James' World 2

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But I make up for it by saving snippets of their childhood in another way. Like that of many parents, my phone contains lots of videos of my kids. In addition to the delightful sprinkler showdown, there are clips of soccer games, recitals, birthdays. It is a robust repository—hundreds of videos taking up hundreds of gigabytes.

Whenever the time comes for me to upgrade to a new phone, these old videos come with me, thank you very much. I have, at the ready and at any moment, easy access to their early years—from a first encounter with snow to their budding inquiries at dinnertime (“What do badgers eat?” “Were you and Abraham Lincoln friends?”).

Some find the fact that Generation Alpha has such hyperdocumented childhoods to be alarming and potentially harmful. But as long as your knee-jerk reaction isn’t to immediately put all these photos and videos online and you can balance being present in the moment, these gigabytes of still and moving images are an unalloyed blessing.

But I make up for it by saving snippets of their childhood in another way. Like that of many parents, my phone contains lots of videos of my kids. In addition to the delightful sprinkler showdown, there are clips of soccer games, recitals, birthdays. It is a robust repository—hundreds of videos taking up hundreds of gigabytes.

Whenever the time comes for me to upgrade to a new phone, these old videos come with me, thank you very much. I have, at the ready and at any moment, easy access to their early years—from a first encounter with snow to their budding inquiries at dinnertime (“What do badgers eat?” “Were you and Abraham Lincoln friends?”).

Some find the fact that Generation Alpha has such hyperdocumented childhoods to be alarming and potentially harmful. But as long as your knee-jerk reaction isn’t to immediately put all these photos and videos online and you can balance being present in the moment, these gigabytes of still and moving images are an unalloyed blessing.

It’s a privilege to be able to so effortlessly indulge my nostalgia whenever I want. For many adults my age, seeing snaps of our childhood might be limited to whenever we have a chance to visit our parents’ house. It requires some effort to unearth dusty albums from basements and closets. The ritual of sitting together to watch family videos also requires some time. Set up the VCR; dig up the tapes. Rewind, fast-forward, rewind.

There is a redemptive element at play here. My childhood lives in the carefully curated and compartmentalized memory of my mind. There is virtually no record of my own early years, with only a handful of photos and certainly no videos. In the 1980s, the time of camera film and camcorders, my parents didn’t invest in making a record, and the dysfunction of my fractured family life ensured that there were very few moments worth committing to film or ever watching on playback.

But I’m not alone when it comes to my fierce attachment to these old videos. It turns out, the subjects of these videos are kind of obsessed with watching themselves.

My kids eagerly press Play and relive it all: the unmistakable lilt of their little baby voices, unsteady first steps, charmingly off-key renditions of Disney songs, and wary standoffs with anything remotely resembling a vegetable on their plate.

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For those who have wrestled a bulky couch around a tight corner and lamented, “Will this even fit?” mathematicians have heard your pleas. Geometry’s “moving sofa problem” asks for the largest shape that can turn a right angle in a narrow corridor without getting stuck. The problem sat unsolved for nearly 60 years until November, when Jineon Baek, a postdoc at Yonsei University in Seoul, posted a paper online claiming to resolve it. Baek’s proof has yet to undergo thorough peer review, but initial passes from mathematicians who know Baek and the moving sofa problem seem optimistic. Only time will tell why it took Baek 119 pages to write what Ross Geller of the sitcom Friends said in one word.

The solution is unlikely to help you on moving day, but as frontier math grows more abstruse, mathematicians hold a special fondness for unsolved problems that anybody can understand. In fact, the popular math forum MathOverflow maintains a list of “Not especially famous, long-open problems which anyone can understand,” and the moving sofa problem currently ranks second on the list. Still, every proof expands our understanding, and the techniques used to resolve the moving sofa problem will likely lend themselves to other geometric puzzles down the road.

The rules of the problem, which Canadian mathematician Leo Moser first formally posed in 1966, involve a rigid shape—so the cushions don’t yield when pressed—turning a right angle in a hallway. The sofa can be any geometric shape; it doesn’t have to resemble a real couch. Both the shape and the hallway are two-dimensional. Imagine the sofa weighs too much to lift, and you can only slide it.

A quick tour through the problem’s history reveals the extensive effort that mathematicians have poured into it—they were no couch potatoes. Faced with an empty hallway, what is the largest shape you could squeeze through it? If each leg of the corridor measures one unit across (the specific unit doesn’t matter), then we can easily scoot a one-by-one square through the passage. Elongating the square to form a rectangle fails instantly, because once it hits the kink in the hallway, it has no room to turn.

Yet mathematicians realized they can go bigger by introducing curved shapes. Consider a semicircle with a diameter (the straight base) of 2. When it hits the turn, much of it still overhangs in the first leg of the hallway, but the rounded edge leaves just enough room to clear the corner.

Remember the goal is to find the largest “couch” that slides around the corner. Dusting off our high school geometry formulas, we can calculate the area of the semicircle as π/2, or approximately 1.571. The semicircle gives a significant improvement over the square, which had an area of only 1. Unfortunately, both would look strange in a living room.

Solving the moving sofa problem requires that you not only optimize the size of a shape but also the path that shape traverses. The setup permits two types of motion: sliding and rotating. The square couch only slid, whereas the semicircle slid, then rotated around the bend, and then slid again on the other side. But objects can slide and rotate at the same time. Mathematician Dan Romik of the University of California, Davis, has noted that a solution to the problem should optimize both types of motion simultaneously.

British mathematician John Hammersley discovered in 1968 that stretching the semicircle can buy you a larger sofa if you carve out a chunk to deal with that pesky corner. Furthermore, Hammersley’s sofa takes advantage of a hybrid sliding plus rotating motion. The resulting sofa looks like a landline telephone:

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These days, if you hear about the birth of an Olivia or a Liam, you might feel a pang of sympathy—the poor child has been cursed with the most popular name of their time and might be at risk of sharing it with a kindergarten classmate.

This wasn’t always considered an undesirable outcome. The name Mary, for instance, was the most popular girls’ name for all but six years from 1880 to 1961, and “if you talk to people from earlier generations, [they’ll say] ‘Well, of course, there were five Marys in the class,’” Laura Wattenberg, the founder of the naming-trends site Namerology, told me. “That didn’t matter. There wasn’t that kind of fear.”

In the past 60 or so years, American parents’ approach to naming their kids has undergone a profound shift. Today, many parents seek out less popular names to help their kids stand out. But in the past, parents typically picked common names, consciously or not, so that their kids would fit in.

In 1880, the percentage of babies who got a top-10 most popular name was in the neighborhood of 32 percent, according to Wattenberg’s calculations. In 1950, it was about 28 percent. And in 2020, it had fallen to an all-time low of 7 percent. “We are deep in an era of naming individuality, where parents assume that having a [name] sound distinctive and unique is a virtue,” Wattenberg said.

For much of American history, many people just named their kids after someone on the family tree, which helped keep names in circulation for a long time. This was especially true for baby boys, who have historically had less varied names than baby girls in part because they were more likely to inherit a family name. For instance, in Raleigh Colony, roughly one in two boys had the name John, William, or Thomas. Those three names remained in or near the top 10 from the 1880s, when the Social Security Administration’s records begin, through the 1960s.

Of course, some names from earlier eras did stand out. Puritan names like Patience, Temperance, and Standfast had explicit moral heft. Immigrants injected some variety by using names from their home countries, but also sometimes opted for (or felt pressured to pick) “whiter-sounding” names in hopes of fitting in. And there was some charming regional diversity. Early-20th-century Oklahoma produced names like Ovonual and Odelene. In southern Appalachia, there were kids named Meek, Bent, Wild, Whetstone, Speed, and AnvilThe last decades of relatively uniform naming were the 1940s and ’50s. In 1955, for example, half of all American babies born had one of just 78 names, according to Wattenberg. In 2019, that number was 520. Parents’ inclination toward sameness in the ’40s and ’50s might have had to do with the unifying effect of living through the Great Depression and World War II. Those events “gave them a sense of solidarity with the whole culture, the whole country,” Cleveland Evans, a professor emeritus of psychology at Bellevue University and an expert on names, told me. At a time when the path to success seemed communal, being like other people wasn’t seen as a bad thing.

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