His second wife, Jeanne, described him as the least curious man she had ever known; he never read a paper, and boasted that he never had, nor ever would read a book. She attributed the break-up of their marriage to the fact that he was never at home - not because of work or women, but because he was forever playing golf. There were no family holidays, no big events in his life. In the 1980s, he dropped out of a Rat Pack reunion tour because he couldn't stand the late nights. All his life, it seemed, he just muddled on, armoured by indifference and passivity; and in his seventies, when the routine had finally palled, he just stopped.
This passive quality afflicts his singing. One marvellous moment in Elaine Donnelly's film had Dorman Panebianco, a barber in Martin's hometown of Steubenville, Ohio, analysing his vocal style: "He had romance in his voice and that's what made him... He brought the moon, he brought the stars, and he made a string of pearls for the girls and he sang them beautiful songs and they closed their eyes and dreamed. And that's the way it was." (It seems incredible that Mr Panebianco has been stuck in a barbershop all his life.) But if he did have sex appeal in his early days, it wore off; mostly, he had a baritone too smooth, too unruffled to catch the attention.
But the singing was just one element in a marvellously composed stage persona - the tipsy, self-deprecating lounge Lothario. In fact, the tipsiness was an act - he never drank on stage (the glass he always held was filled with apple juice). He was a terrific actor and comedian: extracts from his own television series demonstrated a gift for ad-libbing ("Don't bite your nails, look what happened to Venus de Milo") and uncanny timing. At one point, taking the mickey out of a Sinatra record, he inserted his jibes with a swing and precision that Sinatra himself would have envied.
For some reason, the programme felt the need to go into the question of who was more talented - Lewis or Martin. If anybody thought there was any argument, the footage of Lewis crossing his eyes and making goofy noises should have put paid to it. There were also some gaps in the chronology, and once or twice the commentary showed an annoying urge to make Martin mean something. He did nothing and he meant nothing; he just did it with style and humour.
These were qualities last night's Equinox (C4) was short of, from the weakly punning title ("Storm in a D-Cup") onwards. The subject of the programme was silicone breast implants. In recent years, there have been numerous scare stories about the health risks associated with them, but more recent studies suggest that not only are they not harmful, they may even provide some protection against cancer (though the reasons for this seem to be imperfectly understood).
The evidence that implants are harmful ranged from the anecdotal to the downright kookie - the actress Sally Kirkland explained how her implants had caused agony in her left arm: but "I would put this little doggie [indicating a small spaniel-type mutt] on my arm and he was so filled with love that I would gradually feel life-force energy coming back". The evidence in favour of implants was far more impressive, supported by a battery of experimental statistics. This is important, because on the basis of the anti-implant lobby's horror stories, some women have done themselves terrible damage having their implants removed.
Still, that hardly appeared to excuse the programme's gung-ho, pro-big ones approach, emphasising how good it can be for a woman's psychological well-being to have the operation. The lesson seemed to be: if you have implants, let them be; if you don't, learn to be happy some other way.