KOS, Greece >> Dawn was breaking over a beach near Kos harbor, and the first swimmers threaded their way between orange beach umbrellas into the sea.

Suddenly, a black rubber dinghy burst out of the grayness. It tacked rapidly toward the beach, and the life-jacketed young men on board began ululating with joy. Migrants, they had made it across the narrow stretch of water from Turkey to the Greek island of Kos, and what they hope will be a safer and more prosperous life in the European Union.

One punctured the boat. Most of the others scrabbled onto the sand, dropped their life jackets and quickly vanished into the nearby alleyways.

Two young friends, Shady Khilel and Akram Dakdk, both 21, stopped for just a moment to take a selfie. In their Bermuda shorts and T-shirts, with beards and tousled hair, they could have passed for tourists. Only Khilel’s scratched and swollen feet hinted that they had to hike through thorny underbrush on the other side of the channel to get to their boat.

After taking the photo, Khilel made three phone calls. “Allahu akbar,” he crowed to the first person. “Mama,” he explained, laughing joyfully. The next call was to his best friend.

The third was to a friend in Kos, who had made the same journey by boat from the Bodrum peninsula in Turkey a few days earlier — Ayman Almotlak, a teacher of Arabic.

Almotlak instructed the two young men to meet him at a cafe near the medieval fortress, less than a mile from where they had washed up.

At the cafe, another friend, Nour Hamad, a veterinarian, explained why they had made the journey.

“We lost everything in Syria,” Hamad said.

Khilel said something, and Almotlak translated: “My friend says he lost his humanity.”

On Wednesday, five days after he reached the beach, Khilel sent a reporter two photographs and a brief voice message. It said, “I am in Macedonia.”

His timing may have been lucky. On Thursday, Macedonia declared a state of emergency and said it was tightening security on its normally porous border with Greece, stranding thousands of migrants who are trying to move north to more prosperous European countries.

Traveling With Dignity

On Kos, the clean white tables and chairs of a seaside cafe overlook a small yachting marina, and a few miles away across the blue Aegean waters, the whitewashed houses of Bodrum can be seen sparkling in the sun.

In between are new additions to the scene this summer: the tents, clotheslines and playing children belonging to thousands of refugees who have fled destitution and war.

A group of elderly Greek men in crisp shirts sipping coffee at the cafe could be overheard saying that the Greeks, too, were once refugees. “But we always traveled with dignity,” one added.

Dignity, or axioprepeia in Greek, is the word of the hour in Greece. The prime minister, Alexis Tsipras, frequently used it as a battle cry against the austerity demands of eurozone creditors. But it seems to have a special resonance here, where the promise and the reality of modern Europe meet.

Salvage Operations

A peculiar industry has sprung up on the island: salvaging the migrant boats. Every morning, a small group of enterprising Greek men cruise the beaches in jeeps, picking up the punctured dinghies, the abandoned motors, the discarded inner tubes and life jackets.

One of them is Grigoris, 72, who rides barefoot across the beaches at 5 a.m. in his open jeep. He specializes in life jackets, and every morning he collects a pile of them, as hundreds more migrants arrive in Kos. The jackets generally do not meet European Union standards, so they cannot be legally reused in Greece, he said; instead, he removes the foam from them and turns them into reflective vests, which he sells or gives away.

“I do this just to keep busy,” Grigoris said. “Anything illegal, I like.”

In his youth he was an itinerant acrobat, he says, traveling as far as Brazil to perform. Now his bare feet are hard enough to walk on glass, he says. He lives on the produce he grows in his garden, while collecting antiques, and now life jackets. He is proud of his cunning.

“People like me, we are not educated,” he said. “But we are more intelligent than many educated people.”

Common Ground

Dealing with the onslaught of migrants has forced the Greeks, who could be excused for being consumed with their own country’s never-ending economic crisis, into a strange kind of double-think. On the one hand, their fundamental hospitality comes out, and they want to help. On the other, they see the flood of migrants as detrimental to tourism and their own economic interests. In public they express compassion; in private, they are very often angry and resentful.

In this resentment, Turks and Greeks, enemies for centuries, find common ground.

In Bodrum on the Turkish side of the channel, a tour guide and a restaurant waiter ask a visitor whether Kos is overrun with migrants. Yes, they are told, the influx already exceeds 20 percent of the island’s population of about 33,000.

That is nothing, the Turks reply. Turkey has nearly 2 million refugees on its hands just from the Syrian civil war, more than any other country.

Priority for Syrians

Last Friday, three days after a near riot in a stadium on Kos where migrants were being held, a giant ferry that once cruised between Athens and Crete docked at the island. The ferry was pressed into service as a floating processing center, dormitory and refectory. The hope is that it will take some of the migrants off the streets and beaches of Kos, where they have been camping out while waiting for papers that would allow them to move legally inside Greece.

Mayor George Kiritsis of Kos announced that Syrian migrants would be given first priority. Syrians receive preferential treatment in many ways, because the Greeks consider them most likely to be actual war refugees rather than economic migrants.

Migrants were told to assemble at midnight Saturday to board the boat. Several hundred men, women and children milled anxiously at the dock. A man brought a feverish baby to the coast guard officers providing security for the ferry, and was told to take the child to a hospital instead.

The Syrians in the crowd began complaining that many of those assembled at the boat were not Syrian.

“Passports!” the Greek authorities demanded, in English. When most of the crowd did not seem to understand, they called for refugees who understood English and Arabic to step forward and translate for the rest. Christian Salloum, a Syrian in a new blue and white souvenir Kos cap, volunteered.

Salloum, who said he had worked as a journalist before fleeing Syria, organized the waiting Syrians into two lines, one for those who had already registered with the authorities and the other for those who had not.

A group of men suddenly started jumping up and down, chanting and clapping in protest that they were not being allowed onto the ferry. “They are saying, ‘We are Iraqis,’” Salloum explained.

The disturbance passed, and the Syrians began boarding the ship.

Asked about his hat, Salloum said he had gotten it to remember Kos.

“It’s a nice place, but we don’t have the heart to enjoy it,” he said. “For us, it’s a road. I hope someday to come here not being a refugee.”