Jérôme Bel, Cédric Andrieux, Royal Opera House Linbury Studio

Dance is eating itself. Or dancers are eating themselves, rather. It's on-trend to defy the idea of the mute dancer, and instead have them verbally explaining themselves, their motivation, their art. This year’s Dance Umbrella launched last night with the “self-contemplation” of Cédric Andrieux, a handsome blond Frenchman, who regales us in a charming murmur for 80 minutes with the story of his career, with danced illustrations.

I have nothing against a chap expressing himself to me, especially when he has as gentle and self-deprecating a delivery as Andrieux, but I'm largely with Ray McCooney in Little Britain here: "Let me tell you through the medium of dance." Anyway, Andrieux (now 34) recounts deadpan how as a child he was fired by seeing the title credits for Fame on TV, and how when he was to be accepted into the Paris National Conservatoire of Dance, it was the French version of Fame.

That may be as side-splitting as it gets for the general watcher. If you know who Trisha Brown, Maguy Marin, Angelin Preljocaj, Merce Cunningham and Dominique Bagouet are, you’re in for a banquet of dropped names. The Cunningham connection in particular is germane, as Andrieux spent eight years in the celebrated New York company, and his faintly satirical demonstration of a typical daily class (metronomically clicking tongues the only sound) sheds more light on the late, great choreographer’s remote personality than usually emerged in interviews. No corrections afterwards from the master, no comments - "totally depressing". (Andrieux contemplates his unitard, pictured below © PICA Portland Festival 2010/Wayne Bund.)

He also demonstrates the cruelly laborious choreographic process of the computer methods used by Cunningham - the legs doing a chain of very difficult disconnected things, the torso adding almost sadistic counter-intuition, the arms then rigidly applied in dogmatic shapes. None of it logical to the body, none of it flowing, all of it hard, emotionless graft. "I often had this feeling of humiliation," Andrieux murmurs.

Then he performs a section of BIPED, one of Cunningham’s most haunting pieces, but in which he is just one small moving part in the construction kit. Even a short stretch has him panting too hard to speak for a while, and you wonder what possible reward he derived from his years of dully exacting class and incomprehensible dance orders. What he doesn’t talk about is how all that Meccano with its wonky angles turned magically on stage into purest, most delicate, most suggestive dance filigree, as incomprehensible as spring water, because what wasn’t in the computer was Cunningham’s incorrigible showmanship.

That is the key dimension missing here, the insight that doesn’t come. The dancer's self-contemplation is just about disarming enough to avoid being conceited, but it cuts out where it ought to become interesting: how it is that the dancer may sense that the choreography he is doing, even if he doesn’t understand it, has a mighty integrity and super-dimension of its own, offered as a privilege to the audience. What is it like to be a vessel? Can you tell the difference between carrying holy water and bog-standard not-drinking water, choreographically speaking?

I’m not sure whether one can blame Andrieux for this or the evening's conceiver/creator Jérôme Bel (another name to drop in the elite cloisters of European dance), who's made a name for himself by creating solos of self-contemplation for other dancers, including one at the Paris Opera Ballet. So perhaps it's Bel who doesn't want Andrieux to spill the secrets.

Still, when Cunningham’s company performs its last ever British performances this week at the Barbican, Andrieux will have at least provided an elementary primer, and some wicked thoughts about how bored even the most devoted dancers might be as they chop and mutate their bodies into those strangely delicious shapes.

• The Merce Cunningham Dance Company's farewell London visit, with three programmes, is at the Barbican Centre, London 5-8 October. BIPED will be performed on the Saturday, 8 October programme

Watch the opening section of Jérôme Bel's "self-contemplation" film of Paris Opera Ballet dancer Véronique Doisneau