The Kazakh nomad's hand rocks forwards in a gentle stroking motion and the eagle needs no keener reminder of the business of the day, springing from her master's wrist like a fluid extension of his will, gaining the thin, freezing-cold upper air with a few strokes of her vast wings. From there she sees the province of Bayan-Olgii spread out below, the bare, dun-brown, ice-streaked mountains culminating in Mongolia's highest, Khuiten Uul, climbing 13,000ft into the sky.
On the arid plains at the foot of the mountains, those dirty grey specks are hundreds of head of scrawny sheep and goats, tearing at the sparse vegetation — but it's not on them that the eagle's eyes are fixed but rather that fox down there, invisible to human eye, even if one could get up to that height and look where the eagle is looking, creeping from the shade of a rock.
In less time than it takes to tell, she is on to it, screaming in like a racing yacht with a fierce wind behind it, slicing diagonally across the sky, then with a sudden, stunning turn of speed just a few feet above the ground she has the scruff of the fox's fur in her talons, its feet leave the ground then crash back on it as all 15lb of the eagle's weight descends like doom on its neck.
Within minutes the fox is no more than another fine trophy hat for the berkutchi (Kazakh for eagle hunter) in the making.
Kazakhstan and Mongolia share no common border, but at the closest point, where China to the south meets Russia to the north, they are less than 40km apart. And the two countries share much else: the world's first- and second-biggest landlocked countries respectively, both are heirs to the legacy of Genghis Khan and his many and varied successors and imitators; both have tiny populations considering their vast size; both amaze the eye with their endless perspectives; both gladly discarded their Soviet overlords and sent the Red Army packing when the Bolshevik experiment bit the dust.
Long before the bug for drawing hard and fast borders reached these latitudes, this region was home, it is believed, to the first domesticated horses in the world and the first hunting eagles: falconry, we are told, was invented here, the use of these beautiful and powerful raptors to hunt where no other means would have a chance.
And through all the barbaric vicissitudes of the 20th century, the habit of nomadism, of moving from the uplands to the plains with the flocks, and back again as the seasons turn, persisted, as did the love and knowledge of falconry of which it was an intrinsic element: a source of pride and a badge of identity, as much as the extravagant fur coats and hats in which it resulted.
Yet the Kazakh nomads of the far west of Mongolia, though they accepted — Islamic religion, Turkic language and all — as part of the traditional Mongolian mix, had a hankering for the company of their co-nationals. So when Nursultan Nazarbayev, the ruler of Kazakhstan since before the collapse of the Soviet empire, invited them to return 'home' en masse, many heeded the call: the population of their Mongolian province, Bayan-Olgii, crashed from 102,000 in 1991 to 75,000 in 1993 as they streamed west along the jagged Russian-Chinese border to rejoin their country.
Twenty years on, many say the experiment has failed. Although Nazarbayev's appeal, post-Communism, was to Kazakh nationalism, the native traditions which the nomads represented, whatever their sentimental value, have no place in the country he has engineered — a place which today, thanks to its huge oil reserves and the ambition of Nazarbayev himself, has more in common with the hyper-modern monarchies of the Gulf than with Mongolia. Lured by the call of home, the Kazakhs from Mongolia found themselves trapped on their country's margins. Less than ever was there a call for the traditions by which they defined themselves.
It has dawned on many of the Kazakh nomads that the siren song of nationalism means less in the long run than the company of Mongolians who, however different in language, ethnicity and religion (most Mongolians are devout Buddhists in the Tibetan style), still find a place in their lives for yurts (the Mongolians call them gers).
So the exodus has been inverted: though many of the Kazakhs confronted previously unimagined obstacles of passports, visas and guarded frontiers, many have returned to Mongolia: the slump in the population of Bayan-Olgii reversed, and at the last estimate, in 2009, had increased to more than 93,000.
And if, even in Mongolia, the old ways seem increasingly anachronistic, the fascination of hunting with eagles, and the winter festivals in which the sport is celebrated, attract a growing following among visitors from Europe and the United States.