For the past half century, I’ve run thousands of hours with my brother, and with my sister Natalie’s husband and her son. We are all marathoners. Running is our thing. I’ve done no training with Nat; she can’t run. She was born with lymphangioma in the right foot and had a just-below-the-knee amputation at age 9. I was 15 at the time, her oldest sibling.

I am a pitiful swimmer. I’ve tried several times to add swimming to my exercise repertoire, but my efforts never lasted long. In water, I sink. Nat rises. She finds liberation in water, which frees her from gravity’s clutch. In the sea, she cavorts like a porpoise.

In early July, my sister and I began swimming in Long Island Sound every morning.

Turning right onto her street, I looked first for the battered wooden crutches.

A moment later, Nat would bustle through the rickety screen door in her blue bathing suit. She is a strong woman who has moved through her 67 years with clear intent. Her determination is so great that I rarely notice the prosthesis below her right knee.

At the beach, I pull off my shirt, tug on my goggles and toss a towel on the empty lifeguard stand. I’m ready. (I also wear a rubbery flotation belt around my hips.) On the horizon I see Fishers Island and the Orient Point ferry churning into nearby New London.

Nat’s process is longer and more complicated. She drags her crutches and a lightweight beach chair to the water’s edge. Sitting, she rolls down her stump sock, and tucks it in a plastic bag. If the sock collects sand now, it might later rub her leg raw and bleeding. She loosens her prosthesis and pulls it off, revealing a pointy, wrinkled stump.

Nat grabs the crutches and hops into shallow water. She stops briefly to steady herself, then tosses the crutches backward while simultaneously making a shallow dive. It’s my job to fetch the crutches, and return them to her chair.

At this early hour, we’re alone on the beach. During sultry afternoons, however, I have seen curious young children congregate around her. “What happened to your leg?” one always asks. Nat doesn’t hesitate to answer.

“When I was a little girl, my leg was sick,” she says. “The doctors took it off and gave me this artificial leg. Do you want to see how it works?”

The day she came home from the hospital post-amputation, I couldn’t look at her heavily bandaged stump. I wondered: How does someone play sports with one leg? Climb trees? Go to school dances?

I need not have worried about Nat. She thrived in high school and college, and became a psychiatric nurse. In her first job, she worked with Vietnam vets suffering from PTSD.

After placing Nat’s crutches on her chair, I plunge into the water behind her. We will swim from one set of buoy lines to another a quarter-mile away, and then return.

In sports training, it’s crucial to have a workout partner at your same level. Otherwise, you strain too hard to keep up, or get little benefit if you surge ahead. Although I am more fit than my sister over all, her swimming experience pays off: Our differences cancel each other out in the water.

I take about 10 strokes and lift my head in search of Nat. She’s lined up shoulder to shoulder with me, just a couple of feet to my side. I go another 20 strokes, and look again. Same result. This isn’t anything we’ve concocted or practiced for decades. We’re no synchronized-swimming duo. We just seem instinctively connected in the water.

Nat’s more independent than just about anyone I know. I suspect going through life with one leg teaches autonomy. She has friends, yes, but also follows her particular passions: singing, attending national ice-skating competitions, organizing the local Democrats, and many more. I grew up in an era when the phrase “loneliness of the long distance runner” was more apt than today. You could call us both staunch individualists.

Except when we swim together. Once or twice, we bump, startling ourselves. Shark!? Of course not, but we slant away from each other for several strokes. A minute later, we have drifted back. We seem connected by some force that is elastic enough to allow us personal space, but soon tugs us back.

At the halfway buoy line, we stop for 15 seconds to check in. “Ready to turn around?” I ask. Nat usually is. But the other day she surprised me. “I feel good,” she said. “Let’s keep going to the house with the flagpole.”

What? I’m not expecting this. I’m a man of rigid habits. I like to swim to the buoy line and return. Yesterday. Today. Tomorrow. Can I go farther? I pause, feeling stupid.

This reminds me of my early days in running. Extending my distance from two miles to three seemed difficult, from 10 miles to 15 impossible. But the barrier turned out to be mental, not physical. If I didn’t give up, I could cover more miles with little additional effort.

“Sure, let’s do it,” I say finally. We begin swimming again, and the extra distance passes with little effort. Sometimes it’s easier to keep on keeping on rather than stopping to ponder and debate. Go with the activity’s flow, not the mind’s limitations.

The last five minutes of our swim feel the smoothest, and my stopwatch shows that we have sped up. Physiologists have investigated how distance runners can sprint at the end of an exhausting race, but have gained little insight.

Perhaps it’s more about euphoria than muscle and oxygen. Oliver Sacks, the neurologist, writer, and addicted swimmer, once said: “Swimming gives me a sort of joy, a sense of well-being so extreme that it becomes at times a sort of ecstasy.” I imagine ecstasy helps you go faster.

At my age, 73, I could list any number of physical ailments (I know you don’t want to hear them). Though she’s six years younger, Nat must have even more. Still, I’ve never heard her complain. She tells me the secret is acceptance — Zen Buddhism. She’s no card-carrying zealot, but a damn good role model. I’m trying to learn from her.

I finish the swim feeling relaxed and refreshed. “The cure for anything is salt water — sweat, tears or the sea,” Isak Dinesen wrote. We’ve knocked off two out of three. Not bad. And when I think about this summer of daily swims with Nat, I come close to a trifecta.

Amby Burfoot, winner of the 1968 Boston Marathon, is the author of “First Ladies of Running: 22 Inspiring Profiles of the Rebels, Rule Breakers and Visionaries Who Changed the Sport Forever.”