One of the foundations of scientific research is that an experimental

One of the foundations of scientific research is that an experimental result is credible only if it can be replicated—only if performing the experiment a second time leads to the same result. But physicists John Sommerer and Edward Ott have conceived of a physical system in which even the least change in the starting conditions—no matter how small, inadvertent, or undetectable—can alter results radically. The system is represented by a computer model of a mathematical equation describing the motion of a particle placed in a particular type of force field.

Sommerer and Ott based their system on an analogy with the phenomena known as riddled basins of attraction. If two bodies of water bound a large landmass and water is spilled somewhere on the land, the water will eventually make its way to one or the other body of water, its destination depending on such factors as where the water is spilled and the geographic features that shape the water’s path and velocity. The basin of attraction for a body of water is the area of land that, whenever water is spilled on it, always directs the spilled water to that body.

In some geographical formations it is sometimes impossible to predict, not only the exact destination of the spilled water, but even which body of water it will end up in. This is because the boundary between one basin of attraction and another is riddled with fractal properties; in other words, the boundary is permeated by an extraordinarily high number of physical irregularities such as notches or zigzags. Along such a boundary, the only way to determine where spilled water will flow at any given point is actually to spill it and observe its motion; spilling the water at any immediately adjacent point could give the water an entirely different path, velocity, or destination.

In the system posited by the two physicists, this boundary expands to include the whole system: i.e., the entire force field is riddled with fractal properties, and it is impossible to predict even the general destination of the particle given its starting point. Sommerer and Ott make a distinction between this type of uncertainty and that known as “chaos”; under chaos, a particle’s general destination would be predictable but its path and exact destination would not.

There are presumably other such systems because the equation the physicists used to construct the computer model was literally the first one they attempted, and the likelihood that they chose the only equation that would lead to an unstable system is small. If other such systems do exist, metaphorical examples of riddled basins of attraction may abound in the failed attempts of scientists to replicate previous experimental results—in which case, scientists would be forced to question one of the basic principles that guide their work.

1) Which one of the following most accurately expresses the main point of the passage?

(A) Sommerer and Ott’s model suggests that many of the fundamental experimental results of science are unreliable because they are contaminated by riddled basins of attraction.
(B) Sommerer and Ott’s model suggests that scientists who fail to replicate experimental results might be working within physical systems that make replication virtually impossible.
(C) Sommerer and Ott’s model suggests that experimental results can never be truly replicated because the starting conditions of an experiment can never be re-created exactly.
(D) Sommerer and Ott’s model suggests that most of the physical systems studied by scientists are in fact metaphorical examples of riddled basins of attraction.
(E) Sommerer and Ott’s model suggests that an experimental result should not be treated as credible unless that result can be replicated.



2) The discussion of the chaos of physical systems is intended to perform which one of the following functions in the passage?

(A) emphasize the extraordinarily large number of physical irregularities in a riddled basin of attraction
(B) emphasize the unusual types of physical irregularities found in Sommerer and Ott’s model
(C) emphasize the large percentage of a riddled basin of attraction that exhibits unpredictability
(D) emphasize the degree of unpredictability in Sommerer and Ott’s model
(E) emphasize the number of fractal properties in a riddled basin of attraction



3) Given the information in the passage, Sommerer and Ott are most likely to agree with which one of the following?

(A) It is sometimes impossible to determine whether a particular region exhibits fractal properties.
(B) It is sometimes impossible to predict even the general destination of a particle placed in a chaotic system.
(C) It is sometimes impossible to re-create exactly the starting conditions of an experiment.
(D) It is usually possible to predict the exact path water will travel if it is spilled at a point not on the boundary between two basins of attraction.
(E) It is usually possible to determine the path by which a particle traveled given information about where it was placed and its eventual destination.



4) Which one of the following most accurately describes the author’s attitude toward the work of Sommerer and Ott?

(A) skeptical of the possibility that numerous unstable systems exist but confident that the existence of numerous unstable systems would call into question one of the foundations of science
(B) convinced of the existence of numerous unstable systems and unsure if the existence of numerous unstable systems calls into question one of the foundations of science
(C) convinced of the existence of numerous unstable systems and confident that the existence of numerous unstable systems calls into question one of the foundations of science
(D) persuaded of the possibility that numerous unstable systems exist and unsure if the existence of numerous unstable systems would call into question one of the foundations of science
(E) persuaded of the possibility that numerous unstable systems exist and confident that the existence of numerous unstable systems would call into question one of the foundations of science



5) According to the passage, Sommerer and Ott’s model differs from a riddled basin of attraction in which one of the following ways?

(A) In the model, the behavior of a particle placed at any point in the system is chaotic; in a riddled basin of attraction, only water spilled at some of the points behaves chaotically.
(B) In a riddled basin of attraction, the behavior of water spilled at any point is chaotic; in the model, only particles placed at some of the points in the system behave chaotically.
(C) In the model, it is impossible to predict the destination of a particle placed at any point in the system; in a riddled basin of attraction, only some points are such that it is impossible to predict the destination of water spilled at each of those points.
(D) In a riddled basin of attraction, water spilled at two adjacent points always makes its way to the same destination; in the model, it is possible for particles placed at two adjacent points to travel to different destinations.
(E) In the model, two particles placed successively at a given point always travel to the same destination; in a riddled basin of attraction, water spilled at the same point on different occasions may make its way to different destinations.



6) Which one of the following best defines the term “basin of attraction,” as that term is used in the passage?

(A) the set of all points on an area of land for which it is possible to predict the destination, but not the path, of water spilled at that point
(B) the set of all points on an area of land for which it is possible to predict both the destination and the path of water spilled at that point
(C) the set of all points on an area of land that are free from physical irregularities such as notches and zigzags
(D) the set of all points on an area of land for which water spilled at each point will travel to a particular body of water
(E) the set of all points on an area of land for which water spilled at each point will travel to the same exact destination



7) Which one of the following is most clearly one of the “metaphorical examples of riddled basins of attraction” mentioned in lines 52–53?

(A) A scientist is unable to determine if mixing certain chemicals will result in a particular chemical reaction because the reaction cannot be consistently reproduced since sometimes the reaction occurs and other times it does not despite starting conditions that are in fact exactly the same in each experiment.
(B) A scientist is unable to determine if mixing certain chemicals will result in a particular chemical reaction because the reaction cannot be consistently reproduced since it is impossible to bring about starting conditions that are in fact exactly the same in each experiment.
(C) A scientist is unable to determine if mixing certain chemicals will result in a particular chemical reaction because the reaction cannot be consistently reproduced since it is impossible to produce starting conditions that are even approximately the same from one experiment to the next.
(D) A scientist is able to determine that mixing certain chemicals results in a particular chemical reaction because it is possible to consistently reproduce the reaction even though the starting conditions vary significantly from one experiment to the next.
(E) A scientist is able to determine that mixing certain chemicals results in a particular chemical reaction because it is possible to consistently reproduce the reaction despite the fact that the amount of time it takes for the reaction to occur varies significantly depending on the starting conditions of the experiment.