If you’ve ever tried to remain friends with both halves of a couple going through a nasty divorce, or hung out with a crowd of mutuals that also includes someone you can’t stand, you’ll know what an unbalanced social network feels like.

You’ll probably also sympathize with the 20^th-century social psychologist Fritz Heider, who theorized that humans strive to avoid such awkward, unbalanced situations, and instead favour “balanced” networks that obey rules like “the friend of my friend is also my friend” and “the enemy of my enemy is my friend”.

But striving and favouring aren’t the same thing as achieving, and the question of whether real-world social networks exhibit balance has proved surprisingly hard to answer. Some studies suggest that they do. Others say they don’t. And annoyingly, some “null models” – that is, models used to assess the statistical significance of patterns observed in real networks – fail to identify balance even in artificial networks expressly designed to have it.

Two physicists at Northwestern University in the US now report that they’ve cracked this problem – and it turns out that Heider was right. Using data collected from two Bitcoin trading platforms, the tech news site Slashdot, a product review site called Epinions, and interactions between members of the US House of Representatives, István Kovács and Bingjie Hao showed that most social networks do indeed demonstrate strong balance. Their result, they say, could be a first step towards “understanding and potentially reducing polarization in social media” and might also have applications in brain connectivity and protein-protein interactions.

Positive and negative signs

Mathematically speaking, social networks look like groups of nodes (representing people) connected by lines or edges (representing the relationships between them). If two people have an unfriendly or distrustful relationship, the edge connecting their nodes carries a negative sign. Friendly or trustful relationships get a positive sign.

Under this system, the micro-network described by the statement “the enemy of my enemy is my friend” looks like a triangle made up of one negative edge connecting you to your enemy, another negative edge connecting your enemy to their enemy, and one positive edge connecting you to your enemy’s enemy. The total number of negative edges is even, so the network is balanced.

Complicating factors

While the same mathematical framework can be applied to networks of any size and complexity, real-world social networks contain a few wrinkles that are hard to capture in null models. One such wrinkle is that not everyone knows each other. If the enemy of your enemy lives overseas, for example, you might not even know they exist, never mind whether to count them as a friend. Another complicating factor is that some people are friendlier than others, so they will have more positive connections.

In their study, which they describe in Science Advances, Kovács and Hao created a new null model that preserves both the topology (that is, the structure of the connections) and the “signed node degree” (that is, the “friendliness” or otherwise of individual nodes) that characterize real-world networks. By comparing this model to three- and four-node mini-networks in their chosen datasets, they showed that real-world networks are indeed more balanced than would be expected based on the more accurate null model.

So the next time you have to choose between two squabbling friends, or decide whether to trust someone who dislikes the same people as you, take heart: you’re performing a simple mathematical operation, and the most likely outcome will be a social network with more balance. Problem solved!

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Physics World’s office is a long way from the path of totality for yesterday’s solar eclipse, which covered a swathe of North America from the Pacific coast of Mexico to Newfoundland in Canada. Here in Bristol, UK, we didn’t even get to see a partial eclipse, thanks to the heavy cloud that often afflicts the UK at this time of year. But some of our readers were more fortunate, so here’s a quick round-up of their experiences.

The first of our correspondents to see the Moon’s shadow slide across the face of the Sun was Adrian Carreón, who observed the eclipse in Torreón, a city in the southwestern corner of Coahuila state, Mexico. “It was my first eclipse that I’ve seen, or at least that I remember, but it was awesome,” he says. “The best part was when day turned into night in just minutes, and in the sky I could see a light ring over my head.” Carreón captured a shot of this famous “ring of fire” on his phone.

Next up were John, Barb and Kirsten Harris (my uncle, aunt and cousin), who travelled to Little Rock, Arkansas from their homes in Chicago and New York for a better view. An hour or so before totality, things were looking good. According to my uncle, who has an ironic sense of humour, the sky above their chosen viewing spot in a University of Arkansas car park was “clear except for the chemtrails”.

Afterwards, he was full of praise for university staff who put on the event. “They had several rows of telescopes for kids, plus more for adults,” he reported. “Their biggest telescope was feeding a big screen so everybody could see the action.”

The telescopes, he added, will be ready again for the next total solar eclipse in Little Rock on 12 August 2045, when the city should experience 5 minutes and 39 seconds of totality instead of a mere two and a half – “which will be good, as we will all be slower then,” he concluded.

Our next correspondent – a friend of Physics World’s resident Canadian, Hamish Johnston – didn’t have quite so far to travel. A 20-minute drive to a friend’s cottage on the northern shore of Lake Erie was enough to put Peggy Shepherd Johnson in the zone of totality. At that location, the Sun was fully obscured for less than a minute, but she says it felt like longer.

“It was absolutely beautiful,” she told Johnston by email. “We were able to clearly view the ‘ring of fire’ around the Sun and see a few stars and (we believe) a planet at the totality. The temperature dropped significantly – a local brewery recorded a drop from 24 °C down to 12 °C – and it was eerie. We could view areas that were [outside full totality] in the near distance and see brightness and sunset-like views, but we were dark. The birds went quiet, and we heard what sounded like a very loud rumble of thunder with no storm system around. We’re all absolutely amazed – intellectually, we knew what to expect, but it was so much more to experience. We were simply blown away.”

Even those who couldn’t travel far managed to get in on the action. Norm Johnston, Hamish’s 90-year-old father, noticed some extra traffic in the streets from people headed out to view the eclipse from Canada’s Lake Ontario shoreline, but chose to watch television coverage of the eclipse from a viewing site at Niagara Falls rather than going out. “The streetlights came on,” he reported laconically. “Hope this helps!”

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On 12 April 1961 Yuri Gagarin became the first human to orbit the Earth, launching into space in his Vostok-1 craft with an enthusiastic shout of “Poekhali!” (“Let’s go!”). A quarter of a century later, and more than a decade after Gagarin’s death, his “Poekhali!” was considered so iconic that Soviet media included it in the opening sequence for the country’s nightly TV news programme. By the early 2000s, though, the fall of the Soviet Union had taken some of the shine off Gagarin’s legacy. When a survey (one of several carried out in Russia by local newspapers on anniversaries of Gagarin’s flight) asked students in Siberia to name the person who said “Poekhali!”, a 12-year-old boy called Vasia Maskalov suggested it might have been the Formula One driver Michael Schumacher.

The 40-year period between Gagarin’s triumph and Maskalov’s ignorance of it offers rich pickings for Cathleen S Lewis’ book Cosmonaut: a Cultural History. As a Soviet and Russian specialist at the US National Air and Space Museum, Lewis has a keen eye for differences between the rival Cold War space programmes. After noting in her introduction that American astronauts were required to have what the journalist and author Tom Wolfe termed “the Right Stuff”, Lewis coins a similar phrase for their Soviet counterparts. Cosmonauts, she writes, were expected to have “the Red Stuff” – a nebulous set of qualities that owed as much to Russian ideals (the association between red and Russia predates Lenin) as to Communist ones.

According to Lewis, the differences between the Right Stuff and the Red Stuff played out in several ways. Although the Americans and the Soviets both chose their early space farers from shortlists heavily (and, in the US, completely) dominated by military pilots, the first cosmonauts were too young to have fought in the Second World War. Instead, their authorized biographies emphasized their wartime experiences as children who suffered alongside every other Soviet citizen. Hence, if America’s astronauts were lionized as heroic individuals, the early cosmonauts were promoted as heroic everymen (and, in one case, everywoman).

For the Soviet leadership, the Red Stuff also made cosmonauts a convenient new focus for the personality cult that formerly centred on Josef Stalin. The ruthless dictator’s posthumous fall from favour coincided with the rise of the Soviet space programme, and both were strongly linked to his successor Nikita Khrushchev, who used the cosmonauts’ accomplishments to buttress his domestic and international support. Luckily for Khrushchev, the propagandists were pushing at an open door; in Lewis’ view, people would have adored Gagarin and his colleagues even without official encouragement.

Curious as to how far this sentiment penetrated, I asked a friend who grew up in Soviet-controlled Lithuania (and who, accordingly, detests the Soviet Union and all it stood for) what she remembered about Gagarin. “He was a hero,” she texted back. “Boys wanted to be cosmonauts when they grew up.” The cosmonauts’ achievements, she added, were viewed as “genuinely impressive” – even though “you could go to prison for joking about Gagarin”.

If Kennedy-era NASA officials felt that women didn’t have the Right Stuff, why did their counterparts in Khrushchev’s space programme come to such a different conclusion about women and the Red Stuff?

For me, the most fascinating chapter of Cosmonaut focuses not on the first man in space, but the first woman. Valentina Tereshkova’s history-making flight came barely two years after Gagarin’s, and I have often wondered why it took more than two decades for the US to repeat this Soviet “first”. If Kennedy-era NASA officials felt that women didn’t have the Right Stuff, why did their counterparts in Khrushchev’s space programme come to such a different conclusion about women and the Red Stuff?

The answer, Lewis suggests, is complicated. “According to Communist Party doctrine, there was equal opportunity to toil and labour for women in the USSR,” she writes. “The repeated need to demonstrate that equality indicated that reality was far different.” Although Soviet women flew combat missions, commanded partisan bands and directed factories during the Second World War, by the early 1960s a patriarchal backlash was in full swing. Like their Western counterparts, Soviet women were under enormous pressure to give up their former leadership roles in favour of men. They were also urged to have lots of babies (to replace the 11 million Soviet soldiers and perhaps 20 million civilians who died during the war) and to continue doing low-level work (because the staggering loss of life meant there wasn’t anyone else to do it).

Tereshkova’s flight was thus simultaneously the last gasp of wartime feminism; a means of pretending that the Soviet Union was winning the race for equality at the same time as it was dominating the space race; and a patronizing way to suggest that Soviet spacecraft were so well-designed that even a woman could fly them.

Lewis is a museum curator, and substantial portions of her book focus on the material artefacts of cosmonaut culture. For non-specialist readers, these lengthy discussions of cosmonaut-themed stamps, collectible badges and other memorabilia may have limited appeal. Similarly, I could have done without the summaries that appear at the beginning and end of each chapter, as well as in the introduction and epilogue. A more interesting option for the latter might have been to explore what cosmonaut culture looks like in today’s Russia – something that Lewis, who has clearly put in the hard yards in the Soviet and Russian archives, is well placed to do. Alas, though she notes in passing that “the Putin government has not enthusiastically and wholeheartedly embraced the Red Stuff”, she never explains why this is so. It’s a disappointing omission, and it means that, like the Soviet space programme itself, Cosmonaut peters out rather than living up to its early promise.

• 2023 University Press of Florida 324pp £37.95/$38.00hb

The post Never mind the right stuff, here’s the red stuff: how Yuri Gagarin and the cosmonauts shaped Soviet space culture appeared first on Physics World.