In his biography of Edward Lear, the landscape painter and author of nonsense verse, Vivien Noakes points out that when he began writing his famous works sometime around 1860,
there was no such thing as an established literary genre of nonsense. To him the word meant something happy and inconsequential like the limericks [written a decade and a half earlier], but he and Carroll both altered that meaning. Even now it is difficult to define succincthy, and any definition needs qualifying clauses: perhaps it could be said that incongruity of characters, situations, or words, plus a predictable, stable element such as numbers, choruses, alliteration or, paradoxically, an insistence on the correct use of words, equals nonsense. Without this unifying element it tends towards dream: with it, it is more logical, and nonsense is a game played by a rational, methodical mind. Carroll was a professional mathematician, and though Lear wasn't trained in logic his mind was "concrete and fastidious." 
In working towards a definition, Noakes further explains that "Nonsense is a universe of words" (224) and we may add that it is a universe of words that only occasionally hold tight to what we think of as accepted reality. Sound plays a great part in nonsense, since the relations of sounds to one another counts far more than rtheir relation to something they denote. Sound dominates. Lear, notorious for bad puns, "was unusually aware of the sounds words make and he would analyse them phonetically." In fact,
With his strong musical sense he would mull over the words and phrases he heard, so that Dighi Doghi Da reappears twenty years later as the Yonghy-Bonghy-Bo, and Mr & Mrs Discobbolos are named after the Grecian sculpture a cast of which still stands in the Royal Academy Schools. He would use words incongruously as in "The Cummerbund," and he liked rounded words like promiscuous and pusillanimous which he used out of their place as meaningless, musical adjectives. And of course he invented words, like runcible, because he liked the sound they made. 
In addition to (1) a combination of incongrous and stable elements, (2) words floating somewhat free of their usual acceptations, and (3) an emphasis upon sound, Naokes sees detatchment as another key element. According to him, nonsense writing permits neither readers nor writers to become emotionally involved with the characters, and "once this detachment has been established it is quite acceptable and not at all distressing to find a man being baked in an oven or coiled up like a length of elastic" (224).
Noakes's discussion of nonsense suggests, however, that this detatchment can vary widely, for "nonsense characters can have alarming physical defects," which an author like Lear can make self-referential: "Lear returns often to the feature of himself that most bothered him — the size of his nose. There are people with noses which reach to the ground, noses which finish in tassels, noses like trumpets and noses which simply disappear out of sight, and the Dong gathered the bark of the Twangum tree and 'he wove him a wondrous nose'" (224).
I should also point out that the two key kinds of detatchment found in nonsense — emotional detachment and detachment from meaning — can derive from historical amnesia, since once the original referents of satire become forgotten by all except a few specialists, something orginally intended as pointed criticism floats free from history and meaning. Take nursery rhymes, for example, one of which goes something like this: "King William had ten thousand men. He marched them up to the top of the hill, and he marched them down again." Originally, this was a pointed politicism criticism of royal indecision and ineptitude. In a book of hursery rhymes it has floated free of its original historical connections, and all that remains are echoing sounds and apparently silly actions — but they are silly and nonsensical in a way different than originally intended and understood.
Noakes, Vivien. Edward Lear, The Life of a Wanderer. Boston: Houghton-Mifflin, 1968.
Last modified 2 July 2007