Now look at another portrait. It’s the same man. Placed side by side with the first portrait, it immediately raises new questions. The look is almost the same: the tanned face, the small mouth, the dark, slightly furrowed brows. With his narrowed eyes, he seems a bit more preoccupied. His white goatee is fuller and more neatly shaped, giving him the debonair look of a knight in a Renaissance painting. In this second portrait, the man is all buttoned up, and he wears an ocher bow tie. Behind him this time is a different crowd, and instead of the taxi seen in the first picture, there is an armored truck.

It’s not that hard to go out into the street and take a stranger’s picture. It is legal and, with the right equipment, technically simple. But how do you arrive at two pictures of the same person, with almost the same expression, on what seem to be different days? These photographs were made by the Danish artist Peter Funch, and they are part of a series of many such pairs. For nine years, from 2007 until 2016, Funch hung around Grand Central Terminal and watched commuters during the morning rush between 8:30 and 9:30 a.m. Using a long-lensed digital camera, he made countless portraits, an intriguing face here, another one there, yet another over there. He began to notice repetitions, the same people, the same faces, the same gestures, the same clothes. Each person was in the self-enclosed reverie of getting somewhere. The photos were all taken in May, June or July, in bright summer sunshine. The resulting project, published last year in a monograph titled “42nd and Vanderbilt,” is named for the street corner on which Funch stationed himself. It contains dozens of pairs of portraits (and a few in sequences of three), all of strangers.

Funch’s book contains women and men, the old and the young, people of all races and social classes. It looks like New York. One woman strides by with her chin raised and eyes closed. She wears a green blouse in one photo and a purple sweater in another. A man in a dark suit wears a peach-colored shirt in one photo and a blue one in the other, and he holds a cellphone in his right hand in both portraits. A woman crosses her arms, twice; another smokes, twice; another smiles, twice. There are two men walking side by side, and the same men walking side by side again. Do they know each other? They seem not to. There are three young women in medical scrubs, and surely they do know each other. One of them checks her phone, twice; another glances downward, twice.

Funch’s project is a feat of both patience and memory. But it is also a record of the many individual rhythms that collectively make up city life. “42nd and Vanderbilt” evokes “Many Are Called,” the series of subway portraits made between 1938 and 1941 by Walker Evans. Evans sat across from fellow passengers with a 35-millimeter Contax concealed in his coat. He wasn’t after repetition, but he did want to capture New Yorkers unawares. “The guard is down and the mask is off,” he wrote. “People’s faces are in naked repose down in the subway.” What he found was a repetition across selves: when we are unguarded, all artifice is gone and we begin to resemble one another.

This kind of photography is unquestionably invasive. After all, we ease into our resting faces precisely at those moments when we don’t expect to be scrutinized. But in neither Evans’s nor Funch’s project is there any sense of hostility toward their subjects. If the resulting photographs are slightly discomfiting, they are also humane and compassionate, because they make us see that even within the incessant repetitions that constitute capitalist society, there is always a hidden and highly personal pattern to our movements. What the Scottish poet Thomas A. Clark wrote about walking in the country is applicable to city commuters too:

Always, everywhere, people have

walked, veining the earth with

paths, visible and invisible, symmetri-

cal and meandering.

There are walks in which we tread in

the footsteps of others,

walks on which we strike out entirely

for ourselves.

Many photographers, since Evans’s influential work, have been tempted to try to see without being seen. They have come up with various ways to record the poignant individuality of others against the backdrop of public space, many arriving at the idea that transience is best caught in literal moments of transit.

In the mid-1990s, John Schabel used a 500-millimeter lens to take photographs of airplane passengers framed by the windows of the plane. The work, “Passengers,” which wasn’t published until 2011, captures an eerie isolation in each frame, a grainy and pensive head behind the glass. Also in the ’90s, Luc Delahaye’s series, “L’Autre,” revisited Evans’s approach and subject, but this time on the Paris Metro. Cropped, the individual faces fill up the frame. The film director Chris Marker also made a series of pictures of strangers on the Metro between 2008 and 2010, also called “Passengers.” Marker shot in wider views, in color and with a digital camera, creating lo-fi images that were poignant without being pretty.

Philip-Lorca diCorcia’s “Heads” (2001) was made in Times Square with a camera on a tripod and an elaborate strobe-light setup. The resulting high-resolution portraits of strangers are poised between the cinematic and the uncanny. One unhappy passer-by sued diCorcia for photographing him without permission and for profiting from his image. It was an important case: The court dismissed the suit, deciding that street photographs count as a form of artistic expression that may not be infringed.

The Dutch photographer Hans Eijkelboom is more interested in typologies than in faces. His “People of the Twenty-First Century” (2014) presents, in vast arrays, fashion choices in cities around the world: fur hoods, trench coats, leopard prints, a certain kind of T-shirt or hairstyle. And Peter Funch himself, in an earlier project, “Babel Tales” (2006-11), created dense assemblages of repeated gestures or outfits (people carrying yellow envelopes or black umbrellas, people wearing red or posing for a photograph) by digitally layering a large number of figures into a single street scene. When you encounter an image from “Babel Tales,” it seems improbable and utterly mysterious. How on earth was it made? Once you do know how, the mystery is solved. The appeal of the work is largely in its technical achievement. But this was the work that led Funch to “42nd and Vanderbilt,” a project that tapped into some of the same energies, with less artfulness and more art.

The portraits in “42nd and Vanderbilt” are labeled in quasi-scientific manner with the date and time they were taken. The first portrait of the tanned man with the white goatee, for instance, is captioned “2007.06.28 08:59:39.” The people photographed most likely could not say exactly where they were at that time or what they were wearing or what sort of look was on their faces. The photographer, having recorded these things, knows them all, while knowing very little else about the person photographed, not even his or her name. The caption for the second portrait of this pair reveals a particular surprise. While most of the image pairings in the book are indeed taken days or weeks apart, this one had a gap of more than five years between the first image and the second: “2012.07.03 08:54:01.” The subject has aged and is still himself.

Looking more closely at “42nd and Vanderbilt,” I noticed another kind of repetition. Many of the dates recur, and a dozen of the portraits that made it into the book were taken on just one day: 2012.06.27. A man wearing a checked red shirt, a man wearing a checked blue shirt, a woman with dark brown hair and folded arms, a man wearing a burgundy tie and looking directly at the camera, a woman wearing a delicate necklace, and so on, all seen within the same hour. Street photography, like basketball, can be streaky, and June 27, 2012, seems to have been a great day for Funch. His intuition led him into an unpredictable and productive dance. About one in every five matchups in “42nd and Vanderbilt” contains a photo taken on that day.

Photography can remember for us what we didn’t think or were not able to remember for ourselves. I was in New York on Funch’s productive day, but I wasn’t at Grand Central. I know what I was thinking about that day because, quite by chance, it was my birthday. I know my head was filled with the thoughts that tend to preoccupy me each year on the anniversary of my birth: the mystery of time, the habits of a self, how the face in the mirror has changed, the meaning of our lives with others, how beautiful it all is and how soon it will all be gone.