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ON the "golden afternoon" of 4 July 1862, the Reverend Charles Dodgson, his friend Robinson Duckworth and the three young daughters of the Dean of Christ Church college in Oxford went on the boating trip up the Thames towards Godstow during which the main part of Alice's Adventures in Wonderland was composed, extempore, by Dodgson. It surprised Duckworth so much that he turned round and asked the provenance of the story. "I'm inventing it as we go along," came the reply. The children were delighted, especially ten-year-old Alice Liddell, who had been cast as the heroine, and it was at her insistence that Dodgson wrote out the tale. Two years later, the story was published under the pseudonym Dodgson used for his comic verse contributions to magazines, "Lewis Carroll".

The day and the outing were of undoubted significance and are recounted with forensic exactitude in both new biographies of Lewis Carroll, one by Michael Bakewell, the broadcaster and former television drama executive, the other by Donald Thomas of the University of Wales, a prolific novelist and biographer. But if it was the most significant day in Dodgson's life, it was probably also the least characteristic. The spontaneous composition of "Alice's Adventures" was possible because it was demanded by a girl he idolised (and later possibly wanted to marry); he was otherwise oddly without motivation to write any of his stories down.

Dodgson's genius for entertaining children with puzzles, conundrums and stories had been evident from his youth, when, as the eldest of 11 clever children, he organised games and home-produced magazines. The essence of his entertainments, from the simple magic tricks he would perform for strangers in railway carriages to the extraordinary anarchic energy of Alice in Wonderland and Through the Looking Glass, is their unpredictability, and his gratification came from eliciting a satisfactory response from a specific child. This held true even when he had become one of the most famous authors of his day. He had virtually no patience with his public persona, consigning to the bin unread any post that was addressed to "Lewis Carroll", and yet was delighted to hear of the books giving pleasure to individuals. His interest in publication was primarily a social one, a way of making hordes of the "child friends" whom he admitted were "three- fourths" of his life.

Those three-fourths were hardly visible to casual acquaintance, who saw only Dodgson the fastidious, shy and stammering mathematician whose whole adult life was spent at an Oxford college at a period when celibacy was still a condition of holding a fellowship. The protective life of the college suited his temperament admirably, and the events of his 47 years there are limited to internal controversies of astonishing triviality, such as the question of whether or not to buy any more green Chartreuse for the Senior Common Room. Even his pleasures, such as theatre-going, were restrained, and his taste in plays almost perversely undemanding for a highly intelligent man. He knew many of the most famous artists and writers of the day, but failed to form any close friendship with them, his detachment embodied in his preoccupation with taking photographs of "lions" more in the spirit of a collector or voyeur than as a possible peer. "The Reverend C L Dodgson had no life," Virginia Woolf wrote, clearly puzzled by the apparent incongruity of such a man fathering the unfettered fantasy of Wonderland.

The incongruity seems less jarring if one takes Dodgson's restraint as a deliberate strategy for self-control, as both his latest biographers do. Dodgson had a keen, not to say morbid, sense of sin and hinted darkly in his early diaries at his own persistent lapses. Michael Bakewell's suggestion that Dodgson felt unworthy to take full Holy Orders would square with what otherwise might seem an odd lack of ambition in a committed and pious clergyman. "There is but one step from prudishness to pruriency," he said late in his life, and clearly felt the only safe option was to be a prude, whom even one of his best child friends recollected as being "old-maidishly prim". The astonishing mental vigour that whips through the Alice books was, however, not suppressible, only convertible. Donald Thomas makes the convincing argument that Dodgson's fiendishly difficult "Pillow Problems" for insomniacs arose from his own relentless efforts to block unwholesome thoughts with complex ones. Why else should he have lain awake trying to divide 876815922485703152764092 by 9993?

The increasing pleasure Dodgson took in the company of little girls - which had already attracted enough notoriety to warrant 70 pages in the first biography, published in the 1890s - was probably part of the same process of sublimation. The question of how to assess, or even describe, Dodgson's obsession without overlaying it with contemporary sexual sensibilities is about as knotty a problem as any contemporary biographer could face. Bakewell's conviction that the "key" lies in Dodgson's happy childhood lording it over his sisters seems crudely reductivist, whereas Thomas's approach is at once more forthright and analytical, and avoids any implied moral judgements. Dodgson's "oddity" would of course not be tolerated today, and the virtual certainty that he never did anything improper with his "little nudities" as they cavorted round his rooms in Christ Church in "Eve's original dress" does little to mitigate the shock of distaste which many modern viewers will get from the photographs he took of them.

Donald Thomas helps to elucidate the change in sensitivities between Dodgson's age and our own in a wide-ranging section on child prostitution, Krafft-Ebing's definition of sexual psychopathology and the sudden and drastic raising of the age of consent in 1885 from 13 to 16, but there is still much left to be accounted for in Dodgson's psychology. Many of the mothers of his "girl-friends" were wary of him and incurred his wrath by wanting to chaperone their daughters, and Christina Rossetti expressed her disquiet at the nude drawings of children by Dodgson's co-enthusiast Gertrude Thomson: "I do not think to call a figure a 'fairy' settles the right and wrong of such matters." Even Dodgson himself acknowledged that his behaviour was at variance with bourgeois ideas of propriety, referring frequently in his letters and diaries to what the mythical "Mrs Grundy" would say, and taking pleasure in open defiance of her when he felt himself, significantly, too old to rouse anyone's suspicions.

Dodgson's curious sexuality now seems in danger of eclipsing his achievement as the author of one of the most extraordinary books for children ever written, if only for the reason that it invites the very sort of analytical attention which Alice in Wonderland defies and renders absurd. Both Bakewell and Thomas begin to trip over superlatives when they come to discuss the book, but unsurprisingly don't stress the fact that it was virtually a one-off inspiration which Dodgson reprised and diluted throughout his life, from its somewhat inferior sequel, Through the Looking Glass, to the stage and musical versions that appeared decades later, and the surprisingly mawkish "Nursery Alice". Dodgson was still chewing on its success in the 1890s, arranging for publication of the original manuscript containing his own illustrations, which he had to ask to borrow from Alice, now the mature and intimidating "Dear Mrs Hargreaves".

Dodgson was the author of some 200 pamphlets on mathematics, logic and brain teasers, but with the exception of "The Hunting of the Snark", the only other work he wrote as "Lewis Carroll" was the tortuous fairy-story, Sylvie and Bruno, about as unlike the Alice books as possible. Neither of his latest biographers feel confident enough to omit the pseudonym in favour of Dodgson's real name in the titles of their books, but both enforce the impression that "Lewis Carroll" was effectively over even before the boat got back to Folly Bridge.

'Lewis Carroll: A Biography' by Michael Bakewell, William Heinemann pounds 20

'Lewis Carroll: A Portrait with Background' by Donald Thomas, John Murray pounds 25