"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 An Introduction to Astronomy by Forest Ray Moulton (1916 ed.)

The ancient Greeks, at a period four or five hundred years preceding the common era, definitely undertook to find from systematic observation how celestial phenomena follow one another. They determined very accurately the number of days in the year, the period of the moon's revolution, and the paths of the sun and the moon among the stars; they correctly explained the cause of eclipses and learned how to predict them with a considerable degree of accuracy; they undertook to measure the distances to the heavenly bodies, and to work out a complete system that would represent their motions. The idea was current among the Greek philosophers that the earth was spherical, that it turned on its axis, and, among some of them, that it revolved around the sun. They had true science in the modern acceptance of the term, but it was largely confined to the relations among celestial phenomena.

The conception that the heavens are orderly, which they definitely formulated and acted on with remarkable success, has been extended, especially in the last two centuries, so as to include the whole universe. The extension was first made to the inanimate world and then to the more complicated phenomena associated with living beings. Every increase in carefully recorded experience has confirmed and strengthened the belief that nature is perfectly orderly, until now every one who has had an opportunity of becoming familiar with any science is firmly convinced of the truth of this principle, which is the basis of all science.

Which of the following best summarizes this passage’s remarks on Greek science?

Adapted from An Introduction to Astronomy by Forest Ray Moulton (1916 ed.)

The ancient Greeks, at a period four or five hundred years preceding the common era, definitely undertook to find from systematic observation how celestial phenomena follow one another. They determined very accurately the number of days in the year, the period of the moon's revolution, and the paths of the sun and the moon among the stars; they correctly explained the cause of eclipses and learned how to predict them with a considerable degree of accuracy; they undertook to measure the distances to the heavenly bodies, and to work out a complete system that would represent their motions. The idea was current among the Greek philosophers that the earth was spherical, that it turned on its axis, and, among some of them, that it revolved around the sun. They had true science in the modern acceptance of the term, but it was largely confined to the relations among celestial phenomena.

The conception that the heavens are orderly, which they definitely formulated and acted on with remarkable success, has been extended, especially in the last two centuries, so as to include the whole universe. The extension was first made to the inanimate world and then to the more complicated phenomena associated with living beings. Every increase in carefully recorded experience has confirmed and strengthened the belief that nature is perfectly orderly, until now every one who has had an opportunity of becoming familiar with any science is firmly convinced of the truth of this principle, which is the basis of all science.

What is the main idea of the second 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 An Introduction to Astronomy by Forest Ray Moulton (1916 ed.)

It is doubtful if any important scientific idea ever sprang suddenly into the mind of a single man. The great intellectual movements in the world have had long periods of preparation, and often many men were groping for the same truth, without exactly seizing it, before it was fully comprehended.

The foundation on which all science rests is the principle that the universe is orderly, and that all phenomena succeed one another in harmony with invariable laws. Consequently, science was impossible until the truth of this principle was perceived, at least as applied to a limited part of nature.

The phenomena of ordinary observation, as, for example, the weather, depend on such a multitude of factors that it was not easy for men in their primitive state to discover that they occur in harmony with fixed laws. This was the age of superstition, when nature was supposed to be controlled by a great number of capricious gods whose favor could be won by childish ceremonies. Enormous experience was required to dispel such errors and to convince men that the universe is one vast organization whose changes take place in conformity with laws which they can in no way alter.

The actual dawn of science was in prehistoric times, probably in the civilizations that flourished in the valleys of the Nile and the Euphrates. In the very earliest records of these people that have come down to modern times it is found that they were acquainted with many astronomical phenomena and had coherent ideas with respect to the motions of the sun, moon, planets, and stars. It is perfectly clear from their writings that it was from their observations of the heavenly bodies that they first obtained the idea that the universe is not a chaos. Day and night were seen to succeed each other regularly, the moon was found to pass through its phases systematically, the seasons followed one another in order, and in fact the more conspicuous celestial phenomena were observed to occur in an orderly sequence. It is to the glory of astronomy that it first led men to the conclusion that law reigns in the universe.

Which of the following is the best image for the author’s view of the universe?

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 “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?

"Interpreting the Copernican Revolution" by Matthew Minerd (2014)

The expressions of one discipline can often alter the way that other subjects understand themselves. Among such cases are numbered the investigations of Nicolaus Copernicus. Copernicus is best known for his views concerning heliocentrism, a view which eventually obliterated many aspects of the ancient/medieval worldview, at least from the standpoint of physical science. It had always been the natural view of mankind that the earth stood at the center of the universe, a fixed point in reference to the rest of the visible bodies. The sun, stars, and planets all rotated around the earth.

With time, this viewpoint became one of the major reference points for modern life. It provided a provocative image that was used—and often abused—by many people for various purposes. For those who wished to weaken the control of religion on mankind, it was said that the heliocentric outlook proved man’s insignificance. In contrast with earlier geocentrism, heliocentrism was said to show that man is not the center of the universe. He is merely one small being in the midst of a large cosmos. However, others wished to use the “Copernican Revolution” in a very different manner. These thinkers wanted to show that there was another “recentering” that had to happen. Once upon a time, we talked about the world. Now, however, it was necessary to talk of man as the central reference point. Just as the solar system was “centered” on the sun, so too should the sciences be centered on the human person.

However, both of these approaches are fraught with problems. Those who wished to undermine the religious mindset rather misunderstood the former outlook on the solar system. The earlier geocentric mindset did not believe that the earth was the most important body in the heavens. Instead, many ancient and medieval thinkers believed that the highest “sphere” above the earth was the most important being in the physical universe. Likewise, the so-called “Copernican Revolution” in physics was different from the one applied to the human person. Copernicus’ revolution showed that the human point of view was not the center, whereas the later forms of “Copernican revolution” wished to show just the opposite.

Of course, there are many complexities in the history of such important changes in scientific outlook. Nevertheless, it is fascinating to see the wide-reaching effects of such discoveries, even when they have numerous, ambiguous effects.

What can we say, in general, about the interpretations that have been offered for the effects of Copernicus’ discoveries?

"Interpreting the Copernican Revolution" by Matthew Minerd (2014)

The expressions of one discipline can often alter the way that other subjects understand themselves. Among such cases are numbered the investigations of Nicolaus Copernicus. Copernicus is best known for his views concerning heliocentrism, a view which eventually obliterated many aspects of the ancient/medieval worldview, at least from the standpoint of physical science. It had always been the natural view of mankind that the earth stood at the center of the universe, a fixed point in reference to the rest of the visible bodies. The sun, stars, and planets all rotated around the earth.

With time, this viewpoint became one of the major reference points for modern life. It provided a provocative image that was used—and often abused—by many people for various purposes. For those who wished to weaken the control of religion on mankind, it was said that the heliocentric outlook proved man’s insignificance. In contrast with earlier geocentrism, heliocentrism was said to show that man is not the center of the universe. He is merely one small being in the midst of a large cosmos. However, others wished to use the “Copernican Revolution” in a very different manner. These thinkers wanted to show that there was another “recentering” that had to happen. Once upon a time, we talked about the world. Now, however, it was necessary to talk of man as the central reference point. Just as the solar system was “centered” on the sun, so too should the sciences be centered on the human person.

However, both of these approaches are fraught with problems. Those who wished to undermine the religious mindset rather misunderstood the former outlook on the solar system. The earlier geocentric mindset did not believe that the earth was the most important body in the heavens. Instead, many ancient and medieval thinkers believed that the highest “sphere” above the earth was the most important being in the physical universe. Likewise, the so-called “Copernican Revolution” in physics was different from the one applied to the human person. Copernicus’ revolution showed that the human point of view was not the center, whereas the later forms of “Copernican revolution” wished to show just the opposite.

Of course, there are many complexities in the history of such important changes in scientific outlook. Nevertheless, it is fascinating to see the wide-reaching effects of such discoveries, even when they have numerous, ambiguous effects.

Why is the "Copernican revolution" of the human sciences contrary to the literal sense of Copernicus' findings?