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.
Step 1: Understand what the passage actually says about each option.
Option (1): Supported.
The passage explicitly uses runs on banks and toilet paper buying to illustrate contagion-driven cascades that produce extreme, unintended system-wide behaviour.
Hence, this inference is supported.
Option (2): Supported.
The passage discusses no stationarity — how a first-order tail event changes the rules of the system, altering perceived costs and raising the probability of a second-order tail event.
This matches the inference stated.
Option (3): Supported.
The passage stresses that heavy-tailed distributions produce more frequent and larger extreme outcomes than normal distributions, especially in contagion-driven systems.
This is directly stated and therefore supported.
Option (4): Not supported (EXCEPT).
The passage gives the example that former sports bettors might have contributed to market inefficiencies and movements during the COVID–19 rebound.
It does not claim:
that they were the sole cause, nor
that their entry was the overriding cause of market recovery.
The authors clearly treat this factor as one potential contributor, not the decisive explanation.
Thus, Option (4) states something the passage does not support and is therefore the correct answer to an EXCEPT question.
Step 1: Identify the major themes of the passage.
The passage covers three core ideas:
Noise (randomness) in complex systems can surprisingly create orderly collective behaviour.
Complex systems with contagion dynamics are prone to heavy-tailed cascades and extreme events.
Nonstationarity explains how early shocks change the rules of the system, illustrated with stock-market behaviour during COVID-19.
A correct summary must incorporate all three ideas.
Step 2: Evaluate each option.
Option (1): Incorrect.
This contradicts the passage. The passage explicitly argues that complex systems do not follow normal distributions and that extreme events are important, not negligible.
Option (2): Correct.
This option accurately reflects:
the surprising emergence of order from noise,
the vulnerability of contagion-driven systems to heavy-tailed events,
the idea of nonstationarity and how early shocks change rules,
the COVID-19 market example used in the passage.
It is the only option that captures the full scope of the passage.
Option (3): Incorrect.
This overstates the passage. The text says speculative entrants might have contributed to market movements; it emphatically does not say that speculative entrants always cause inefficiency or that long-term investors always profit.
Option (4): Incorrect.
This misrepresents the passage entirely. The passage does not reject applying nonstationarity to markets or public health; in fact, it explicitly applies it to those contexts. The parasite–host example is merely an analogy.
Thus, the best summary is Option (2).
Step 1: Recall the passage’s claim.
The passage states that:
A first-order tail event (a large, rare shock)
raises the probability of second-order tail events,
meaning that after the initial shock, extreme events become more frequent.
Thus, we must choose the option showing clusters of extreme events after an initial extreme event.
Step 2: Evaluate each option.
Option (1): Weakens the claim.
Says tail events remain isolated with no increase afterward — the opposite of what we want.
Option (2): Irrelevant.
Describes a normal distribution with thin tails; nothing about successive extreme events.
Option (3): Strongly supports the claim.
After a major stock market crash, there are:
dense clusters of large daily moves,
extreme events appearing far more often,
a sustained period of elevated tail risk.
This directly confirms that a first-order tail event increases the probability of further tail events.
Option (4): Weakens the claim.
Says seismic activity returns to baseline with no aftershocks — contradicting the idea of second-order tail events.
Thus the best answer is Option (3).
The passage argues that contact-tracing apps, though designed to help individuals avoid risk, could inadvertently create collective patterns that increase risky interactions.
This can only happen if:
This is the hallmark of a complex system with interdependent behaviour.
Option (2) states exactly this assumption:
\(\textit{Individuals change behaviour based on infection data and the behaviour of others, and these interactions scale up.}\)
Without this interdependence, individual actions would stay local, and no large-scale unintended pattern could emerge — which the passage says can happen.
Thus, (2) is the necessary assumption.
Therefore, the assumption most necessary for the passage’s argument is Option (2).