You can buy a pair of designer jeans in Emperor Diocletian's third-century retirement palace, at Split on the Croatian coast. This is where crumbling Roman walls house sleek boutiques and bars, and hundreds of people call a former imperial villa home. The Adriatic port city is a surreal meld of the ancient, the modern and all points between, making it a perfect metaphor for the cruise that brought me here.
A luxury voyage around this part of Europe is like a virtual theme-park ride through 20 centuries of culture. Each day delivers you to a different point in time for a spellbinding meander through its lifestyle, art and architecture. Then it's back to the ship for some very 21st-century pampering while you are transported, through the night, to the next era on the itinerary. It's like a journey in Doctor Who's Tardis: time travel made easy.
The odyssey begins in Rome, where I spend a couple of days hurtling between classical antiquity and the Renaissance before taking the hour-long train ride to the port of Civitavecchia to join the Celebrity Silhouette. The size of the crew alone is almost twice the population of the Vatican – 1,500 to look after 2,886 passengers at full complement, which is a ratio that spoils you rotten.
What I enjoy most about a big ship of this quality is the sheer variety of places to eat, drink, join in, or do nothing. Go to a party or curl up in a quiet corner; there are plenty of places to do both. It is blissful to be able to eat out in a different restaurant almost every night, take in a high-calibre show, and go on for a nightcap or to a nightclub without worrying about transport home.
First stop on the switchback ride through the centuries is Naples; alight here for first-century Pompeii, where Mount Vesuvius stopped the clock in AD79 and gave us a unique window on everyday Roman life. There is so much preserved here it is easy to conjure up the doomed inhabitants, and when the heavens open, sending torrents of water crashing through the streets, my question about the giant stepping stones placed across every road is answered vividly by the gods.
Thoughts of tunics and togas are soon elbowed aside by Silhouette's hi-tech restaurant QSine, where I use an iPad to order an ultra-modern meal of sushi lollipops and flashing LED shrimp cocktail. These cultural contrasts are dizzying.
The ship moves on via Sicily to Malta where I pass up a detour into prehistory (a visit to the Neolithic temples at Tarxien) to spend the day in Valletta, exploring the 16th- to 19th-century era of the Knights of St John and the besieged island's heroic stand during the Second World War. The capital's cathedral, a Baroque marvel decorated by the knights to rival the great churches of Rome, houses the largest Caravaggio in the world, a not-to-be-missed, dark and disturbing 19sq m of The Beheading of St John the Baptist.
Get your breath back at the nearby Caffe Cordina, a Maltese institution since 1837, where you sample homemade pastries inside under the ornate vaulted ceiling or outside under the gaze of Queen Victoria's statue and the pigeons perched on her stone head.
With only one sea day on this packed itinerary, the opportunities to dive deep into another country's history come thick and fast, but every port offers an alternative to full-on sightseeing. At Corfu and Bari I opt instead for a gentle paddle in present-day culture, strolling through the backstreets and finding cafés where the locals go for their ouzo or Campari soda.
But at breathtakingly beautiful Dubrovnik, Croatia, it is back to total immersion in the multilayered history of the place. Get on to the eighth-century walls encircling this medieval city as early as you can before the crowds or the heat diminish the experience. From the highest landward bastion, a terracotta sea of roof tiles ripples beneath you in the foreground with the brilliant blue of the Adriatic sparkling beyond. Later, it is shocking to see those same views rent by war in an exhibition of photographs taken just 20 years ago during the Serbian siege of Dubrovnik after the break-up of Yugoslavia.
Early next morning we sail into the fjord of Kotor Bay, Montenegro, the only point on the voyage where the giant ship is dwarfed by the stunning natural scenery. This medieval town, its narrow, crooked streets strung with laundry and dodgy-looking wiring, is also protected by ancient fortifications, but here they snake for miles up the mountainside and some stretches are in a ruinous state of repair. The first stage is relatively easy going, though, and the view is well worth it.
Day 10 brings us to Split where, after roaming the city-in-a-Roman-palace, I wander off the tourist trail and stumble on modern-day Split at play. Packed Bacvice Beach looks like a poster for a 1970s European holiday resort, with local families enjoying picnics on the sand and ball games in the shallows – and rather too many men in unfeasibly tiny swimming trunks.
Back in Italy the next day, Ravenna's fifth- and sixth-century mosaics are simply dazzling. It is claimed that Cole Porter, who honeymooned here, was inspired to write "Night and Day" by the gorgeous blue and gold-starred cupola of the Mausoleum of Galla Placidia. For the "no mo' duomo" crowd – a phrase coined by one group of American cruisers after a particularly church-heavy sightseeing day – Ravenna is also the gateway to the spanking new Enzo Ferrari museum at Modena.
There is one last dash across the Adriatic to call in at Koper, Slovenia, before final docking in Venice for another cultural banquet, dominated by the Byzantine basilica of St Mark's and the glorious Gothic Doge's Palace. Before leaving home I had paid the princely sum of €1 online to secure timed entry to St Mark's and jump the queue. What a good decision that was.
Fitting this much time travel into less than a fortnight would be exhausting, if not impossible, with any other mode of transport, but on a cruise ship such as the Celebrity Silhouette it is exhilarating. Perhaps Doctor Who should reconsider his undeniably spacious but horribly spartan police box.
Celebrity Cruises (0845 456 0523; celebritycruises.co.uk) offers a 13-night Adriatic fly/cruise on Celebrity Silhouette, departing 26 June, from £1,508 per person, based on two sharing an inside stateroom. The price includes flights from Gatwick to Venice and return from Rome, plus transfers and meals.