Understanding the key properties of complex systems can help us clarify and deal with many new and existing global challenges, from pandemics to poverty . . . A recent study in Nature Physics found transitions to orderly states such as schooling in fish (all fish swimming in the same direction), can be caused, paradoxically, by randomness, or ‘noise’ feeding back on itself. That is, a misalignment among the fish causes further misalignment, eventually inducing a transition to schooling. Most of us wouldn’t guess that noise can produce predictable behaviour. The result invites us to consider how technology such as contact-tracing apps, although informing us locally, might negatively impact our collective movement. If each of us changes our behaviour to avoid the infected, we might generate a collective pattern we had aimed to avoid: higher levels of interaction between the infected and susceptible, or high levels of interaction among the asymptomatic.

Complex systems also suffer from a special vulnerability to events that don’t follow a normal distribution or ‘bell curve’. When events are distributed normally, most outcomes are familiar and don’t seem particularly striking. Height is a good example: it’s pretty unusual for a man to be over 7 feet tall; most adults are between 5 and 6 feet, and there is no known person over 9 feet tall. But in collective settings where contagion shapes behaviour – a run on the banks, a scramble to buy toilet paper – the probability distributions for possible events are often heavy-tailed. There is a much higher probability of extreme events, such as a stock market crash or a massive surge in infections. These events are still unlikely, but they occur more frequently and are larger than would be expected under normal distributions.

What’s more, once a rare but hugely significant ‘tail’ event takes place, this raises the probability of further tail events. We might call them second-order tail events; they include stock market gyrations after a big fall and earthquake aftershocks. The initial probability of second-order tail events is so tiny it’s almost impossible to calculate – but once a first-order tail event occurs, the rules change, and the probability of a second-order tail event increases.

The dynamics of tail events are complicated by the fact that they result from cascades of other unlikely events. When COVID-19 first struck, the stock market suffered stunning losses followed by an equally stunning recovery. Some of these dynamics are potentially attributable to former sports bettors, with no sports to bet on, entering the market as speculators rather than investors. The arrival of these new players might have increased inefficiencies and allowed savvy long-term investors to gain an edge over bettors with different goals. . . .

One reason a first-order tail event can induce further tail events is that it changes the perceived costs of our actions and changes the rules that we play by. This game-change is an example of another key complex systems concept: nonstationarity. A second, canonical example of nonstationarity is adaptation, as illustrated by the arms race involved in the coevolution of hosts and parasites [in which] each has to ‘run’ faster, just to keep up with the novel solutions the other one presents as they battle it out in evolutionary time.

Correct Option: 2

Rationale:

This option provides the most accurate and structurally complete summary, capturing the three sequential topics presented in the passage: 1. The introduction of the paradox that noise can create order (Paragraph 1); 2. The discussion of heavy-tailed distributions and cascades in complex systems (Paragraphs 2 and 3); and 3. The explanation of nonstationarity and its market illustration during the COVID-19 disruption (Paragraphs 4 and 5).

Why other options wrong:

Option 1 is incorrect because it uses overly generalized and definitive language (“always produce inefficiency,” “invariably profit”) that contradicts the passage’s cautious phrasing (“might have increased,” “potentially attributable”). It also fails to summarize the passage’s introductory concepts of noise and heavy-tailed distributions.

Option 3 is factually incorrect because the passage argues that social outcomes involving contagion often do not follow normal distributions and that extreme events are significant, not negligible.

Option 4 is incorrect because the passage uses the host-parasite system as an illustration only, and then explicitly applies the concept of nonstationarity to markets and public health dynamics, rather than rejecting these applications.

Difficulty: Medium

Correct Option: 3

Rationale:

The passage describes how complex systems, like the contact tracing scenario, exhibit behavior where local, individual changes (noise) feed back into the system to generate a collective pattern that may be contrary to the intended goal. This requires a feedback mechanism driven by interdependence. The fish schooling example illustrates this: one fish’s misalignment causes further misalignment, leading to a collective, predictable pattern (schooling). The contact tracing analogy follows the same logic: individual changes in behavior (avoiding the infected) interact to create a large-scale, undesirable pattern (higher interaction between infected and susceptible). Option 3 captures this necessary condition by stating that individuals base choices on observed infections and the behavior of others, causing local responses to interact and turn small adjustments into large-scale, potentially frustrating patterns.

Why other options wrong:

Option 1 is incorrect because it contradicts the fundamental premise of complex systems described in the passage. The suggestion that interdependence is negligible would mean individual choices do not feed back to create collective patterns, which is the opposite of the author’s argument.

Option 2 is incorrect because it focuses on participation rates and data bias, which are not the necessary conditions for the paradoxical feedback mechanism described. The suggested outcome relies on the interaction of behavioral changes, not the number of users.

Option 4 is incorrect because the suggestion focuses on the collective response to information, not the accuracy of the data feed itself. The paradoxical outcome occurs even if the local information is accurate, because of the behavioral feedback loop it triggers.

Difficulty: Medium

Correct Option: 4

Rationale:

The passage claims that a first-order tail event (a major shock) “raises the probability of further tail events.” This happens because the shock “changes the rules” of the system, leading to nonstationarity. To strengthen this claim, one needs evidence that the frequency of extreme events increases immediately after the first shock, rather than the system quickly returning to normal. Option 4 provides this evidence directly: A major equity crash (first-order tail event) is followed by “dense clusters of large daily moves” for several weeks (second-order tail events), which occur “far more often than in normal circumstances” (elevated probability). This directly confirms the cascading effect described in the text.

Why other options wrong:

Option 1, Option 2, and Option 3 describe scenarios where extreme events are independent or the system returns to a baseline quickly.

Option 2 explicitly contradicts the passage’s claim by suggesting “independence across events” and “no aftershock sequence” after a large earthquake, which is the opposite of strengthening the argument.

Option 3 also weakens the claim by stating that outbreak sizes return to the “baseline distribution” after initial spikes, meaning the probability of later extreme clusters is not raised.

Option 1 suggests that river levels fit a normal distribution, weakening the general claim about heavy-tailed distributions in complex systems.

Difficulty: Easy

Correct Option: 2

Rationale:

The inference that the text attributes the COVID-19 pandemic rebound in financial markets solely to displaced sports bettors and treats their entry as the overriding cause of the rapid recovery across assets and time horizons is not supported by the passage. The text uses highly cautious and speculative language regarding the cause of the market dynamics. It states that the dynamics are only “potentially attributable to former sports bettors” and that their arrival “might have increased inefficiencies.” The use of the words “solely” and “overriding cause” in the option is a strong overstatement and direct contradiction of the passage’s tentative wording.

Why other options wrong:

Option 1 is supported by Paragraph 2, which states that heavy-tailed events “occur more frequently and are larger than would be expected under normal distributions,” which is the definition of complicating forecasting.

Option 3 is supported by Paragraph 5, which discusses how a shock changes the rules (nonstationarity) and Paragraph 3, which notes that this change “raises the probability of further tail events” (second-order tail events).

Option 4 is supported by the combination of Paragraph 2 (bank runs and toilet paper scrambles are examples of collective settings where contagion shapes behaviour) and Paragraph 1 (which illustrates how local changes or ‘noise’ can amplify into collective patterns that were “aimed to avoid,” meaning unintended).

Difficulty: Easy