The movie was never for the faint of heart. The Los Angeles Times chief film critic, Charles Champlin, harpooned it. He was horrified by the severed limbs; “Jaws,” he wrote, “is nightmare time.” As for Spielberg: “Intimacy is not yet his strength.” Of course, Champlin missed the point. Seventies America was high on cocaine and disco and thoroughly disenchanted with almost everything else, which is to say no one was particularly interested in intimacy. It was a paranoid decade, a decade in which shark attacks resonated, as such a thing could stand for any number of demonic threats.

In 1975, the country was reeling from the oil crisis, inflation of 8%, and a battered economy. That year saw two assassination attempts on the president and ended in an act of terrorism as a bomb exploded at New York’s LaGuardia airport, killing 11 — a crime that to this day remains unsolved. America was no longer captain of the ship, master of her fate. The Grammy-winning song of the year was “The Way We Were”.

The tone of the movie is set from the opening scene: sun sinking into the ocean behind a bevy of beach-guitar-strumming, pot-smoking, long-haired college students, blissfully unaware that one of their crowd will soon be destined for dismemberment. There was something satisfying in that realization that the Age of Aquarius was about to get its just deserts. Saigon had fallen and Richard Nixon along with it, suggesting that America, naked and vulnerable, was swimming through dangerous waters in a sexed-up haze, gloriously ignorant of the savage appetites lurking beneath the surface. Of course it’s the Fourth of July. Of course it’s an allegory.

In the face of clear and present carnivorous danger, the ambitious mayor and his well-fed lawyer sidekick spew pure greed. “We need summer dollars,” rumbles Murray Hamilton, who had caught Spielberg’s notice by playing Mr Robinson in The Graduate, in yet another Seventies harbinger of American decline.

Soon, yet another corpse sinks into a blood-stained sea, but these are not the crimson beaches of America’s bravest, sacrificed for world democracy on the sands of Normandy or Iwo Jima, the men Spielberg would glorify in Saving Private Ryan. The shark-chomped bodies of 1975 were the first articulations of what would come to be called American carnage. The cop, the child, the old-salt sonofabitch, the naked hippie doing water ballet — the beast from the deep knows no difference. Not even fancy college kids who had escaped the draft were safe.

Peter Benchley was one of those fancy college kids who dreamed of writing the Great American novel. His grandfather, the journalist and novelist Robert Benchley, had been a stalwart of the Algonquin Round Table of New York’s finest wits, along with Dorothy Parker and Harpo Marx. Yet Peter had found little success in the writing world. He was about to quit when he came across an interview with a Montauk sport fisherman who once hauled in a 3,427-pound Great White.

Jaws was Benchley’s last attempt to make it as a writer — and the resulting novel was smattered with faux-deep social commentary and small-town drama, including a sprinkling of the mafia and a dash or two of adultery, none of which would survive the great sausage-making of what would be heralded as the first Hollywood blockbuster. Benchley’s total advance from Doubleday was a meager $7,500.

While Benchley was laboring over drafts, another drama was unfolding 3,000 miles to the west, where Richard Darryl Zanuck, reeling from the failure of 1967’s Doctor Dolittle, was in the midst of losing his job as president of 20th Century Fox. He was fired by his own father, company founder Darryl F. Zanuck, which may have sparked Richard’s fascination with claustrophobic dramas of men intent on out-manning one another and killing the monstrous father beast. But as is generally the case with nepo babies, Zanuck fils landed on his feet. He became partners with the erstwhile head of his story department, David Brown, and the collaboration promptly blossomed into 1974’s Best Picture, The Sting.

Zanuck and Brown suddenly had some money to invest, which is why before Benchley’s novel ever hit bookstores, they could afford to see if they could develop the book into a screenplay, rustle up a director and a few actors, and make a movie. They spent $175,000 for a book that still didn’t have a title — which, in retrospect, was a bargain. Twenty minutes before the deadline, Benchley finally came up with the word that summed it all up. And just like that, Jaws hit the bestseller list and remained there for the next 44 weeks.

Zanuck was not the only one to have understood that this was the key to the American zeitgeist. The pages also landed on the desk of young Spielberg, who was disappointed to discover another director, Dick Richards, had already got his hands on it. Luckily, Richards made the mistake of repeatedly referring to the shark as “the white whale” in front of Benchley, who, instead of being flattered by the comparison with Melville, became incensed. The macropredator was the whole point — not some humpbacked vacuum cleaner of microscopic krill.

Spielberg got the job. He hired Robert Shaw to play the manliest of men — that is, the most homicidal — as a farcical send-up of the Hemingway man. Richard Dreyfuss became the preppy ichthyologist, and Roy Scheider became the New York cop, a stand-in for the urban everyman, now on notice that being a landlubber didn’t exempt you from the horrors of the deep.

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At the film’s first screening at the Medallion theatre in Dallas, the audience cheered and screamed — and one of them vomited. What followed was a tidal wave of publicity, with Jaws merch of every sort, from trading cards to beach towels. It was a kids’ movie — the bloodiest ever — and the gory opus summarily grossed more than $470 million worldwide (at that point, the top-grossing film of all time), and established its place in Hollywood iconography. Pauline Kael gushed: “The film belongs to the pulpiest sci-fi monster-movie tradition.”

As it turns out, old men and the sea never get old. Fifty years after the closing credits of Jaws, the model of what Kael called the “primal-terror comedy” has endured: shark eats man, shark eats ship, shark gets blown to smithereens. Swap shark for evil alien or mechanical dinosaur. Rinse, repeat. It’s horror. It’s comedy. And what is striking is that after half a century, the two have become one, which is perhaps a reflection on American culture more generally, arching from one hysterical pole to the next.

In October 1975, Spielberg was asked at the San Francisco Film Festival whether he would direct Jaws II. “Making a sequel to anything is just a cheap carny trick,” he responded (don’t mention Jurassic Park). Of course, Spielberg’s opinion hardly mattered. What ensued was a school of fishy spawn: Jaws II, Jaws III, Jaws: The Revenge, Cruel Jaws, Santa Jaws.

Beneath it all lurks the secret of the movie’s extraordinary staying power. It was then, and remains to this day, a metric not only of American fear but of American aggression, a foreshadowing of a future not only of Hollywood big-budget gore-bloated extravaganzas, but of a country declining into numbness that only the most sensational of spectacles could touch. Hollywood was the first to perceive that our taste for apocalypse, once the niche purview of melodrama, had expanded its market.

Half a century later, we don’t know whether to laugh or cry as we swim, if only a little less innocently, into the depths. Because as it turns out, no one cares about old men and the sea. It’s the Great Whites, symbol of American paranoia, predation, and violence, which adorn our whiskey bottles and popcorn buckets. D.H. Lawrence had it right when he commented: “The essential American soul is hard, isolate, stoic, and a killer.”

He didn’t say it was a shark.

Prevent is a much-mocked government counter-terrorism strategy, which looks out for warning signs that someone is at risk of being radicalised into some form of violent extremism. About 6,000 people are referred to it each year. 

Every high-profile murder or act of terrorism appears to be followed by a story like this. The Manchester Arena suicide bomber was known to the security services. Lee Rigby’s killers were known to the security services. At least one of the London Bridge attackers was known to the security services. It’s not just in cases of terrorism: the murderer of Alice Gross had a criminal record for sexual assault. Sarah Everard’s killer had a history of indecent exposure.

There is a further sense of inevitability over the fact that, three days after Sir David’s murder, Priti Patel, the home secretary, declared that Prevent is “under review” to ensure that it is “fit for purpose”. This is, in fact, an ongoing review that was launched in 2019 and due to report in December, rather than a response to the atrocity. Yet the announcement was clearly intended to suggest that the murder represented a failure on the part of the surveillance and deradicalisation system.

But is it? The sense of inevitability is real: these stories crop up a lot. But the truth is they will continue to keep cropping up, almost every time there is a terror attack, and almost no matter what we do with Prevent or whatever its successor is. Prevent may be failing — though I’ll happily defer judgment until the publication of the review — but even if it were successful, when terrorist attacks happen, it is likely that the perpetrators would be on its books, or known to the security services.

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And more than that: as callous as it sounds, that may be for the best. To give a sense of why that is, it’s helpful to look at another system for spotting future risks: cancer screening.

You screen for prostate cancer with a blood test, which looks for levels of something called “prostate-specific antigen”, or PSA. If you’re between 50 and 69 years old, the “normal” level of PSA is given as below three nanograms per millilitre (ng/ml). If your test comes back higher than that, you are flagged as at risk of having prostate cancer.

But according to the NHS, about 15% of men who do have prostate cancer actually have “normal” levels of PSA: that is, below 3ng/ml. If you run a screening test like this, you’ll falsely reassure about one cancer sufferer in six that they are cancer-free.

There’s a straightforward solution to that, of course. Instead of putting your cut-off at 3ng/ml, you could make it 2.5ng/ml. Then you’d miss fewer cancers.

You can probably guess the outcome, though. If you move the cut-off lower, you’ll miss fewer real cancers, but you’ll scare more men unnecessarily. If you move the cut-off higher, you’ll get fewer false positives — you won’t tell as many men that they have cancer when they don’t — but you’ll get more false negatives: you’ll miss more real cancers.

You might think that it’s a pretty straightforward decision. Telling people that they have cancer when they don’t is inconvenient and alarming; telling people that they don’t have cancer when they do might kill them. So you err on the side of caution.

But that’s not how it works. False positives on cancer screenings can literally kill. People can end up having unnecessary surgeries, X-rays, chemo or radiotherapy. Complications are sufficiently common that the NHS says that the benefits of prostate cancer screening do not outweigh the risks.

The cost of getting it wrong is real with terrorism, too. The process is somewhat different, though. When it comes to the risk of someone being radicalised, unlike a blood test, there isn’t a number that you can read off. That doesn’t mean there can’t be one: it could be that the people who are passed on to Prevent are given a quasi-objective score. We do exactly that for, say, suicidality risk or autism or happiness, or any one of a thousand psychological functions. You tick boxes on a questionnaire about someone’s isolation, their anger, their ideologies, and if the score on the questionnaire adds up to more than 40 or whatever you declare them a terrorism risk. That is precisely what goes on, in a less obvious and open way, with things like AI parole decisions. 

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But as it happens, there isn’t an explicit number. The Prevent guidance says: “There is no fixed profile of a terrorist, so there is no defined threshold to determine whether an individual is at risk of being drawn into terrorism.” So there’s no nice straightforward “Terrorism risk: 13.6” readout.

Nonetheless, the same process is going on. A person comes into contact with the counterterrorism services. Of the 6,000 or so who are referred to Prevent each year, about 500 or so are deemed “vulnerable” to radicalisation and are passed on to a subgroup called “Channel”. 

Since referral to Channel is not based on an objective score, it’s based on a subjective feeling (or “expert judgment”): people will be flagged up if the panel judging them feels sufficiently strongly that they’re a risk. They might not explicitly say “Terrorism risk: 13.6”, but still, there is a threshold of risk, over which someone is considered a threat.

And just like the PSA levels in the blood, that assessment will be imperfect. If you read some young man saying something disturbing online, is it harmless anger and braggadocio, or are they a terrorist? You can raise your implicit threshold and avoid harassing innocent people, at the cost of an increased risk of missing a genuine terrorist, or you can lower it and correctly identify more terrorists, but at the cost of labelling a lot of harmless people as potential terrorists.

It might seem, like the cancer test in reverse, that there’s an asymmetry here: a false positive annoys people; a false negative kills people. But also like the cancer test, it’s not as simple as that. The false positives will be a lot more common than the false negatives — simply put, there are more mouthy non-terrorists than actual terrorists in the world. As I said before, there were 6,000 people referred to Prevent every year, and 500 or so were judged to be of sufficiently high risk to be passed on to Channel. But there have been only four actual terror attacks in the last two years. 

If you lower your threshold, raise the alarm on more borderline cases, then you will waste more police time, put more innocent people under needless scrutiny and stigmatise more communities. (It seems inevitable that a lowered threshold will mean more young Muslim men, in particular, being picked up by the security services.) That may be a price worth paying — but, let’s be clear, it will be a price that you pay. If you take in everybody suspicious for questioning — every misogynist loser on incel subreddits, every angry racist or radical Islamist on dark-web chatrooms — you may prevent one or two more attacks, but you will undoubtedly fill up your jails and enrage the populace.

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This doesn’t mean there’s nothing you can do. Moving your threshold is zero-sum. But you can change your test: if instead of testing for PSA you looked for some other marker, you might be able to tell whether someone had cancer with more accuracy. In the case of counter-terrorism, you could do things like increasing police funding for surveillance, rather than simply being more strict about your criteria — although of course that would mean less money elsewhere.

An alternative suggestion might be to abandon “expert judgment” and introduce something like I talked about above, an explicit algorithm: human judgment is famously terrible at predicting complex things like the likelihood of a criminal to reoffend, and algorithms consistently outperform us, as the psychologist Paul Meehl demonstrated way back in 1954. They beat humans at predicting the price of wine, how long a cancer patient will live, who will win a football match, how likely a business is to succeed and dozens of other subjects. It is likely that some fairly simple algorithm could do significantly better than the best experts at predicting who is a terror risk, as well.

But it could only ever be a partial improvement. Humans are stubbornly hard to predict. Part of the reason why algorithms can outperform human judgment in those fields is because human judgment is consistently terrible: we are very often wrong about who will reoffend, who will live and die, who will win a football match. It is not that algorithmic prediction is great; the future is still hard to know. However good we make our systems for detecting terrorists, they will never be very good. So terrible things will always happen, and when they do, we will assume our systems are too lax and need to be tightened.

It is tempting to think like that in the wake of an atrocity such as David Amess’s murder: to think that we ought to lower our thresholds of what counts as a risk. Perhaps it’s even true. But just as it is an unavoidable fact of reality that reducing false alarms means missing more real ones, a world in which Sir David’s murderer was caught ahead of time could be grimly authoritarian.