemispheres and the cerebellum that are superadded in us mammals upon the simple sense-centers of lower creatures. Besides the eye, with its optic nerve and optic perceptive organs—besides the ear, with its similar mechanism—we mammalian lords of creation have a higher and more genuine brain, that collects and compares the information given to the senses, and sends down the appropriate messages to the muscles accordingly. Now, bees and flies and ants have got much the same sort of arrangement, on a smaller scale, within their tiny heads. On top of the little knots that do duty as nerve centers for their eyes and mouths, stand two stalked bits of nervous matter, whose duty is analogous to that of our own brains. And that is why these three sorts of insects think and reason so much more intellectually than beetles or butterflies, and why the larger part of them have organized their domestic arrangements on such an excellent cooperative plan.

We know well enough what forms the main material of thought with bees and flies, and that is visible objects. For you must think about something if you think at all; and you can hardly imagine a contemplative blow-fly setting itself down to reflect, like a Hindu devotee, on the syllable Om, or on the oneness of existence. Abstract ideas are not likely to play a large part in apian consciousness. A bee has a very perfect eye, and with this eye it can see not only form, but also color, as Sir John Lubbock's experiments have shown us. The information that it gets through its eye, coupled with other ideas derived from touch, smell, and taste, no doubt makes up the main thinkable and knowable universe as it reveals itself to the apian intelligence. To ourselves and to bees alike the world is, on the whole, a colored picture, with the notions of distance and solidity thrown in by touch and muscular effort; but sight undoubtedly plays the first part in forming our total conception of things generally.

One of the main points made in the second paragraph is __________.

Adapted from Common Diseases of Farm Animals by R. A. Craig (1916, 2nd ed.)

The common bot-fly of the horse (G. equi) has a heavy, hairy body. Its color is brown, with dark and yellowish spots. The female fly can be seen during the warm weather, hovering around the horse, and darting toward the animal for the purpose of depositing the egg. The color of the egg is yellow, and it adheres firmly to the hair. It hatches in from two to four weeks, and the larva reaches the mouth through the animal licking the part. From the mouth, it passes to the stomach, where it attaches itself to the gastric mucous membrane. Here it remains until fully developed, when it becomes detached and is passed out with the feces. The third stage is passed in the ground. This takes place in the spring and early summer and lasts for several weeks, when it finally emerges a mature fly.

The bot-fly of the ox (H. lineata) is dark in color and about the size of a honey-bee. On warm days, the female may be seen depositing eggs on the body of the animal, especially in the region of the heels. This seems to greatly annoy the animal, and it is not uncommon for cattle to become stampeded. The egg reaches the mouth through the animal licking the part. The saliva dissolves the shell of the egg and the larva is freed. It then migrates from the gullet, wanders about in the tissue until finally it may reach a point beneath the skin of the back. Here the larva matures and forms the well-known swelling or warble. In the spring of the year it works out through the skin. The next stage is spent in the ground. The pupa state lasts several weeks, when the mature fly issues forth.

The bot-fly of sheep (O. ovis) resembles an overgrown house-fly. Its general color is brown, and it is apparently lazy, flying about very little. This bot-fly makes its appearance when the warm weather begins, and deposits live larvae in the nostrils of sheep. This act is greatly feared by the animals, as shown by their crowding together and holding the head down. The larva works up the nasal cavities and reaches the sinuses of the head, where it becomes attached to the lining mucous membrane. In the spring, when fully developed, it passes out through the nasal cavities and nostrils, drops to the ground, buries itself, and in from four to six weeks develops into the mature fly.

SYMPTOMS OF BOT-FLY DISEASES.—The larvae of the bot-fly of the horse do not cause characteristic symptoms of disease. Work horses that are groomed daily are not hosts for a large number of "bots," but young and old horses that are kept in a pasture or lot and seldom groomed may become unthrifty and "pot bellied," or show symptoms of indigestion.

Cattle suffer much pain from the development of the larva of the H. lineata. During the spring of the year, the pain resulting from the presence of the larvae beneath the skin and the penetration of the skin is manifested by excitement and running about. Besides the loss in milk and beef production, there is a heavy yearly loss from the damage to hides.

The life of the bot-fly of sheep results in a severe catarrhal inflammation of the mucous membrane lining the sinuses of the head, and a discharge of a heavy, pus-like material from the nostrils. The irritation produced by the larvae may be so serious at times as to result in nervous symptoms and death.

Based on the passage, the primary purpose for the farm animals in the life cycle of the various types of bot-flies is to __________.

Adapted from Common Diseases of Farm Animals by R. A. Craig (1916, 2nd ed.)

The common bot-fly of the horse (G. equi) has a heavy, hairy body. Its color is brown, with dark and yellowish spots. The female fly can be seen during the warm weather, hovering around the horse, and darting toward the animal for the purpose of depositing the egg. The color of the egg is yellow, and it adheres firmly to the hair. It hatches in from two to four weeks, and the larva reaches the mouth through the animal licking the part. From the mouth, it passes to the stomach, where it attaches itself to the gastric mucous membrane. Here it remains until fully developed, when it becomes detached and is passed out with the feces. The third stage is passed in the ground. This takes place in the spring and early summer and lasts for several weeks, when it finally emerges a mature fly.

The bot-fly of the ox (H. lineata) is dark in color and about the size of a honey-bee. On warm days, the female may be seen depositing eggs on the body of the animal, especially in the region of the heels. This seems to greatly annoy the animal, and it is not uncommon for cattle to become stampeded. The egg reaches the mouth through the animal licking the part. The saliva dissolves the shell of the egg and the larva is freed. It then migrates from the gullet, wanders about in the tissue until finally it may reach a point beneath the skin of the back. Here the larva matures and forms the well-known swelling or warble. In the spring of the year it works out through the skin. The next stage is spent in the ground. The pupa state lasts several weeks, when the mature fly issues forth.

The bot-fly of sheep (O. ovis) resembles an overgrown house-fly. Its general color is brown, and it is apparently lazy, flying about very little. This bot-fly makes its appearance when the warm weather begins, and deposits live larvae in the nostrils of sheep. This act is greatly feared by the animals, as shown by their crowding together and holding the head down. The larva works up the nasal cavities and reaches the sinuses of the head, where it becomes attached to the lining mucous membrane. In the spring, when fully developed, it passes out through the nasal cavities and nostrils, drops to the ground, buries itself, and in from four to six weeks develops into the mature fly.

SYMPTOMS OF BOT-FLY DISEASES.—The larvae of the bot-fly of the horse do not cause characteristic symptoms of disease. Work horses that are groomed daily are not hosts for a large number of "bots," but young and old horses that are kept in a pasture or lot and seldom groomed may become unthrifty and "pot bellied," or show symptoms of indigestion.

Cattle suffer much pain from the development of the larva of the H. lineata. During the spring of the year, the pain resulting from the presence of the larvae beneath the skin and the penetration of the skin is manifested by excitement and running about. Besides the loss in milk and beef production, there is a heavy yearly loss from the damage to hides.

The life of the bot-fly of sheep results in a severe catarrhal inflammation of the mucous membrane lining the sinuses of the head, and a discharge of a heavy, pus-like material from the nostrils. The irritation produced by the larvae may be so serious at times as to result in nervous symptoms and death.

For what purpose does the author reference different types of bot-fly?

Adapted from Ice-Caves of France and Switzerland by George Forrest Browne (1865)

This account states that the cave is in the county of Thorn, among the lowest spurs of the Carpathians. The entrance, which faces the north, and is exposed to the cold winds from the snowy part of the Carpathian range, is eighteen fathoms high and nine broad; and the cave spreads out laterally, and descends to a point fifty fathoms below the entrance, where it is twenty-six fathoms in breadth, and of irregular height. Beyond this no one had at that time penetrated, on account of the unsafe footing, although many distant echoes were returned by the farther recesses of the cave; indeed, to get even so far as this, much step-cutting was necessary.

When the external frost of winter comes on, the account proceeds, the effect in the cave is the same as if fires had been lighted there: the ice melts, and swarms of flies and bats and hares take refuge in the interior from the severity of the winter. As soon as spring arrives, the warmth of winter disappears from the interior, water exudes from the roof and is converted into ice, while the more abundant supplies which pour down on to the sandy floor are speedily frozen there. In the dog-days, the frost is so intense that a small icicle becomes in one day a huge mass of ice; but a cool day promptly brings a thaw, and the cave is looked upon as a barometer, not merely feeling, but also presaging, the changes of weather. The people of the neighborhood, when employed in field-work, arrange their labour so that the mid-day meal may be taken near the cave, when they either ice the water they have brought with them, or drink the melted ice, which they consider very good for the stomach. It had been calculated that six hundred weekly carts would not be sufficient to keep the cavern free from ice. The ground above the cave is peculiarly rich in grass.

In explanation of these phenomena, Bell threw out the following suggestions, which need no comment. The earth being of itself cold and damp, the external heat of the atmosphere, by partially penetrating into the ground, drives in this native cold to the inner parts of the earth, and makes the cold there more dense. On the other hand, when the external air is cold, it draws forth towards the surface the heat there may be in the inner part of the earth, and thus makes caverns warm. In support and illustration of this view, he states that in the hotter parts of Hungary, when the people wish to cool their wine, they dig a hole two feet deep, and place in it the flagon of wine, and, after filling up the hole again, light a blazing fire upon the surface, which cools the wine as if the flagon had been laid in ice. He also suggests that possibly the cold winds from the Carpathians bring with them imperceptible particles of snow, which reach the water of the cave, and convert it into ice. Further, the rocks of the Carpathians abound in salts, nitre, alum, etc., which may, perhaps, mingle with such snowy particles, and produce the ordinary effect of the snow and salt in the artificial production of ice.

Based on the passage, the primary reason for the lack of full exploration of the cave was that __________.

Adapted from A Practical Treatise on the Hive and Honey-Bee by Lorenzo Lorraine Langstroth (1857 ed.)

Of all the numerous enemies of the honey-bee, the Bee-Moth (Tinea mellonella), in climates of hot summers, is by far the most to be dreaded. So widespread and fatal have been its ravages in this country that thousands have abandoned the cultivation of bees in despair, and in districts which once produced abundant supplies of the purest honey, bee-keeping has gradually dwindled down into a very insignificant pursuit. Contrivances almost without number have been devised to defend the bees against this invidious foe, but still it continues its desolating inroads, almost unchecked, laughing as it were to scorn at all the so-called "moth-proof" hives, and turning many of the ingenious fixtures designed to entrap or exclude it into actual aids and comforts in its nefarious designs.

I should feel but little confidence in being able to reinstate bee-keeping in our country into a certain and profitable pursuit if I could not show the apiarian in what way he can safely bid defiance to the pestiferous assaults of this, his most implacable enemy. I have patiently studied its habits for years, and I am at length able to announce a system of management founded upon the peculiar construction of my hives, which will enable the careful bee-keeper to protect his colonies against the monster. The bee-moth infects our apiaries, just as weeds take possession of a fertile soil. Before explaining the means upon which I rely to circumvent the moth, I will first give a brief description of its habits.

Swammerdam, towards the close of the seventeenth century, gave a very accurate description of this insect, which was then called by the very expressive name of the "bee-wolf." He has furnished good drawings of it, in all its changes, from the worm to the perfect moth, together with the peculiar webs or galleries that it constructs and from which the name of Tinea galleria or “gallery moth” has been given to it by some entomologists. He failed, however, to discriminate between the male and female, which, because they differ so much in size and appearance, he supposed to be two different species of the wax-moth. It seems to have been a great pest in his time, and even Virgil speaks of the "dirum tineæ genus," the dreadful offspring of the moth; that is the worm.

This destroyer usually makes its appearance about the hives in April or May, the time of its coming depending upon the warmth of the climate or the forwardness of the season. It is seldom seen on the wing (unless startled from its lurking place about the hive) until towards dark, and is evidently chiefly nocturnal in its habits. In dark cloudy days, however, I have noticed it on the wing long before sunset, and if several such days follow in succession, the female, oppressed with the urgent necessity of laying her eggs, may be seen endeavoring to gain admission to the hives. The female is much larger than the male, and "her color is deeper and more inclining to a darkish gray, with small spots or blackish streaks on the interior edge of her upper wings." The color of the male inclines more to a light gray; they might easily be mistaken for different species of moths. These insects are surprisingly agile, both on foot and on the wing. The motions of a bee are very slow in comparison. "They are," says Reaumur, "the most nimble-footed creatures that I know." "If the approach to the apiary be observed of a moonlight evening, the moths will be found flying or running round the hives, watching an opportunity to enter, whilst the bees that have to guard the entrances against their intrusion will be seen acting as vigilant sentinels, performing continual rounds near this important post, extending their antenna to the utmost, and moving them to the right and left alternately. Woe to the unfortunate moth that comes within their reach!" "It is curious," says Huber, "to observe how artfully the moth knows how to profit, to the disadvantage of the bees, which require much light for seeing objects; and the precautions taken by the latter in reconnoitering and expelling so dangerous an enemy."

What is the main idea of the second paragraph?

Adapted from "Recent Views as to Direct Action of Light on the Colors of Flowers and Fruits" in Tropical Nature, and Other Essays by Alfred Russel Wallace (1878)

The theory that the brilliant colors of flowers and fruits is due to the direct action of light has been supported by a recent writer by examples taken from the arctic instead of from the tropical flora. In the arctic regions, vegetation is excessively rapid during the short summer, and this is held to be due to the continuous action of light throughout the long summer days. “The further we advance towards the north, the more the leaves of plants increase in size as if to absorb a greater proportion of the solar rays. M. Grisebach says that during a journey in Norway he observed that the majority of deciduous trees had already, at the 60th degree of latitude, larger leaves than in Germany, while M. Ch. Martins has made a similar observation as regards the leguminous plants cultivated in Lapland.” The same writer goes on to say that all the seeds of cultivated plants acquire a deeper color the further north they are grown, white haricots becoming brown or black, and white wheat becoming brown, while the green color of all vegetation becomes more intense. The flowers also are similarly changed: those which are white or yellow in central Europe becoming red or orange in Norway. This is what occurs in the Alpine flora, and the cause is said to be the same in both—the greater intensity of the sunlight. In the one the light is more persistent, in the other more intense because it traverses a less thickness of atmosphere.

Admitting the facts as above stated to be in themselves correct, they do not by any means establish the theory founded on them; and it is curious that Grisebach, who has been quoted by this writer for the fact of the increased size of the foliage, gives a totally different explanation of the more vivid colors of Arctic flowers. He says, “We see flowers become larger and more richly colored in proportion as, by the increasing length of winter, insects become rarer, and their cooperation in the act of fecundation is exposed to more uncertain chances.” (Vegetation du Globe, col. i. p. 61—French translation.) This is the theory here adopted to explain the colors of Alpine plants, and we believe there are many facts that will show it to be the preferable one. The statement that the white and yellow flowers of temperate Europe become red or golden in the Arctic regions must we think be incorrect. By roughly tabulating the colors of the plants given by Sir Joseph Hooker as permanently Arctic, we find among fifty species with more or less conspicuous flowers, twenty-five white, twelve yellow, eight purple or blue, three lilac, and two red or pink; showing a very similar proportion of white and yellow flowers to what obtains further south.

The purpose of this passage is ___________.

Adapted from "Recent Views as to Direct Action of Light on the Colors of Flowers and Fruits" in Tropical Nature, and Other Essays by Alfred Russel Wallace (1878)

The theory that the brilliant colors of flowers and fruits is due to the direct action of light has been supported by a recent writer by examples taken from the arctic instead of from the tropical flora. In the arctic regions, vegetation is excessively rapid during the short summer, and this is held to be due to the continuous action of light throughout the long summer days. "The further we advance towards the north, the more the leaves of plants increase in size as if to absorb a greater proportion of the solar rays. M. Grisebach says that during a journey in Norway he observed that the majority of deciduous trees had already, at the 60th degree of latitude, larger leaves than in Germany, while M. Ch. Martins has made a similar observation as regards the leguminous plants cultivated in Lapland.” The same writer goes on to say that all the seeds of cultivated plants acquire a deeper color the further north they are grown, white haricots becoming brown or black, and white wheat becoming brown, while the green color of all vegetation becomes more intense. The flowers also are similarly changed: those which are white or yellow in central Europe becoming red or orange in Norway. This is what occurs in the Alpine flora, and the cause is said to be the same in both—the greater intensity of the sunlight. In the one the light is more persistent, in the other more intense because it traverses a less thickness of atmosphere.

Admitting the facts as above stated to be in themselves correct, they do not by any means establish the theory founded on them; and it is curious that Grisebach, who has been quoted by this writer for the fact of the increased size of the foliage, gives a totally different explanation of the more vivid colors of Arctic flowers. He says, “We see flowers become larger and more richly colored in proportion as, by the increasing length of winter, insects become rarer, and their cooperation in the act of fecundation is exposed to more uncertain chances.” (Vegetation du Globe, col. i. p. 61—French translation.) This is the theory here adopted to explain the colors of Alpine plants, and we believe there are many facts that will show it to be the preferable one. The statement that the white and yellow flowers of temperate Europe become red or golden in the Arctic regions must we think be incorrect. By roughly tabulating the colors of the plants given by Sir Joseph Hooker as permanently Arctic, we find among fifty species with more or less conspicuous flowers, twenty-five white, twelve yellow, eight purple or blue, three lilac, and two red or pink; showing a very similar proportion of white and yellow flowers to what obtains further south.

The author’s critique of the theory presented in the first paragraph is that __________.

"The Multiple Sides of Computer Science" by Matthew Minerd (2014)

It often takes some time for a new discipline to become recognized as an independent science. An excellent example of this is computer science. In many ways, this science still is a hodgepodge of several different sciences, each one having its own distinct character. For example, some computer scientists are almost indistinguishable from mathematicians. Many of the most difficult topics in pattern recognition and data communications require intensive mathematics in order to provide software solutions. Years of training in the appropriate disciplines are necessary before the computer scientist can even begin to work as a programmer in such areas. In contrast to those computer scientists who work with complex mathematics, many computer scientists work on areas of hardware development that are similar to disciplines like electrical engineering and physics.

However, computer science has its own particular problems regarding the unity of its subject matter. There are many practical applications for computing work; therefore, many computer scientists focus on learning a large set of skills in programming languages, development environments, and even information technology. All of these disciplines have a certain practical coloration that is quite distinct from the theoretical concepts used in other parts of the field. Nevertheless, these practical topics add to the broad range of topics covered by most academic programs that claim to focus on “computer science.” It can only be hoped that these disciplines will increase in orderliness in the coming decades.

What is the main point introduced in the second paragraph?

"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?