“In the past few years both the methods of ‘lie detection’ and the polygraph itself have been subjected to increasing scrutiny. Although the polygraph was developed as an aid in police work, enterprising practitioners have long since discovered new applications for the device, and since about 1950 the polygraph has become firmly established in industry and government. There are some 500 commercial polygraph firms. Many companies retain polygraph examiners not only to investigate specific losses but also to conduct routine preemployment interviews in an attempt to identify applicants who are likely to be disloyal to the company. Outside the Federal Government the polygraph remains largely uncontrolled. So far only Illinois, Kentucky and New Mexico have adopted legislation requiring polygraph operators to be licensed.”
—Scientific American, January 1967
More gems from Scientific American’s first 175 years can be found on our anniversary archive page.
When I talk to my students about the tempestuous relationship between science and religion, I like to bring up the case of Francis Collins. Early in his career, Collins was a successful gene-hunter, who helped identify genes associated with cystic fibrosis and other disorders. He went on to become one of the world’s most powerful scientists. Since 2009, he has directed the National Institutes of Health, which this year has a budget of over $40 billion. Before that he oversaw the Human Genome Project, one of history’s biggest research projects. Collins was an atheist until 1978, when he underwent a conversion experience while hiking in the mountains and became a devout Christian. In his 2006 bestselling book The Language of God, Collins declares that he sees no incompatibility between science and religion. “The God of the Bible is also the God of the genome,” he wrote. “He can be worshipped in the cathedral or in the laboratory.” Collins just won the $1.3 million Templeton Prize, created in 1972 to promote reconciliation of science and spirituality. (See my posts on the Templeton Foundation here and here). This news gives me an excuse to post an interview I carried out with Collins for National Geographic in 2006, a time when Richard Dawkins, Daniel Dennett and others were vigorously attacking religion. Below is an edited transcript of my conversation with Collins, which took place in Washington, D.C. I liked Collins, whom I found to be surprisingly unassuming for a man of such high stature. But I was disturbed by our final exchanges, in which he revealed a fatalistic outlook on humanity’s future. Collins, it seems, has lots of faith in God but not much in humanity. – John Horgan
Horgan: How does it feel to be at the white-hot center of the current debate between science and religion?
Collins: This increasing polarization between extremists on both ends of the atheism and belief spectrum has been heartbreaking to me. If my suggestion that there is a harmonious middle ground puts me at the white-hot center of debate–Hooray! It’s maybe a bit overdue.
Horgan: The danger in trying to appeal to people on both sides of a polarized debate is–
Collins: Bombs thrown at you from both directions!
Horgan: Has that happened?
Collins [sighs]: The majority have responded in very encouraging ways. But some of my scientific colleagues argue that it’s totally inappropriate for a scientist to write about religion, and we already have too much faith in public life in this country. And then I get some very strongly worded messages from fundamentalists who feel that I have compromised the literal interpretation of Genesis 1 and call me a false prophet. I’m diluting the truth and doing damage to the faith.
Horgan: Why do you think the debate has become so polarized?
Collins: It starts with an extreme articulation of a viewpoint on one side of the issue and that then results in a response that is also a little bit too extreme, and the whole thing escalates. Every action demands an equal and opposite reaction. This is one of Newton’s laws playing out in an unfortunate public scenario.
Horgan: I must admit that I’ve become more concerned lately about the harmful effects of religion because of religious terrorism like 9/11 and the growing power of the religious right in the United States.
Collins: What faith has not been used by demagogues as a club over somebody’s head? Whether it was the Inquisition or the Crusades on the one hand or the World Trade Center on the other? But we shouldn’t judge the pure truths of faith by the way they are applied any more than we should judge the pure truth of love by an abusive marriage. We as children of God have been given by God this knowledge of right and wrong, this “Moral Law,” which I see as a particularly compelling signpost to His existence. But we also have this thing called free will which we exercise all the time to break that law. We shouldn’t blame faith for the ways people distort it and misuse it.
Horgan: Isn’t the problem when religions say, This is the only way to truth? Isn’t that what turns religious faith from something beautiful into something intolerant and hateful?
Collins: There is a sad truth there. I think we Christians have been way too ready to define ourselves as members of an exclusive club. I found truth, I found joy, I found peace in that particular conclusion, but I am not in any way suggesting that that is the conclusion everybody else should find. To have anyone say, “My truth is purer than yours,” that is both inconsistent with what I see in the person of Christ and incredibly off-putting. And quick to start arguments and fights and even wars! Look at the story of the Good Samaritan, which is a parable from Jesus himself. Jews would have considered the Samaritan to be a heretic, and yet clearly Christ’s message is: That is the person who did right and was justified in God’s eyes.
Horgan: How can you, as a scientist who looks for natural explanations of things and demands evidence, also believe in miracles, like the resurrection?
Collins: My first struggle was to believe in God. Not a pantheist God who is entirely enclosed within nature, or a Deist God who started the whole thing and then just lost interest, but a supernatural God who is interested in what is happening in our world and might at times choose to intervene. My second struggle was to believe that Christ was divine as He claimed to be. As soon as I got there, the idea that He might rise from the dead became a non-problem. I don’t have a problem with the concept that miracles might occasionally occur at moments of greatsignificance where there is a message being transmitted to us by God Almighty. But as a scientist I set my standards for miracles very high. And I don’t think we should try to convince agnostics or atheists about the reality of faith with claims about miracles that they can easily poke holes in.
Horgan: The problem I have with miracles is not just that they violate what science tells us about how the world works. They also make God seem too capricious. For example, many people believe that if they pray hard enough God will intercede to heal them or a loved one. But does that mean that all those who don’t get better aren’t worthy?
Collins: In my own experience as a physician, I have not seen a miraculous healing, and I don’t expect to see one. Also, prayer for me is not a way to manipulate God into doing what we want Him to do. Prayer for me is much more a sense of trying to get into fellowship with God. I’m trying to figure out what I should be doing rather than telling Almighty God what He should be doing. Look at the Lord’s Prayer. It says, “Thy will be done.” It wasn’t, “Our Father who are in Heaven, please get me a parking space.”
Horgan: Many people have a hard time believing in God because of the problem of evil. If God loves us, why is life filled with so much suffering?
Collins: That is the most fundamental question that all seekers have to wrestle with. First of all, if our ultimate goal is to grow, learn, discover things about ourselves and things about God, then unfortunately a life of ease is probably not the way to get there. I know I have learned very little about myself or God when everything is going well. Also, a lot of the pain and suffering in the world we cannot lay at God’s feet. God gave us free will, and we may choose to exercise it in ways that end up hurting other people.
Horgan: The physicist Steven Weinberg, who is an atheist, has written about this topic. He asks why six million Jews, including his relatives, had to die in the Holocaust so that the Nazis could exercise their free will.
Collins: If God had to intervene miraculously every time one of us chose to do something evil, it would be a very strange, chaotic, unpredictable world. Free will leads to people doing terrible things to each other. Innocent people die as a result. You can’t blame anyone except the evildoers for that. So that’s not God’s fault. The harder question is when suffering seems to have come about through no human ill action. A child with cancer, a natural disaster, a tornado or tsunami. Why would God not prevent those things from happening?
Horgan: Some theologians, such as Charles Hartshorne, have suggested that maybe God isn’t fully in control of His creation. The poet Annie Dillard expresses this idea in her phrase “God the semi-competent.”
Collins: That’s delightful–and probably blasphemous! An alternative is the notion of God being outside of nature and of time and having a perspective of our blink-of-an-eye existence that goes both far back and far forward. In some admittedly metaphysical way, that allows me to say that the meaning of suffering may not always be apparent to me. There can be reasons for terrible things happening that I cannot know.
Horgan: I think you’re an agnostic.
Horgan: You say that, to a certain extent, God’s ways are inscrutable. That sounds like agnosticism.
Collins: I’m agnostic about God’s ways. I’m not agnostic about God Himself. Thomas Huxley defined agnosticism as not knowing whether God exists or not. I’m a believer! I have doubts. As I quote Paul Tillich: “Doubt is not the opposite of faith. It’s a part of faith.” But my fundamental stance is that God is real, God is true.
Horgan: I’m an agnostic, and I was bothered when in your book you called agnosticism a “copout.” Agnosticism doesn’t mean you’re lazy or don’t care. It means you aren’t satisfied with any answers for what after all are ultimate mysteries.
Collins: That was a putdown that should not apply to earnest agnostics who have considered the evidence and still don’t find an answer. I was reacting to the agnosticism I see in the scientific community, which has not been arrived at by a careful examination of the evidence. I went through a phase when I was a casual agnostic, and I am perhaps too quick to assume that others have no more depth than I did.
Horgan: Free will is a very important concept to me, as it is to you. It’s the basis for our morality and search for meaning. Don’t you worry that science in general and genetics in particular—and your work as head of the Genome Project–are undermining belief in free will?
Collins: You’re talking about genetic determinism, which implies that we are helpless marionettes being controlled by strings made of double helices. That is so far away from what we know scientifically! Heredity does have an influence not only over medical risks but also over certain behaviors and personality traits. But look at identical twins, who have exactly the same DNA but often don’t behave alike or think alike. They show the importance of learning and experience–and free will. I think we all, whether we are religious or not, recognize that free will is a reality. There are some fringe elements that say, “No, it’s all an illusion, we’re just pawns in some computer model.” But I don’t think that carries you very far.
Horgan: What do you think of Darwinian explanations of altruism, or what you call agape, totally selfless love and compassion for someone not directly related to you?
Collins: It’s been a little of a just-so story so far. Many would argue that altruism has been supported by evolution because it helps the group survive. But some people sacrifically give of themselves to those who are outside their group and with whom they have absolutely nothing in common. Like Mother Teresa, Oscar Schindler, many others. That is the nobility of humankind in its purist form. That doesn’t seem like it can be explained by a Darwinian model, but I’m not hanging my faith on this.
Horgan: If only selflessness were more common.
Collins: Well, there you get free will again. It gets in the way.
Horgan: What do you think about the field of neurotheology, which attempts to identify the neural basis of religious experiences?
Collins: I think it’s fascinating but not particularly surprising. We humans are flesh and blood. So it wouldn’t trouble me–if I were to have some mystical experience myself–to discover that my temporal lobe was lit up. I’d say, “Wow! That’s okay!” That doesn’t mean that this doesn’t have genuine spiritual significance. Those who come at this issue with the presumption that there is nothing outside the natural world will look at this data and say, “Ya see?” Whereas those who come with the presumption that we are spiritual creatures will go, “Cool! There is a natural correlate to this mystical experience! How about that!” I think our spiritual nature is truly God-given, and may not be completely limited by natural descriptors.
Horgan: What if this research leads to drugs or devices for artificially inducing religious experiences? Would you consider those experiences to be authentic? You probably heard about the recent report from Johns Hopkins that the psychedelic drug psilocybin triggered spiritual experiences.
Collins: Yes. If you are talking about the ingestion of an exogenous psychoactive substance or some kind of brain-stimulating contraption, that would smack of not being an authentic, justifiable, trust-worthy experience. So that would be a boundary I would want to establish between the authentic and the counterfeit.
Horgan: Some scientists have predicted that genetic engineering may give us superhuman intelligence and greatly extended life spans, and possibly even immortality. We might even engineer our brains so that we don’t fear pain or grief anymore. These are possible long-term consequences of the Human Genome Project and other lines of research. If these things happen, what do you think would be the consequences for religious traditions?
Collins: That outcome would trouble me. But we’re so far away from that reality that it’s hard to spend a lot of time worrying about it when you consider all the truly benevolent things we could do in the near term. If you get too hung up on the hypotheticals of what night happen in the next several hundred years, then you become paralyzed and you fail to live up to the opportunities to reach out and help people now. That seems to be the most unethical stance we could take.
Horgan: I’m really asking, Does religion requires suffering? Could we reduce suffering to the point where we just won’t need religion?
Collins: In spite of the fact that we have achieved all of these wonderful medical advances and made it possible to live longer and eradicate diseases, we will probably still figure out ways to argue with each other and sometimes to kill each other, out of our self-righteousness and our determination that we have to be on top. So the death rate will continue to be one per person by one means or another. We may understand a lot about biology, we may understand a lot about how to prevent illness, and we may understand the life span. But I don’t think we will figure out how to stop humans from doing bad things to each other. That will always be our greatest and most distressing experience here on this planet, and that will make us long the most, perhaps, for something more.
In Defense of Disbelief: An Anti-Creed
Can Faith and Science Coexist?
Richard Dawkins Offers Advice for Donald Trump, and Other Wisdom
What Should We Do With Our Visions of Heaven and Hell?
Mind-Body Problems (free online book, also available as Kindle e-book and paperback).
For decades the number of satellites orbiting Earth rose at a gentle pace, but growth has soared recently. By July 2019 more than 2,200 satellites were aloft. In the 1980s and 1990s the action was in geosynchronous orbit (blues), says Jonathan McDowell, an astrophysicist at the Center for Astrophysics|Harvard & Smithsonian. But now the action is in the lowest Earth orbits (yellows), he says, and increasingly dominated by young companies rather than government, military or academic owners. Today the push is from Starlink—constellations of satellites weighing 260 kilograms, being launched by SpaceX to deliver high-speed Internet.
The uptick started around 2014, stemming largely from CubeSats—diminutive satellites, each lighter than 12 kilograms, that were lofted in groups. They are fulfilling a desire to observe changes on Earth every day. CubeSats could reveal, for example, how people were moving around Wuhan, China, during the coronavirus outbreak. And instead of Google Earth showing driveways with cars from 10 years ago, it could display vehicles purchased last week.
A massive galaxy similar to our own Milky Way spotted shockingly early in the universe’s history is challenging astrophysicists’ understanding of galaxy formation. Witnessed just 1.5 billion years after the big bang, when the universe was some 10 percent of its current age, the spinning disk of gas and stars is the earliest of its type ever identified. And it provides strong evidence that some of the first galaxies got off to a cold start.
In standard formation models, galaxies coalesce as gas collects in and around diffuse “halos” of dark matter. All that gas becomes extremely hot as it funnels down into the heart of the newborn galaxy, and it must take time to cool down before it can begin forming stars. In contrast, more recent simulations suggest that gas flowing into young galaxies along long filaments of dark matter can remain relatively cool, allowing star formation to begin sooner. These “cold start” galaxies should form spiral-like disks that resemble the Milky Way.
So far most of the early galaxies observers have managed to identify have been irregular blobs without disks, their shapes distorted, and their gas heated, by repeated collisions with protogalaxies. Astronomers have indeed found a handful of disk galaxies from the first few billion years of the universe’s history. But some researchers argue that these objects are old enough for their gas to have already cooled down, making their origins indefinite.
This particular disk galaxy, however, defies such objections. “We found a galaxy that has a lot of cold gas in it,” says Marcel Neeleman, an astronomer at Max Planck Institute for Astronomy in Heidelberg, Germany, and first author of a study reporting the observations, which was published in the May 21 issue of the journal Nature. “If it had formed through hot-mode accretion, it wouldn’t be there.”
Coral Wheeler, an astronomer who studies galaxy evolution at the University of California, San Diego, agrees. The galaxy provides “very strong evidence of cold-mode accretion,” she says. (Wheeler was not part of the paper.)
Neeleman and his colleagues claim that the new finding means that most of the first generation of galaxies formed through either cold-mode accretion or collisions with other young galaxies.
Researchers have long argued over whether gas pouring into the earliest galaxies was hot or cold. Simulations favor cold gas, but skeptics have raised questions about the validity of those virtual conclusions. And they have done so for good reason: by necessity, those models have simplified many of a galaxy’s most salient environmental effects, such as feedback processes from supernovae and black holes that could heat otherwise cool gas.
“There’s been a controversy about this over the last couple decades now,” says Ryan Trainor, an astrophysicist at Franklin & Marshall College, who was not involved in the Nature study. One of the challenges of hunting for early galaxies is the need for targets that are big and bright enough to be seen across immense cosmic distances. As a result, the most luminous objects are the ones most likely to be observed. To overcome this bias, Neeleman and his colleagues decided to utilize a method pioneered by the late astronomer Arthur Wolfe. Using the Atacama Large Millimeter/Submillimeter Array (ALMA) in Chile, they hunted for galaxies in front of quasars, the brightest known objects in the universe. As light from a quasar passes through a foreground galaxy, the gas from that galaxy absorbs some of the light, creating what Neeleman calls “shadows.”
By studying the shadows, or absorption lines, with ALMA, the astronomers could track the rotating motion of the dim gas of the galaxy DLA0817g, which they discovered in 2017. They nicknamed it the “Wolfe Disk” in honor of the team members’ former adviser and colleague. Follow-up observations with the Hubble Space Telescope revealed some of the galaxy’s brightest stars, which the scientists used to estimate that the Wolfe Disk is churning out an average of 16 sun-sized stars each year. Hubble’s scrutiny also revealed that the gas blocking the quasar came not from the heart of DLA0817g but from the galaxy’s outer edges—a region where gas would be expected to thin out rather than thicken. The researchers suspect what they are seeing is one of the dark matter filaments funneling gas into the Wolfe Disk.
“We can’t prove it’s a filament, but it’s well beyond the star-forming region of the galaxy,” says team member and study co-author J. Xavier Prochaska, an astronomer at the University of California, Santa Cruz.
By using quasars, the team hoped to overcome the observing bias faced by previous studies. To some degree, they were successful. “You probably end up with a fairer sampling of the galaxy population this way,” says Alfred Tiley, an astronomer at the University of Western Australia. Tiley, who was not involved in the research, authored an accompanying commentary about it in Nature.
Not everyone is convinced. Trainor thinks Neeleman and his colleagues’ new method avoids the bias of brightness but may come with its own prejudices. “Their technique is biased toward finding stable rotating disks,” he says. The extended disks created by cool galaxies are more likely to obscure a quasar than a more compact galaxy might. “It’s like throwing darts at a dartboard,” Trainor says. “The larger dartboard is more likely going to get hit.” That analogy does not diminish the technique, which he calls “a really useful and complementary tool.”
While Prochaska agrees that larger galaxies are more likely to block quasars, he argues that the Wolfe Disk’s extended gas in front of the background quasar does not necessarily have a bearing on the galaxy’s structure. The large distribution of gas around a quasar-blocking object could come from a spheroidal shell of gas around the galaxy or from extended filaments funneling gas into it.
Trainor also questions how common galaxies like the Wolfe Disk might be in the early universe. He is not convinced that a single galaxy is enough to demonstrate that cold accretion dominated early galaxy formation. But new galaxies may be uncovered soon. Neeleman’s team plans to continue using ALMA to study quasar-shadowed galaxies in hopes of finding more.
“It’s clear now that you can do this in a subset of cases very early on,” Prochaska says of cold-mode accretion. “We’re all a bit surprised.”
Native to the Indian and Pacific oceans, lionfish invaded coral reefs in the Bahamas beginning in the early 2000s—likely when multiple aquarium owners surreptitiously liberated some of these fast-growing tank menaces into the Atlantic. As new predators with no enemies and venomous spines, lionfish have multiplied almost unimpeded and have wreaked havoc on Bahamian coral reef fish species, especially little ones. Invasive predators often capitalize on the naivete of native species that do not recognize them as a threat—at least initially. But heavy predation is presumed, over time, to place intense selection pressure on prey to develop a fear of the new species.
In 2015, a decade after the lionfish invasion took hold in her study area, coral reef ecologist Isabelle Côté was curious: Are native Caribbean fish becoming wary of these dangerous newcomers? She and her graduate student Adrienne Berchtold, both then at Simon Fraser University in British Columbia, conducted a series of experiments at the Cape Eleuthera Institute in the Bahamas to find out. They published their results on Tuesday in Animal Behaviour.
First, the researchers donned scuba gear and collected baby striped parrotfish, which lionfish commonly eat. The scientists took some of these specimens from two reefs known to have many predators (including lionfish) and others from two reefs with few of them. Côté and Berchtold placed the parrotfish in tanks with a sandy bottom and hiding places made of PVC pipe. Then they watched the parrotfish’s behavior before and after lifting a barrier to an adjacent tank so the animals could see one of three things: a lionfish, a grouper (a scary-looking native predator that eats parrotfish) or a control environment containing only seawater.
Fish can also smell predators. So the scientists further tested the parrotfish’s response by injecting lionfish and grouper effluent—an excretory soup from the predators’ water—into their tanks. (For a control condition, the researchers used a squirt of plain seawater.) Additional trials simultaneously combined the visual and olfactory cues.
After all of these evasion tests, the same parrotfish fish were subjected to studies of survival. If specific fish in the evasion trials had been deemed relatively naive because they exhibited less fearful behavior, it was predicted they would be more likely to get eaten. The parrotfish were placed in tanks containing a hungry lionfish, as well as conch shells for shelter. The researchers then recorded the ensuing drama for up to two hours.
What happened? In the evasion trials, when most of the parrotfish saw or smelled a grouper, they swam less, frequently froze and cowered away. But their reaction to a lionfish did not significantly vary from their response to the plain-seawater control.
In the survival trials, 57 percent of the parrotfish tested were eaten. And the best predictor of a fish’s survival was how long it had hidden during the evasion trials. The length of this period was interpreted as a measure of “shyness” or “boldness.”
Bold fish were more likely to come from the low-predation reefs—and to be gobbled up. Shy fish mainly came from high-predation reefs. They had a significantly higher chance of surviving—not because they recognized lionfish as predators, but because they were simply more afraid in general. “To me, that’s the coolest part,” Côté says. These scaredy-fish were neophobic, even fearing empty neighboring tanks and squirts of plain seawater.
Fear ecologist Liana Zanette of Western University in Ontario, who was not involved with the study, calls it “extremely thorough, thoughtful, and well designed.” She suggests the research indicates that striped parrotfish do not recognize lionfish as predators, despite 10 years of cohabiting with them.
So how long does it take for native prey to develop recognition of a new predator on the block? It depends. Previous studies involving other species reveal huge variations, from a few years to centuries. Some species have been wiped out because they never adapted to invasive predators at all.
One big implication of the new paper, says University of Washington predator biologist Aaron Wirsing, who was not involved in the study, is that “lionfish may be selecting for more cautious prey populations.”
“To be shy is usually a lousy lot in life,” Côté says, referring to other studies that found guarded fish get less to eat. With lionfish in the mix, however, shyness is a major survival advantage. Being generally scared of everything helps when encountering a new predator. Strong selection for shy fish may not bode well for the hunting success of native predators—but Côté speculates it may underpin declining lionfish numbers recently observed in the northern Caribbean.
“Some years ago Eugène Dubois discovered in the island of Java some bones from a prehistoric animal, which might have formed the so-called missing link in the chain of descent of man from monkey. Julius Kollman is rather of the opinion that the direct antecedents of man should not be sought among the species of anthropoid apes of great height and with flat skulls, but much further back in the zoological scale, among the small monkeys with pointed skulls; from these he believes were developed the human pygmy races of prehistoric ages, with pointed skulls. Thus may be explained the persistency with which mythology and folk lore allude to pygmy people.”
—Scientific American, August 1906
More gems from Scientific American’s first 175 years can be found on our anniversary archive page.
At least 3,700 years ago, Babylonian mathematicians approximated the ratio of a circle’s circumference to its diameter. They inscribed their answer, the first discovered value of pi, on a humble clay tablet: 25/8, or 3.125. Now Carl-Johan Haster, a theoretical astrophysicist at the Massachusetts Institute of Technology, has managed to do almost as well: in a study uploaded to the preprint server arXiv.org, he measured pi to be about 3.115.
In the intervening years, researchers have calculated the true value of the ratio to a modest 50 trillion decimal places with the aid of powerful computers (you probably know how it starts: 3.141592653… and on into infinity). Haster’s approximation of it may be a couple of millennia behind in terms of accuracy, but that fact is of little relevance to his real goal: testing Einstein’s general theory of relativity, which links gravity with the dynamics of space and time.
Information about the laws of physics is effectively baked into gravitational waves, the ripples in spacetime created when massive objects such as black holes spiral into one another. Haster, a member of the Laser Interferometer Gravitational-Wave Observatory (LIGO) Scientific Collaboration, noticed pi appeared in several terms of an equation describing the waves’ propagation.
“What Carl did was say, ‘Look, all of these coefficients depend on pi. So let’s change pi, and let’s check whether the measurements are consistent [with general relativity],’” says Emanuele Berti, a theoretical physicist at Johns Hopkins University, who was not involved in the new study and is not part of the LIGO collaboration.
Haster realized that he could treat pi as a variable instead of a constant. Then he could check the equation for gravitational waves against LIGO’s experimental measurements of them. Einstein’s theory should have matched the measurements if and only if Haster used values of pi close to that already determined by other methods. If general relativity matched LIGO’s measurements when pi was not close to its true figure, that would be a sign that the theory was only half-baked. By trying values of pi from –20 to 20, Haster checked more than 20 observed candidate gravitational-wave eventsand found that the figure that matched theory to experiment was about 3.115. So Einstein’s recipe does not seem to need any tweaking just yet. “In my head, at least, [the study] has a nice mix of being both kind of cute and amusing and also actually producing a valid and fairly strong test of general relativity,” Haster says.
Pi seems to pop up all the time—not just explicitly in circles but in the hydrogen atom and the way needles fall across lines. The reason a factor of pi appears in an equation for gravitational waves is a little headier, however: the waves interact with themselves.
“When a gravitational wave is traveling out, it sees the the curvature of spacetime, including the energy that was generated by the gravitational waves produced in the past,” Berti says. The first stone you drop into a calm pond sends out smooth ripples across the surface. If you drop another stone immediately after, the surface is no longer smooth—leftover ripples from the previous stone will interfere with new ripples from the second one. Gravitational waves work similarly, but the medium is spacetime itself, not water.
The equation describing this self-interacting effect contains factors of pi as a piece of several numerical terms. A previous examination of Einstein’s theory by LIGO in 2016 varied individual terms instead of slicing out a common factor across several terms such as pi. Although this approach sufficed as a test of general relativity, physicists have wanted to see all the terms changing together, and Haster’s method using pi offers a way of doing just that.
But it remains a far from transcendental test of the theory. One issue is the relative uncertainty of Haster’s figures: his approximation of pi currently ranges from 3.027 to 3.163. Significantly sharpening it will require observing mergers of lighter objects such as neutron stars, which create drawn-out gravitational waves that can last 300 times longer than those from a colliding pair of massive black holes. Like trying to identify an unknown song, the more one can listen, the better. Currently, there are only two recorded confirmed neutron star mergers in the available data. And until LIGO—which is shut down because of COVID-19—resumes operations, that number will not change.
Not everyone is worried about the flakiness of this pi-scrying technique, though. “Many people have been discussing the fact that we could maybe change Pi Day (March 14) into ‘Pi Two Weeks’ (March 2 to March 15) to account for current uncertainty,” jokes Chris Berry, an astrophysicist at Northwestern University, who was not involved in the new study and is part of the LIGO collaboration.
This proposal would, of course, likely increase the number of pastries for a pi-loving physicist to consume. But Berry maintains that calorie increase would not be altogether a bad thing. A fortnight of feasting, he says, would eventually give researchers another way to approximate pi: measuring their own rotund circumference.
On February 22 “Mad” Mike Hughes died when his self-built steam rocket crashed shortly after takeoff. Hughes was a famous flat-earther, one of a growing group who do not accept that Earth is an oblate spheroid (which it is). His fatal launch was apparently general daredevilry and not an attempt to gather data for flatearthism. Although coverage by our friends at Space.com quoted him as saying in a 2017 documentary, “I’m going to build my own rocket right here, and I’m going to see it with my own eyes what shape this world we live on.”
When a virus invades your cells, it changes your body. But in the process, the pathogen changes its shape, too. A new mathematical model predicts the points on the virus that allow this shape-shifting to occur, revealing a new way to find potential drug and vaccine targets. The unique math-based approach has already identified potential targets in the coronavirus that causes COVID-19.
Outlined in April in the Journal of Computational Biology, the strategy predicts protein sites on viruses that stash energy—important spots that drugs could disable. In a rare feat, the work proceeds from pure mathematics, says study author and mathematician Robert Penner of the Institute of Advanced Scientific Studies in France. “There’s precious little pure math in biology,” he adds. The paper’s predictions face a long road before they can be verified experimentally, says John Yin, who studies viruses at the University of Wisconsin–Madison and was not involved in the research. But he agrees that Penner’s approach has potential. “He’s coming at this from a mathematician’s point of view—but a very scientifically informed mathematician,” Yin says. “So that’s highly rare.”
Penner’s method takes advantage of the fact that certain viral proteins alter their shape dramatically when viruses breach cells, and this transformation depends on unstable features. (A stable protein site, by definition, resists change.) By identifying “high free energy sites”—areas on a viral protein that store lots of energy—Penner realized he could spot likely “spring” points that mediate this change in shape. He calls such high-energy spots exotic sites. Finding them required some complex math.
Penner focused on the backbones of the proteins that undergo the most change during cell fusion and entry. He examined the hydrogen bonds that form between backbone sections when proteins fold. A protein consists of a series of individual units, or residues, with two such units forming hydrogen bonds. The bonded units rotate relative to each other, and those twists imply varying amounts of free energy in the residues involved.
To isolate the exotic rotations, Penner cranked a few mathematical levers on a giant collection of protein shapes. He and his colleagues had previously gathered a representative sample of proteins from a database, and looked at the roughly 1.17 million backbone hydrogen bonds in the set. He then needed to establish how frequently different rotations appeared.
To find that information, Penner turned to geometry. In the 19th century, German mathematician Carl Friedrich Gauss showed that you can describe each unique rotation of three-dimensional space by specifying the axis around which that rotation turns and the amount by which it does so (picture a wheel turning around car axle by anywhere from zero to 360 degrees, or zero to two pi radians). You can represent each rotation with a vector, a measurement that has both a magnitude and a direction and that is usually pictured as an arrow of a certain length pointing in a specific direction. This arrow’s orientation describes the rotation’s axis, and the vector’s length gives the amount of rotation (imagine an axle that lengthens with further rotation). Collect all the vector arrows pointing out every which way from a central point, and you have all possible axes for a rotation to spin about. Spots along each axis (the arrow points of different vectors) identify all unique rotations: the possible amounts of rotation, from zero to two pi radians, around every axis.
Altogether these arrows make up a 3-D ball (imagine a spiny Koosh ball or a rolled-up hedgehog). This structure is what Penner wanted, because it allowed him to do some math on the points appearing in it. Penner mapped the rotations found in the database onto the ball. Then he calculated the frequency of each one by looking at the density of its surrounding region in the structure: rotations in less dense parts of the ball are rarer.
Scientists know that the frequency of a protein feature is related to a function of its free energy, such that rarer features have higher energies. So using established equations and the densities on the ball, Penner computed the free energy of different rotations, revealing exotic sites. One indication that the approach works is that it predicted already known functional sites, Penner says. But previously unknown sites discovered by this method could prove to be promising targets for drugs to attack.
If experiments verify Penner’s predicted sites—a big if—the approach holds promise, says Arndt Benecke, a biological researcher at the French National Center for Scientific Research, who advises the mathematician. “If that were the case, then automatically, the free energy is something you could target that we’re not currently doing,” he says. “The whole thought of what could or should a drug or antibody do might change.”
In a follow-up study published in the same journal on Wednesday, Penner pinpointed three exotic “sites of interest” on the coronavirus behind COVID-10. But now, they must survive the rigors of the lab. Experimenters need to show that knocking out the sites indeed releases free energy, Benecke says. Even then, they may remain inaccessible to drugs, he adds. And any treatments targeting the sites must survive the usual tests for efficacy and safety in animal models and then in people. “The literature is littered with failures,” Penner says.
Still, if the method works, it could have applications for a wider range of targets, from the signaling proteins that allow cells to communicate with their environment to prions, the misfolded proteins behind conditions such as mad cow disease. “This could go far beyond the viruses,” Benecke says.
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