NEW YORK — “The New York State Thruway is closed. Isn’t that far out?!”

So says the 22-year-old Arlo Guthrie in one of the more humorous moments in the motion picture “Woodstock,” the essential document of the culture-shifting concert/event celebrating its 50th anniversary. Bad traffic is not normally a point of pride, but in this case it is understandable.

While it wasn’t the first large scale “hippie” concert, Woodstock (the festival’s actual mouthful of a title being “Woodstock Music & Art Fair’s Aquarian Exposition: 3 Days of Peace & Music”) was still fundamentally an underground, countercultural thing, a rebuke of uptight square society. Just a month earlier industry and government worked to put a man on the moon. Here, a bunch of longhair guitar freaks worked to put a generation in touch with themselves, man.

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It’s easy to get philosophical about Woodstock, even with its ambiguous legacy. One can easily connect the dots from it to the disastrous Fyre Festival, or simply wince at the recycled use of its brand for lame-o anniversary concerts (the latest was actually canceled before it happened, probably for the best.)

But for a time, those two syllables, named for the Hudson Valley town not far from where the actual event took place, meant Utopia for idealistic, anti-war agents of change. And while the most prominent performers were artists such as Jimi Hendrix, Janis Joplin and The Who, the event was a lot more Jewish than people realize.

Arlo Guthrie, quoted above, is a great example of Woodstock’s somewhat veiled Jewishness. He was and is the famous son of legendary Oklahoma “dustbowl balladeer” Woody Guthrie, but his mother was born Marjorie Greenblatt, daughter of Yiddish poet Aliza Greenblatt. (Here’s a weird factoid: Arlo, author of “Alice’s Restaurant,” studied for his bar mitzvah under a young Rabbi Meir Kahane.)

Arlo was one of 32 acts that played over three days/nights/mornings in August 1969. His catchy tune “Coming Into Los Angeles” is used to great comic effect in the documentary film, as something of a celebratory anthem to smoking marijuana. (Indeed, were it not for Arlo, millions of people might never have learned how to create a makeshift pipe out of some aluminum foil and a pen.)

A lot of other performers at Woodstock fit the “oh, they’re Jewish?” bill (and more detail on that in a moment), but behind that there’s a more important factor. The concert itself would not exist if not for a squad of heimish young men.

Michael Lang, 24 at the time, could be considered the “face” of Woodstock from a business point of view. He was a Jewish kid from Brooklyn who ended up in Florida and became a concert promoter. In 1968 he co-produced the Miami Pop Festival, which featured Jimi Hendrix, John Lee Hooker, Frank Zappa and Chuck Berry. A solid warm-up to Woodstock.

He’s the one you see in the documentary zooming around on his motorcycle as they are setting up the stage, seemingly unfazed by the rain or the fact that the larger-than-expected crowd makes selling or even collecting tickets impossible. Once a fence is breached, he declares it a free concert, knowing the investors will lose their shirts.

Lang’s main partner was Artie Kornfeld, then 26, another Jewish kid from Brooklyn. He worked at Capitol Records as a young executive and also wrote or co-wrote a number of forgettable tunes. (“The Pied Piper,” recorded by Crispian St. Peters, and “Dead Man’s Curve” by Jan & Dean are two examples.)

Lang and Kornfeld hooked up and planned to open a recording studio somewhere near Woodstock. The area, a little over two hours’ drive from New York City, is quite close to the Catskills and all the Jewish Borscht Belt hotels and bungalows associated with it. But the little town of Woodstock and its immediate neighbors have long had an association with artists going back to the Hudson Valley School of painters and the Arts & Crafts movement.

In the 1960s it was an oasis for the counterculture scene, and, famously, home to Bob Dylan (née Zimmerman, if you need reminding) after his motorcycle crash in mid-1966. He dug in with some musician friends (The Band) at a house up there (Big Pink) to explore “the old, weird America,” inadvertently creating pop culture’s first widely circulated bootleg album (“The Basement Tapes.”)

To get financing for the studio Lang and Kornfeld got in touch with Joel Rosenman, also Jewish but older at a whopping 27, who had some success building a studio in Manhattan. He suggested that they could better promote the area and its social justice causes with a festival. Rosenman’s partner was John R. Roberts, dangerously close to 30, and heir to the Block Drugs fortune.

That’s right, Polident paid for Jimi Hendrix!

If you watch the 1970 Woodstock documentary (four hours of anthropology, psychedelia and split-screen singalongs) Lang seems sincere when he says he cares more about proving a large gathering of young people can be peaceful than about making a buck. But there still is some sechel (common sense) there. The concert was a financial flop. The soundtrack album and the movie were a smash. In other words, don’t worry: they all recouped.

But beyond the producers and Arlo Guthrie, what else was kosher at Woodstock?

The only artist to get billed twice, both as a solo artist and with his backing group The Fish, doesn’t have a very Jewish sounding name: Country Joe McDonald. But the folk-rocker who sang the Vietnam protest song “The-I-Feel-Like-I’m-Fixing-To-Die Rag” is the son of one Florence Plotnick. The Plotnicks were Russian immigrants and Country Joe’s parents were Communist Party members who, before they renounced the party, named their son after Joseph Stalin. The guitarist in The Fish, Barry “Fish” Melton, was another Jew from Brooklyn. Maybe they all rented a bus together.

One of the most important psychedelic bands of the era was San Francisco’s Jefferson Airplane. Its lead singer, Marty Balin, was born Martyn Buchwald and his father was Jewish. Their lead guitar player, Jorma Kaukonen, had a Jewish mother (Beatrice Levine). Since we’re at it, we’ll add that Jefferson Airplane bassist Jack Casady had one Jewish grandparent. I looked it up.

Less groovy and more jazzy was a band that isn’t quite so celebrated today, but back then sold a ton of albums. Blood, Sweat & Tears was wall-to-wall Jews, with Fred Lipsius, Lew Soloff, Bobby Colomby and Steve Katz in the 1969 lineup. You may not know this band by name but you definitely know some of their songs (put “Spinning Wheel” into YouTube, trust me.)

Also in that vein is one of Woodstock’s top curiosities: the inclusion of Sha-Na-Na. The 1950s nostalgia act that later had a television variety show was, for some reason, the band that played just before Jimi Hendrix’s closing act. Sha-Na-Na was created by a group of Columbia University alumni (its founder, Robert A. Leonard, later became a celebrated forensic linguist) and its revolving door of members includes a wide swath of “New York types.” The last names are all Jewish and Italian. Alas, “Bowzer” (Jon Bauman) was not with the group at Woodstock; he joined a year later.

There’s more. The band Mountain? Headed by Leslie West, born Leslie Weinstein. (Yes, the “Mississippi Queen” is Jewish.) The Grateful Dead performed and, of course, their very far-out percussionist and space ranger Mickey Hart was born Michael Hartman. (Their set was not included in the album or the movie, and the band was displeased with their performance.) Folkie Bert Sommer, probably best known for being in the original production of “Hair,” did an early set on Woodstock weekend, and the band Canned Heat had a Jewish bassist and guitarist, Larry Taylor and Harvey Mandel.

Also, Robbie Robertson, guitarist and principal songwriter with The Band, discovered in his teens that the biological father he did not know was Jewish. (He was raised in Toronto and his mother was Cayuga and Mohawk.) The Queens-born folk singer Melanie (Melanie Safka) is not Jewish, even though she is often mistaken for being so (she’s still great!) and Mike Bloomfield, the principal Jewish electric guitar player of the era, had already left the Paul Butterfield Blues Band by the time Woodstock rolled around, so he wasn’t there.

But the political agitator/trickster/clown/dissident Abbie Hoffman was there, and interrupted The Who’s set to yell about the recent arrest of activist/music manager John Sinclair. (Pete Townshend wasn’t too impressed, ordering him off the stage with some expletives.) Surely other Members of the Tribe, tucked away as bassists in some group or other, performed that weekend. But there are two other important names to mention.

First, the man who wasn’t there: Bob Dylan. The New York State Thruway shut down, as Arlo Guthrie celebrated, in part because so many kids were certain the reclusive Dylan would play. He actually turned down the offer and was on his way to Britain to play the Isle of Wight, but since Woodstock was his home base and The Band was on the bill, the rumors were rampant.

Then there was the land itself, owned by a Jewish farmer named Max Yasgur. Like Tevye before him, he was a dairy man, and was close to 50 at the time of the concert. When the promoters were having trouble finding a suitable location, a local kid (Elliot Tiber, also Jewish) made the connection.

Yasgur was a conservative, but he was troubled by the growing social divide and hoped the concert could act as a balm. While he did get a nice check, he also sprang into action bringing free food and water to the concertgoers when the overcrowding got dangerous. He was later shunned by the community (not everyone was thrilled with the hippies) and he moved to Florida.

Immediately after the show, the legend grew. Joni Mitchell didn’t attend, but she penned “Woodstock” for Crosby, Stills, Nash & Young, who did. When the movie came out, everyone who got too high during a screening later told their kids they were there. The key images of nude young people frolicking in “the Garden” began to stick. The biblical implications may be a bit much, but the social impact can’t be denied. That so much of it happened on Shabbat doesn’t make it any less Jewish.