"Alif'. Lam. Mîm." are each like the rap of a knocker; they rouse the listener, alerting him through their singularity that they are the harbingers of something strange and remarkable. This topic also contains a number of subtleties.
Firstly: The disjointing of the letters and their being spelled out by name indicates that what they signify is of the same kind as themselves.
Secondly: These letters being disjointed indicates that what they signify is assumedly one and not compound.
Thirdly: The spelling out of the letters by disjoining them is an indication that it is alluding to the material of the art, as though providing pen and paper for those wanting to dispute them by writing. It is as if the Qur'an is saying: "Hey you obstinate rivals, you're the masters of fine speech! You have at your disposal the materials I had when I devised these. You do likewise if you can!"
Fourthly: Being devoid of meaning, the disjointing of the letters indicates that [the Qur'an's] opponents have been left without proof. For they say: "We don't know the facts, stories, and ordinances that we might dispute you." So it appears the Qur'an is saying: "I only want you to produce [something similar to] the eloquent ordering (nazm al-balâgha) [of the letters], even if it's made up."
Fifthly: Calling the letters by their names is the custom of scholars and writers. But both the one uttering this speech and those listening to him were unlettered. Considering its character, therefore, the letters being in this unexpected form infers that "this speech is not his but was imparted to him."
Sixthly: Spelling out letters syllable by syllable is particular to learners of reading and writing. It is understood from this then that the Qur'an was establishing a new way and was teaching illiterate people.
Those who cannot see the elevated art in the interweaving of these lines - though admittedly some are very fine - are novices to the art of eloquence, so should apply to its adepts!