Forget 1 January, 2000, reckons Robin Catchpole, the real third millennium starts the following year. But if you want to cheat, here's how the intrepid traveller can catch the last sunset of the old millennium and the first sunrise of the new ...
What do the Nicobar Islands, the Balleny Islands, Caroline Island and a sixth-century monk have in common? If I tell you that the monk's name is Dionysius Exiguus, or Denys the Little, then you may just guess that it is all to do with when the next millennium starts, and where to see the first sunrise.

When and where will the last sunset of this millennium occur? Does it come before or after the first sunrise of the next, and can you see them both? If you are not too much of a purist, you will be pleased to hear that you can do all this from exotic tropical islands.

The purist will ask: whose millennium, as there are about 40 different calendars in use in the world today. But the populist knows that it is the Christian calendar that is about to reach the magic 2000. The first question to decide is when we should celebrate the start of the third millennium. Should it be on 1 January 2000, as common sense suggests, and when all the numbers change, or on 1 January 2001, as purists like myself insist? To understand why this dispute arises we have to go back to the time of Denys the Little. When he was busy making a table giving the dates of Easter he decided to abandon counting years since the beginning of the reign of the Roman emperor Diocletian, in favour of a system starting with the birth of Christ. The year 248 Anno Diocletiani would henceforth be known as the year 532 Anni Domini Nostri Jesu Christi.

Denys made two mistakes. First, and quite understandably, he left out the year nought, because the number zero had not yet been discovered in the West. He called the first year of his era year one, with the understanding that Christ was born at the end of the previous year. This was his second mistake. Modern scholars think that Christ was probably born in 6BC, and certainly not after 4BC, when Herod died.

The first mistake rankles with the purist. Most of us think that at the beginning of the year 2000, 2,000 years will have passed since the start of the Christian era. This is not so. Because there was no year zero, 2,000 years will have passed only at the end of the year 2000, or the start of the year 2001. So the 21st century and the third millennium begin only at the start of 1 January 2001.

We have fixed the year and the day, but when during the day should we celebrate? As a purist I must now draw your attention to the "International Conference Held At Washington For The Purpose Of Fixing A Prime Meridian And A Universal Day" in October 1884. Resolution one resolved to adopt a prime meridian, while resolution two decided this would be the Greenwich meridian. Interestingly, at this point the French abstained. Resolution five decided that the day is to begin "for all the world" at midnight at Greenwich. This was carried 15 to two, although the French, Germans, Dutch, Swedes and Swiss abstained, and the Austro-Hungarians and the Spanish voted against. Some attitudes in Europe never change.

From this we purists must conclude that the next millennium will start for "all the world" at the last stroke of midnight GMT on 31 December 2000 or, more exactly and identically, at zero hours Universal Time on 1 January 2001. So if we want to see the first sunrise of the new millennium we must find the place, preferably on a tropical island, where the sun is rising at that moment, which happens to be Katchall Island in the Nicobar Islands.

It is a matter of deep regret to purists like myself that "all the world" does not normally wait until midnight Universal Time before celebrating the New Year. Indeed in resolution four of the 1884 conference we find that the "universal day shall not interfere with the use of local or other standard time where desirable". Put simply, this means that in Sydney they don't have to wait until 10 next morning before celebrating the New Year.

To proceed, we must come to grips with the International Date Line, which, incidentally, is neither international nor mentioned in the conference of 1884, and can, as we shall see, be changed by anyone at will. We ask: where does the sun first rise this side of the Date Line? At first we thought of Cape Elsworth, a 1,000ft-high, sheer rock bluff in the ice- capped Balleny Island, just north of Antarctica. The problem is that the sun only half sets before rising again, so that does not count. At this point the super-purist, determined to find somewhere even colder and more miserable to celebrate, will point out that the first sunrise of the new millennium will take place at the South Pole in September at the time of the equinox of the previous year. We can also ignore this, because Antarctica is a continent not an island.

Our most plausible candidate after the Balleny Islands would have been Pitt Island in the Chatham Islands, were it not for an announcement from the Ministry of Foreign Affairs in the Republic of Kiribati (the "ti" to be pronounced like the letters "ti" in station). This declared that from 1 January 1995 all the islands in their jurisdiction would take the same day of the week. This seems quite reasonable when you imagine the chaos there must have been, having part of the country not just an hour or two but a whole day behind the rest. The result of this decision is to put an enormous eastward bulge into the not-so-International Date line, which now includes Caroline Island at the southern end of the Line Islands. It is a warmer and more hospitable place to celebrate than the South Pole, the Balleny Islands or even Pitt Island.

Finally, if you are not too much of a purist, you have the chance to celebrate the first sunrise of the new millennium before you race off to Western Samoa to mourn the last sunset of the old millennium. You have a mere 14 hours and 14 minutes to complete the 1,528-mile westerly dash from Caroline Island. I am sorry I shall not be able to join you because, as a super-purist, I shall be obliged to watch sunrise from the Nicobar Islands. And, by the way, the year 2000 is a leap year.

Travel: Sunset in Western Samoan

The Western Samoan tourist officer leaned back in his squeaky chair with a sigh. "It's a problem," he said. "Samoans are just too hospitable."

I had just told him that within four hours of arriving in his postcard- perfect tropical paradise, while I was standing on a street corner, a young woman named Pesi had struck up a conversation in stilted English. Within five hours we had taken a bus to her modest concrete-and-Plexiglas house. Within six hours, her daughter had stopped crying at the strange sight of the seemingly bleached visitor, and her mother was feeding me banana after banana as a sign of welcome. Within seven hours, Pesi had enacted that age-old rite of female bonding and had French-braided my hair. Within nine hours, the mother, making up for her lack of English, had tied a lava-lava around my waist and was teaching me a spirited Samoan dance. About then, I threw away my watch, lost track of my shoes, and swore eternal friendship.

The tourist officer did not seem surprised. "It's the Fa'a Samoa," he said, "the Samoan Way".

The Fa'a Samoa is often invoked when Samoans won't or can't explain the complex interlacing of duty, pride and humanity that keeps their society so tightly knit - a society that has been largely untouched by the 20th century and is desperately trying not to unravel under the pressures of the 21st.

One of those pressures is tourism. Samoan hospitality is so renowned that American Peace Corps volunteers proudly report they regularly go on bike trips without their wallets. They are invariably fed and housed by people they meet along the way.

The problem for the Department of Tourism is: how you introduce more tourists without impoverishing your hospitable citizens? The answer seems to be to offer visitors a small selection of extremely good accommodation at reasonable prices, hoping they will win out over free turf floors and no electricity.

The legendary Aggie Grey's, in the capital, Apia, is a surprisingly big, colonial-era hotel in the grand old South Sea tradition. Rooms are bright and airy, with the compulsory ceiling fan (backed up by the practical air conditioner) laconically swishing in the hibiscus-scented air. Many of the staff are tattooed from waist to mid-thigh.

The road north from Apia, through the centre of the island - past waterfalls, rolling hills and Vailima, the house (now a museum) where Robert Louis Stevenson died while making mayonnaise - arrives at a white-sand, swaying- palm-tree, South Sea idyll. The Coconut Beach Club, owned and run by two Americans who understand luxury, is a bar, restaurant, motel and a clutch of detached, sumptuously appointed cabins. All with Jacuzzi and private beach access, of course.

Jacuzzi by Jacuzzi, air-con by air-con, Samoa is changing, with all the good and the bad that modernising implies. But, for a few more years, at least, the Fa'a Samoa will cocoon the country in its past - and for the time being, at any rate, it will remain a place where old women take strangers by the hand and teach them how to dance..

On the cusp of tomorrow in Kiribati

The Republic of Kiribati (formerly the "Gilbert" of the Gilbert and Ellis Islands) is still shuffling and shifting, trying to get comfortable in its new chair of nationhood.

It became independent only in 1979; one side of its story of British rule was told in the school classic A Pattern of Islands, by Arthur Grimble. This has been (and to some extent continues to be) an area of geographical awkwardness. Kiribati's 33 islands, almost all coral atolls, are scattered over 3.5 million square kilometres of the Pacific, and at Independence these straddled both the equator and the International Date Line.

The Date Line was particularly irksome. With half the country 23 hours ahead of the other half, there were only three working days in each week when the entire nation could be expected to be in the office. Slack, even by the standards of a south seas paradise. So, in 1994, in a move initially not much noticed outside Kiribati, President Teburoro Tito unilaterally shifted the International Date Line to the country's eastern extremity. The entire country now lives on the cusp of tomorrow, with Caroline Island getting the best view of what's to come.

Hidden away in the Southern Line Islands, Caroline is a 10-kilometre- by-1-kilometre atoll, made up of more than 20 tiny islets. It bustled with 27 citizens in 1868, but since then numbers have dwindled. The shores, lined with coconut trees, have seen few people this century, though roving colonisers occasionally stopped off long enough to rename the place. Over the years, the atoll has been variously called Hirst, Clark, Carolina, Independence and Thornton.

Party-goers wishing to get to the island before the year 2000 may want to leave soon. There is no good anchorage or proper airstrip at Caroline Island. And, at the last count, Kiribati's domestic airline had only one (mostly) functioning plane (a 10-seater with such an unreliable schedule that flights are generally announced only on Radio Kiribati and usually never more than 24 hours before departure). In fact, with pristine beaches, aquamarine lagoons, tropical-fish-encrusted coral reefs, deserted equatorial islands and largely pre-cash and pre-electricity economy, the outer atolls of Kiribati may well be the best place in the world to forget the new millennium.

Cleo Pascal

Kiribati Visitors Bureau, PO Box 261, Bikenibeu, Tarawa, (00 686 28287)

Dawn over Nicobar's silver sands

The Andaman and Nicobar Islands straggle languidly across the ocean far to the east of the Indian mainland, to which they are technically joined. For years the authorities in Delhi have kept a tight grip on all developments, for political reasons. The islands are close to Burma, with whose government India has uneasy relations. In addition, Indian efforts to absorb the native peoples has resulted in the importation of thousands of Bengali settlers, who now form the bulk of the population of 280,000. The only native group to survive and thrive are the Nicobarese, in the southern islands that are still largely out of bounds to foreigners. The rest of the tribes are teetering on the brink of extinction: the comparatively friendly Onges, of whom just 98 remain; the Andamanese (reduced by "diseases from the outside world" to 36 souls); a couple of hundred Jawaras (it seems that no one can get close enough to count them); and the hostile inhabitants of North Sentinel Island who will, with bad grace, accept gifts dropped overboard in watertight containers. The closest we got to a genuine "tribal" was to stand in front of a grainy photograph in the half-light of the museum. Sensitivity about the tribals helps to explain why visitors are allowed access only to a handful of islands. Indeed our guidebook informed us that there was only one place outside the capital, Port Blair, where foreigners were allowed to make an overnight stay: Havelock Island.

Havelock is four hours' sailing from Port Blair. We steamed along a rich, green coastline spattered with silver sand. There was not a soul to be seen until we reached the little settlement that clustered round the port. Our motley band of tourists emerged and boarded a decrepit bus, which trundled down a narrow lane to the new government guest house, Yatri Niwas. It was one of the most peaceful places we have ever found: simple beach cabins looking out through palm trees across a bay of filmic azure. We didn't mind when we failed to reach the finest snorkelling beach on Havelock, Radha Nagar because the coach broke down. For the same reason, our return to the port was on the back of a filthy lorry. But it did not matter. This was something rare: a place which still seemed pleasantly surprised to meet a visitor - with an open smile, rather than an open palm. My guess is that the remains of this century constitute the perfect time to go to the Andaman and Nicobar Islands, while there is still a real sense of discovery and while people are keen to help, without feeling the desire to milk tourists for every last penny they can get. You can investigate empty island roads by moped, or seek out deserted corners of coastline. You can hunt out the spices which once made the islands prosperous, or watch birds, such as the white-bellied sea eagle, drifting across the sky. It may not be always be comfortable, it's pretty much guaranteed not to be convenient, but it certainly will not be dull.

Nick Clarke