James' World 2

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You’re at the checkout screen after an online shopping spree, ready to enter your credit card number. You type it in and instantly see a red error message: “Please enter a valid credit card number.” Annoyed, you scan back through each digit and spot the culprit: you tapped the 6 key where a 5 belonged. Typo corrected; purchase complete. But how did the website detect your error so quickly? Does the online platform keep a master list of every valid credit card number to compare your entry against? Did it ping your bank in a split second? The explanation is much cleverer.

All mainstream credit card numbers obey a mathematical trick designed to catch the most common typos. It’s called the Luhn algorithm, named after IBM researcher Hans Peter Luhn, who patented it in 1960. Similar error-checking schemes lurk in many of the numbers you encounter daily: barcodes, package tracking numbers, bank account numbers, and even ISBNs on books.

Grab a credit card from your wallet, and you’ll find it contains more structure than first glance suggests. The anatomy of a credit card number includes four main parts. To demonstrate, I’ll use my personal Visa. [Stretch your math muscles with these puzzles]

The first digit is the major industry identifier. Visas always begin with a 4, and Discover always start with a 6. The next five to seven digits pinpoint the bank or institution that issued the card. What remains (sans the final digit) is your specific account number within that bank. The final digit, sometimes called the “check digit,” has nothing to do with financial institutions. Issuers tack it on so that the whole card number will satisfy a specific mathematical test—the Luhn algorithm. Here’s how the algorithm works:

1. Write out all but the last digit of the card number.
2. Double every other number starting at the right.
3. Sum the resulting digits (not numbers). E.g., if you doubled a 7 to become a 14 in Step 2, this will become 1 + 4 = 5 in this step.
4. Add the check digit to the sum. If the result is not a multiple of 10, then the credit card number is invalid.

I’ll show the Luhn algorithm in action on my Visa, but you should try it with your credit card, too.

The number crunching culminates in 75, which is not a multiple of 10. So this cannot be my real credit card number; I must have mistyped it.

Credit card issuers first assign the account numbers and then compute steps one through three of the Luhn algorithm to determine the appropriate check digit. In this case, the card number should have ended in a 3 because 67 + 3 = 70, a multiple of 10.

This particular dance of digits has come to dominate credit card verification because of its simplicity and powerful set of features. If you mess up any single digit when entering your card number, the Luhn algorithm will detect it. If you accidentally swap adjacent card digits while inputting, it will detect that, too (with the one exception of flipping 09 to 90, or vice versa).

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Isabel Pavia/Getty Images

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Suze Orman, the New York Times best-selling author of “The Ultimate Retirement Guide for 50+,” podcaster, finance guru and motivational speaker, has seen it all when it comes to retirement mistakes.

In her nearly forty years as a financial adviser, people have come to her when they’ve spent too much money, paid too much in taxes, or made hasty decisions that lost them too much money.

But the biggest mistake, the one that Orman sees all the time, the one that people lose thousands of dollars over, is claiming Social Security early.

What constitutes early for Orman? Claiming anytime before at least your full retirement age, which is 67 for anyone born after 1960.

“Everybody thinks Social Security isn’t going to be there. Everybody is scared to death, but I wouldn’t be,” says Orman. By claiming early, “you’re passing up an 8% increase each year in your Social Security from your full retirement age all the way to 70.”

You may not think delaying filing for Social Security makes that big a difference in terms of your benefit amount, but it could add up to a lot more money than you realize. The maximum a 62-year-old can receive monthly in 2025 is $2,831. If that person waits until they turn age 66/67 to file for benefits, their monthly check increases to $4,018. If they hold off until age 70, their check increases to $5,108.

Don’t let fear cost you money

Many people collect Social Security early out of fear it won’t be around for much longer. But Orman doesn’t think that’s a viable reason to claim benefits. While it’s true that the Old-Age and Survivors Insurance Trust Fund, which pays Social Security retiree benefits, is projected to become insolvent in the first quarter of 2033, that doesn’t mean it will collapse. If nothing is done by then, benefits would face a 23% cut, and beneficiaries would then receive 77% of their benefits.

Sure, if you have a serious illness or need the money to get by, then you may have to collect Social Security early. But otherwise, collecting Social Security before you’ve at least reached your full retirement age can backfire, leaving you short on cash over your lifetime. Retirement can last 20 years or more for many people.

“They find out it’s a lot more expensive in retirement than they thought,” says Orman. They are spending the same, if not more, and they are dealing with inflation. At the same time, they are withdrawing from their retirement accounts and depleting their savings. Their Social Security payment is already locked in at a lower rate, and it’s not enough. As a result, they are now either forced to change their lifestyle or return to work, she says.

“Where else are you going to make that money? You’re not,” says Orman. “Claiming Social Security before full retirement age is one of the biggest mistakes you could possibly make.”

Second place: ignoring the Roth option

In wanting to be generous with Orman’s advice, we are also sharing her second-place all-time mistake — and this one is geared toward pre-retirees.

Ignoring the Roth conversion

“You don’t want to be partners with Uncle Sam,” says Orman. “A big mistake everybody is making leading up to retirement is not taking advantage of the Roth 401(k), 403(b), or Roth IRA.”

Pre-retirees and retirees like traditional 401(k)s, funded by pre-tax dollars, because they get a tax break now while they’re still working and potentially are in a higher tax bracket than when they retire. They figure their income tax bracket will be lower when they are retired and start withdrawing from their retirement accounts.

But what some people don’t take into account are required minimum distributions or RMDs, says Orman. RMDs kick in when you turn 73 and require you to withdraw a percentage of your 401(k) or IRA each year. The withdrawal is treated as ordinary income, which can be a big tax hit if the RMD is large enough.

“The money in your retirement account is compounding and growing and it’s growing and it’s growing for you and Uncle Sam,” says Orman. “Why do you think Uncle Sam is allowing you that long (before RMDs). Because the more time it’s in there, the larger it grows, the more they are going to get in income taxes.”

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(Image credit: MARC ROYCE)

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Representative James R. Comer, the Kentucky Republican who leads the Oversight Committee, at the Capitol in Washington on Monday for a deposition with former Attorney General Bill Barr.Credit…J. Scott Applewhite/Associated Press

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Rachel Feltman: For Scientific American’s Science Quickly, I’m Rachel Feltman.

When it comes to birth control, men have exactly two reliable options: condoms or a vasectomy. That’s it. For decades, researchers have been working to expand those choices, but progress has been slow.

Now, a new pill for men has just passed its first safety trial in humans. What’s particularly exciting about this daily pill, which works by blocking a key step in sperm production, is that it’s hormone-free.

Here to tell us more about the latest progress on male contraception is Hannah Seo, a freelance science journalist based in Brooklyn.

Hannah, thanks so much for coming on to chat today.

Hannah Seo: Thanks for having me. It’s exciting.

Feltman: So you recently wrote a story for Scientific American about some advances in male birth control. Could you start by just telling us what this particular method is and, and how it works?

Seo: Yeah, I was really fascinated to read about this trial because it’s the first nonhormonal male birth control pill. So a lot of the birth control methods that we think about usually involve hormones of some kind or involve some sort of surgery, right, like a vasectomy. But this does neither of those things. It is a pill that’s supposed to be taken daily, and it just kind of stops sperm production from happening through nonhormonal methods, so I thought this was a really innovative piece of medicine that is being—in development right now.

Feltman: Could you tell us more about the mechanism by which it prevents sperm production?

Seo: Yes, absolutely. So one thing that’s interesting to note is that in people of all sexes, if you have a severe vitamin A deficiency, that can really impact your fertility, and so the makers of this drug were really focused on this detail. And what they found out is that cells in the testes will take up vitamin A, metabolize vitamin A into this metabolite called retinoic acid; retinoic acid will bind to a receptor, and in that binding it’ll drive changes in gene expression that leads to sperm production—there’s, like, a cascade of effects, and the consequence is that you get sperm.

And so what this drug does is it prevents that binding from happening …

Feltman: Mm.

Seo: It prevents retinoic acid from binding to its receptor. And as a consequence, it sort of breaks the chain, and, you know, all the various effects can’t really cascade the way they would—normally would, and you prevent sperm production that way. And then once you’ve stopped taking the drug, after a while, you eventually regain that function.

Feltman: Just, you know, remind us: Where are we at with male birth control in general right now? You know, what’s available, what’s in the works?

Seo: Yeah, right now, what people can currently get include just two things: you can get a vasectomy, or you can use condoms. And so, as far as male contraception goes, those are really the only two options, and neither one of those is particularly ideal, especially if you’re someone who wants a reversible option to control your fertility.

At the moment, there are several options in development, including this pill, which is a nonhormonal birth control pill taken daily. There’s also a gel—I think a lot of people will have heard of this gel. It’s called Nest/T, which stands for a progestin called Nestorone, as well as testosterone. People who are doing hormone-replacement therapy will use a similar gel on their shoulders. It’s a very, very similar mechanism. And this works a little bit similarly to the nonhormonal pill in that it stops sperm production reversibly. So that is probably the male contraceptive that is furthest along in development. That is currently on the cusp of starting phase 3 clinical trials.

There’s also a reversible vasectomy. Some vasectomies, currently, surgically are reversible, but not all of them, and this, quote, unquote, “reversible vasectomy” is really an implant. And what it is, is that it’s a tiny, little hydrogel that can be inserted into the vas deferens, and it just physically blocks sperm from being able to escape into the ejaculate. And so that is also pretty far along in development.

And those are really the two that are kind of closest to becoming released onto the market. Besides those two we then have this nonhormonal contraceptive pill that stops sperm production and, like, a few other smaller options that are also kind of in early, early development.

Feltman: Yeah, so speaking of which: Where in development is this pill? I know there [was] some recent news about progress, but where does that leave us?

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Carol Yepes/Getty Images; Scientific American illustration

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The State Department has revoked more than 6,000 student visas this year, a State Department official said Monday, as the Trump administration continues its crackdown on some international students it says have broken the law.

The visas were revoked because people had stayed after their visas expired or broken the law, the official said, noting that the “vast majority” of those legal violations were for cases of assault, driving under the influence, burglary, and “support for terrorism.”

According to the official, approximately 4,000 of the 6,000 visas were revoked because the visa holders “broke the law.”

Approximately 200 to 300 of those visas were yanked for alleged terrorism under part of the Immigration and Nationality Act that says that foreign nationals may be inadmissible to the US “due to terrorist related activities.”

The thousands of revocations, first reported by Fox News, come as the Trump administration has undertaken aggressive actions towards universities and related to student visas.

Administration officials have particularly targeted international students active in protests against the war in Gaza, accusing those students of antisemitism and of supporting terrorism.

In one high profile case, Tufts University PhD student Rumeysa Ozturk’s visa was canceled, and she was seized by masked federal agents in March and put into ICE detention. A judge ordered her release in May.

In June, the State Department told its embassies and consulates it must vet student visa applicants for “hostile attitudes towards our citizens, culture, government, institutions, or founding principles.” Applicants will be asked to set their social media profiles to public as part of the vetting, and a diplomatic cable noted that “limited access to, or visibility of, online presence could be construed as an effort to evade or hide certain activity.”

Secretary of State Marco Rubio has vigorously defended the Trump administration’s policies on student visa revocation.

“There is no constitutional right to a student visa. A student visa is something we decide to give you,” he said in an interview with EWTN in early August. “Visas of every kind are denied every day all over the world. As I speak to you now, someone’s visa application to the US is being denied. So, if I would have denied you a visa had I known something about you, and I find out afterwards that I gave you a visa and I found this out about you, why wouldn’t I be able to revoke your visa?”

According to the State Department, roughly 400,000 student visas, otherwise known as F1 visas, were issued in fiscal year 2024.

Far fewer are expected to be issued this calendar year after new appointments were temporarily suspended, and the new vetting requirements were put in place.

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President Volodymyr Zelensky of Ukraine met with President Trump and an extraordinary delegation of European leaders at the White House on Monday, seeking to defend his nation’s interests as Mr. Trump presses for a quick peace agreement with Russia that would require Ukraine to make sweeping concessions.

Mr. Trump and Mr. Zelensky huddled for several hours in the East Room with the small group of European leaders, who had rushed to Washington to support the Ukrainian president in talks about how to end the war despite serious disagreements over the path forward. After the meetings, Mr. Trump called President Vladimir V. Putin of Russia while Mr. Zelensky and the other European leaders were still at the White House, two people briefed on the call said.

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Rabbits in northern Colorado have been spotted with bizarre, somewhat grisly horns on their face. But wildlife officials say the bunnies are likely ultimately going to be okay.

They’re also not a danger to others—at least, not to nonrabbits. The tentacle-faced bunnies are infected with Shope papillomavirus, a member of the same viral family that can cause warts in humans. Shope papillomavirus is known to affect only rabbits and hares, not humans or other animals, says Kara Van Hoose, a spokesperson for Colorado Parks & Wildlife (CPW). For most rabbits, it’s also a harmless infection.

Infected animals “are able to clear it from their system on their own,” Van Hoose says. Once the virus is gone, the growths, which are made of the same keratin found in hair and nails, eventually fall off. In a minority of cases, the infection can induce squamous cell cancer. The infection can also cause problems if the associated growths pop up near the eyes or mouth, where they might interfere with foraging and eating, Van Hoose says.

It’s not clear whether there are actually more rabbits than usual infected with Shope papillomavirus in northern Colorado this summer, Van Hoose says. CPW had not received any reports of horned-faced rabbits before a local news story published on August 8 drew attention to sightings in Fort Collins, Colo. Since then, multiple people have called the agency, Van Hoose says, but it’s hard to tell how many infected rabbits there really are.

“It’s also difficult to say, if we get 10 reports, if it’s 10 different rabbits or if it’s two rabbits that maybe we’re seeing five different times,” she says.

The growths themselves are not infectious. The virus spreads through bites from mosquitoes, ticks, and fleas, so it tends to peak in summer and fade away in the colder months.

The discoverer and namesake of the virus, virologist Richard Shope, first identified the pathogen in 1933 in the U.S. Midwest. Shope also was the first to identify the influenza A virus and was among the first to pinpoint that particular flu pathogen as the culprit of the deadly 1918 pandemic. His work on rabbit papillomavirus formed the basis of understanding human papillomavirus (HPV) strains, some of which can cause cancer. This line of research ultimately led to the development of the HPV vaccine, which dramatically reduces the risk of cervical and other cancers linked to HPV.

Though the horned rabbits aren’t a danger to humans or pets, Van Hoose advises people to keep their distance from the creatures, as they should with any wild animal, because rabbits can pass along other pathogens. “Once you realize these [growths] probably aren’t harmful to rabbits, you can kind of appreciate the science at work,” she says.

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Photo: Allison Johnson / The Verge

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“The statute would have no meaning at all if the president can just say, ‘We’re taking over your police department,’” said Judge Reyes, who was nominated to the federal bench by President Biden.

The judge made clear that she was considering a ruling that would block the administration’s entire order as unlawful, but said she would prefer if the lawyers on both sides worked out some modifications to the order. After several hours, the Justice Department lawyers reissued the order, leaving the city in control of the police force.

City officials praised the outcome on Friday as an affirmation of the Washington’s autonomy.

Speaking to reporters, Brian Schwalb, the D.C. attorney general, said the law makes clear “that the authority to appoint a chief of police sits squarely with the mayor, and the right to control the local policing of our city sits with the mayor and the chief of police, notwithstanding the government, the president and the attorney general’s efforts to suggest that they had taken control of our police force.”

In a post on social media announcing the redrafted order, U.S. Attorney General Pam Bondi criticized Mr. Schwalb for, she said, opposing the administration’s “efforts to improve public safety.” But she said the administration remained committed to working closely with D.C. Mayor Muriel Bowser, “who is dedicated to ensuring the safety of residents, workers, and visitors” in the city.

Local officials were taken by surprise on Thursday evening when Ms. Bondi issued an order naming Terrance C. Cole, the head of the Drug Enforcement Administration, as an “emergency police commissioner.” The directive came after days of assurances by local officials, including the mayor and the police chief, that they would work as partners alongside federal law enforcement.

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Amtrak police officers and National Guard troops patrolling at Union Station in Washington on Thursday.Credit…Eric Lee for The New York Times

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Researchers have captured the very first real-time, three-dimensional images and videos of a human embryo implanting into collagen designed to mimic uterine tissue —a key stage in reproduction. The resulting footage, which shows how embryos push and pull to anchor themselves in the uterus in vivid detail, could lead to improvements for in vitro fertilization (IVF) techniques, the scientists say.

“This will allow us to develop treatments specifically targeting implantation, which is the biggest roadblock in human reproduction,” says Samuel Ojosnegros, a bioengineer at the Barcelona Institute of Science and Technology in Spain and a co-author of the new study, which was published in Science Advances.

Five days after an embryo is fertilized artificially, fertility doctors must implant it into the body so it can continue to grow. “What happens between the transfer and the first ultrasound weeks later is a black box,” says Ojosnegros, who is also co-founder of the biotech company Serabiotics. Implantation failure is one of the main causes of infertility —up to 60 percent of miscarriages occur during this process.

The first successful culture of human embryos beyond implantation was demonstrated in a petri dish in a lab in 2016, but Ojosnegros and his team wanted to see what this process would look like in 3D tissue that was more similar to that of the uterus.

To do this, the team designed a special ex vivo system made of gel and collagen—a protein found in the uterine lining—and used embryos donated by people who had completed an assisted reproduction process. The system works, Ojosnegros says, because the network of collagen fibers signals to the embryo at a molecular level that this is a natural matrix.

By using advanced 3D microscopes, the researchers recorded the action over time. Tracking tiny movements in the gel’s fibers allowed them to map exactly where and how strongly the embryos were pulling. The researchers did the same with mouse embryos to compare movement patterns.

The footage showed that human embryos generate a network of tiny pulling forces that ripple through the womb. They burrow into the surrounding tissue from one side, creating multiple small traction points that tug the lining in all directions. Mouse embryos, on the other hand, spread out more across the surface and pull mainly along two or three strong lines.

When the researchers applied external tension to the matrix, tugging it with tiny forceps, they noticed the embryos reoriented toward those areas. The scientists suggest micro contractions might be guiding the embryo to implant in the optimal direction in the uterus. “We believe these micro contractions are what the embryo uses to guide itself toward the blood vessels and the nutrients it needs,” Ojosnegros explains, adding that more studies are needed to confirm this hypothesis.

In both mouse and human experiments, the strength and pattern of these forces were linked to the embryo’s health, meaning embryos that pulled less were less likely to successfully invade the tissue. Observing implantation in real-time in a 3D model is a “quantum leap” compared with the two-dimensional observations that already exist, says developmental biologist Claudia Spits of the Free University of Brussels, who was not involved in the research. Keeping an embryo alive under these conditions is extremely difficult, she says. “What you see in a 10-second video is years of setting these [conditions] up so that the embryo can survive,” Spits adds.

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