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‘Boycott French products’ launched over Macron’s Anti Islam comments

Several Arab companies withdraw French products from supermarkets in response to Macron’s statements on Islam.

Empty shelves cleared of French products after Kuwaiti supermarkets declared a boycott of French goods. Kuwait City, October 25, 2020 [Ahmed Hagagy/Reuters] (Reuters)
Empty shelves cleared of French products after Kuwaiti supermarkets declared a boycott of French goods. Kuwait City, October 25, 2020 [Ahmed Hagagy/Reuters] (Reuters)

Several Arab trade associations have announced a boycott of French products, in response to recent comments made by President Emmanuel Macron on Islam.

Earlier this month, Macron pledged to fight “Islamist separatism”, which he said was threatening to take control in some Muslim communities around France.

He also described Islam as a religion “in crisis” worldwide and said the government would present a bill in December to strengthen a 1905 law that officially separated church and state in France.

His comments, in addition to his backing of satirical outlets publishing caricatures of the Prophet Muhammad, has led to a social media campaign calling for the boycott of French products from supermarkets in Arab countries and Turkey.


Hashtags such as the #BoycottFrenchProducts in English and the Arabic #NeverTheProphet trended across countries including Kuwait, Qatar, Palestine, Egypt, Algeria, Jordan, Saudi Arabia and Turkey.

In Kuwait, the chairman and members of the board of directors of the Al-Naeem Cooperative Society decided to boycott all French products and to remove them from supermarket shelves.

The Dahiyat al-Thuhr association took the same step, saying: “Based on the position of French President Emmanuel Macron and his support for the offensive cartoons against our beloved prophet, we decided to remove all French products from the market and branches until further notice.”




In Qatar, the Wajbah Dairy company announced a boycott of French products and pledged to provide alternatives, according to their Twitter account.

Al Meera Consumer Goods Company, a Qatari joint stock company, announced on Twitter: “We have immediately withdrawn French products from our shelves until further notice.”

“We affirm that as a national company, we work according to a vision consistent with our true religion, our established customs and traditions, and in a way that serves our country and our faith and meets the aspirations of our customers.”

Qatar University also joined the campaign. Its administration has postponed a French Cultural Week event indefinitely, citing the “deliberate abuse of Islam and its symbols”.


In a statement on Twitter, the university said any prejudice against Islamic belief, sanctities and symbols is “totally unacceptable, as these offences harm universal human values ​​and the highest moral principles that contemporary societies highly regard”.

The Gulf Cooperation Council (GCC) described Macron’s statements as “irresponsible”, and said they are aimed at spreading a culture of hatred among peoples.

“At a time when efforts must be directed towards promoting culture, tolerance and dialogue between cultures and religions, such rejected statements and calls for publishing insulting images of the Prophet (Muhammad) – may blessings and peace be upon him – are published,” said the council’s secretary-general, Nayef al-Hajraf.

Al-Hajraf called on world leaders, thinkers and opinion leaders to reject hate speech and contempt of religions and their symbols, and to respect the feelings of Muslims, instead of falling captive to Islamophobia.

In a statement, Kuwait’s foreign ministry warned against the support of abuses and discriminatory policies that link Islam to terrorism, saying it “represents a falsification of reality, insults the teachings of Islam, and offends the feelings of Muslims around the world”.

On Friday, the Organisation of Islamic Cooperation (OIC) condemned what it said was France’s continued attack against Muslims by insulting religious symbols.

The secretariat of the Jeddah-based organisation said in a statement it is surprised at the official political rhetoric issued by some French officials that offend French-Islamic relations and fuels feelings of hatred for political party gains.


Khabib Nurmagomedov is one of the great champions whose glory all Muslims enjoy sharing.


Every generation has its sporting heroes, some of whom transcend the sports they are famous for and use their platform to do good that is far bigger than them. 

For a globally persecuted community, reviled and degraded at every turn by politicians and the mainstream media in the West and elsewhere, Muslims have often sought comfort and a sense of sharing in the glory of sporting legends who share their faith – and have managed, despite the odds, to force the public consciousness to acknowledge them and their efforts and to recognise that they are clearly Muslims.

In today’s world, perhaps no other athlete represents the ideals of Islamic piety, humbleness, and being a master of one’s craft more than mixed martial arts legend Khabib “The Eagle” Nurmagomedov.

Tonight, he once again proved that he is the most dominant fighter to grace the cage after defeating top contender Justin Gaethje, bringing his undefeated record to 29-0. Now one step closer to fulfilling his father’s plan of crafting an unparalleled martial artist with a clean 30-0 record*, he is an athlete all Muslims can admire both for his prowess and his behaviour in and out of the cage. He is also the kind of champion his late father and trainer Abdulmanap Nurmagomedov would have been proud to say is his son.

Carrying out Abdulmanap’s plan

Khabib, born in the mountainous and rugged climes of the Dagestan region of Russia, has been raised since birth to be a warrior, and not simply just a prizefighter. Throughout his entire career, his father Abdulmanap had been by his side, guiding him to success even when he was denied visas to corner his son’s UFC bouts in the United States. 

Abdulmanap’s Islamic faith used to shine through in all his interviews, as his son would ultimately emulate, and he also clearly had faith in the training he gave his son knowing he would reach the top.

Sadly, and as a result of the coronavirus pandemic that has ground the world to a standstill, Abdulmanap fell ill and died at the age of 57 in July. Tonight’s fight was the first time that Khabib had to compete without the comfort a son feels by having his father’s guidance and wisdom to hand. 

However, the lightweight champion showed his mettle and demonstrated that he had absorbed his late and great father’s lessons and would continue to honour his memory by achieving at the very highest levels by establishing a sporting legacy inside and outside the cage. His father could not have been prouder.

The keys to Khabib’s success are not a secret. Every fighter who has ever fought against him knew well in advance what he was going to do, yet remained incapable of stopping him from executing Abdulmanap’s tried and tested formula of hard work, discipline, technical excellence, and spiritual conviction.

Khabib’s training regimen is legendarily rigorous, bringing together the sheer toughness the people of the Caucasus are renowned for with the technical excellence his father’s Sambo martial arts imparted upon him, as well as keeping himself mentally and spiritually strong by finding comfort and strength in Islam. 

He has been known to wrestle bears as a child, swims against the powerful currents of icy rivers, and to fight against elite training partners until they, and not he, became exhausted and could no longer continue. As Abdulmanap once said about his son, “a child always wants his father to see what his son is capable of” to prove his strength of character.

The Eagle has spent his entire life honouring his father’s mission, showing what he was capable of, and defeating the very best the world had to offer. He not only dominated the Combat Sambo world championships two years in a row in his early twenties but has fought against some of the toughest fighters in the world in MMA competition, becoming the lightweight champion in April 2018 after defeating “Raging” Al Iaquinta, a tough-as-leather New York brawler. He has since defended his title thrice with Gaethje as the latest to fall before him. 

Notably, he defended his title once against disgraced superstar Conor McGregor who spent much of 2018 insulting Khabib’s father, wife, and religion only to be smashed by the Dagestani champion, and once in a more respectful but nevertheless decisive bout against Dustin Poirier in 2019.

Abdulmanap’s plan for Khabib was for him to at least reach a pristine 30-0 before retiring. By all accounts, it seems that the Dagestani is just one step away from fulfilling his father’s dream. 

Unashamedly Muslim in an Islamophobic world

But what makes Khabib so special is not only his professional performance in the cage and his conduct out of it, but also his impact on his fanbase and in his ability to effectively portray practising Muslims as committed, hardworking, and successful people. 

Notably, Khabib often keeps himself out of political affairs. Unlike boxing legend Muhammad Ali, who absolutely dominated the heavyweight division in the 1960s and 1970s, Khabib has chosen a more restrained approach.

An early pillar of the black civil rights movement in America, Ali famously refused to be drafted into the US army to fight the Vietcong in Vietnam, exclaiming in 1967: “They [the Vietcong] never called me nigger”. 

Ali was convicted of draft-dodging, refused a boxing license to compete across the United States, was stripped of his heavyweight title, and would not compete again until 1971, stealing four years of a potentially long reign at the top of the sweet science, as boxing is affectionately known. 

Nevertheless, “The Greatest” had his unjust conviction overturned and came back to establish himself as one of the all-time most successful and outspoken boxers in history.

Interestingly, Khabib was recently interviewed regarding his own impact in society and if he was the modern-day equivalent of Ali, the People’s Champ. Ever the example of the humble Muslim warrior, the Eagle refused to be compared to Ali, citing the persecution of black Americans at the time Ali was building his legend and said: “To be able to be compared with him, I need to go back to those years and be Black and be a champion. Afterwards, we would see how I would behave in such a situation.”

While Khabib’s political quietism cannot be compared to Ali’s lionhearted defence of his racial and religious background, we now tragically live in an era where Muslims are deemed to be national security threats for daring to be outwardly Muslim, either by women donning hijabs or by men growing beards. They are persecuted across the globe, whether in Indian occupied Kashmir, Myanmar’s Rohingya minority, China’s Uyghur and Hui Muslim populations, or even in the heart of the secular West where French politicians across the political spectrum, including President Emmanuel Macron, are courting Islamophobic votes by making xenophobic statements and pillorying the entire Muslim community due to the actions of an extreme minority.

It is in this way that Khabib’s public speeches broadcast before tens of millions globally of “alhamdulillah”, “inshallah”, and indicating that his success only comes from Allah all while wearing his traditional papakha hat indicating his Avar Muslim heritage send a powerful message. 

The bearded Khabib in traditional Dagestani garb, praising his Lord, imbued with a religious conviction that fuels his training, and achieving the highest success in an environment dominated by all the trappings of Western culture, from show-offs like McGregor flashing their wealth, to scantily clad ring girls to ensure a “sex sells” degrading visual feast for a largely male fanbase, sends a powerful message. 

Khabib rises above it all, averting his gaze, and dedicating himself to the mastery of his craft as Islamic teachings command.

This model of the Muslim champion, true to his faith, his principles, and with the utmost characteristics of filial piety forces people to respect Muslims for who they are. It also serves as an inspiration for young Muslims around the world who feel under siege because of their identity, yet now can look at Khabib and feel proud of being unabashedly Muslim while aiming to reach the very pinnacle of their field. 

For this alone, Khabib’s impact transcends his sport, and I am certain that if he were alive today, Abdulmanap would be praising Allah for the blessing his son has been to his name in life and now in death.

*Editor’s Note: Khabib Nurmagomedov announced retirement soon after the publishing of this article.

Disclaimer: The viewpoints expressed by the authors do not necessarily reflect the opinions, viewpoints and editorial policies of TRT World.

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Muslim man denied German citizenship over handshake





A German court ruled a Muslim man should be denied citizenship after he refused to shake the hand of a female immigration official due to religious reasons.

The 40-year-old unidentified doctor from Lebanon applied for citizenship in 2012 and then aced the exam with a perfect score, German newspaper Deutsche Welle (DW) reported.

As part of the process, he also signed a declaration denouncing extremism and expressing loyalty to the German constitution.

But when he rejected a female official’s handshake at his 2015 naturalization ceremony, she withheld his certificate and ultimately denied his application, the paper reported.

The doctor argued he had only refused to shake her hand because he promised his wife he would not shake another woman’s hand, and his religious beliefs forbid him from doing so.

He unsuccessfully brought his case to the Stuttgart Administrative Court before appealing to the Administrative Court of Baden-Wurttemberg.

But the higher court ruled that anyone who refuses to shake hands on gender-specific grounds was violating terms about equality in the German constitution.

The handshake could be considered a “fundamentalist conception of culture and values” and this could be interpreted as a rejection of “integration into German living conditions,” the Independent reported.

The court also found that the handshake has legal significance since it symbolizes the conclusion of a contract, the DW reported.

The doctor can now appeal the ruling to the federal court, the outlet said.

Was Columbus’ Voyage to the “New World” Driven by Islamophobia?

Was Columbus’ Voyage to the “New World” Driven by Islamophobia?

Popular views of the explorer see him as intrepid adventurer or bungling murderer. But he was also a religious crusader.

A racist drawing of Christopher Columbus meeting Native people.
A hagiographic take of Christopher Columbus’ arrival. Images Plus

Tucked inside historian Alan Mikhail’s new biography of Sultan Selim, the ambitious early-16th-century ruler of the Ottoman Empire, is a riveting series of chapters about Christopher Columbus. Mikhail’s ambition in writing God’s Shadow: Sultan Selim, His Ottoman Empire, and the Making of the Modern World was to restore the place of the Ottoman Empire in the global history of the early modern period. To that end, the Columbus chapters make the argument that at its inception, European exploration of the New World can be understood as an ideological extension of the Crusades—a new effort to circumvent the ever-more-powerful Islamic presence in Europe.

Because this argument is somewhat hidden inside a big biography of an Ottoman ruler, it’s not been as controversial with traditionalists as the 1619 Project’s recasting of American history around slavery, but it’s got a similar power to make you look at a major historical happening in a completely new way. I asked Mikhail to explain how Columbus came to commit himself to combating Islam, how his feelings about Muslims affected his approach to the New World, and whether the Europeans of this time could rightly be called “Islamophobic.”


This conversation has been condensed and edited for clarity.

Rebecca Onion: There are a few common popular stories of Columbus. The first one is the elementary school version, where a brave explorer sets out for strange worlds—basically, a hagiographic take. Then there’s the revisionist one: Columbus was a blunderer who didn’t know what he was doing and just kind of happened onto the “New World.” But this is another twist, what you’re writing about.

Alan Mikhail: Yes, and of course there are also corollaries of the two versions of Columbus you talked about: the Italian American hero and the genocidal murderer.

Oh! Of course, I assumed the “genocidal murderer” part was understood, but thank you for making that clear.

Ha, yes. What I’m hoping to do is to point out something else that’s crucial to his biography, and that’s right there in his own writings and in the understanding of his age: He was a crusader.

Columbus was born in 1451 in Genoa—a really important mercantile port city but also a crusader port city. He was born two years before the Ottomans captured Constantinople, in 1453. And that was seen as an apocalyptical loss for Christian Europe. The Ottomans had—in the words of one of the Popes—“plucked out one of the two eyes of Christendom,” which were Rome and Constantinople, the Eastern capital.

In very real terms for a place like Genoa, this made a difference, because Constantinople, through the Bosphorus strait, had provided access to the eastern Black Sea; that is where Genoa had many of its trading ports, to connect to places further East. So there was this sense of loss in Genoa that was religious but also economic.

Genoa also had lots of crusaders going in and out of its port, when Columbus was young. We think of the Crusades as only happening in the medieval period, in the 11th and 12th centuries, but there were calls for Crusades up through the 17th century. To various degrees of effectiveness, of course. But Columbus was alive when there were crusaders going in and out of his city, and one of the crusading orders had a hospital in Genoa.

So Columbus was brought up on this story of loss. And he also read works like Marco Polo’s. One of the things that would become very important for Columbus, that he took from reading Marco Polo, is the idea of the “Grand Khan.” This is a person Polo wrote about that maybe has some connection to various actual historical figures. He’s supposed to be a ruler in a far-off place in Asia, who Polo says has shown interest in converting to Christianity. If this “Grand Khan” would convert, Polo’s readers were thinking, he would bring his subjects along with him, and there’d be this big Christian ally way off in Asia that would let Christians surround the Muslims in the Middle East and basically crush them.

That idea was very important to Columbus. On the first page of his logbook recording his voyage, Columbus writes to Isabella and Ferdinand, the Spanish sovereigns, that they had sent Columbus on a mission to India to find the Grand Khan. He’s very explicit about this being a reason for the trip.

These were ideas he absorbed when he was young, but he had personal experience encountering Muslims, too, before he set off on the voyage.

Yes, when he finally set to the sea as a teenager, in his early ventures as a sailor for hire, a couple of voyages took him to various parts of the Muslim world. He was hired by the king of Anjou in France to retrieve a ship of his that had been captured by pirates based in Tunis, on the North African coast. That was the first time that Columbus was face to face with a living, breathing Islam—not the kind of fantasy he had read about or heard about in Genoa. We don’t know the outcome of that voyage—he probably didn’t retrieve the ship—but that’s the first time he encountered the Muslim world in any kind of way.

There was another voyage that took him to Chios, an island off the Anatolian Coast in the Aegean Sea, and there he met Greek soldiers who had fought in defense of Constantinople. So he heard these real-life stories about this loss of a Christian city to this Muslim power. He sailed with Portuguese navigators down the West Coast of Africa, and there again, encountered Muslim powers. He got this sense that, even once you sail out of the Mediterranean, and are in this very different kind of place, West Africa—Islam is going to be there to greet you.

Then he was present at the siege of Granada in 1492, when Isabella and Ferdinand captured Granada. And in that logbook I spoke about, he connects that event—the expulsion of the last Muslim ruler from Spain—with the sovereigns’ decision to send him on the voyage, to find a new route to Asia and to connect with the Grand Khan. To him, these things were all tied together.

To what degree was this idea that his voyage would be a way to outflank Islam explicit in the way he lobbied Ferdinand and Isabella to support him—if we know?  

Famously, he went to a lot of people to try to get them to fund his voyages. And during that process, he did cite what he saw as the existential battle between Christendom and Islam as one of the reasons for his voyages.

And this worked with Isabella and Ferdinand in part because of the politics of European rulership. They controlled property in Italy, specifically Sicily, that the Ottomans, or so they thought, were poised to invade, at various points. And of course, there were still many Muslims in Spain after the conquest of Granada; the sovereigns saw those Muslims that remained as a potential fifth column—internal enemies, maybe allies to the Ottoman Empire, the Mamluks, or Muslim powers in North Africa.

They sort of felt like Islam was breathing down their necks.

There are a lot of examples of the ways Columbus and other explorers approached the Native people in the New World, primed to perceive them in the same way they thought of the Muslims they had encountered in Europe.

This is the other half of the story, which is that the explorers used language around Islam to frame their experience of the Old World, once they got to the New World. Some examples: Columbus described the weapons of the Taíno—the Indigenous people of the Caribbean—as alfanjes, which was the Spanish name for the scimitars used by Muslim soldiers. Hernán Cortés said that there were 400 “mosques” in Mexico, by which he probably meant Aztec temples, and that Aztec women look like “Moorish women.” He describes Montezuma, the Aztec leader, as a “sultan.” This first generation of conquistadors were forged in this world of warfare between Islam and Christendom, and that’s what they thought of in their minds’ eye, when they thought of enemies.

And they also thought maybe they were seeing these signs of Islam because they were in Asia, where it would make sense, right?

Yes, well, it depends on who you’re talking about; Columbus, until the day he died in 1506, thought he’d landed in Asia. So he thought all he needed to do was find the right path in, to the Grand Khan. But even much later, way beyond Columbus’ time, in the 1580s or something, when it was clear the Americas weren’t Asia, the Spanish authorities in what is today Peru reported rumors that Ottoman ships were off the West Coast of South America. There’s zero historical evidence so far that this was true—I mean, I’m open to change my mind if somebody finds evidence!—but what I’m interested in is this idea they still seemed to have that Islam is everywhere; Muslims are all around us.

Is it possible to use the word Islamophobia to describe the way Columbus, Isabella, Ferdinand, and other Christian Europeans felt at this time? I don’t know if that’s ahistorical. What was the motivation for their animus? Anxiety about territory? Religious fear?

I didn’t use the word Islamophobia in the book. That’s a very modern term; I would be hesitant to apply it to this period. Maybe something like “anti-Muslim sentiment,” which, to be fair, is clunkier.

It’s very tricky, the answer to this question. The idea is that there’s a thread of anti-Muslim sentiment from this period, and maybe even before, to today. In some ways you can draw a throughline. But I don’t want to buy into a story about some kind of eternal “clash of civilizations,” because there are plenty of examples of Christian Europeans and Muslims having quite positive interactions at the same time I’m talking about: the sharing of ideas, the exchange of goods, diplomatic relationships, fighting on the same side of wars against other enemies. And that’s part of the book, too—to point out that the Ottoman Empire has been part of “our history.”

Why do you think it was important to highlight this angle on Columbus’ story?

As I started writing this as an epic history, curious about the Western perspective on this, I thought, Why isn’t this motivation—this crusading motivation—part of the Columbus story? I mean, if you go back to Columbus and the Spanish sovereigns we are talking about, who wanted to deny and defeat Islam, they succeeded, in that the narratives about the New World do exclude Muslims. That’s part of the legacy.

If you think of the imports, if that’s what you want to call them, that Columbus brought with him in 1492, you have disease, an ambition to find Asia, and a crusading spirit of anti-Muslim sentiment. And very tragically, to write this history of what happened next, you then have to fold what happened to the Native people of the Americas into Europe’s anti-Islamic history.

And again, I don’t want to get too transhistorical here, but there are some ways in the modern American psyche that there are still connections between Muslims and Native Americans. You see that today, in the way the main American theater of warfare is the Muslim world, and so much American weaponry used there is named after Native Americans—Apache helicopters, Black Hawk helicopters, Tomahawk missiles. There’s a history of American warfare with Native peoples that’s playing out again, in different ways in the Muslim world.

You could say, Those are just names, it’s language, that doesn’t mean anything. But it does! There are reasons why discursive echoes like these exist. There’s a reason that Columbus and Cortés used language referring to Islam, when they encountered the New World, and not the language of anti-Judaism. They didn’t talk about, I don’t know, “the dirty French,” or something like that. There are particular reasons for that, that have to be explained.

Computer Scientists Break Traveling Salesperson Record
After 44 years, there’s finally a better way to find approximate solutions to the notoriously difficult traveling salesperson problem.

An illustration of computer scientists looking down a new road that breaks open a traveling salesperson route.

Islenia Mil for Quanta Magazine

When Nathan Klein started graduate school two years ago, his advisers proposed a modest plan: to work together on one of the most famous, long-standing problems in theoretical computer science.

Even if they didn’t manage to solve it, they figured, Klein would learn a lot in the process. He went along with the idea. “I didn’t know to be intimidated,” he said. “I was just a first-year grad student — I don’t know what’s going on.”

Now, in a paper posted online in July, Klein and his advisers at the University of Washington, Anna Karlin and Shayan Oveis Gharan, have finally achieved a goal computer scientists have pursued for nearly half a century: a better way to find approximate solutions to the traveling salesperson problem.

This optimization problem, which seeks the shortest (or least expensive) round trip through a collection of cities, has applications ranging from DNA sequencing to ride-sharing logistics. Over the decades, it has inspired many of the most fundamental advances in computer science, helping to illuminate the power of techniques such as linear programming. But researchers have yet to fully explore its possibilities — and not for want of trying.

The traveling salesperson problem “isn’t a problem, it’s an addiction,” as Christos Papadimitriou, a leading expert in computational complexity, is fond of saying.

Most computer scientists believe that there is no algorithm that can efficiently find the best solutions for all possible combinations of cities. But in 1976, Nicos Christofides came up with an algorithm that efficiently finds approximate solutions — round trips that are at most 50% longer than the best round trip. At the time, computer scientists expected that someone would soon improve on Christofides’ simple algorithm and come closer to the true solution. But the anticipated progress did not arrive.

“A lot of people spent countless hours trying to improve this result,” said Amin Saberi of Stanford University.

Now Karlin, Klein and Oveis Gharan have proved that an algorithm devised a decade ago beats Christofides’ 50% factor, though they were only able to subtract 0.2 billionth of a trillionth of a trillionth of a percent. Yet this minuscule improvement breaks through both a theoretical logjam and a psychological one. Researchers hope that it will open the floodgates to further improvements.

Nathan Klein (left), a graduate student at the University of Washington, and his advisers, Anna Karlin and Shayan Oveis Gharan.

Flora Hollifield; from “ Embracing Frustration,” with permission from Microsoft; courtesy of Shayan Gharan.

“This is a result I have wanted all my career,” said David Williamson of Cornell University, who has been studying the traveling salesperson problem since the 1980s.

The traveling salesperson problem is one of a handful of foundational problems that theoretical computer scientists turn to again and again to test the limits of efficient computation. The new result “is the first step towards showing that the frontiers of efficient computation are in fact better than what we thought,” Williamson said.

Fractional Progress

While there is probably no efficient method that always finds the shortest trip, it is possible to find something almost as good: the shortest tree connecting all the cities, meaning a network of connections (or “edges”) with no closed loops. Christofides’ algorithm uses this tree as the backbone for a round-trip tour, adding extra edges to convert it into a round trip.

Any round-trip route must have an even number of edges into each city, since every arrival is followed by a departure. It turns out that the reverse is also true — if every city in a network has an even number of connections then the edges of the network must trace a round trip.

The shortest tree connecting all the cities lacks this evenness property, since any city at the end of a branch has just one connection to another city. So to turn the shortest tree into a round trip, Christofides (who died last year) found the best way to connect pairs of cities that have odd numbers of edges. Then he proved that the resulting round trip will never be more than 50% longer than the best possible round trip.

In doing so, he devised perhaps the most famous approximation algorithm in theoretical computer science — one that usually forms the first example in textbooks and courses.

“Everybody knows the simple algorithm,” said Alantha Newman of Grenoble Alpes University and the National Center for Scientific Research in France. And when you know it, she said, “you know the state of the art” — at least, you did until this past July.

Computer scientists have long suspected that there should be an approximation algorithm that outperforms Christofides’ algorithm. After all, his simple and intuitive algorithm isn’t always such an effective way to design a traveling salesperson route, since the shortest tree connecting the cities may not be the best backbone you could choose. For instance, if this tree has many branches, each city at the end of a branch will need to be matched with another city, potentially forming lots of expensive new connections.

In 2010, Oveis Gharan, Saberi and Mohit Singh of the Georgia Institute of Technology started wondering if it might be possible to improve on Christofides’ algorithm by choosing not the shortest tree connecting all the cities, but a random tree from a carefully chosen collection. They took inspiration from an alternate version of the traveling salesperson problem in which you are allowed to travel along a combination of paths — maybe you get to Denver via 3/4 of the route from Chicago to Denver plus 1/4 of the route from Los Angeles to Denver.

Unlike the regular traveling salesperson problem, this fractional problem can be solved efficiently. And while fractional routes don’t make physical sense, computer scientists have long believed that the best fractional route should be a rough guide to the contours of good ordinary routes.

So to create their algorithm, Oveis Gharan, Saberi and Singh defined a random process that picks a tree connecting all the cities, so that the probability that a given edge is in the tree equals that edge’s fraction in the best fractional route. There are many such random processes, so the researchers chose one that tends to produce trees with many evenly connected cities. After this random process spits out a specific tree, their algorithm plugs it into Christofides’ scheme for matching cities with odd numbers of edges, to convert it into a round trip.


Samuel Velasco/Quanta Magazine

This method seemed promising, not just to the three researchers but to other computer scientists. “The intuition is simple,” said Ola Svensson of the Swiss Federal Institute of Technology Lausanne. But “to prove it turns out to be a different beast.”

The following year, though, Oveis Gharan, Saberi and Singh managed to prove that their algorithm beats Christofides’ algorithm for “graphical” traveling salesperson problems — ones where the distances between cities are represented by a network (not necessarily including all connections) in which every edge has the same length. But the researchers couldn’t figure out how to extend their result to the general traveling salesperson problem, in which some edges may be vastly longer than others.

“If we have to add a super expensive edge to the matching then we’re screwed, basically,” Karlin said.

Pushing Back

Nevertheless, Oveis Gharan emerged from that collaboration with an unshakable belief that their algorithm should beat Christofides’ algorithm for the general traveling salesperson problem. “I never had a doubt,” he said.

Oveis Gharan kept turning the problem over in his mind over the years that followed. He suspected that a mathematical discipline called the geometry of polynomials, little known in the theoretical computer science world, might have the tools he needed. So when Karlin came to him two years ago suggesting that they co-advise a brilliant new graduate student named Nathan Klein who had double-majored in math and cello, he said, “OK, let’s give it a try — I have this interesting problem.”

Karlin thought that, if nothing else, it would be a fun opportunity to learn more about the geometry of polynomials. “I really didn’t think we would be able to solve this problem,” she said.

She and Oveis Gharan had no hesitation about throwing Klein into the deep end of computer science research. Oveis Gharan had himself cut his teeth on the traveling salesperson problem as a graduate student back in 2010. And the two advisers agreed about the merits of assigning hard problems to graduate students, especially during their first couple of years, when they are not under pressure to get results.

The three dived into an intense collaboration. “It’s all I was thinking about for two years,” Klein said.

They spent the first year solving a simplified version of the problem, to get a sense of the challenges they were facing. But even after they accomplished that, the general case still felt like a “moonshot,” Klein said.

Still, they had gotten a feel for their tools — in particular, the geometry of polynomials. A polynomial is a combination of terms made out of numbers and variables raised to powers, such as 3x2y + 8xz7. To study the traveling salesperson problem, the researchers distilled a map of cities down to a polynomial that had one variable for each edge between cities, and one term for each tree that could connect all the cities. Numerical factors then weighted these terms to reflect each edge’s value in the fractional solution to the traveling salesperson problem.

This polynomial, they found, has a coveted property called “real stability,” which means that the complex numbers that make the polynomial evaluate to zero never lie in the upper half of the complex plane. The nice thing about real stability is that it stays in force even when you make many kinds of changes to your polynomial. So, for example, if the researchers wanted to focus on particular cities, they could use a single variable to represent all the different edges leading into a city, and they could set the variables for edges they didn’t care about equal to 1. As they manipulated these simplified polynomials, the results of their manipulations still had real stability, opening the door to a wide assortment of techniques.

This approach enabled the researchers to get a handle on questions like how often the algorithm would be forced to connect two distant cities. In a nearly 80-page analysis, they managed to show that the algorithm beats out Christofides’ algorithm for the general traveling salesperson problem (the paper has yet to be peer-reviewed, but experts are confident that it’s correct). Once the paper was completed, Oveis Gharan dashed off an email to Saberi, his old doctoral adviser. “I guess I can finally graduate,” he joked.

Amin Saberi (left) of Stanford University and Mohit Singh of the Georgia Institute of Technology.

Courtesy of Amin Saberi; Lance Davies

While the improvement the researchers established is vanishingly small, computer scientists hope this breakthrough will inspire rapid further progress. That’s what happened back in 2011 when Oveis Gharan, Saberi and Singh figured out the graphical case. Within a year, other researchers had come up with radically different algorithms that greatly improved the approximation factor for the graphical case, which has now been lowered to 40% instead of Christofides’ 50%.

“When they announced their result [about the graphical case], … that made us think that it’s possible. It made us work for it,” said Svensson, one of the researchers who made further progress in that case. He’s been trying for many years to beat Christofides’ algorithm for the general traveling salesperson problem. “I will try again now I know it’s possible,” he said.

Over the decades, the traveling salesperson problem has launched many new methods into prominence. Oveis Gharan hopes that it will now play that role for the geometry of polynomials, for which he has become an eager evangelist. In the decade or so since he started learning about this approach, it has helped him prove a wide range of theorems. The tool has “shaped my whole career,” he said.

The new traveling salesperson result highlights the power of this approach, Newman said. “Definitely it’s an inspiration to look at it more closely.”

Klein will now have to find a new problem to obsess over. “It’s a bit sad to lose the problem, because it just built up so many structures in my head, and now they’re all kind of gone,” he said. But he couldn’t have asked for a more satisfying introduction to computer science research. “I felt like we pushed back a little bit on something that was unknown.”

This Twist on Schrödinger’s Cat Paradox Has Major Implications for Quantum Theory

A laboratory demonstration of the classic “Wigner’s friend” thought experiment could overturn cherished assumptions about reality

This Twist on Schrödinger's Cat Paradox Has Major Implications for Quantum Theory
Credit: Getty Images

What does it feel like to be both alive and dead?

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That question irked and inspired Hungarian-American physicist Eugene Wigner in the 1960s. He was frustrated by the paradoxes arising from the vagaries of quantum mechanics—the theory governing the microscopic realm that suggests, among many other counterintuitive things, that until a quantum system is observed, it does not necessarily have definite properties. Take his fellow physicist Erwin Schrödinger’s famous thought experiment in which a cat is trapped in a box with poison that will be released if a radioactive atom decays. Radioactivity is a quantum process, so before the box is opened, the story goes, the atom has both decayed and not decayed, leaving the unfortunate cat in limbo—a so-called superposition between life and death. But does the cat experience being in superposition?

Wigner sharpened the paradox by imagining a (human) friend of his shut in a lab, measuring a quantum system. He argued it was absurd to say his friend exists in a superposition of having seen and not seen a decay unless and until Wigner opens the lab door. “The ‘Wigner’s friend’ thought experiment shows that things can become very weird if the observer is also observed,” says Nora Tischler, a quantum physicist at Griffith University in Brisbane, Australia.

Now Tischler and her colleagues have carried out a version of the Wigner’s friend test. By combining the classic thought experiment with another quantum head-scratcher called entanglement—a phenomenon that links particles across vast distances—they have also derived a new theorem, which they claim puts the strongest constraints yet on the fundamental nature of reality. Their study, which appeared in Nature Physics on August 17, has implications for the role that consciousness might play in quantum physics—and even whether quantum theory must be replaced.

The new work is an “important step forward in the field of experimental metaphysics,” says quantum physicist Aephraim Steinberg of the University of Toronto, who was not involved in the study. “It’s the beginning of what I expect will be a huge program of research.”


Until quantum physics came along in the 1920s, physicists expected their theories to be deterministic, generating predictions for the outcome of experiments with certainty. But quantum theory appears to be inherently probabilistic. The textbook version—sometimes called the Copenhagen interpretation—says that until a system’s properties are measured, they can encompass myriad values. This superposition only collapses into a single state when the system is observed, and physicists can never precisely predict what that state will be. Wigner held the then popular view that consciousness somehow triggers a superposition to collapse. Thus, his hypothetical friend would discern a definite outcome when she or he made a measurement—and Wigner would never see her or him in superposition.

This view has since fallen out of favor. “People in the foundations of quantum mechanics rapidly dismiss Wigner’s view as spooky and ill-defined because it makes observers special,” says David Chalmers, a philosopher and cognitive scientist at New York University. Today most physicists concur that inanimate objects can knock quantum systems out of superposition through a process known as decoherence. Certainly, researchers attempting to manipulate complex quantum superpositions in the lab can find their hard work destroyed by speedy air particles colliding with their systems. So they carry out their tests at ultracold temperatures and try to isolate their apparatuses from vibrations.

Several competing quantum interpretations have sprung up over the decades that employ less mystical mechanisms, such as decoherence, to explain how superpositions break down without invoking consciousness. Other interpretations hold the even more radical position that there is no collapse at all. Each has its own weird and wonderful take on Wigner’s test. The most exotic is the “many worlds” view, which says that whenever you make a quantum measurement, reality fractures, creating parallel universes to accommodate every possible outcome. Thus, Wigner’s friend would split into two copies and, “with good enough supertechnology,” he could indeed measure that person to be in superposition from outside the lab, says quantum physicist and many-worlds fan Lev Vaidman of Tel Aviv University.

The alternative “Bohmian” theory (named for physicist David Bohm) says that at the fundamental level, quantum systems do have definite properties; we just do not know enough about those systems to precisely predict their behavior. In that case, the friend has a single experience, but Wigner may still measure that individual to be in a superposition because of his own ignorance. In contrast, a relative newcomer on the block called the QBism interpretation embraces the probabilistic element of quantum theory wholeheartedly (QBism, pronounced “cubism,” is actually short for quantum Bayesianism, a reference to 18th-century mathematician Thomas Bayes’s work on probability.) QBists argue that a person can only use quantum mechanics to calculate how to calibrate his or her beliefs about what he or she will measure in an experiment. “Measurement outcomes must be regarded as personal to the agent who makes the measurement,” says Ruediger Schack of Royal Holloway, University of London, who is one of QBism’s founders. According to QBism’s tenets, quantum theory cannot tell you anything about the underlying state of reality, nor can Wigner use it to speculate on his friend’s experiences.

Another intriguing interpretation, called retrocausality, allows events in the future to influence the past. “In a retrocausal account, Wigner’s friend absolutely does experience something,” says Ken Wharton, a physicist at San Jose State University, who is an advocate for this time-twisting view. But that “something” the friend experiences at the point of measurement can depend upon Wigner’s choice of how to observe that person later.

The trouble is that each interpretation is equally good—or bad—at predicting the outcome of quantum tests, so choosing between them comes down to taste. “No one knows what the solution is,” Steinberg says. “We don’t even know if the list of potential solutions we have is exhaustive.”

Other models, called collapse theories, do make testable predictions. These models tack on a mechanism that forces a quantum system to collapse when it gets too big—explaining why cats, people and other macroscopic objects cannot be in superposition. Experiments are underway to hunt for signatures of such collapses, but as yet they have not found anything. Quantum physicists are also placing ever larger objects into superposition: last year a team in Vienna reported doing so with a 2,000-atom molecule. Most quantum interpretations say there is no reason why these efforts to supersize superpositions should not continue upward forever, presuming researchers can devise the right experiments in pristine lab conditions so that decoherence can be avoided. Collapse theories, however, posit that a limit will one day be reached, regardless of how carefully experiments are prepared. “If you try and manipulate a classical observer—a human, say—and treat it as a quantum system, it would immediately collapse,” says Angelo Bassi, a quantum physicist and proponent of collapse theories at the University of Trieste in Italy.


Tischler and her colleagues believed that analyzing and performing a Wigner’s friend experiment could shed light on the limits of quantum theory. They were inspired by a new wave of theoretical and experimental papers that have investigated the role of the observer in quantum theory by bringing entanglement into Wigner’s classic setup. Say you take two particles of light, or photons, that are polarized so that they can vibrate horizontally or vertically. The photons can also be placed in a superposition of vibrating both horizontally and vertically at the same time, just as Schrödinger’s paradoxical cat can be both alive and dead before it is observed.

Such pairs of photons can be prepared together—entangled—so that their polarizations are always found to be in the opposite direction when observed. That may not seem strange—unless you remember that these properties are not fixed until they are measured. Even if one photon is given to a physicist called Alice in Australia, while the other is transported to her colleague Bob in a lab in Vienna, entanglement ensures that as soon as Alice observes her photon and, for instance, finds its polarization to be horizontal, the polarization of Bob’s photon instantly syncs to vibrating vertically. Because the two photons appear to communicate faster than the speed of light—something prohibited by his theories of relativity—this phenomenon deeply troubled Albert Einstein, who dubbed it “spooky action at a distance.”

These concerns remained theoretical until the 1960s, when physicist John Bell devised a way to test if reality is truly spooky—or if there could be a more mundane explanation behind the correlations between entangled partners. Bell imagined a commonsense theory that was local—that is, one in which influences could not travel between particles instantly. It was also deterministic rather than inherently probabilistic, so experimental results could, in principle, be predicted with certainty, if only physicists understood more about the system’s hidden properties. And it was realistic, which, to a quantum theorist, means that systems would have these definite properties even if nobody looked at them. Then Bell calculated the maximum level of correlations between a series of entangled particles that such a local, deterministic and realistic theory could support. If that threshold was violated in an experiment, then one of the assumptions behind the theory must be false.

Such “Bell tests” have since been carried out, with a series of watertight versions performed in 2015, and they have confirmed reality’s spookiness. “Quantum foundations is a field that was really started experimentally by Bell’s [theorem]—now over 50 years old. And we’ve spent a lot of time reimplementing those experiments and discussing what they mean,” Steinberg says. “It’s very rare that people are able to come up with a new test that moves beyond Bell.”

The Brisbane team’s aim was to derive and test a new theorem that would do just that, providing even stricter constraints—“local friendliness” bounds—on the nature of reality. Like Bell’s theory, the researchers’ imaginary one is local. They also explicitly ban “superdeterminism”—that is, they insist that experimenters are free to choose what to measure without being influenced by events in the future or the distant past. (Bell implicitly assumed that experimenters can make free choices, too.) Finally, the team prescribes that when an observer makes a measurement, the outcome is a real, single event in the world—it is not relative to anyone or anything.

Testing local friendliness requires a cunning setup involving two “superobservers,” Alice and Bob (who play the role of Wigner), watching their friends Charlie and Debbie. Alice and Bob each have their own interferometer—an apparatus used to manipulate beams of photons. Before being measured, the photons’ polarizations are in a superposition of being both horizontal and vertical. Pairs of entangled photons are prepared such that if the polarization of one is measured to be horizontal, the polarization of its partner should immediately flip to be vertical. One photon from each entangled pair is sent into Alice’s interferometer, and its partner is sent to Bob’s. Charlie and Debbie are not actually human friends in this test. Rather, they are beam displacers at the front of each interferometer. When Alice’s photon hits the displacer, its polarization is effectively measured, and it swerves either left or right, depending on the direction of the polarization it snaps into. This action plays the role of Alice’s friend Charlie “measuring” the polarization. (Debbie similarly resides in Bob’s interferometer.)

Alice then has to make a choice: She can measure the photon’s new deviated path immediately, which would be the equivalent of opening the lab door and asking Charlie what he saw. Or she can allow the photon to continue on its journey, passing through a second beam displacer that recombines the left and right paths—the equivalent of keeping the lab door closed. Alice can then directly measure her photon’s polarization as it exits the interferometer. Throughout the experiment, Alice and Bob independently choose which measurement choices to make and then compare notes to calculate the correlations seen across a series of entangled pairs.

Tischler and her colleagues carried out 90,000 runs of the experiment. As expected, the correlations violated Bell’s original bounds—and crucially, they also violated the new local-friendliness threshold. The team could also modify the setup to tune down the degree of entanglement between the photons by sending one of the pair on a detour before it entered its interferometer, gently perturbing the perfect harmony between the partners. When the researchers ran the experiment with this slightly lower level of entanglement, they found a point where the correlations still violated Bell’s bound but not local friendliness. This result proved that the two sets of bounds are not equivalent and that the new local-friendliness constraints are stronger, Tischler says. “If you violate them, you learn more about reality,” she adds. Namely, if your theory says that “friends” can be treated as quantum systems, then you must either give up locality, accept that measurements do not have a single result that observers must agree on or allow superdeterminism. Each of these options has profound—and, to some physicists, distinctly distasteful—implications.


“The paper is an important philosophical study,” says Michele Reilly, co-founder of Turing, a quantum-computing company based in New York City, who was not involved in the work. She notes that physicists studying quantum foundations have often struggled to come up with a feasible test to back up their big ideas. “I am thrilled to see an experiment behind philosophical studies,” Reilly says. Steinberg calls the experiment “extremely elegant” and praises the team for tackling the mystery of the observer’s role in measurement head-on.

Although it is no surprise that quantum mechanics forces us to give up a commonsense assumption—physicists knew that from Bell—“the advance here is that we are a narrowing in on which of those assumptions it is,” says Wharton, who was also not part of the study. Still, he notes, proponents of most quantum interpretations will not lose any sleep. Fans of retrocausality, such as himself, have already made peace with superdeterminism: in their view, it is not shocking that future measurements affect past results. Meanwhile QBists and many-worlds adherents long ago threw out the requirement that quantum mechanics prescribes a single outcome that every observer must agree on.

And both Bohmian mechanics and spontaneous collapse models already happily ditched locality in response to Bell. Furthermore, collapse models say that a real macroscopic friend cannot be manipulated as a quantum system in the first place.

Vaidman, who was also not involved in the new work, is less enthused by it, however, and criticizes the identification of Wigner’s friend with a photon. The methods used in the paper “are ridiculous; the friend has to be macroscopic,” he says. Philosopher of physics Tim Maudlin of New York University, who was not part of the study, agrees. “Nobody thinks a photon is an observer, unless you are a panpsychic,” he says. Because no physicist questions whether a photon can be put into superposition, Maudlin feels the experiment lacks bite. “It rules something out—just something that nobody ever proposed,” he says.

Tischler accepts the criticism. “We don’t want to overclaim what we have done,” she says. The key for future experiments will be scaling up the size of the “friend,” adds team member Howard Wiseman, a physicist at Griffith University. The most dramatic result, he says, would involve using an artificial intelligence, embodied on a quantum computer, as the friend. Some philosophers have mused that such a machine could have humanlike experiences, a position known as the strong AI hypothesis, Wiseman notes, though nobody yet knows whether that idea will turn out to be true. But if the hypothesis holds, this quantum-based artificial general intelligence (AGI) would be microscopic. So from the point of view of spontaneous collapse models, it would not trigger collapse because of its size. If such a test was run, and the local-friendliness bound was not violated, that result would imply that an AGI’s consciousness cannot be put into superposition. In turn, that conclusion would suggest that Wigner was right that consciousness causes collapse. “I don’t think I will live to see an experiment like this,” Wiseman says. “But that would be revolutionary.”

Reilly, however, warns that physicists hoping that future AGI will help them home in on the fundamental description of reality are putting the cart before the horse. “It’s not inconceivable to me that quantum computers will be the paradigm shift to get to us into AGI,” she says. “Ultimately, we need a theory of everything in order to build an AGI on a quantum computer, period, full stop.”

That requirement may rule out more grandiose plans. But the team also suggests more modest intermediate tests involving machine-learning systems as friends, which appeals to Steinberg. That approach is “interesting and provocative,” he says. “It’s becoming conceivable that larger- and larger-scale computational devices could, in fact, be measured in a quantum way.”

Renato Renner, a quantum physicist at the Swiss Federal Institute of Technology Zurich (ETH Zurich), makes an even stronger claim: regardless of whether future experiments can be carried out, he says, the new theorem tells us that quantum mechanics needs to be replaced. In 2018 Renner and his colleague Daniela Frauchiger, then at ETH Zurich, published a thought experiment based on Wigner’s friend and used it to derive a new paradox. Their setup differs from that of the Brisbane team but also involves four observers whose measurements can become entangled. Renner and Frauchiger calculated that if the observers apply quantum laws to one another, they can end up inferring different results in the same experiment.

“The new paper is another confirmation that we have a problem with current quantum theory,” says Renner, who was not involved in the work. He argues that none of today’s quantum interpretations can worm their way out of the so-called Frauchiger-Renner paradox without proponents admitting they do not care whether quantum theory gives consistent results. QBists offer the most palatable means of escape, because from the outset, they say that quantum theory cannot be used to infer what other observers will measure, Renner says. “It still worries me, though: If everything is just personal to me, how can I say anything relevant to you?” he adds. Renner is now working on a new theory that provides a set of mathematical rules that would allow one observer to work out what another should see in a quantum experiment.

Still, those who strongly believe their favorite interpretation is right see little value in Tischler’s study. “If you think quantum mechanics is unhealthy, and it needs replacing, then this is useful because it tells you new constraints,” Vaidman says. “But I don’t agree that this is the case—many worlds explains everything.”

For now, physicists will have to continue to agree to disagree about which interpretation is best or if an entirely new theory is needed. “That’s where we left off in the early 20th century—we’re genuinely confused about this,” Reilly says. “But these studies are exactly the right thing to do to think through it.”

Disclaimer: The author frequently writes for the Foundational Questions Institute, which sponsors research in physics and cosmology and partially funded the Brisbane team’s study.

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How Many Aliens Are in the Milky Way? Astronomers Turn to Statistics for Answers

The tenets of Thomas Bayes, an 18th-century statistician and minister, underpin the latest estimates of the prevalence of extraterrestrial life

How Many Aliens Are in the Milky Way? Astronomers Turn to Statistics for Answers
Credit: Zihao Chen Getty Images

In the 12th episode of Cosmos, which aired on December 14, 1980, the program’s co-creator and host Carl Sagan introduced television viewers to astronomer Frank Drake’s eponymous equation. Using it, he calculated the potential number of advanced civilizations in the Milky Way that could contact us using the extraterrestrial equivalent of our modern radio-communications technology. Sagan’s estimate ranged from “a pitiful few” to millions. “If civilizations do not always destroy themselves shortly after discovering radio astronomy, then the sky may be softly humming with messages from the stars,” Sagan intoned in his inimitable way.

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Sagan was pessimistic about civilizations being able to survive their own technological “adolescence”—the transitional period when a culture’s development of, say, nuclear power, bioengineering or a myriad of other powerful capabilities could easily lead to self-annihilation. In essentially all other ways, he was an optimist about the prospects for pangalactic life and intelligence. But the scientific basis for his beliefs was shaky at best. Sagan and others suspected the emergence of life on clement worlds must be a cosmic inevitability, because geologic evidence suggested it arose shockingly quickly on Earth: in excess of four billion years ago, practically as soon as our planet had sufficiently cooled from its fiery formation. And if, just as on our world, life on other planets emerged quickly and evolved to become ever more complex over time, perhaps intelligence and technology, too, could be common throughout the universe.

In recent years, however, some skeptical astronomers have tried to put more empirical heft behind such pronouncements using a sophisticated form of analysis called Bayesian statistics. They have focused on two great unknowns: the odds of life arising on Earth-like planets from abiotic conditions—a process called abiogenesis—and, from there, the odds of intelligence emerging. Even with such estimates in hand, astronomers disagree about what they mean for life elsewhere in the cosmos. That lack of consensus is because even the best Bayesian analysis can only do so much when hard evidence for extraterrestrial life and intelligence is thin on the ground.

The Drake equation, which the astronomer introduced in 1961, calculates the number of civilizations in our galaxy that can transmit—or receive—interstellar messages via radio waves. It relies on multiplying a number of factors, each of which quantifies some aspect of our knowledge about our galaxy, planets, life and intelligence. These factors include ƒp, the fraction of stars with extrasolar planets; ne, the number of habitable planets in an extrasolar system; ƒl, the fraction of habitable planets on which life emerges; and so on.

“At the time Drake wrote [the equation] down—or even 25 years ago—almost any of those factors could have been the ones that make life very rare,” says Ed Turner, an astrophysicist at Princeton University. Now we know that worlds around stars are the norm, and that those similar to Earth in the most basic terms of size, mass and insolation are common as well. In short, there appears to be no shortage of galactic real estate that life could occupy. Yet “one of the biggest uncertainties in the whole chain of factors is the probability that life would ever get started—that you would make that leap from chemistry to life, even given suitable conditions,” Turner says.

Ignoring this uncertainty can lead astronomers to make rather bold claims. For example, last month Tom Westby and Christopher Conselice, both at the University of Nottingham in England, made headlines when they calculated that there should be at least 36 intelligent civilizations in our galaxy capable of communicating with us. The estimate was based on an assumption that intelligent life emerges on other habitable Earth-like planets about 4.5 billion to 5.5 billion years after their formation.

“That’s just a very specific and strong assumption,” says astronomer David Kipping of Columbia University. “I don’t see any evidence that that’s a safe bet to be making.”

Answering questions about the likelihood of abiogenesis and the emergence of intelligence is difficult because scientists just have a single piece of information: life on Earth. “We don’t even really have one full data point,” Kipping says. “We don’t know when life emerged, for instance, on the Earth. Even that is subject to uncertainty.”

Yet another problem with making assumptions based on what we locally observe is so-called selection bias. Imagine buying lottery tickets and hitting the jackpot on your 100th attempt. Reasonably, you might then assign a 1 percent probability to winning the lottery. This incorrect conclusion is, of course, a selection bias that arises if you poll only the winners and none of the failures (that is, the tens of millions of people who purchased tickets but never won the lottery). When it comes to calculating the odds of abiogenesis, “we don’t have access to the failures,” Kipping says. “So this is why we’re in a very challenging position when it comes to this problem.”

Enter Bayesian analysis. The technique uses Bayes’s theorem, named after Thomas Bayes, an 18th-century English statistician and minister. To calculate the odds of some event, such as abiogenesis, occurring, astronomers first come up with a likely probability distribution of it—a best guess, if you will. For example, one can assume that abiogenesis is as likely between 100 million to 200 million years after Earth formed as it is between 200 million to 300 million years after that time or any other 100-million-year-chunk of our planet’s history. Such assumptions are called Bayesian priors, and they are made explicit. Then the statisticians collect data or evidence. Finally, they combine the prior and the evidence to calculate what is called a posterior probability. In the case of abiogenesis, that probability would be the odds of the emergence of life on an Earth-like planet, given our prior assumptions and evidence. The posterior is not a single number but rather a probability distribution that quantifies any uncertainty. It may show, for instance, that abiogenesis becomes more or less likely with time rather than having a uniform probability distribution suggested by the prior.

In 2012 Turner and his colleague David Spiegel, then at the Institute for Advanced Study in Princeton, N.J., were the first to rigorously apply Bayesian analysis to abiogenesis. In their approach, life on an Earth-like planet around a sunlike star does not emerge until some minimum number of years, tmin, after that world’s formation. If life does not arise before some maximum time, tmax, then, as its star ages (and eventually dies), conditions on the planet become too hostile for abiogenesis to ever occur. Between tmin and tmax, Turner and Spiegel’s intent was to calculate the probability of abiogenesis.

The researchers worked with a few different prior distributions for this probability. They also assumed that intelligence took some fixed amount of time to appear after abiogenesis.

Given such assumptions, the geophysical and paleontological evidence of life’s genesis on Earth and what evolutionary theory says about the emergence of intelligent life, Turner and Spiegel were able to calculate different posterior probability distributions for abiogenesis. Although the evidence that life appeared early on Earth may indeed suggest abiogenesis is fairly easy, the posteriors did not place any lower bound on the probability. The calculation “doesn’t rule out very low probabilities, which is really sort of common sense with statistics of one,” Turner says. Despite life’s rapid emergence on Earth, abiogenesis could nonetheless be an extremely rare process.

Turner and Spiegel’s effort was the “first really serious Bayesian attack on this problem,” Kipping says. “I think what was appealing is that they broke this default, naive interpretation of the early emergence of life.”

Even so, Kipping thought the researchers’ work was not without its weaknesses, and he has now sought to correct it with a more elaborate Bayesian analysis of his own. For instance, Kipping questions the assumption that intelligence emerged at some fixed time after abiogenesis. This prior, he says, could be another instance of selection bias—a notion influenced by the evolutionary pathway by which our own intelligence emerged. “In the spirit of encoding all of your ignorance, why not just admit that you don’t know that number either?” Kipping says. “If you’re trying to infer how long it takes life to emerge, then why not just also do intelligence at the same time?”

That suggestion is exactly what Kipping attempted, estimating both the probability of abiogenesis and the emergence of intelligence. For a prior, he chose something called the Jeffreys prior, which was designed by another English statistician and astronomer, Harold Jeffreys. It is said to be maximally uninformative. Because the Jeffreys prior doesn’t bake in massive assumptions, it places more weigh on the evidence. Turner and Spiegel had also tried to find an uninformative prior. “If you want to know what the data is telling you and not what you thought about it previously, then you want an uninformative prior,” Turner says. In their 2012 analysis, the researchers employed three priors, one of which was the least informative, but they fell short of using Jeffreys prior, despite being aware of it.

In Kipping’s calculation, that prior focused attention on what he calls the “four corners” of the parameter space: life is common, and intelligence is common; life is common, and intelligence is rare; life is rare, and intelligence is common; and life is rare, and intelligence is rare. All four corners were equally likely before the Bayesian analysis began.

Turner agrees that using the Jeffreys prior is a significant advance. “It’s the best way that we have, really, to just ask what the data is trying to tell you,” he says.

Combining the Jeffreys prior with the sparse evidence of the emergence and intelligence of life on Earth, Kipping obtained a posterior probability distribution, which allowed him to calculate new odds for the four corners. He found, for instance, that the “life is common, and intelligence is rare” scenario is nine times more likely than both life and intelligence being rare. And even if intelligence is not rare, the life-is-common scenario has a minimum odds ratio of 9 to 1. Those odds are not the kind that one would bet the house on, Kipping says. “You could easily lose the bet.”

Still, that calculation is “a positive sign that life should be out there,” he says. “It is, at least, a suggestive hint that life is not a difficult process.”

Not all Bayesian statisticians would agree. Turner, for one, interprets the results differently. Yes, Kipping’s analysis suggests that life’s apparent early arrival on Earth favors a model in which abiogenesis is common, with a specific odds ratio of 9:1. But this calculation does not mean that model is nine times more likely to be true than the one that says abiogenesis is rare, Turner says, adding that Kipping’s interpretation is “a little bit overly optimistic.”

According to Turner, who applauds Kipping’s work, even the most sophisticated Bayesian analysis will still leave room for the rarity of both life and intelligence in the universe. “What we know about life on Earth doesn’t rule out those possibilities,” he says.

And it is not just Bayesian statisticians who may have a beef with Kipping’s interpretation. Anyone interested in questions about the origin of life would be skeptical about claimed answers, given that any such analysis is beholden to geologic, geophysical, paleontological, archaeological and biological evidence for life on Earth—none of which is unequivocal about the time lines for abiogenesis and the appearance of intelligence.

“We still struggle to define what we mean by a living system,” says Caleb Scharf, an astronomer and astrobiologist at Columbia. “It is a slippery beast, in terms of scientific definition. That’s problematic for making a statement [about] when abiogenesis happens—or even statements about the evolution of intelligence.”

If we did have rigorous definitions, problems persist. “We don’t know whether or not life started up, stopped, restarted. We also don’t know whether life can only be constructed one way or not,” Scharf says. When did Earth become hospitable to life? And when it did, were the first molecules of this “life” amino acids, RNAs or lipid membranes? And after life first came about, was it snuffed out by some cataclysmic event early in Earth’s history, only to restart in a potentially different manner? “There’s an awful lot of uncertainty,” Scharf says.

All this sketchy evidence makes even Bayesian analysis difficult. But as a technique, it remains the best–suited method for handling more evidence—say, the discovery of signs of life existing on Mars in the past or within one of Jupiter’s ice-covered, ocean-bearing moons at the present.

“The moment we have another data point to play with, assuming that happens, [the Bayesian models] are the ways to best utilize that extra data. Suddenly, the uncertainties shrink dramatically,” Scharf says. “We don’t necessarily have to survey every star in our galaxy to figure out how likely it is for any given place to harbor life. One or two more data points, and suddenly, we know about, essentially, the universe in terms of its propensity for producing life or possibly intelligence. And that’s rather powerful.”

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