COVID-19 has turned our usual routines on their heads, and we are all scrambling to figure out how to live in this new time, however long it lasts. Many parents have found themselves suddenly thrust in the role of teacher, trying to keep their children on pace in school, often while working from home remotely to boot.
Math can be a challenge for parents trying to help their kids with homework in the best of times, and these are decidedly not those times. If you need someone to tell you it’s okay not to be a superparent who makes sure all the homework gets done perfectly right now, I am happy to be that person. To adapt a meme I’ve seen, you’re not homeschooling. Your kids are staying home during a crisis, and you are trying to help them learn. In my view, it’s okay if you don’t prioritize classroom math. (If you are looking for resources for supporting your kids’ classroom math, math Twitter might be helpful.)
Perhaps a more feasible goal right now than keeping up with classroom math (and one that will be even more relevant over the summer) is having joyful, open-ended experiences with math that cultivate mathematical curiosity and pattern-finding. I think of these activities as being analogous to reading for pleasure rather than to write a paper for a class, or running around outside instead of participating in organized sports.
Resource lists can be overwhelming. If I’m trying to figure out what to cook for dinner tonight with my leftover squash, a list of seven recipes is often more helpful than a list of 87. For that reason, I have limited my list to six (my favorite number) sites. There are a lot of other wonderful resources out there, but these are a few I’ve stumbled on that give a wide range of opportunities for engaging with math in a playful, creative way. I’ve tried to arrange these roughly from sites geared towards younger learners to those for math undergraduates and mathematicians, but there is a lot of overlap in what different groups might find enjoyable.
Math for Love by Dan Finkel and Katherine Cook is chock full of math games and more structured curriculum materials for elementary school students. Since schools started closing as a result of the pandemic, they have been sending out email newsletters with resources and games to help parents help their kids. Which One Doesn’t Belong is a website by Mary Bourassa, inspired by Christopher Danielson’s book of the same name. The concept is simple: there are four numbers, shapes, or graphs, and you have to find a reason each one is the odd one out. If the numbers are 9, 16, 25, and 43, you could say 9 is the odd one out because it has only one digit, 16 is the odd one out because it’s not odd (the even one out, I suppose), 25 is the odd one out because it does not end in a multiple of three, or 43 is the odd one out because it is not a square. (Maybe you can come up with some of your own reasons for each one.) There is no right answer, and each activity can be a jumping-off point for mathematical creativity. Annie Perkins’ #MathArtChallenge is an open-ended way to explore math by creating and noticing patterns. Perkins is sharing daily prompt to inspire mathematical play — everything from Islamic geometry constructions to toilet paper roll polyhedra — and other participants are sharing their creations on Twitter and Instagram. Paula Krieg’s blog Bookzoompa has a wealth of paper-folding activities that engage with mathematics. Disclosure: Krieg recently mailed me a beautiful example of one of the more challenging crafts she’s written about on her blog: Jo Nakashima’s origami fireworks. You might want to try some of her simpler crafts first, like these pentagons and stars or this eight-page origami booklet. Aperiodical’s Big Lock-Down Math-Off is a version of the summer math communication competition they have run for the past couple of years. Participants submit write-ups of favorite bits of math(s), and readers can vote on their favorites. I believe submissions are still open if you want to toss your hat in the ring. Talk Math with Your Friends is a series of Zoom talks organized by Steven Clontz, T.J. Hitchman, Brian Katz, Drew Lewis, and Kate Owens. Each Thursday, a mathematician talks about their work to a friendly online audience. The talks are designed to be as accessible as possible to math undergraduates and beginning graduate students. Stay tuned—a TMWYF My Favorite Theorem live taping is in the works for this summer!
On a recent episode of our podcast My Favorite Theorem, my cohost Kevin Knudson and I had the opportunity to talk with Ben Orlin, a math educator and author of the popular blog Math With Bad Drawings as well as two books, Math With Bad Drawings and Change Is the Only Constant. You can listen to the episode here or at kpknudson.com, where there is also a transcript.
Orlin decided to talk not about a theorem but about a favorite mathematical object, Weierstrass’s function. This function, sometimes known as a “monster,” answers the question of how closely continuity and differentiability are related. In mathematics, continuity is roughly what you might think it should be: a function is continuous if nearby inputs are sent to nearby outputs. (Is there a more rigorous definition? Yes! Here, if you insist.) A function is differentiable if at every point, you can find a tangent line, a straight line that approximates the function’s path near that point.
In rough terms, when you think about graphs of functions, a continuous function is one that doesn’t have jumps, and a differentiable function is one that doesn’t have corners or spikes. It seems clear that a function must be continuous in order to be differentiable A function with one corner in it—an example is the absolute value function f(x)=|x|, where |x|=x if x is greater than or equal to 0 and |x|= −x if x is less than 0—is continuous everywhere and differentiable everywhere except at x=0, where it has that corner.
It’s not too hard to cook up a function that has a lot of corners like that. You can make a sawtooth function with a peak or valley at every integer, for example. That function would be differentiable everywhere except at those isolated points, which are infinite in number but politely spaced out. Weierstrass wanted to know whether there was a limit to how not differentiable a continuous function could be, and this example shows that it can be pretty darn non-differentiable! While the function is continuous everywhere, it is not differentiable at any point.
An illustration of the Weierstrass function, showing the way its cragginess shows up at every scale. Credit: Eeyore22 Wikimedia
To be pedantic, it is not quite accurate to say the Weierstrass function. Weierstrass’s original construction allowed for two parameters to be chosen, so there is a whole family of these functions. Since Weierstrass first published his curves, other mathematicians have defined more such monsters, and even proved that in a sense, most continuous curves are nowhere-differentiable. It’s a blow to those of us who like our math neat and tidy, but perhaps we can think of it as an invitation to think bigger and weirder about what we should expect in mathematics.
In each episode of My Favorite Theorem, we ask our guest to pair their theorem with something. You’ll have to check out the episode to see why Orlin thinks molecular gastronomy is the ideal accompaniment to Weierstrass’s function.
Back in the pre-pandemic era, I was really looking forward to April 8. On that date, Carl Zimmer was going to give a talk at my school, Stevens Institute of Technology, about his latest book, She Has Her Mother’s Laugh. For decades, Zimmer has reported on biology in The New York Times and other publications and in books, 13 so far. Mother’s Laugh tells the epic tale of our attempts to plumb the mysteries of heredity and to improve ourselves with that knowledge. The book is a marvelous work of history—Zimmer’s account of the early days of eugenics in the U.S. is especially gripping—as well as a detailed, up-to-date report on CRISPR and other advances that add urgency to old debates about human enhancement. Zimmer is an engaging story-teller and insatiable reporter, who visits scientists in their labs and even volunteers to be a subject. As a result, while discussing the remarkable diversity of creatures dwelling on and in our bodies, he can tell you that his own bellybutton harbors a bacterium, Marimonas, also found in the Mariana Trench. In lieu of Carl’s April 8 talk, here he answers questions about genetics and related topics. – John Horgan
Horgan: How did you end up in the science-writing racket, anyway? Any regrets?
Zimmer: I feel incredibly lucky to have this job. It wasn’t anything I thought about with any foresight. I loved to write, and I loved science. A couple years out of college, I got a job as an assistant copy editor at the science magazine Discover. There, I got a great training in how to fact-check and report on science. I stayed there for ten years before heading out on my own.
Horgan: Why the focus on biology? When you started out, wasn’t physics going to solve everything?
Zimmer: As a junior reporter at Discover, I had to write about all sorts of stuff–astronomy, geoscience, physics, technology, and so on. But I found that biology was always the field that managed to surprise me the most. Evolution has gone off in such crazy directions in the past four billion years, and the tools biologists have to study life have grown incredibly powerful over the past few decades.
Horgan: I sometimes worry I’m too mean to scientists. Do you ever worry you’re too nice?
Zimmer: As a fact-checker, you learn that no one should be given a pass. When I report on a story, I talk with outside experts to see if researchers I’m writing about are really delivering on what they claim. And it’s also important to keep up with what social scientists and philosophers have to say–because science doesn’t happen in a vacuum and can have dangerous consequences.
Horgan: What’s the biggest thing that’s happened in science since you started writing about it?
Zimmer: DNA sequencing. It changed everything, from the study of Neanderthals to tracking the covid-19 pandemic.
Horgan: In 2009 you quit the online chat show Bloggingheads.tv, on which we once spoke, because it gave a platform to creationists. Have your feelings about creationism evolved over the past decade?
Zimmer: No. Creationists have not done any good science since then, while evolutionary biology has leapt forward in dramatic fashion.
Horgan: Whenever I criticize scientific racism, or sexism, people call me an unscientific social justice warrior. I know this happens to you, too. How do you deal with these people?
Zimmer: People try to deflect from weak arguments by accusing their opponents of being contemptible.
Horgan: Is CRISPR living up to its hype? If so, will it help gene therapy, finally, take off?
Zimmer: CRISPR is already a mainstay of scientific research, for testing how genes work and how mutations affect health. It’s already into clinical trials for diseases like sickle cell anemia just few years after its invention. We have yet to see how well it will work in those applications. But it’s unquestionably one of the most important advances in the history of biology.
Horgan: By the time I reached the end of She Has Her Mother’s Laugh, I wasn’t sure whether you think genetic enhancement of humans is feasible, or desirable. Could you clarify?
Zimmer: I think anyone who pretends to have a simple answer is wrong. The answer depends not only on the complexity of biology, but also on what we really want from genetic enhancement. We are already carrying out genetic enhancement when parents with Huntington’s disease pick embryos for IVF without the mutation. But I’m skeptical that any manipulation will affect, say, intelligence–certainly not more than what a decent education and a healthy childhood can offer.
Horgan: Will there be any more revolutions in our understanding of heredity?
Zimmer: It’s not possible to predict revolutions that haven’t happened. But I think that scientists will learn a lot about how epigenetic changes can be carried down through generations–if not in humans, then in other animals and plants.
Horgan: Will our knowledge ever be so complete that the nature/nurture debate finally ends?
Zimmer: I can’t rule it out, but it won’t be easy. It’s relatively easy to study how genes influence variation, but the environment is so vast and complex it may not submit to simple experiments with clear results. Still, there are some very impressive experiments that are grappling with these challenges.
Horgan: Are radical life extension, and possibly immortality, feasible?
Zimmer: I’m not holding my breath. Aging is the result of so many factors that it’s hard to see how any simple intervention can change it much. Immortality just seems biologically silly to me.
Horgan: I can’t resist asking: what do you think of the U.S. response to the coronavirus?
Zimmer: A disaster.
Was Darwin Wrong?
How Can We Curb the Spread of Scientific Racism?
Should Research on Race and IQ Be Banned?
My Problem with “Taboo” Behavioral Genetics? The Science Stinks!
Quest for Intelligence Genes Turns Out More Dubious Results
Have Researchers Really Discovered Any Genes for Behavior?
Defending Stephen Jay Gould’s Crusade Against Biological Determinism
Darwin Was Sexist, and So Are Many Modern Scientists
Do Women Want to be Oppressed?
Google Engineer Fired for Sexist Memo Isn’t a Hero
See also my free, online book Mind-Body Problems: Science, Subjectivity & Who We Really Are, also available as a Kindle e-book and paperback.
The thin atmosphere of Pluto may be far more resilient than scientists thought
The dwarf planet’s thin shell of air is generated by the vaporization of surface ices, which leads to the lofting of nitrogen and small amounts of methane and other gases. That vaporization is driven by sunlight, the intensity of which varies greatly during Pluto’s highly elliptical, 248-year-long trek around the sun.
Many scientists have thought that Pluto’s atmosphere waxes and wanes dramatically as a result, probably even collapsing completely when the dwarf planet is at its farthest from the sun. However, recently published results based on observations by NASA’s Stratospheric Observatory for Infrared Astronomy (SOFIA) may force scientists to rethink such notions.
“Now, we’re questioning if Pluto’s atmosphere is going to collapse in the coming years — it may be more resilient than we thought,” study lead author Michael Person, director of the Massachusetts Institute of Technology’s Wallace Astrophysical Observatory, said in a statement this week.
Most of what we know about that atmosphere, and Pluto itself, comes courtesy of NASA’s New Horizons mission, which flew by the dwarf planet in July 2015.
Two weeks before that epic flyby, SOFIA got a much longer-range look at Pluto’s air, studying the dwarf planet as it passed in front of a distant star. SOFIA, a modified Boeing 747 jet outfitted with a nearly 9-foot-wide (2.7 meters) telescope, stared as starlight streamed through Pluto’s atmosphere.
This “occultation” was visible for just 2 minutes, and only from a small patch of the Pacific Ocean near New Zealand. SOFIA got into position in plenty of time initially, but the plane had to course-correct just two hours before the event when updated predictions revealed that the faint shadow would actually settle onto the waves 200 miles (320 kilometers) farther north than previously thought.
“Capturing that shadow required a bit of scramble. SOFIA has the benefit of being mobile, but the revised flight plan had to be cleared by air traffic control,” William Reach, SOFIA’s associate director for science operations, said in the same statement.
“There were a few tense moments, but the team worked together, and we got clearance,” Reach said. “We reached Pluto’s shadow at exactly the right time and were very happy to have made it!”
SOFIA was able to peer into the middle layers of the dwarf planet’s atmosphere, gathering data in infrared and visible-light wavelengths. Two weeks later, during its flyby, New Horizons collected information about the upper and lower layers, in radio and ultraviolet frequencies.
“These combined observations, taken so close in time, have provided the most complete picture yet of Pluto’s atmosphere,” NASA officials wrote in the same statement.
For example, New Horizons’ imagery revealed that the atmosphere has a distinct blue tint, like the air of Earth. The color is thought to come courtesy of tiny haze particles, which reflect short-wavelength blue light preferentially.
SOFIA’s observations confirmed the existence of those particles and characterized them, revealing that each fleck is just 0.06 to 0.10 microns wide, study team members said—about 1,000 times thinner than a human hair.
After analyzing these and other results—including information gathered by SOFIA’s predecessor, the Kuiper Airborne Observatory, which operated from 1975 to 1995—Person and his colleagues determined that Pluto’s haze likely evolves on short timescales, fading and thickening over the course of just a few years.
This brief cycle suggests that something other than Pluto’s distance from the sun is driving the abundance of haze particles. For example, periods of thick haze may result when particularly ice-rich regions of Pluto’s surface get their time in the sun, the researchers said.
“There’s still a lot we don’t understand, but we’re forced now to reconsider earlier predictions,” Person said. “Pluto’s atmosphere may collapse more slowly than previously predicted, or perhaps not at all. We have to keep monitoring it to find out.”
The study was published online in November 2019 in the journal Icarus.
It’s unclear how many more occultations SOFIA will be able to chase down: President Donald Trump’s proposed budget for 2021 would eliminate funding for the program. But that’s not necessarily a death sentence. No budget is final until Congress passes it, and SOFIA—a joint project of NASA and the German Aerospace Center, known by its German acronym DLR—has escaped proposed termination before.
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Scientists are scrambling to learn how the novel coronavirus, SARS-CoV-2, causes disease, as well as racing to develop treatments and, critically, a vaccine. The work relies heavily on a rarely acknowledged player: research animals. One of the most unusual things about SARS-CoV-2 is the wide range of disease severity it has in humans—from mild or asymptomatic infections to deadly ones. Creating animal models that reflect such clinical diversity will be important, albeit difficult. Creatures ranging from the humble laboratory mouse to hamsters and baboons are in the mix. We do not yet know which animals will prove most useful; different species may be best suited to answering different questions.
Reproducing serious disease is especially tricky, but studies of the coronaviruses that cause severe acute respiratory syndrome (SARS) and Middle East respiratory syndrome (MERS) have laid important groundwork. The go-to medical research animals are mice: they can be quickly bred and cheaply obtained, and researchers already have many tools for working with them. Unfortunately, these rodents—although not immune to infection—do not appear to suffer any ill effects from the new virus. The same was true for SARS, but two strategies proved effective: adapting mice to the virus or adapting the virus to mice.
In 2007 microbiologist Stanley Perlman of the University of Iowa and his colleagues genetically engineered mice to produce the human version of the angiotensin-converting enzyme 2 (ACE2) receptor that the original SARS virus used to latch onto cells. The disease was lethal to these “hACE2” mice. SARS-CoV-2 uses the same receptor, so hACE2 mice should likewise be vulnerable to the new virus, Perlman says. He has sent frozen mouse sperm samples to the Jackson Laboratory, which is breeding the animals and gearing up to distribute them to other labs around the world. “We should have enough for the scientific community to conduct its experiments by mid-June,” says neuroscientist Cat Lutz, who directs the Jackson Laboratory’s mouse repository—one of the largest in the U.S.
Virologist Kanta Subbarao, then at the National Institute of Allergy and Infectious Diseases, and her colleagues took another route: they created a strain of the SARS virus that was lethal to ordinary mice. The researchers employed a technique called serial passage, which involves extracting virus from the lungs of an infected mouse, using it to inoculate another one and then repeating the process in additional mice. After 15 cycles, they created a SARS strain that was 100 percent lethal to mice. Studying the genetic mutations involved also enabled them to learn something about how the virus caused disease. Although hACE2 mice are very likely to be susceptible to the new coronavirus, they may exhibit much milder disease than they did with SARS. “The expectation is that SARS-CoV-2 will have to be adapted by [serial] passage in hACE2 mice,” says Subbarao, now at the Peter Doherty Institute for Infection and Immunity in Australia. Researchers also have more prosaic tools at their disposal. “We can possibly manipulate [the viral] dose and route of administration to get a range of severity,” Lutz says.
Perlman has not waited around to see how his hACE2 mouse strain responds to SARS-CoV-2. He used an unrelated virus as a “vector” to carry the human ACE2 gene into adult mouse cells, rendering them temporarily susceptible to the new coronavirus—an approach he pioneered while studying MERS. This method is faster than those that involve altering sperm or egg cells. The technique is useful for testing therapeutics given around the time an animal is infected. But it is not good for “pathogenesis” studies that attempt to help scientists understand how a virus enters cells and replicates or which cells that virus attacks. Perlman is also using gene editing to alter the mouse ACE2 receptor so SARS-CoV-2 can recognize it. Others are editing the virus’s genome to allow it to attach to the mouse receptor. “They may well be able to use any mouse strain” to study COVID-19, Perlman says. “That would be a huge step forward.”
Hamsters, Ferrets and Cats
Researchers are also looking beyond mice. Subbarao and her colleagues found hamsters were useful for studying SARS, so some researchers are using them again for COVID-19. A team at the University of Hong Kong showed that SARS-CoV-2 replicates in hamsters, producing some of the lung damage seen in humans. None of the animals died, but there were signs of illness, including weight loss. The hamsters produced antibodies. And blood serum from recovered animals that was given to others prior to infection lowered viral levels but did not significantly reduce the lung pathology.
Scientists often study respiratory diseases in ferrets, because their lung physiology is similar to that of humans. A team in South Korea found that ferrets infected with SARS-CoV-2 had an elevated temperature and mild lung disease. A paper published days later, however, showed that the virus replicated efficiently only in ferrets’ upper respiratory tract rather than their lower one, which is not reflective of severe disease in humans. That study also found the virus was transmitted between cats in adjacent cages—suggesting transmission by respiratory droplets. So cats may be useful for examining how the virus spreads. Some animals are more difficult to work with than others, though. “A lot of the tools for studying the immune system that we have in mice aren’t nearly as well developed for ferrets or hamsters,” says pathologist David O’Connor of the University of Wisconsin–Madison, who is studying nonhuman primates as part of a large collaboration of researchers using various methods and putting all their data in an online portal called CoVen. “There’s even less research on cats, so there are even fewer tools.” Some animals are also more difficult to obtain or take care of or are costlier, but researchers need more information before ruling any species out. “In an emergency like this, where we don’t have the luxury of time, we have to let the biology guide us,” O’Connor says. “It may turn out these less conventional models are the best approach, in which case we’re going to have to develop the expertise to study them.”
Nonhuman primates are “the gold standard when it comes to testing vaccines and therapeutics,” says virologist Barry Rockx of Erasmus University Medical Center in the Netherlands. A preprint paper by virologist Chuan Qin of the Chinese Academy of Medical Sciences and Peking Union Medical College and colleagues, posted online in March, found that the virus replicated in the noses, lungs and guts of rhesus macaques. The animals also lost weight and showed signs of pneumonia. The study grabbed attention because the researchers showed that recovered monkeys could not be reinfected. “That provided good news: that protective immune responses can be elicited by natural infection,” O’Connor says, “though the durability still needs to be figured out.” A U.S. team has also demonstrated in a preprint study that infected rhesus macaques given the antiviral remdesivir (which was recently approved for emergency use in treating COVID-19 patients) had milder symptoms and lung pathology.
Cynomolgus (crab-eating) macaques are also being studied as a possible model of COVID-19. Credit: Hendra Su
One of the main factors influencing COVID-19 severity in humans is how old an individual is, so some researchers are studying animals at a range of ages. Rockx led a recent study using both young and old cynomolgus macaques—none of which displayed overt symptoms. “There are no clinical signs, but you do see lesions in the lung,” he says. This animal model could be useful for testing whether drugs reduce the transmission of disease or have adverse effects, Rockx adds. He and his colleagues detected more virus lingering longer in older monkeys, but those animals’ disease was not more severe. Meanwhile researchers at Texas Biomedical Research Institute (Texas Biomed) are studying rhesus macaques, baboons and marmosets simultaneously. “We’re comparing multiple nonhuman primate species, to see if we can recapitulate the [range of disease] observed in humans,” says Deepak Kaushal, director of Texas Biomed’s Southwest National Primate Research Center. His team is also not seeing significant differences in severity with age.
Recall, though, that only a small fraction of people with COVID-19 become critically ill. And these studies used relatively small numbers of monkeys. These caveats illustrate a drawback of nonhuman primates: because of ethical and practical concerns, it is not possible to study large enough numbers of them to reveal all facets of the disease—or even to calculate meaningful statistics. But doing so is not the primary goal. O’Connor’s studies involve injecting virus deep inside the lungs of cynomolgus macaques to elicit measurable disease. “We have lung disease that’s quantifiable, which means we can measure a reduction in that as a readout for medical countermeasures,” he says. The issue of severe disease becomes “academic,” he adds, “because if you can’t get the same readout consistently, you don’t have a good system for testing vaccines and drugs.” Nonhuman primates are subject to the highest ethical bar for research, however, so they are used sparingly.
The End Goal
A crucial advantage of animal studies is control. “With humans, you don’t know when they get infected, what exactly happens,” Perlman says. “You can understand disease much better in an experimentally infected animal, because you can manipulate parameters,” such as exposure route, dose and time of infection. The same principle applies to generating efficacy and safety data. “You’ll never have that sort of control in a clinical trial,” O’Connor says. “That’s where animal models are essential.”
Existing vaccine strategies—partly based on those developed for SARS—have led to some candidates for a COVID-19 vaccine skipping the animal testing phase. “It’s challenging in the COVID-19 era, because people don’t want to wait,” Perlman says. “For drugs, it’s not a good idea to skip the animal steps. But for vaccines, they’re really being skipped or minimized.” The urgent need, the lack of well-established animal models and previous experience with some vaccine platforms have all sped up the time line. The fact that vaccine strategies have been tested in humans, even if for different pathogens, provides some reassurance about safety, but there is also a specter raised by previous animal studies: vaccines can sometimes enhance disease, including via a phenomenon known as antibody-dependent enhancement. If that problem were to occur with a COVID-19 vaccine, “you would want to know that,” says Larry Schlesinger, president of Texas Biomed. Scientists also need to understand immune responses. Recent data from China suggests not everyone infected with the virus generates enough protective, or “neutralizing,” antibodies to become immune. And SARS-CoV-2 has not been around long enough for us to know how long people who may be protected remain so. “This has important implications for what a vaccine would look like,” O’Connor says.
Just last week in Science, Qin and colleagues published results from a study of an inactivated SARS-CoV-2 virus vaccine candidate that produces neutralizing antibodies that bind to the virus’s “spike” protein, which allows it to enter cells. The researchers showed that the vaccine, called PiCoVacc, generated immune responses that protected against several strains of the virus in mice, rats and rhesus macaques. Reassuringly, they saw no signs of antibody-dependent enhancement. And human trials are expected to begin later this year. If none of these initial attempts are successful, however, basic research may become critical. Better understanding may be required to pursue more sophisticated strategies. And to understand a virus, researchers need to study it in living organisms. “Everyone hopes the generic approaches we’re already testing are going to be spectacularly successful,” O’Connor says. Developing a vaccine “might be straightforward, but we have to prepare people for the possibility it might not be.”
Read more about the coronavirus outbreak from Scientific American here. And read coverage from our international network of magazines here.
“The press of the Soviet Union has been astounding its readers with accounts of a ‘revolution’ in science and a ‘miracle’ of technology. Nikolai A. Kozyrev, an astrophysicist, was said to have wrought the revolution, with his hypothesis that the passage of time is the source of cosmic energy. The miracle was the harnessing of a ‘concentration of energy.’ Speaking for the Presidium of the U.S.S.R. Academy of Sciences, three distinguished physicists joined in a public rebuke to the press for ‘cheap sensationalism’ and for placing its pages ‘at the disposal of absolutely incompetent people.’ They declared: ‘We are not against bold hypotheses, provided they are given substantiation.’ However, ‘This is not a case of the concentration of energy but of the concentration of amazing ignorance.’”
—Scientific American, January 1960
More gems from Scientific American’s first 175 years can be found on our anniversary archive page.
“Photography is the general name now applied to sun painting on paper and glass, as being different from the daguerreotype, which is produced on metallic plates. The inventor of photographs is Fox Talbot, of England, who secured patents in Britain and America, but has thrown them open to the public. Photography is destined apparently to supersede the art of Daguerre. In France, the splendid display of photographs in the Great Exhibition of Industry, and the limited number of pictures on metallic plates, affords conclusive proof that, with the French artists, the daguerreotype is becoming obsolete.”
—Scientific American, November 1855
More gems from Scientific American’s first 175 years can be found on our anniversary archive page.