Science – artdiamondblog.com

Clarity Is Rewarded, at Least Among Cave Experts

After Deirdre McCloskey published her classic “Economical Writing” in Economic Inquiry, Jack High published a critique in the same journal arguing that young economists would ruin their careers if they followed McCloskey’s advice to write clearly. High claimed that clear writing would be less published and economists who wrote more clearly would therefore be less likely to receive tenure. McCloskey published a rebuttal saying that clear writing was more likely to be published, to be read, and to help the writer receive tenure. But she added that even if she was wrong about that, we should try to write clearly because it is the right thing to do.

The study mentioned below provides some evidence to support McCloskey’s claim that clarity is rewarded.

(p. D2) . . . a team of researchers has analyzed jargon in a set of over 21,000 scientific manuscripts. The study focused on manuscripts written by scientists who study caves, . . .

They found that papers containing higher proportions of jargon in their titles and abstracts were cited less frequently by other researchers. Science communication — with the public but also among scientists — suffers when a research paper is packed with too much specialized terminology, the team concluded.

For the full story, see:

Katherine Kornei. “Confused by All That Scientific Jargon? So Are the Scientists.” The New York Times (Tuesday, April 13, 2021): D2.

(Note: ellipses added.)

(Note: the online version of the article has the date April 9, 2021, and has the title “Are You Confused by Scientific Jargon? So Are Scientists.” Where the wording in the online version differs from the wording in the print version, the passages quoted above follow the print version.)

The study discussed in the passages quoted above is:

Martínez, Alejandro, and Stefano Mammola. “Specialized Terminology Reduces the Number of Citations of Scientific Papers.” Proceedings of the Royal Society of Britain (April 7, 2021)
https://doi.org/10.1098/rspb.2020.2581.

The McCloskey classic article, and the exchange with Jack High, are:

McCloskey, Deirdre. “Economical Writing.” Economic Inquiry 23, no. 2 (April 1985): 187-222.

High, Jack C. “The Costs of Economical Writing.” Economic Inquiry 25, no. 3 (July 1987): 543-45.

McCloskey, Deirdre. “Reply to Jack High.” Economic Inquiry 25, no. 3 (July 1987): 547-548.

Still Plenty of Fruit to Pick from the Tree of Science

Some pessimists have argued for imminent economic stagnation on the grounds that technological progress depends on new scientific knowledge and that we already pretty much know all there is to know about science. One way in which they are wrong is that the process of scientific discovery still has a long way to go before we fully understand the world. (If C.S. Peirce was right in saying that truth is the result of infinite inquiry, then we will never fully understand the world.)

(p. A1) Evidence is mounting that a tiny subatomic particle seems to be disobeying the known laws of physics, scientists announced on Wednesday, a finding that would open a vast and tantalizing hole in our understanding of the universe.

The result, physicists say, suggests that there are forms of matter and energy vital to the nature and evolution of the cosmos that are not yet known to science. The new work, they said, could eventually lead to breakthroughs more dramatic than the heralded discovery in 2012 of the Higgs boson, a particle that imbues other particles with mass.

“This is our Mars rover landing moment,” said Chris Polly, a physicist at the Fermi National Accelerator Laboratory, or Fermilab, in Batavia, Ill., who has been working toward this finding for most of his career.

The particle célèbre is the muon, which is akin to an electron but far heavier, and is an integral element of the cosmos. Dr. Polly and his colleagues — an international team of 200 physicists from seven countries — found that muons did not behave as predicted when shot through an intense magnetic field at Fermilab.

The aberrant behavior poses a firm challenge to the Standard Model, the suite of equations that enumerates the fundamental particles in the universe (17, at last count) and how they interact.

“This is strong evidence that the muon is sensitive to something that is not in our best theory,” said Renee Fatemi, a physicist at the University of Kentucky.

. . .

(p. A19) For decades, physicists have relied on and have been bound by the Standard Model, which successfully explains the results of high-energy particle experiments in places like CERN’s Large Hadron Collider. But the model leaves many deep questions about the universe unanswered.

Most physicists believe that a rich trove of new physics waits to be found, if only they could see deeper and further. The additional data from the Fermilab experiment could provide a major boost to scientists eager to build the next generation of expensive particle accelerators.

For the full story, see:

Dennis Overbye. “A Particle’s Tiny Wobble Could Upend the Known Laws of Physics.” The New York Times (Friday, April 16, 2021): A1 & A19.

(Note: ellipsis, and bracketed year, added.)

(Note: the online version of the article was updated April 9, 2021, and has the title “A Tiny Particle’s Wobble Could Upend the Known Laws of Physics.”)

My point at the start of this entry is directly relevant to my argument in the first half of the last chapter of:

Diamond, Arthur M., Jr. Openness to Creative Destruction: Sustaining Innovative Dynamism. New York: Oxford University Press, 2019.

Distinguished French Scientists Spearhead International Effort to Investigate Possible Wuhan Lab Origin of Covid-19

(p. A8) BEIJING—A World Health Organization team investigating the origins of Covid-19 is planning to scrap an interim report on its recent mission to China amid mounting tensions between Beijing and Washington over the investigation and an appeal from one international group of scientists for a new probe.

The group of two dozen scientists is calling in an open letter on Thursday [March 4,2021] for a new international inquiry. They say the WHO team that last month completed a mission to Wuhan—the Chinese city where the first known cases were found—had insufficient access to adequately investigate possible sources of the new coronavirus, including whether it slipped from a laboratory.

. . .

WHO chief Tedros Adhanom Ghebreyesus said on Feb. 12 [2021] that the team would release an interim report briefly summarizing the Wuhan mission, possibly the following week, with a full report coming weeks later. But that summary report has yet to be published and the WHO team is now scrapping that plan, said Peter Ben Embarek, the food-safety scientist who led the team.

. . .

According to an advance copy of the open letter, the group of 26 scientists and other experts in areas including virology, zoology and microbiology said that it was “all but impossible” for the WHO team to conduct a full investigation, and that any report was likely to involve political compromises as it had to be approved by the Chinese side.

A credible investigation required, among other things, confidential interviews and fuller access to hospital records of confirmed and potential Chinese coronavirus cases in late 2019, when the outbreak was first identified in Wuhan, said the letter signed by experts from France, the U.S., India, Australia and other countries.

Investigators should also be allowed to view records including maintenance, personnel, animal breeding and experiment logs from all laboratories working with coronaviruses, the letter said.

“We cannot afford an investigation into the origins of the pandemic that is anything less than absolutely thorough and credible,” the letter said. “Efforts to date do not constitute a thorough, credible, and transparent investigation.”

The appeal is unlikely to gain traction, as any future probes would require Beijing’s cooperation. Moreover, many leading infectious-disease experts are skeptical that a lab accident could plausibly explain the origins of the pandemic.

Still, it expresses what has become a more widely shared dissatisfaction, voiced by the U.S. and U.K. governments and many scientists world-wide, that China has provided too little information and data to the WHO to guide researchers trying to determine where the virus originated and how it jumped to humans.

. . .

A laboratory accident is “definitely not off the table,” Dr. Ben Embarek told a seminar last week. Dr. Tedros said in February after the team’s trip that “all hypotheses remain open and require further analysis.”

The signatories of the open letter are mostly members of a broader group, spearheaded by French scientists, who have been sharing research papers and other information on Covid-19 since around December. None are associated with the WHO investigation.

Among the signatories are Etienne Decroly and Bruno Canard, molecular virologists at AFMB Lab, which belongs to Aix-Marseille University and the French National Centre for Scientific Research, France’s state research agency.

Dr. Decroly said he became involved after concluding that on the basis of available data, it was impossible to determine whether SARS-CoV-2 “is the result of a zoonosis from a wild viral strain or an accidental escape of experimental strains.”

The letter was co-organized by Gilles Demaneuf, a French data scientist based in New Zealand, and Jamie Metzl, a U.S.-based senior fellow for the Atlantic Council and adviser to the WHO on human genome editing.

Prominent critics of the laboratory hypothesis have in recent weeks published new research on bat coronaviruses found in Southeast Asia and Japan that they say shows that SARS-CoV-2 most likely evolved naturally to infect humans.

Robert Garry, a virologist at the Tulane University School of Medicine who was involved in that research, said he and other colleagues had initially considered the possibility of a leak or accident from a laboratory, but ultimately deemed it “nearly impossible.”

The Biden administration hasn’t publicly repeated its predecessor’s specific assertions regarding Wuhan laboratories.

Signatories of the open letter say they don’t back any one hypothesis but think it is premature to exclude the possibility of a leak or accident at or connected with a research facility such as the Wuhan Institute of Virology, or WIV, which runs high-security laboratories and has conducted extensive research on bat coronaviruses.

WIV scientists deny the virus came from there, saying they neither stored nor worked on SARS-CoV-2 before the pandemic and none of their staff tested positive for the virus.

Signatories said investigators should look at several possible scenarios, including whether a laboratory employee became infected with a naturally evolving virus while sampling bats in the wild, during transport of infected animals, or during disposal of lab waste.

They also said investigators should probe whether SARS-CoV-2 could have stemmed from “gain-of-function” experiments, in which viruses found in the wild are genetically manipulated to see if they can become more infectious or deadly to humans.

For the full story, see:

Betsy McKay, Drew Hinshaw, and Jeremy Page. “WHO Delays Release of Virus Origin Report.” The Wall Street Journal (Friday, March 5, 2021): A8.

(Note: ellipses, and bracketed dates, added.)

(Note: the online version of the story was updated March 5, 2021, and has the title “WHO Investigators to Scrap Plans for Interim Report on Probe of Covid-19 Origins.” The online edition says that the title in the print edition was “WHO Team Delays Release of Report on Virus’s Origin.” But my copy of the print edition had the title “WHO Delays Release of Virus Origin Report.”
The last 11 paragraphs quoted above appear in the online version, but not the print version, of the article.)

The open letter mentioned above, signed by 26 scientists from Australia, Austria, Belgium, France, Germany, India, New Zealand, Spain, the United Kingdom, and the United States, is:

Butler, Colin D., Bruno Canard, Henri Cap, Y. A. Chan, Jean-Michel Claverie, Fabien Colombo, Virginie Courtier, Francisco A. de Ribera, Etienne Decroly, Rodolphe de Maistre, Gilles Demaneuf, Richard H. Ebright, André Goffinet, François Graner, José Halloy, Milton Leitenberg, Filippa Lentzos, Rosemary McFarlane, Jamie Metzl, Dominique Morello, Nikolai Petrovsky, Steven Quay, Monali C. Rahalkar, Rossana Segreto, Günter Theißen, and Jacques van Helden. “Open Letter: Call for a Full and Unrestricted International Forensic Investigation into the Origins of Covid-19.” March 4, 2021.

Quiet, Modest Steinsberger Said Scientists Should “Be Interested in Learning About Nature,” Not in Seeking Prizes

(p. B12) Jack Steinberger, who shared the 1988 Nobel Prize in Physics for expanding understanding of the ghostly neutrino, a staggeringly ubiquitous subatomic particle, died on Saturday [Dec. 12, 2020] at his home in Geneva.

. . .

In 1988, The Economist said Dr. Steinberger “enjoys a reputation as one of the finest experimental physicists in the world.” The magazine continued, “In a field full of flamboyance and a fair bit of arrogance, he is a quiet, modest man; something of a physicist’s physicist.”

As if to prove the point, Dr. Steinberger told a meeting of Nobel laureates in 2008 that scientists should “be interested in learning about nature,” not prizes.

“The pretension that some of us are better than others,” he said, “I don’t think is a very good thing.”

For the full obituary, see:

Douglas Martin. “Jack Steinberger, Physicist Awarded a Joint Nobel Prize, Is Dead at 99.” The New York Times (Thursday, December 17, 2020): B12.

(Note: ellipses, and bracketed date, added.)

(Note: the online version of the obituary was updated Jan. 20, 2021, and has the title “Jack Steinberger, Nobel Winner in Physics, Dies at 99.”)

The Curious Still Have a Lot to Learn

(p. 22) Earlier this week, and more than 2,700 feet underwater by the northern Great Barrier Reef, a remotely operated vehicle named SuBastian engaged in a stare-off with a burrito. That’s what the creature looked like from a distance: an untoasted cylinder floating eerily upright in the ocean’s twilight zone, like takeout from Triton.

. . .

When Dr. Vecchione got a good look at the image, he knew exactly what it was: Spirula spirula, or the ram’s horn squid. Spirula is the only living squid to have an internal coiled shell, which it tucks under the fleshy flaps of its rear end, according to Jay C. Hunt, a biologist at East Stroudsburg University. The squid can also emit lime-green light from a large photophore, also located on its behind.

. . .

Although the Spirula sighting may be a scientific first, it did not make a strong initial impression on the researchers onboard. “We’ve seen bobtail squids and dumbo octopuses where we say, ‘Wow, this is the cutest thing,’” Ms. Cornet said. “This one was weird-looking, and looking at us with its weird eye.”

Perhaps even more surprising than the creature’s cameo was its strange positioning. Scientists had always assumed that Spirula swam with its head pointed down and its gas-filled bottom in the air. When Dr. Vecchione caught living Spirulas in trawl nets and plopped them in cold water onboard, the “sort of alive” squids always floated rump-up, he said.

This hypothesis made sense; the squid’s gas-chambered shell buoyed it like a nautilus, after all. But it raised another question. Deeper-living creatures often point their photophores downward, disguising their silhouettes from predators lurking below. Beaming a green light toward the sky, on the other hand, serves no clear purpose. “This is neither common nor does it make sense,” Dr. Vecchione said.

But the Spirula caught on camera was clearly head-up, suggesting that its downward-gazing photophore was most likely used for counterillumination after all. “This makes sense,” Dr. Vecchione said.

Although the photophore mystery may now be solved, a right-side-up Spirula would seem to have a balancing problem, with the squid’s body mass precariously balanced on its buoyant shell. “When you design an R.O.V. you don’t put the heavy stuff on top and the floats on the bottom,” Dr. Lindsay said.

For the full story, see:

Sabrina Imbler. “A Squid Seen in the Wild, Perhaps for the First Time.” The New York Times, First Section (Sunday, November 8, 2020): 22.

(Note: ellipses added.)

(Note: the online version of the story was updated Oct. 31, 2020, and has the title “‘They’re Calling You on the Squid Phone’.” In the last sentence of the first paragraph quoted above, the phrase “like takeout from Triton” appears in the online, but not the print, version.)

2016 Law Requires FDA to Move to Mining Real-World Data and Away from Costly and Slow Clinical Trials

(p. A1) Drugmakers are trying to win drug approvals by parsing vast data sets of electronic medical records, shifting away from lengthy, and costly, clinical trials in patients.

. . .

For the companies, the use of real-world data can cut costs and shorten drug-development times. Instead of finding trial subjects, companies simply mine hospital and doctor files for cases where patients already took a drug in routine medical care, looking for changes in blood pressure, tumor size and other readings to see if the medicine is helping or causing a side effect.

. . .

(p. A2) . . . for rare diseases especially, it can take a while to even enroll enough patients in studies. And their cost can limit the number of trials that companies can fund, drugmakers say.

A 2016 law required the FDA to explore greater use of real-world data, and the agency is developing standards to assess the reliability of different data sources and which kinds of decisions the data support.

“Real-world evidence should not be a means toward dropping standards, but rather a mechanism to have more efficiency in evidence generation while maintaining standards,” said FDA Principal Deputy Commissioner Amy Abernethy, a former executive at health-data firm Flatiron Health.

A market has emerged in recent years for digital drug-use information. Iqvia Inc., which tracks prescription and health data, has about a dozen projects under way, said Nancy Dreyer, the company’s chief scientific officer of real-world evidence.

For the full story, see:

Peter Loftus. “Drugmakers Mine Data to Avoid Clinical Trials.” The Wall Street Journal (Tuesday, Dec. 24, 2019): A1-A2.

(Note: ellipses added.)

(Note: the online version of the story was updated Dec. 23, 2019, and has the title “Drugmakers Turn to Data Mining to Avoid Expensive, Lengthy Drug Trials.”)

“Normal” Human Temperature May Be Lower When Baseline Inflammation Is Lower

When I was a child my mother would hand me an oral thermometer to take my temperature and often the temperature would come out below 98.6 degrees. She would be annoyed and hand it back to me, saying that I should put it in right this time. I would painfully jab the thermometer back under my tongue, discouraged that I would never figure out what I was doing wrong. So several decades later, I smiled when I read the commentary quoted below. (Hey mom, maybe I was doing it OK all along.)

(p. A2) Nearly 150 years ago, a German physician analyzed a million temperatures from 25,000 patients and concluded that normal human-body temperature is 98.6 degrees Fahrenheit.

That standard has been published in numerous medical texts and helped generations of parents judge the gravity of a child’s illness.

But at least two dozen modern studies have concluded the number is too high.

The findings have prompted speculation that the pioneering analysis published in 1869 by Carl Reinhold August Wunderlich was flawed.

Or was it?

In a new study, researchers from Stanford University argue that Wunderlich’s number was correct at the time but is no longer accurate because the human body has changed.

Today, they say, the average normal human-body temperature is closer to 97.5 degrees Fahrenheit.

. . .

“Wunderlich did a brilliant job,” Dr. Parsonnet said, “but people who walked into his office had tuberculosis, they had dysentery, they had bone infections that had festered their entire lives, they were exposed to infectious diseases we’ve never seen.”

For his study, he did try to measure the temperatures of healthy people, she said, but even so, life expectancy at the time was 38 years, and chronic infections such as gum disease and syphilis afflicted large portions of the population. Dr. Parsonnet suspects inflammation caused by those and other persistent maladies explains the temperature documented by Wunderlich and that a population-level change in inflammation is the most plausible explanation for a decrease in temperature.

For the full commentary, see:

Jo Craven McGinty. “THE NUMBERS; 98.6 Degrees Is No Longer the Body’s Norm.” The Wall Street Journal (Saturday, January 18, 2020): A2.

(Note: ellipsis added.)

(Note: the online version of the commentary has the date January 17, 2020, and has the title “THE NUMBERS; 98.6 Degrees Fahrenheit Isn’t the Average Anymore.”)

Mathematical Disciplines Need the “Re-injection” of “Empirical Ideas”

(p. C4) Mathematicians have faced a similar choice between pure and applied work for millennia. In his 1940 book “A Mathematician’s Apology,” G.H. Hardy made a hard-core case for purity: “But is not the position of an ordinary applied mathematician in some ways a little pathetic?…‘Imaginary’ universes are so much more beautiful than this stupidly constructed ‘real’ one.”

On the other hand, John von Neumann rebuked purity in his 1947 essay “The Mathematician”: “As a mathematical discipline travels far from its empirical source…it is beset with very grave dangers. It becomes more and more purely aestheticizing,…whenever this stage is reached, the only remedy seems to me to be the rejuvenating return to the source: the re-injection of more or less directly empirical ideas.”

I think von Neumann has the better of this argument. In his own career, he used his mathematical talents to pioneer fields like game theory and computer science, leaving a titanic legacy, practical as well as intellectual.

For the full commentary, see:

Frank Wilczek. “WILCZEK’S UNIVERSE; Beautiful, Impractical Physics.” The Wall Street Journal (Saturday, Oct. 31, 2020): C4.

(Note: ellipses in original.)

(Note: the online version of the commentary has the date October 29, 2020, and has the same title as the online version.)

The John von Neumann essay mentioned above is:

Neumann, John von. “The Mathematician.” In Works of the Mind, edited by Robert B. Heywood. Chicago: University of Chicago Press, 1947, pp. 180-96.

Scientists Shocked to Discover a New Structure in Human Body

Some have claimed that we have picked all the low-hanging fruit and that there is little yet to be discovered. But if we remain curious, alert to serendipitous inconsistencies or surprises, we still have a lot to be learned. The default is to not see, or at least to soon forget, when we see the unexpected. To see and remember is hard enough. In the passages quoted below the researchers saw, remembered, and followed up. (Another example would be when Nick Steinsberger saw, remembered, and followed-up on the unexpected positive effects of the accidentally too watery fracking mixture injected into a well.)

(p. D5) A team of researchers in the Netherlands has discovered what may be a set of previously unidentified organs: a pair of large salivary glands, lurking in the nook where the nasal cavity meets the throat. If the findings are confirmed, this hidden wellspring of spit could mark the first identification of its kind in about three centuries.

Any modern anatomy book will show just three major types of salivary glands: one set near the ears, another below the jaw and another under the tongue. “Now, we think there is a fourth,” said Dr. Matthijs Valstar, a surgeon and researcher at the Netherlands Cancer Institute and an author on the study, published last month in the journal Radiotherapy and Oncology.

The study was small, and examined a limited patient population, said Dr. Valerie Fitzhugh, a pathologist at Rutgers University who wasn’t involved in the research. But “it seems like they may be onto something,” she said. “If it’s real, it could change the way we look at disease in this region.”

Even without a direct therapeutic application, Dr. Yvonne Mowery, a radiation oncologist at Duke University, said she “was quite shocked that we are in 2020 and have a new structure identified in the human body.”

Dr. Valstar and his colleagues, who usually study data from people with prostate cancer, didn’t set out on a treasure hunt for unidentified spit glands.

. . .

While perusing a set of scans from a machine that could visualize tissues in high detail, the researchers noticed two unfamiliar structures dead center in the head: a duo of flat, spindly glands, a couple of inches in length, draped discreetly over the tubes that connect the ears to the throat.

Puzzled by the images, they dissected tissue from two cadavers and found that the glands bore similarities to known salivary glands that sit below the tongue. The new glands were also hooked up to large draining ducts — a hint that they were funneling fluid from one place to another.

It’s not completely clear how the glands eluded anatomists. But “the location is not very accessible, and you need very sensitive imaging to detect it,” said Dr. Wouter Vogel, a radiation oncologist at the Netherlands Cancer Institute and an author on the study.

. . .

Dr. Fitzhugh added that it should be easier to spot the camera-shy glands with traditional techniques “now that they know to look for it.”

For the full story, see:

Katherine J. Wu. “The Human Anatomy Yields a New Surprise.” The New York Times (Tuesday, October 27, 2020): D5.

(Note: ellipses added.)

(Note: the online version of the story was updated on Oct. 21, 2020, and has the title “Doctors May Have Found Secretive New Organs in the Center of Your Head.”)

The academic article mentioned above is:

Valstar, Matthijs H., Bernadette S. de Bakker, Roel J. H. M. Steenbakkers, Kees H. de Jong, Laura A. Smit, Thomas J. W. Klein Nulent, Robert J. J. van Es, Ingrid Hofland, Bart de Keizer, Bas Jasperse, Alfons J. M. Balm, Arjen van der Schaaf, Johannes A. Langendijk, Ludi E. Smeele, and Wouter V. Vogel. “The Tubarial Salivary Glands: A Potential New Organ at Risk for Radiotherapy.” Radiotherapy and Oncology (published online in advance of print on Sept. 23, 2020).

Costs and Difficulties of Clinical Trials Delay “Most Promising Experimental Drugs”

(p. A6) As the coronavirus pandemic continues to wreak havoc in the United States and treatments are needed more than ever, clinical trials for some of the most promising experimental drugs are taking longer than expected.

Researchers at a dozen clinical trial sites said that testing delays, staffing shortages, space constraints and reluctant patients were complicating their efforts to test monoclonal antibodies, man-made drugs that mimic the molecular soldiers made by the human immune system.

As a result, once-ambitious deadlines are slipping. The drug maker Regeneron, which previously said it could have emergency doses of its antibody cocktail ready by the end of summer, has shifted to talking about how “initial data” could be available by the end of September [2020].

And Eli Lilly’s chief scientific officer said in June that its antibody treatment might be ready in September, but in an interview this week, he said he now hopes for something before the end of the year.

“Of course, I wish we could go faster — there’s no question about that,” said the Eli Lilly executive, Dr. Daniel Skovronsky. “I guess in my hopes and dreams, we enroll the patients in a week or two, but it’s taking longer than that.”

For the full story, see:

Katie Thomas. “Clinical Trials of Drugs For Virus Are Delayed By a Swamped System.” The New York Times (Saturday, August 15, 2020): A6.

(Note: bracketed year added.)

(Note: the online version of the story has the date Aug. 14, 2020, and has the title “Clinical Trials of Coronavirus Drugs Are Taking Longer Than Expected.”)

Bayesian Updating, Not Clinical Trials, Is Key to Advancing Medical Knowledge

(p. D8) In the early pandemic era, for instance, airborne transmission of Covid-19 was not considered likely, but in early July the World Health Organization, with mounting scientific evidence, conceded that it is a factor, especially indoors. The W.H.O. updated its priors, and changed its advice.

This is the heart of Bayesian analysis, named after Thomas Bayes, an 18th-century Presbyterian minister who did math on the side. It captures uncertainty in terms of probability: Bayes’s theorem, or rule, is a device for rationally updating your prior beliefs and uncertainties based on observed evidence.

. . .

As Marc Lipsitch, an infectious disease epidemiologist at Harvard, noted on Twitter, Bayesian reasoning comes awfully close to his working definition of rationality. “As we learn more, our beliefs should change,” Dr. Lipsitch said in an interview.

. . .

But there is little point in trying to establish fixed numbers, said Natalie Dean, an assistant professor of biostatistics at the University of Florida.

“We should be less focused on finding the single ‘truth’ and more focused on establishing a reasonable range, recognizing that the true value may vary across populations,” Dr. Dean said. “Bayesian analyses allow us to include this variability in a clear way, and then propagate this uncertainty through the model.”

. . .

Joseph Blitzstein, a statistician at Harvard, delves into the utility of Bayesian analysis in his popular course “Statistics 110: Probability.” For a primer, in lecture one, he says: “Math is the logic of certainty, and statistics is the logic of uncertainty. Everyone has uncertainty. If you have 100 percent certainty about everything, there is something wrong with you.”

By the end of lecture four, he arrives at Bayes’s theorem — his favorite theorem because it is mathematically simple yet conceptually powerful.

“Literally, the proof is just one line of algebra,” Dr. Blitzstein said. The theorem essentially reduces to a fraction; it expresses the probability P of some event A happening given the occurrence of another event B.

“Naïvely, you would think, How much could you get from that?” Dr. Blitzstein said. “It turns out to have incredibly deep consequences and to be applicable to just about every field of inquiry” — from finance and genetics to political science and historical studies. The Bayesian approach is applied in analyzing racial disparities in policing (in the assessment of officer decisions to search drivers during a traffic stop) and search-and-rescue operations (the search area narrows as new data is added). Cognitive scientists ask, ‘Is the brain Bayesian?’ Philosophers of science posit that science as a whole is a Bayesian process — as is common sense.

. . .

Even with evidence, revising beliefs isn’t easy. The scientific community struggled to update its priors about the asymptomatic transmission of Covid-19, even when evidence emerged that it is a factor and that masks are a helpful preventive measure. This arguably contributed to the world’s sluggish response to the virus.

. . .

In 1650, Oliver Cromwell, Lord Protector of the Commonwealth of England, wrote in a letter to the Church of Scotland: “I beseech you, in the bowels of Christ, think it possible you may be mistaken.”

In the Bayesian world, Cromwell’s law means you should always “keep a bit back — with a little bit of probability, a little tiny bit — for the fact that you may be wrong,” Dr. Spiegelhalter said. “Then if new evidence comes along that totally contradicts your main prior belief, you can quickly ditch what you thought before and lurch over to that new way of thinking.”

“In other words, keep an open mind,” said Dr. Spiegelhalter. “That’s a very powerful idea. And it doesn’t necessarily have to be done technically or formally; it can just be in the back of your mind as an idea. Call it ‘modeling humility.’ You may be wrong.”