Robert Chalmers doesn't like... Mensa

Why is it only the brain? Why is nobody swanking around in public celebrating the impressive qualities of their other organs? Where is the Really Huge Penis Society (to quote the late Kurt Vonnegut: "you never know who's going to get one.") Why no Federation of Perfect Skin? Or Royal Association of 20/20 Vision? You may remember how Roderick Spode, PG Wodehouse's caricature of English fascist Oswald Mosley, developed a curiously plausible obsession with the perfectly formed knee.

There's something very peculiar about vaunting your own IQ. If you're a genius, people tend to notice, not least because you are potentially useful to them. But Mensa attracts individuals, men predominantly, who feel their talents have gone cruelly unrecognised by orthodox establishments: people like co-founder Roland Berrill, who failed the Oxford entrance exam but stayed in the city anyhow. That stratospheric IQ score compensates for a lifetime of crushed aspirations. The Mensa Test: it's the great unwritten episode of Hancock.

Last week, there were a number of articles concerning Saffron Pledger of Southend, a three-year-old inducted into Mensa, which celebrates its 65th birthday in October. BBC Radio Five Live conducted an interview with her mother, because Saffron was talking to another network on the other line. That sounded unlikely to me, but when I turned the volume up I could just make out a precocious voice discussing coded references to Engel's law of dialectics in Gore Vidal's novel, Duluth. How did they judge her? One picture question showed a football and an ice cream and asked: "Which is cold?" I could have a stab at that. Without seeking to question Saffron's extraordinary ability, the history of measuring IQ is hardly without its controversies. At least one expert – Cyril Burt, first president of Mensa – has been shown to have fabricated some of his data.

Saffron's fellow-members include the doyen of green yet stylish motoring, Clive Sinclair; Jimmy Savile, and former hardcore porn-star Asia Carrera. Another is Derek Keith Barbosa, alias rapper Chino XL, who sang "Murder Dem Murderers". ("Hey. Uhh. Uhh. Uhh. Who next of kin/When I bust this iron across yo' chin, nigga?")

It's easy to imagine how the idea of identifying superior intelligence could have interested historical figures; guys like – oh, I don't know – Hitler. Ex-Mensa president Victor Serebriakoff mooted a scheme to establish a sperm bank of "guaranteed material" from donors with two living parents, neither of whom had ever claimed welfare.

Does Mensa make you happy? My own first contact with the organisation was at Telford coroner's court in 1997, following the death of former chairman Howard Gale. Suffering from depression, following accusations of profiteering from fellow-members, Gale left a suicide note, then drove his Mazda 626 into a railway arch at speed, wearing no seatbelt. (Verdict: accidental death.)

The perceived political complexion of Mensa at that time – though certainly not fascist – could fairly be described as right-leaning. Its then magazine editor was Simon Clark, formerly the hub of Lord Chalfont's Media Monitoring Unit. In the dying days of the Thatcher regime, Clark sat in a flat in West London, writing reports on programmes like Panorama which, unsurprisingly, he concluded had a left-wing bias. Simon Clark, a non-smoker, is now director of Forest, which defends the interests of the tobacco lobby.

Clark is long gone, and under current magazine editor Brian Page and chairman Chris Tyler, British Mensa is apparently a far less fractious place. But it's when you see Mensa members relaxing en masse that things get really alarming. I once attended their annual ball. My companion was a young woman who, having whispered a series of mean asides along the lines of "at least this is one place we know we won't meet any Arsenal supporters," scribbled an equation on the back of an envelope.

"What's that?" I asked her. "That 'x'," she told me, "represents IQ. And the 'y' stands for an ability to dance. That symbol in the middle, between the two letters, means 'is inversely proportionate to' ." She had a point. I've never seen such a grotesque menagerie on a dance floor, and I write as someone once forced to attend a Conservative party conference disco where one of the dancers was Ann Widdecombe.

Where – I ask this because I know Mensa people enjoy difficult questions – do they get this impulse to congregate? If there's one thing that unites members, it's their individualism. These are people who often feel unblessed in certain areas of life: I'm thinking of things like personality, inspiration and creativity . Is there any unique purpose a gathering of this dysfunctional organisation could claim to fulfil? One, perhaps. A Mensa party, in these comparatively egalitarian times, is the last remaining placewhere everybody loves a smart-arse.