His tiny four-seater banks sharply at an acute angle, less than 100 metres above the elephant herd - and only when the line of broad orange- grey backs and long Tsavo grass loom towards the window does the question suddenly make sense.
Two "elephant counters", Salome and Catherine, are squeezed into the rear seats. They are well used to this precipitous but effective method. They count the small herd with rapid finger movements and a lot of muttering. "We count the live and the dead," says Dr Douglas-Hamilton, a world expert in his studies of elephant behaviour. Noticing a lone male chasing buffalo and birds by a watering hole, he lifts his hands from the controls in ecstasy: "Wonderful! Great! Full of the joys of life!"
But after the high comes the low. He says he is terrified for the future of the animal whose magnificent tusks are gouging the red dust and mud.
In March, the strict worldwide ban on ivory trading is to be relaxed. One experimental shipment from the African countries relatively well endowed with elephants, Zimbabwe, Namibia and Botswana, will be sold to Japan for domestic use only. But to those who oppose the trade, even this highly regulated sale may have disastrous consequences.
"It is extremely risky to open up the trade, even partially," says Dr Douglas-Hamilton. "To the poachers, it's either open or shut. It will send all the wrong signals and trigger a huge demand for ivory again. We risk seeing again the awful slaughter of the 1980s."
With the Kenya Wildlife Service and other elephant experts, he is leading the most comprehensive elephant count in Kenya's Tsavo eco-system since 1994 - covering an area of 40,000 square kilometres. When the ivory trade opens up, the effects will be carefully monitored.
A steady increase in Kenya's biggestt herd had been expected. But after a five-day count, observers came up with 8,100 elephants in the 21,000- sq km (8,400-sq mile) park. They also counted five fresh carcasses. Since 1990, the rate of growth of Tsavo's herd has averaged about 3.8 per cent, but the last week's count points to a drop of about 1 per cent. No one yet understands why.
Tsavo once held 45,000 elephants, so the recent figures are tiny. But they are considered a triumph by elephant conservationists who saw the decline to an appallingly low level because of poaching and drought over two decades.
Carcasses of elephants horribly mutilated by automatic weapons were so common in Tsavo 10 years ago that in some areas there were more animals dead than alive. That left an indelible mark on populations that can live to 70 years. "You don't see elephants more than about 40," says Paula Kahumbu, the project's overall co-ordinator.
Not all poaching is commercial. John Kagwe, a senior Tsavo warden, says "subsistence poaching" for meat is "wrong, but understandable". As more people eke out a living on the peripheries of the parks, they often resort to snaring animals with homemade wires and cables.
One of the dilemmas of maintaining the parks - and particularly elephants - is convincing the community that the beasts that trample their farms are "beneficial". So far in Kenya, there has been more rhetoric about "community involvement' than success, with continual (and usually uncompensated) destruction of crops.
The fragile recovery of the Tsavo elephant population was attributed to the worldwide ban on ivory trading imposed in 1989 by the Convention of International Trade in Endangered Species. Kenya was one of its most vocal supporters, then led by Dr Richard Leakey, re-appointed director of Kenya Wildlife Service last September. He wants the count done before the ban is relaxed.
"Fresh carcasses have been found during the count," he says. "If that means an increase in poaching, then I've got a problem on my hands."
He believes about 40 elephants have been killed outside the national parks over the past four months.