In George Bernard Shaw’s play Pygmalion, and in the musical version My Fair Lady, Professor Higgins tries to turn a flower-girl into a duchess by improving her accent – a provocative attempt at social engineering. More worrying is the idea of actual human genetic engineering. A famous dancer called Isadora Duncan approached Bernard Shaw and suggested they should have a child together, so that it might have her stunning looks and his amazing brains. ‘Ah, Madam’, he replied, ‘but supposing it should have my looks and your brains?’

Is it possible to breed children with particular desirable characteristics? Certainly many traits run in families; my brother and I are both tall, like our dad, and we are both writers, as he was. On the other hand I don’t think I inherited  my love of science, a subject that interested neither of my parents nor any of their parents; so it must have come from the environment; specifically, I suspect, from a teacher.

Adolf Hitler, who was small and dark, dreamed of creating a master race of tall blond Aryans who would take over the world. He actually attempted to create such a tribe by herding together suitable young men and women, and ordering them to have babies.

In his 1869 book Hereditary Genius, Francis Galton wrote that just as it is easy by careful selective breeding to produce horses that run fast, ‘so it would be quite practicable to produce a highly-gifted race of men by judicious marriages during several consecutive generations.’ In a way Galton himself was living proof that intelligence can be inherited, for he was a brilliant scientist, like his cousin, the famous Charles Darwin. Their grandfather Erasmus Darwin was a skilled doctor, an ingenious inventor, a fine poet, a founder member of the Lunar Society of Birmingham, and a friend and mentor of James Watt.

The latest attempt at breeding intelligence comes from California, where 20 years ago millionaire Robert Graham set up a genius sperm bank. For donors to the bank he allowed only the super-smart, such as Nobel-prize winners, and his goal was to produce tomorrow’s leaders. About 230 children were born to these donors, and are now in their teens and twenties. In Genius Sperm Bank (Discovery, Monday, 10.30) we meet some of them and their families, and find out whether Graham’s dream has succeeded, or whether it is merely another dodgy and doomed attempt at genetic engineering.