Whenever travellers let out a whoop of childish glee in Yosemite National Park — a disturbingly common occurrence, even among the most jaded globetrotters — they’re part of a grand tradition.

Back in 1869, an eccentric Scottish hobo named John Muir let out a shriek of amazement and did a little jig when he first peered over the rim of the yawning Yosemite Valley, having just walked the 186 miles from San Francisco. “I shouted and gesticulated in a wild burst of ecstasy,” Muir later recalled, marvelling at cliffs that were “all a-tremble with the thundering tones of falling water” and sheer granite towers “like the spires of Gothic cathedrals”.

At the time, word was only slowly leaking out that Yosemite was California’s ultimate natural spectacle. It impressed the long-bearded young drifter deeply, and he swore to stay in the valley and explore its every nook and cranny.

Like some Victorian flower child — or, more precisely, a spiritual forebear of Jack Kerouac — Muir took up residence in a shack overlooking a flowing creek, and worked as a freelance hiking guide for the odd adventure tourist who made the arduous journey from San Francisco.

He spent every spare minute climbing Yosemite’s mountains, gazing in rapture at its waterfalls and studying its delicate forest flowers, jotting down his observations in notebooks that explode with a passion for nature.

“Who wouldn’t be a mountaineer?” Muir wrote, in what would become the American wilderness-lover’s creed. “Up here, all the world’s prizes seem nothing.”

Within a decade, Muir — who had emigrated from Dunbar, Scotland, to rural Minnesota at the age of 11 with his dour Calvinist father — was being recognised by the American literati as a self-taught genius; and by the end of the century (when his flowing beard was snow-white, like Methuselah’s), he would be hailed as the heir to Emerson and Thoreau as the leading conservationist in the United States.

His many lyrical books and magazine articles on Yosemite were instrumental in the campaign to turn the Californian Shangri-La into a national park in 1890. Today, travellers will see the name of John Muir emblazoned all over the West, given to high schools, forests, hiking trails, parks, roads and even medical centres — and while he’s not exactly a Scottish national hero, the cottage where he was born in Dunbar has been turned into a little shrine.

Although Yosemite is now one of America’s most popular destinations — it sees 3.5m people a year, turning its main trails into cacophonous conga lines of hikers and its roads into log jams — it takes surprisingly little effort to escape the throngs and slip into the benign natural world Muir loved back in the late 1860s.

Shady bicycle paths lead to silent swimming holes where you can baptise yourself in icy mountain waters. Stroll 100 yards off the main trails and you can be completely alone. And a little knowledge of history helps.

While armies of bus-tour passengers jostle to photograph Yosemite’s most famous vista from the so-called “Tunnel Overlook”, an overgrown trail head just across the road climbs up to the even more impressive vantage called Old Inspiration Point: this was the most beloved of the Victorian-era lookouts, and you can still see the 19th-century carriage-wheel ruts marking the earth. (In the 1940s, the famous Western photographer Ansel Adams took the most iconic images of Yosemite here.)

But really to experience ye olde Yosemite, you have to delve into the park’s high-altitude mountain expanses beyond the valley, just as John Muir did on his days off. Back-country hiking trails weave from the verdant, subalpine Tuolumne Meadow, an hour’s drive from the valley floor (“the most delightful high pleasure-ground I have yet seen”, Muir raved), into a rugged landscape that has not changed since the Scotsman first explored it in hobnailed boots in 1869.

Times recommends

• Travel advice: what to do if your flight is disrupted
• Top 10 unmissable events in 2010
• Seven spa breaks for January