I'm just sitting down with Helga Schmidt when the news breaks that Santiago Calatrava is in the building. The arrival of the great architect generates excitement and apprehension in equal measure. "There are things he is still not happy with," says Mrs Schmidt, the intendant of Calatrava's extraordinary Palau de les Arts Reina Sofía in Valencia.
It's an iconic structure if ever there was one, a great white-beaked spacecraft covered in trencadis (small broken tiles) that seemingly floats on top of a shallow lake. Inside this monumental building, Calatrava has built a concert hall, an opera house, several recital rooms and now an underground theatre. The Teatro Martí*i Soler wasn't in the original plan, but Calatrava decided that the building deserved an extra auditorium for small-scale works – so he went ahead and designed one. "This is my present to you," he told Mrs Schmidt. Now the golden boy has more plans.
Calatrava is one of those architects you don't say no to, especially given that he is Valencia's local boy made good. Born near Valencia 56 years ago, Calatrava made his name with sweeping sculptural buildings such as the gorgeous Auditorio in Tenerife, the 54-storey "Turning Torso" tower in Malmö and the Milwaukee Art Museum. He is currently designing a new transportation hub at Ground Zero in New York City. Likened by some to a bird being released from a pair of hands, it is one of the few buildings on the World Trade Center site liked by everyone.
In Valencia, however, Calatrava has a whole new city to play with. In the Sixties, having grown fed up by frequent flooding, the Generalitat Valenciana diverted the River Turia south to the sea, leaving the old medieval city centre encircled by a large dry river bed. Various ad hoc attempts were made to do something with this empty space; parks, statuary, a football pitch and a stylish sea-life museum called Parque Oceanográfico by Felix Candela were constructed. Then, in 1996, Calatrava was brought in to design a communications tower and the project grew into a grand enterprise called Ciutat de les Arts i les Ciències (City of Arts and Sciences). It's a whole new Valencia.
So far there are four buildings, with work underway on a fifth. On first sighting, these radical white structures give the impression that the 22nd Century has arrived early in Spain. El Palau de les Arts Reina Sofía dominates the complex. Inside here, Mrs Schmidt runs a programme of concerts and operas featuring talents such as Zubin Mehta, Daniel Barenboim and Lorin Maazel. Calatrava's work attracts top names.
It's obvious why everyone defers to him. The Palau has been likened to a supermodel in that it has no bad angles. It is a 17-storey sculpture designed by a master artist, inside which other artists go about their business. The structure is topped by a great 750ft plume and is linked to the rest of Valencia by a Valhalla of a bridge. The vast creation is wholly symmetrical, which appealed to Calatrava, though people say it can be disorientating. Sometimes it's hard to know which side of the building you're in.
To the south of the shallow azure lake below the Palau, Calatrava built El Museu de les Ciències Príncipe Felipe, an interactive science museum with all its supporting ribs on the outside. El Hemisfèrico is in the middle of the lake, seemingly submerging like a submarine, but designed to resemble a great eye peering out of the water. It contains an Imax Cinema, a planetarium and laserium.
Perhaps the most remarkable structure in this part of the complex is El Umbracle, which resembles a long white conservatory with its panes empty of glass. Inside this metal canopy, palm trees line a walkway. The structure is actually sited atop an underground car park and is quite unnecessary, but you don't expect Calatrava to be utilitarian. For example, running along one side of the science museum there is a broad gantry 40ft in the air that is served by two grand staircases 30 feet wide, one at each end. It has no practical purpose unless you want to walk up at one end and come down the other. No one uses it, but it looks fantastic.
The project is far from finished. There really ought to be a restaurant, several in fact, from which you can sit and marvel at all that has come to pass. Worse, transport around the mini-city is currently by one of those twee trains on pneumatic tyres, when this complex absolutely cries out for Calatrava's take on the monorail.
At the moment, Calatrava is building a 6,000-seat open-air auditorium called Agora on the other side of this road bridge, and has begun his own pedestrian bridge to span it (Calatrava's bridges are always something to behold). When Agora is finished, Calatravaland will link up with Parque Oceanográfico to create a futuristic complex longer, if not yet wider, than the old walled city of Valencia that stands to its north. He is also intending to build two blocks of apartments. Knowing Calatrava, he will design every aspect of them and go wonderfully overbudget. Consider the doors at the Palau: not many architects would go to the length of sculpting blue ceramic torsos as door handles.
His splendid new bridge over the Grand Canal in Venice has trebled in price over the last 10 years and is still not finished. But costs are a mere practical consideration. The boy from Valencia is all about vision – and he has that in spades.
Meanwhile, Mrs Schmidt breaks off from discussing the Palau's summer music festival to consult on the latest changes required by her architect. One thing is certain: he hasn't come up with ways of saving her money.
As I kill time outside, I gaze down over the City of Arts and Sciences towards the sea. The complex looks good in all weathers and at any time of day, but what I really like is the way that it acts as a link from the old Valencia to the harbour area. So many of these dockland redevelopments – Cardiff, Oslo, Copenhagen – are detached from the parent city, isolated by derelict interstitial space that is neither city nor marina. The Ciutat de les Arts i les Ciències is using up this space. I reckon in another 10 years Calatrava will have brought the two areas together via a series of amazing buildings – assuming Valencia continues to come up with the money. Personally I hope it does.