Ranthambore National Park, in eastern Rajasthan, is a cross between the Garden of Eden and the setting for Kipling’s The Jungle Book. A short (by Indian standards) train ride from Jaipur, it’s 150 square miles of gentle wooded hills, lakes and meadows, rocky outcrops, cliffs and ravines. At its heart, crowning a tall escarpment, is a sprawling 14^th century fort.

In Ranthambore silent leopards stalk the heights. Monkeys chatter their warnings in the trees below. Huge banyans send down aerial roots like tangles of gothic plumbing. The air rings with birdsong from first light till dusk. Muggers, the great Indian crocodiles, patrol the lakes. Peacocks keep company with the dainty spotted deer that graze the grasslands and spacious woods. Wild boar root through the forest mulch. And then there are the tigers.

‘You may not have much luck,’ said Jaisal Singh, the ebullient owner of our hotel, Sher Bagh, a luxurious tented retreat. ‘We’ve had a late monsoon. There’s still a lot of vegetation and they’re much harder to spot.’ A congenial host, Jaisal is also a seasoned manager of his clients’ expectations. In the event the late monsoon accounted for a dream-like lushness to the landscape and – with exceptional luck – we saw four separate tigers over one-and-a-half days.

These tigers are wild. They are not fed or managed. Nor are they contained within the park – some outcasts have been sighted hundreds of kilometres away – although most have been raised there and being territorial by nature they stick to their own patches. But they are known and studied intimately by the park staff and other specialists. We were lucky on our first afternoon to have as our guide Yusuf Ansari, an English-educated writer, historian and conservationist.

A fount of knowledge about Ranthambore and its residents, Yusuf was with us when we made our first sighting. This was Macchli, the grande dame of Ranthambore and star of the BBC 2 documentary series Queen of Tigers. Macchli is now elderly. She had killed that morning and when we saw her she was moving slowly along the bed of a ravine, a hundred feet or so below us.

It was a thrilling moment, of course, but nothing like as thrilling as what followed the next morning. We had been waiting by a broad, still pool in a river, listening for some time to the alarm calls of monkeys in the trees on the cliff face above. Then the radio crackled. We turned round and a few hundred yards back the way we had come, another jeep had stopped on the track. As we approached, round the corner stepped a large and beautiful tigress. Quite unconcerned, she strolled towards us, stopping to sniff at some grasses, then moving forward again to pass finally within two or three feet of the nose of our jeep before sauntering on to the river.

As I realised that she was coming towards us I felt an instant of elemental terror. This was a three-metre-long killing machine, one of the two or three most formidable predators on the planet, and we were in an open jeep. It would be no exaggeration to say that she could have taken my head off with one swipe of the paw whose dinner-plate-sized imprint we inspected in the dust after she had moved on. (Although in fact, as Yusuf later explained, the tiger’s preferred method of killing is a bite to the neck or, if necessary, the skull, and the shape of a jeep with humans in it is something unrecognisable to a tiger as prey.)

Reason reasserted itself and the moment passed. Wild as they are, these animals have grown up in the presence of vehicles and have never experienced humans as a threat. That the jeeps are open and none of the park staff are armed says all one needs to know.

My breathing slowed and I watched her spellbound as she walked past us, across the river and away down the track. She rippled with muscular grace. Her stripes echoed the bars of shade falling across her path. She embodied a power and majesty that I have never seen before in any living thing. I am the spirit of this place, she seemed to be saying, and I have walked this path for aeons. It was one of the great experiences of my life.

Next week – to the INK (Indian TED) conference in Cochin …