Ḥamiduddīn Farāhī (d. 1930 AD) elaborated an intriguing solution which might hold the key, at least to the significance of the Muqaṭṭa’āt. We shall briefly delineate his theory here.
Any cursory investigation into the origins of the Arabic abjad would reveal that it has much in common with the Hebrew abjad, which itself has roots in the Syriac and Aramaic abjads. Farāhī is of the opinion that the letters of this parent abjad did not just represent phonetic sounds, but also symbolised the shape of certain concrete objects from which the script was ultimately elaborated. He goes on to assert that this acrophonic origin of the letters was influenced by the Phoenicians who had borrowed the concept for the elaboration of their own abjad from the early Egyptians whose hieroglyphic system was primarily based around pictograms.
The science which deciphered the meanings of these letters is now extinct. However, there are some letters whose meanings have persisted to this day, and the way they are written somewhat resembles their ancient forms. For example, it is known about the Arabic letter Alif that it was first used to mean a cow and represented a cow’s head; the letter Bayt in Hebrew means ‘house’; the Hebrew letter Gimel meant camel; Ṭa stood for a snake and its shape resembles that of a serpent; and Mīm represents a water wave and has a similar form.
Farāhi presents Sūrat al-Qalam (also known as ‘Sūrat Nūn’) in support of his theory. The letter Nūn still denotes a fish. In this Sūrah, the Prophet Jonah has been addressed as Ṣāḥib al-Hūt or he who has been swallowed by a whale. Farāhī opines that it is because of this reference that the Sūrah is often referred to by the letter Nūn, which appears disconnected at the beginning of the first verse. He goes on to theorise that if one considers the example given above, it is quite likely that the Muqaṭṭa’āt by which other chapters commence are placed so as to symbolise a relation between the topics of a particular sūrah and their own ancient connotations.
Some other names of the Qur’ānic chapters reinforce Farāhi’s theory. Sūrat Ṭa-Ha, for example, begins with the letter Ṭa, which represents a serpent. After a brief introduction, the tale of Moses and his staff, which is transformed into a snake, is depicted. Chapters 26, 27 and 28, which are also prefixed by Muqaṭṭa’āt containing the letter Ṭa, portray this aforementioned miraculous episode.
Sūrat al-Baqarah, which begins with the letter Alif, is another example that further buttresses Farāhī’s claims. It has been indicated before that the letter Alif was analogous with the cow and represented a cow’s head. Sūrat al-Baqarah contains an anecdote about a cow and its sacrifice.
More research is needed to substantiate this theory across the other chapters prefixed by Muqaṭṭa’āt, and to elaborate the original pictographic meanings of the other letters employed. Nevertheless, given what we know about the origins of early orthography, such an explanation would not be beyond the realms of possibility.
 Islahi, Amin Aḥsan. 2004. Taddabur-i-Quran. Karachi: Faraan Foundation. pp.82-85