The world described by physics is a surprisingly strange world, somewhat distant from our regular experience. Many high school students likely suspect this fact, given the difficulty that they often experience when taking physics courses. However, they are rarely instructed in the explicit difference between the world expressed by their equations and the world that they experience. Many of the concepts used in physics are related to the figures, facts, and equations that are learned in mathematics. The world is recast into a form that looks more like a geometry problem than the world as experienced in day-to-day life. All of this at first seems strange to the budding young physics student. However, after performing a number of experiments, he or she soon sees that these mathematical formulas seem to “work.” That is, these equations really do predict the outcomes of experiments in the real world, not merely in mathematical equations on paper.

Still, it is interesting to notice some examples of how much is overlooked in these kinds of mathematical models. Most obviously, there are few (if any) objects in reality that perfectly match the form and shape of a pure geometric figure. Few physical triangles are exact triangles in the manner of the shapes used in geometric problems. Likewise, motion becomes merely something to be expressed in an equation that has time as a variable. Finally, all of the physical descriptions of light waves tell us about everything except for what it is like to experience color. This last reason is perhaps the most interesting reason of all. No matter how many equations and shapes are used to describe color, none of these will have anything to do with the experience of color itself. To speak of a “rectangular surface” or an “icosahedron-like body” does not tell us anything about colors. Rectangles and icosahedrons can be any color. That is, color does not enter into their definitions at all—a red rectangle is just as much a rectangle as is a green one.

What is the purpose of the closing expression, “a red rectangle is just as much a rectangle as is a green one”?

The world described by physics is a surprisingly strange world, somewhat distant from our regular experience. Many high school students likely suspect this fact, given the difficulty that they often experience when taking physics courses. However, they are rarely instructed in the explicit difference between the world expressed by their equations and the world that they experience. Many of the concepts used in physics are related to the figures, facts, and equations that are learned in mathematics. The world is recast into a form that looks more like a geometry problem than the world as experienced in day-to-day life. All of this at first seems strange to the budding young physics student. However, after performing a number of experiments, he or she soon sees that these mathematical formulas seem to “work.” That is, these equations really do predict the outcomes of experiments in the real world, not merely in mathematical equations on paper.

Still, it is interesting to notice some examples of how much is overlooked in these kinds of mathematical models. Most obviously, there are few (if any) objects in reality that perfectly match the form and shape of a pure geometric figure. Few physical triangles are exact triangles in the manner of the shapes used in geometric problems. Likewise, motion becomes merely something to be expressed in an equation that has time as a variable. Finally, all of the physical descriptions of light waves tell us about everything except for what it is like to experience color. This last reason is perhaps the most interesting reason of all. No matter how many equations and shapes are used to describe color, none of these will have anything to do with the experience of color itself. To speak of a “rectangular surface” or an “icosahedron-like body” does not tell us anything about colors. Rectangles and icosahedrons can be any color. That is, color does not enter into their definitions at all—a red rectangle is just as much a rectangle as is a green one.

Why does the author use quotation marks around the boldfaced word “work”?

Adapted from "The Treatment of Rattlesnake Bite by Permanganate of Potassium, Based on Nine Successful Cases" by Amos W. Barber, M.D. in Scientific American Supplement No. 841, Vol. XXXIII (February 13th 1892)

Poisoned wounds, inflicted by the fangs of the rattlesnake, are happily rarer each year, since, as the country is becoming more populated, the crotalus is rapidly being exterminated. Yet, considering the disregard that characterizes the cowboy in his treatment of this reptile, it is astonishing that this class of injury is not more common.

It is the invariable custom among the cattlemen to dismount and destroy these snakes whenever they are seen. This is readily accomplished, since a slight blow will break the back. This blow is, however, generally delivered by means of the quirt, a whip not over two and a half feet long, and hence a weapon which brings the one who wields it in unpleasant proximity to the fangs of the reptile. A still more dangerous practice, and one which I have frequently seen, is a method of playing with the rattlesnake for the humor of the cowboy at the expense of a "tenderfoot." It is well known that unless a snake is coiled or in other specific positions, it cannot strike. On this theory, a mounted cowboy first puts a rattler to flight, then seizes it by the tail, and, swinging it so rapidly around his head that it is impossible for it to strike, sets off in pursuit of whoever has exhibited the most terror at the sight of the reptile. When within fair distance, he hurls the snake at the unfortunate victim, in the full assurance that even should it hit him it cannot bury its fangs in his flesh, since it cannot coil until it reaches the ground. This is a jest of which I have frequently been the victim, nor have I yet learned to appreciate it with unalloyed mirth.

The first case of rattlesnake wound to which I was called occurred in 1885. A cowboy was bitten on the foot, the fang penetrating through the boot. I saw him about twenty-four hours after he was struck. There was enormous swelling, extending up to the knee. There was no special discoloration about the wound; in fact, the swelling disguised this to such an extent that it was impossible to determine exactly where the fangs had entered. The patient was suffering great pain. His mind was clear, but he was oppressed with a dreadful anxiety.

Why does the author believe the number of rattlesnake poisonings is decreasing each year?

Adapted from "Errors in Our Food Economy" in Scientific American Supplement No. 1082 Vol. XLII (September 26th, 1896)

Scientific research, interpreting the observations of practical life, implies that several errors are common in the use of food.

First, many people purchase needlessly expensive kinds of food, doing this under the false impression that there is some peculiar virtue in the costlier materials, and that economy in our diet is somehow detrimental to our dignity or our welfare. And, unfortunately, those who are most extravagant in this respect are often the ones who can least afford it.

Secondly, the food which we eat does not always contain the proper proportions of the different kinds of nutritive ingredients. We consume relatively too much of the fuel ingredients of food, such as the fats of meat and butter, and the starch which makes up the larger part of the nutritive material of flour, potatoes, sugar, and sweetmeats. Conversely, we have relatively too little of the protein of flesh-forming substances, like the lean of meat and fish and the gluten of wheat, which make muscle and sinew and which are the basis of blood, bone and brain.

Thirdly, many people, not only the well-to-do, but those in moderate circumstances, use needless quantities of food. Part of the excess, however, is simply thrown away with the wastes of the table and the kitchen; so that the injury to health, great as it may be, is doubtless much less than if all were eaten. Probably the worst sufferers from this evil are well-to-do people of sedentary occupations.

Finally, we are guilty of serious errors in our cooking. We waste a great deal of fuel in the preparation of our food, and even then a great deal of the food is very badly cooked. A reform in these methods of cooking is one of the economic demands of our time.

The primary argument of the second paragraph is that _________.

Adapted from "Errors in Our Food Economy" in Scientific American Supplement No. 1082 Vol. XLII (September 26th, 1896)

Scientific research, interpreting the observations of practical life, implies that several errors are common in the use of food.

First, many people purchase needlessly expensive kinds of food, doing this under the false impression that there is some peculiar virtue in the costlier materials, and that economy in our diet is somehow detrimental to our dignity or our welfare. And, unfortunately, those who are most extravagant in this respect are often the ones who can least afford it.

Secondly, the food which we eat does not always contain the proper proportions of the different kinds of nutritive ingredients. We consume relatively too much of the fuel ingredients of food, such as the fats of meat and butter, and the starch which makes up the larger part of the nutritive material of flour, potatoes, sugar, and sweetmeats. Conversely, we have relatively too little of the protein of flesh-forming substances, like the lean of meat and fish and the gluten of wheat, which make muscle and sinew and which are the basis of blood, bone and brain.

Thirdly, many people, not only the well-to-do, but those in moderate circumstances, use needless quantities of food. Part of the excess, however, is simply thrown away with the wastes of the table and the kitchen; so that the injury to health, great as it may be, is doubtless much less than if all were eaten. Probably the worst sufferers from this evil are well-to-do people of sedentary occupations.

Finally, we are guilty of serious errors in our cooking. We waste a great deal of fuel in the preparation of our food, and even then a great deal of the food is very badly cooked. A reform in these methods of cooking is one of the economic demands of our time.

Which of these factors does the author believe is most relevant to why the excessive preparation of food is less injurious to our health than the other mistakes and fallacies he discusses?

"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.

Which of the following would strengthen the author’s main contention?

"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?