• the relations between the four instances mentioned above are stages of transformative processes whereby the world is being regenerated through an exchange between a supernal reality (sometimes called ‘pleroma’) and a lower reality: ‘silence becomes sound’, ‘the invisible name becomes visible…’

Conclusion

Similar to Hermetism in a broad sense of the term, and very closely related to early
magical literature, Gnosticism is another offspring of a syncretist age, and at one time
or another its historical correspondences with Egyptian religion, early Judaism and,
especially, with Platonic metaphysics, have been, and continue to be, brought into
scholarly focus and studied in the context of early Christian theology.<fnref n="109" />

As I hope to have demonstrated in the preceding pages, a distinct shared domain of
these manifestations of Hellenistic religiosity is the cosmogonic and cosmological role
of language and numbers, and even more specifically, the alphanumeric entities which
can spell, or tell, or calculate a λόγος, which in the current context might easily be
translated as an ‘alphanumeric analogy’. Every ‘creation’ at every new level is effected
through a λόγος, that is through a mediating reality which is so close to the Creator that
it can be said to be its child, and which is so close to the Created that it can be identified
with it. This is the foundation of the doctrine of sympathy and its ‘vertical chains’,<fnref n="110" /> for
‘the name is congenital (συγγενές) with the god, the sound (φθόγγος) is consubstantial
(σύντροφος) with the deity.’<fnref n="111" /> The relation is one of *mimesis* or re-presentation or
personation. This intermediate nature is according to the ‘measures’ of the Creator,
measures that are interrelated as the letters of the alphabet are. Indeed, according to
Plotinus, the *logos* is not a separate hypostasis, but it determines the relation of every
hypostasis to its source and its products, serving as a *formative* principle from which
the lower realities evolve.<fnref n="112" />

Moreover, and now with a view to the following pages, it is clear that, from the point
of view of the στοιχεία, every creation as an utterance or an act of writing implies a
change of state and is thus a sort of cosmic alchemical operation. What we have just
seen in the Gnostic literature, where the ‘invisible name is made a visible Son,’ parallels
clearly Athanasius’ ὁ τοῦ Θεοῦ Λόγος ... ἐνηνθρώπησεν, ἵνα ἡμεῖς θεοποιηθῶμεν, ‘the

<footnote n="109">109. E. Moore and J. D. Turner, ‘Gnosticism,’ chap. 10 in *The Cambridge History of Philosophy in Late Antiquity*, ed. L. P. Gerson (Cambridge University Press, 2010), 175.</footnote>

<footnote n="110">110. See D’Alverny, *review of La Révélation d’Hermès Trismégiste. I: L’astrologie et les sciences occultes by A.-J. Festugière*, 268, ‘des « chaînes » verticales allant des planètes aux minéraux’.</footnote>

<footnote n="111">111. Crippa, ‘Les marges du langage,’ 270.</footnote>

<footnote n="112">112. Cf. Enneads, 3, 5, 9; Uždavinys, *Philosophy as a Rite of Rebirth*, 306.</footnote>
Word of God became man so that we might become divine.’<fnref n="113" />

In the following pages I shall start exploring the doctrine of alphanumeric cosmology in Islamic scripture, and then proceed to the first non-scriptural Islamic writings which happen to belong to the alchemical tradition.

<footnote n="113">113. *De incarnatione verbi*, 54, 3; PG, 192B.</footnote>
# Alphanumeric Cosmology in Islamic Scripture and Exegesis

## Introduction

The place of the *logos* and its elements in Islam is not only similar to what we have seen in the preceding Abrahamic revelations, but the status of language in Islam is as it were further specified and amplified in comparison. As in Judaism and Christianity, the creation of the world is enacted by divine speech, 'His command (*amr*), when He intendeth a thing, is only that He saith unto it: Be! (*kun*) and it is,'<fnref n="1" /> but in addition to this acoustic cosmogony, the imagery of the written word acquires in the Qur'ān an exalted level that in earlier traditions is only to be found in the exegetical literature, not in the scriptures themselves. 'If all the trees on earth were pens (*aqlām*) and all the seas, with seven more seas besides, were ink, still God's words (*kalimāt*) would not be exhausted.'<fnref n="2" /> When Muḥammad received his first revelation, he was asked by the archangel to read; *iqra!*, 'read!' was the first word of Islamic scripture,<fnref n="3" /> with the same root as *qur'ān*, literally 'the reading'.<fnref n="4" /> The verses of the Qur'ān are called in

<footnote n="1">1. Qur'ān 36:82. Unless noted, Qur'ānic translations are mine, following mostly Pickthall, Abdul Haleem or the *Study Quran*. Sura 36, Yā Sīn, was called by the Prophet 'the heart of the Qur'ān'.</footnote>

<footnote n="2">2. 31:27, and found also with little variation at 18:109. *Kalima* is the customary rendition of *logos* in the Arabic translations of John; cf. H. Kashouh, *The Arabic Versions of the Gospels: The Manuscripts and their Families*, Arbeiten zur Neutestamentlichen Textforschung 42 (Berlin/Boston: Walter de Gruyter, 2012), 283.</footnote>

<footnote n="3">3. Qur'ān 96:1.</footnote>

<footnote n="4">4. The basic meaning of the root *q-r-’* is ‘to gather’, ‘to collect together’ (see *Lisān*), following the same semantic development of Lat. *lego*. For a rare ‘semantic’ etymology that gives a perfect cognate of *logos* by association with the root *q-r-n*, see T. Mayer, ‘Shahrastānī’s *Mafātīḥ al-Asrār*: A Medieval Ismaili System of Hermeneutics,’ chap. 8 in *The Spirit and the Letter: Approaches to the Esoteric Interpretation of the Qur’an*, ed. A. Keeler, S. H. Rizvi, and M. Nguyen (Oxford University Press, 2016), 281. The Hebrew cognate *miqrah* is a traditional alternative name for the *Tanakh*.</footnote>
Arabic āyāt, ‘signs’, with the basic meaning of a referent, a symbol, ‘any apparent thing inseparable from a thing not equally apparent,’<fnref n="5" /> from a Semitic root found elsewhere with the meaning of ‘letters’.<fnref n="6" /> Followers of the two previous Abrahamic revelations are called in the Qur’ān ‘the people of the Book’ (*ahl al-kitāb*). It can hardly be a surprise that Muslims developed over the centuries such a great esteem of calligraphy,<fnref n="7" /> or that even to these days the recitation of the Qur’ān can enthuse Muslims of all ages around the world, and it will be hardly surprising that Islamic civilization has been described as ‘clearly logocentric’.<fnref n="8" />

Recent overtures in comparative studies of theology and mysticism have been laying bare the deep and very explicit analogies between the ontological status of Christ, *kalimatu Allāh*, the Word of God, and the Qur’ān as *kalām Allāh*, the Speech of God.<fnref n="9" /> In this regard, and following the main thread of this research, I shall once again start by focusing on the ‘letters’, the elementary alphanumeric components of that ‘Word’ and that ‘Speech’.

Based on the Qur’ānic nucleus of terms related to speech, language, reading and writing in different aspects, Abū al-Ḥasan al-Ash‘arī enunciated the mainstream theological position that ‘God’s speech is uncreated and is coeternal with His essence,’ that ‘it is neither a sensory sound (ṣawt) nor a graphical trace that is manifested in the form of a letter (ḥarf, pl. ḫurūf),’ whereas human ‘sounds and letters are created expressive traces (dalā’il) of the uncreated divine word.’<fnref n="10" /> Far from settling the matter, the theological subtleties involved gave rise to a theological topos, ‘the question of God’s speech’ (*al-mas’ala kalām Allāh*), or even more specifically ‘the question of letter and sound’ (*al-mas’ala al-ḥarf wa-al-ṣawt*). Fakhr al-Dīn al-Rāzī (d. 1209) considered the matter too ‘difficult and subtle’,<fnref n="11" /> but it was treated at length by Abū Naṣr al-Sijzī (d. 1052)<fnref n="12" /> in his *Refutation of Those who Deny [that God’s Speech Consists of] Words and Sounds*. Though mostly polemical in tone, and without entering in any detail into

<footnote n="5">5. Lane’s *Lexicon*, I, 135, s.v. ’-y.</footnote>

<footnote n="6">6. The Heb. *ot*, for instance, has two plurals: *otiyot*, with the meaning of ‘letters’, and *otot*, with the meaning of ‘signs’; cf. Klein, s.v.</footnote>

<footnote n="7">7. A. Schimmel, *Islamic Calligraphy*, Iconography of Religions, XXII, 1 (Leiden: Brill, 1970), 1–2.</footnote>

<footnote n="8">8. See W. C. Chittick, *The Sufi Path of Knowledge: Ibn al-Arabi’s Metaphysics of Imagination* (Albany, NY: Suny Press, 2010), xv.</footnote>

<footnote n="9">9. Cf. R. Shah-Kazemi, *A Muslim Perspective on the Christian Mysteries: 1. The Incarnation, 2. The Crucifixion*, Augustana Distinguished Lectures 2012 (Camrose, Alberta: Chester Ronning Centre for the Study of Religion / Public Life, 2015), 15 for detailed argumentation and references.</footnote>

<footnote n="10">10. As summarised by N. El-Bizri, ‘God: Essence and Attributes,’ in *The Cambridge Companion to Classical Islamic Theology* (Cambridge University Press, 2008), 130–31.</footnote>

<footnote n="11">11. Fakhr al-Dīn al-Rāzī, *Mafātiḥ al-ghayb*, 32 vols (Beirut: Dār Ihyā’ Turāth al-‘Arabī, n.d.), 1.45.</footnote>

<footnote n="12">12. Also known as Abū Naṣr al-Wā’ilī; see J. Brown, *The Canonization of Al-Bukhārī and Muslim: The Formation and Function of the Sunnī Hadīth Canon*, Islam History and Civilization, Studies and Texts 69 (Leiden, Boston: Brill, 2007), 196–99.</footnote>
the consideration of the alphabet, al-Sijzī argued that God’s speech necessarily implies
the discreteness of the phonetic elements, that ‘the reality of speech is the articulated
elocution (nuṭq).<fnref n="13" />

The Linguistic-Logical Aspect

The triliteral root *n-ṭ-q* is of particular interest, since it not only refers to language articulated as an uttered reality, in the sense of the phonetic points of articulation (*khawārij*), but also to the concept of logical articulation, in the Latin grammatical sense of *articulatio*,<fnref n="14" /> in close relation to measure (*modus*), and in the sense of the linguistic concept of twofold segmentation, which is very close to the central object of this entire research.<fnref n="15" />

With the development of Arabic philosophy, *manṭiq* was used to translate the Greek λογική for the discipline of reasoning or discerning the laws of truth.<fnref n="16" /> Consequently, later authors speak of *al-nuṭq al-khārijī*, the outer articulation, namely speech (*lafẓ*), and of the inner articulation, *al-nuṭq al-dākhilī*, namely ‘understanding and perception of the universals’ (*al-fahm wa-idrāk al-kulliyāt*). ‘The reality of language (*nuṭq*) is that it is utterance which surrounds and holds fast meaning in the manner of a belt (*niṭāq*).’ It was considered general knowledge that ‘language (*nuṭq*) is discrete sounds (*aṣwāt muqaṭṭaʿa*),’ and that ‘an utterance is not considered language unless it has sound and letters (*ṣawt wa-ḥurūf*) through which meaning is recognised.’<fnref n="17" /> It may be clear by now that the expression *ṣawt wa-ḥurūf* means rather ‘an acoustic continuum divided into a series of discrete elementary units.’

The two aspects of *nuṭq*, that is the phonetic-linguistic and the conceptual-logical,
seem to have inherited in the original usage of the related terms in the Qur’ān, where
God is described as ‘the one who makes everything speak’ (*alladhī anṭaqa kulla shay’in*,
41:21), and where speaking is associated with verification, with the ascertainment of
reality: ‘All this is as real as your speaking’ (*haqqun mithla mā annakum tanṭiqūn*),<fnref n="18" />

<footnote n="13">13. Abū Naṣr al-Wā’ilī al-Sijzī, *Al-radd* ‘alā man ankara al-ḥarf wa-al-ṣawt, ed. Muḥammad Bā ‘Abd Allāh (Riyadh: Dār al-Rāyah, 1994), 148.</footnote>

<footnote n="14">14. See below p. 258.</footnote>

<footnote n="15">15. This ‘duality of patterning’ is Martinet’s *double articulation*. See ‘Zweifache Gliederung’, C. Lehmann, *Phonetik und Phonologie* (Erfurt: Universität Erfurt, 2007), 2.6. More on this topic in my Conclusion below, p. 249.</footnote>

<footnote n="16">16. K. Versteegh et al., eds, *Encyclopedia of Arabic Language and Linguistics*, 5 vols (Leiden: Brill, 2006), 4.459 (hereafter cited as EALL). An alternative name for this discipline is *al-mīzān*, ‘the balance’, see *al-Munjid fī al-lugha* (Beirut: Dār al-mashriq, 2005), 816 (hereafter cited as *Munjid*).</footnote>

<footnote n="17">17. Aḥmad ibn Yūsuf Samīn, ‘Umdat al-ḥuffāz fī tafsīr ashraf al-alfāẓ, 4 vols (Beirut: Dār al-kutub al-‘ilmiyya, 1996), 4.190–92.</footnote>

<footnote n="18">18. 51:23, transl. Abdul Haleem; Yusuf Ali elaborates, ‘this is the very Truth, as much as the fact that ye can speak intelligently to each other.’</footnote>
and ‘Our Book speaks (*kitābuna yanṭiqu*) against you with truth.’<fnref n="19" /> But the most famous
of the occurrences of this root in the Qur’ān is the mention of the *manṭiq al-ṭayr*
(27:16), the language of the birds,<fnref n="20" /> which Solomon is said to have learnt by God’s
favour. It is from this passage that ‘Aṭṭār took the name of his famous poem, often
called in English the *Conference of the Birds*. The language of the birds became a Sufi
image for the understanding of the cosmic language, both by ‘hearing’ and ‘reading’
the signs of nature, granted to the prophets and saints,<fnref n="21" /> and it was perpetuated as
a prerogative of magicians and sages in folk Arabic literature. We had encountered
Solomon previously<fnref n="22" /> as related in rabbinical literature to the origin of acrostics. Indeed,
in the figure of this prophet-king there is much to consider him a representative *par
excellence*, or even the patron of the science of letters as the knowledge of the elements
of the universe, whence his epithet, *Magister omnium physicorum*.<fnref n="23" /> The Qur’ānic
depiction which makes of him, literally, a *manṭiqī* sage, that is, a knower of language in
its various ‘logic’ aspects, is an echo of the verse of the Wisdom of Solomon where he
speaks of having been taught ‘the structure of the world and the activity of the letter-
elements’ (σύστασιν κόσμου καὶ ἐνέργειαν στοιχείων, 7:17). Further comment on this
and on the related significance to Solomon’s architectural work will be left for a later
chapter.

Starting Point and Influences

It would be left to esoteric philosophers and to mystical authors to penetrate the
structure of that mythical bird language, and to elaborate and draw upon the symbolism
of the alphabet and the letters in particular. As tends to be the case with the applied
‘subtle’ sciences, the ‘initiatic arts’ often bundled under the labels of ‘the occult’
or ‘esoterica’, the applications of ‘ilm al-ḥurūf, the ‘science of the letters’, always

<footnote n="19">19. 45:29, transl. S. H. Nasr et al., eds, *The Study Quran: A New Translation and Commentary* (New York: Harper Collins, 2015) (hereafter cited as SQ).</footnote>

<footnote n="20">20. Later also, in the important Persian tradition, lughat wa zabān-i murghān; see O. Mir-Kasimov, *Words of Power – Hurūfī Teachings Between Shi‘ism and Sufism in Medieval Islam* (London: I.B. Tauris, Institute of Ismaili Studies, 2015), 267–71.</footnote>

<footnote n="21">21. Cf. Abū Hāmid al-Ghazālī, *Al-Ghazālī on Conduct in Travel: Book XVII of the Revival of the Religious Sciences*, trans. Leonard Librande, Ghazālī Series (Cambridge: Islamic Texts Society, 2016), 11–12.</footnote>

<footnote n="22">22. See above p. 115.</footnote>

<footnote n="23">23. See P. A. Torijano, *Solomon, the Esoteric King: From King to Magus, Development of a Tradition*, Supplements to the Journal for the Study of Judaism 73 (Leiden, Boston, Köln: Brill, 2002), 92–3, and J. Janssens, ‘The Ikhwān aș-Șafā’ on King-Prophet Solomon,’ in *The Figure of Solomon in Jewish, Christian and Islamic Tradition: King, Sage and Architect*, Themes in Biblical Narrative: Jewish and Christian Traditions 16 (Brill, 2012), 241ff. for references to Solomon’s position in the prophetology of the Ikhwān al-Șafā’.</footnote>
attracted most of the public attention, and have equally continued to attract most
scholarly studies, prompting facile, and sometimes outright dismissive reductions of
their nature to ‘divinatory practices’, to ‘magic’ or ‘pseudo-sciences’. The picture is
clearer, however, and more relevant to the Islamic worldview, when it is understood
that ‘occult beliefs and practices are inextricably embedded in philosophical, scientific,
and religious discourses,’<sup>24</sup> and when the science of letters is thus understood as one
of the natural developments of the language cosmogony mentioned above, and its
applications revealed as instrumental in relation to the doctrine. The occult sciences,
in spite of their proneness to degeneration into superstition, are ‘repositories of
cosmological principles’,<sup>25</sup> and the symbolism of the letters is one of these which finds
macrocosmic and microcosmic applications through different disciplines.<sup>26</sup> This is why
the science of the letter-numbers can be called ‘the place and language that are common
to metaphysics, cosmogony, and cosmology, as well as to the initiatory path.’<sup>27</sup>

As is the case with Greek alphanumeric cosmology, the elaborations on the Arabic
letter-numbers, be they scientific, theological or magical, are based on the perceived
intrinsic nature of the letters themselves and on the nature and structure of the alphabet
which comprises them (and which they constitute). The point of departure of ‘ilm al-
hurūf is that the letters themselves are bearers of a knowledge that is revealed to men
through the messengers and prophets.

As with the Greek letters, we may try to glean some initial knowledge about the
letters from those scholars who study language, namely the grammarians. It turns
out, however, that there is no reliable Arabic grammatical literature prior to the
Qur’ānic revelation, and the greatest authority for the earliest and most authoritative
grammarians, in their struggle to preserve the perceived purity of Old Arabic (al-lugha
al-‘arabiyya al-qadīma al-jayyida),<sup>28</sup> was that of the Bedouin speech and poetry.<sup>29</sup> More
crucially, the description of the alphabet as we know it dates to the times of al-Khalīl ibn

<footnote n="24">24. L. Saif, ‘From Gāyat al-ḥakīm to Šams al-ma‘ārif: Ways of Knowing and Paths of Power in Medieval Islam,’ *Arabica* 64, nos. 3-4 (2017): 297.</footnote>

<footnote n="25">25. S. H. Nasr, *Islamic Science: An Illustrated Study* (London: World of Islam Festival, 1976), 207.</footnote>

<footnote n="26">26. For a very useful and comprehensive summary, see G. Böwering, ‘Sulamī’s Treatise on the Science of the Letters,’ in *In the Shadow of Arabic: The Centrality of Language to Arabic Culture*, ed. B. Orfali (Leiden: Brill, 2011), 341–42.</footnote>

<footnote n="27">27. D. Gril, ‘The Science of Letters,’ in *Ibn al-Arabi, The Meccan Revelations, volume II*, ed. M. Chodkiewicz (New York: Pir Press, 2004), 112–13.</footnote>

<footnote n="28">28. Sībawayh, *Al-Kitāb*, 4 vols (Cairo: Maktaba al-Khanjī, 1982), 4.473.</footnote>

<footnote n="29">29. Cf. F. Corriente, ‘From Old Arabic to Classical Arabic Through the Pre-Islamic Koine: Some Notes on the Native Grammarians’ Sources, Attitudes and Goals,’ *Journal of Semitic Studies* 21, nos. 1-2 (1976): 62–68. For details concerning the earliest inscriptions in Hismaic, Safaitic, Dadanitic, Nabataean and even Greek scripts, see A. Al-Jallad, ‘The Earliest Stages of Arabic and its Linguistic Classification,’ chap. 16 in *The Routledge Handbook of Arabic Linguistics* (Routledge, 2017), 315–16, among a plethora of highly recommended recent articles by this author.</footnote>
Aḥmad al-Farāhīdī (often called simply ‘al-Khalīl’, 718–786), considered the first Arabic lexicographer, and his disciple Sībawayh (c. 760–796), author of the first extant Arabic grammar. This means that the earliest codification of the basic letter correspondences, from a grammatical point of view, cannot really be separated from the influence of Islamic revelation. As a matter of fact, it was not only the Bedouins’ Arabic which would be considered the highest standard on language questions, but more specifically the Hijazi dialect of Quraysh, because it was in that particular form of Arabic that the Prophet Muḥammad had received the revelations.

There has been a long scholarly debate over Greek and Syriac influences on the
development of Arabic grammar, and quite specifically over the extent of the influence
of the *Techne* of Dionysius Thrax on some of the features of Arabic grammar.<fnref n="30" />
While there seem to be some unsolvable issues, it appears clear now that the Greek
influence would have been mediated by Syriac authors, not only grammarians but also
philosophers, to whom would have befallen the major task of adapting the grammar
and the logical structures of a Indo-European language to those of a Semitic one;<fnref n="31" />
the detailed study of this process of adaptation is in its early stages and exceeds the
boundaries of this research. What I intend to do in the following pages is to trace the
development of Islamic letter cosmology by examining selected passages taken from a
wide range of sources, but there are at least two main points which should be retained
about the origin of Arabic grammar:

* grammatical reflection developed ‘at the same time (eighth century), in the same place (Mesopotamia), in three different languages (Syriac, Arabic, and Hebrew).’<fnref n="32" />

* grammar developed as an ancillary discipline in relation to Qur’ānic sciences, not unlike the other grammatical traditions developed in the wake of a scriptural corpus.<fnref n="33" />

The Arabic Alphabet Order

The Arabic alphabet as we know it today (alif, bā', tā', thā'...), and as used in practically every dictionary, follows a shape-oriented sequence introduced during the 1st century

<footnote n="30">30. See King, *Elements of the Syriac Grammatical Tradition*, 201–206.</footnote>

<footnote n="31">31. See G. Bohas, ‘Le traitement de la conjugaison du syriaque chez Bar Zo‘bî : une langue sémitique dans le miroir de la grammaire grecque,’ *Parole de l’Orient* 40 (2015): 18–19.</footnote>

<footnote n="32">32. King, *Elements of the Syriac Grammatical Tradition*, 204.</footnote>

<footnote n="33">33. Cf. W. J. van Bekkum et al., *The Emergence of Semantics in Four Linguistic Traditions: Hebrew, Sanskrit, Greek, Arabic*, Amsterdam Studies in the Theory and History of Linguistic Science 82 (Amsterdam/Philadelphia: John Benjamins Publishing, 1997), 285–96.</footnote>
AH.<fnref n="34" /> It is called ḫurūf al-hijā' or ḫurūf al-tahjī, 'the letters of spelling',<fnref n="35" /> and it is formed by 28 or 29 consonants and semi-consonants.

Another curious and very common designation for the alphabet is ḫurūf al-muʻjam, which means literally ‘letters of confusion’, from a triliteral root ᶜ-j-m<fnref n="36" /> which parallels closely, from the Arab point of view, the meaning of Greek βάρβαρος as ‘non-Greek-speaking’, foreigner. ‘Alā ḫurūf al-muʻjam meant simply ‘in alphabetical order’,<fnref n="37" /> but Arab lexicographers were at pains over the centuries to explain the expression,<fnref n="38" /> and two distinct traits of the alphabet can be retained from their attempts: 1) that there was some perceived foreignness to the alphabet, and 2) that the letters, when unconnected and not forming words, were conspicuously meaningless, as foreign bodies. The word ᶜujma, from the same root ᶜ-j-m, refers to the diacritic dots which distinguish, for example, between ṣ and ṣ̱, a distinction compared to the irruption of light at dawn. The elaborations of the grammarians and lexicographers on the different qualities of the letters, their degrees, their nature and properties, including their astronomical associations and their correspondences with the four elements and the elementary qualities, are clear reminders of this same mixture of grammar and cosmology found in the corpus of Greek grammarians; a notable example is furnished by the introductory pages of Lisān al-ʻarab, the preeminent dictionary of the language, which starts with a chapter ‘On the Disjointed (muqaṭṭaʻa) Letters,’ followed by ‘On the Names, Natures and Properties of Letters.’<fnref n="39" /> The sense of foreignness ascribed to the letters when in isolation also brings to mind the Greek grammarians’ insistence on the fact of the indeclinability of the names of the letters, and on the lack of meaning of the originally Phoenician names of the letters.<fnref n="40" />

There was also an original letter sequence inherited, with minor regional variations, from the Phoenician alphabet, a sequence shared with the Aramaic, Hebrew and Greek alphabets, starting *alif, bā, jīm, dāl, and known as abjad, ḫurūf al-abjadiyya* ('letters of the abjad'), or even personified as 'Abū Jād'.<fnref n="41" /> In fact, and strictly speaking, *abjad* means

<footnote n="34">34. A. Al-Nāṣīr, 'Sibawayh the Phonologist: A Critical Study of the Phonetic and Phonological Theory of Sibawayh as Presented in his Treatise *Al Kitāb*' (PhD diss., University of York, 1985), 25–6.</footnote>

<footnote n="35">35. Cf. Lisān 4627c s.v. *h-j-a*: *al-hijāʾ taqtīʿ al-lafẓah bi-ḥurūfihā, ʿal-hijāʾ* is the cutting of a word in its letters.</footnote>

<footnote n="36">36. *Muʿjam* is a *maṣdar mīmī* of ʿ*ajama*, that is, a ʿ*mīm* infinitive*’ used customarily as a kind of aorist, i.e. to express action abstracted from duration.</footnote>

<footnote n="37">37. Cf. Bukhārī 64:13.</footnote>

<footnote n="38">38. Cf., s.v. ᶜ-j-m, Ibn Manẓūr, *Lisān al-ʿarab*, 15 vols (Qum, Iran, 1405 AH), 12.387a; G. Freytag, *Lexicon Arabico-Latinum*, 4 vols (Berlin: C.A. Schwetschke & Son, 1837), 3.116; Samīn, *Umdat al-ḥuffāz*, 3.33–4.</footnote>

<footnote n="39">39. Ibn Manẓūr, *Lisān al-ʿarab*, 1.10–16.</footnote>

<footnote n="40">40. See above, p. 36.</footnote>

<footnote n="41">41. ‘*Ka-ṣighat al-kunya*’, ‘in the form of a surname’, see M. al-Zabīdī, *Tāj al-ʿarūs min jawāhir al-qāmūs*, ed. A. Hārūn, 40 vols (Kuwait: Ministry of Guidance / Information, 1994), 7.401ff (hereafter cited as Tāj).</footnote>
‘the first of the words in which are grouped the letters of the Arabic alphabet.’<fnref n="42" /> The *abjad* is customarily grouped in eight subsets of letters for ease of memorisation, and like its Semitic relatives it lends itself from early times to the representation of numeric values,<fnref n="43" /> to the point that *abjad* will often simply mean ‘the letters in their numeric values.’ The eight mnemonic sets of this arrangement, namely, *abjad*, *hawwaz*, *huṭaya*, *kalamun*, *saʾfaṣ*, *qarashat*, *thakhadha*, *daẓagha*,<fnref n="44" /> or more often only the first six—thus corresponding to the twenty-two letters of Hebrew—are traditionally matched to the Kings of Madyan (the biblical Midian), ‘whose names were laid upon the number of letters of the Arabic writing,’ or to some devils, or to ‘sons of Persia’,<fnref n="45" /> who invaded the Hijaz like the rays of the sun.<fnref n="46" />

## The Arabic Letters as Numerals

The evidence for the earliest uses of the Arabic letters as numbers is currently under
scholarly scrutiny, with conclusive evidence found only for as late as the tenth century,
but it is generally accepted that, as in the case of Hebrew and Syriac, the influence of the
Greek alphanumeric system was decisive,<fnref n="47" /> and it is known from alchemical literature,
as I shall explain below, that some form of alphanumeric notation was already in use
from at least as early as the eighth century.

The *abjad* sequence serves as the practical basis of Arabic isopsephy, *hisāb al-abjadiyya* or *hisāb al-jummal*, ‘the reckoning of the total’,<fnref n="48" /> which, depending on the authors and the periods, has been more or less identified to related forms of onomatomancy like *jafr* (sometimes *jafr jāmiʿ*, often simply identified to ‘ilm al-*hurūf*),<fnref n="49" /> *sīmiyā*’ (letter magic), *zā’iraja* (art of the diviner’s board or geomantic

<footnote n="42">42. *Munjid*, 1.</footnote>

<footnote n="43">43. Cf. Chrisomalis, *Numerical Notation*, 134ff.</footnote>

<footnote n="44">44. The vocalisation can vary. The ‘Western’ variant of this arrangement, where five letters occupy different positions, is laid out clearly in C. Bonmariage and S. Moureau, *Le Cercle des lettres de l’alphabet* (Dā’irat al-aḥruf al-abjadiyya) (Leiden: Brill, 2016), 11.</footnote>

<footnote n="45">45. Muḥammad ibn Yaʻqūb al-Fīrūzābādī, *al-Qāmūs al-muḥīt* (Beirut: Mu’assasa al-risāla, 1998), 266.</footnote>

<footnote n="46">46. Tāj, 7.401a.</footnote>

<footnote n="47">47. See J. Thomann, ‘The Two Arabic Abjad Numeral Systems: Scientific Innovation and Archaic Tradition,’ pre-publication:7–10. I am very grateful to Johannes Thomann for kindly sharing this still unpublished article.</footnote>

<footnote n="48">48. Although *jummal* has been also thought to be a foreign term, see Ibn Manẓūr, *Lisān al-ʿarab*, 11.128a, Lane, s.v. *j-m-l*, and especially Thomann, ‘The Two Arabic Abjad Numeral Systems,’ 5.</footnote>

<footnote n="49">49. *Munjid*, 94b. Confusion and lack of clarity seem to have surrounded for centuries the definition of *jafr*—cf. M. Ebstein, *Mysticism and Philosophy in al-Andalus* (Leiden: Brill, 2014), 121; S. Nizamuddin Ahmad calls it ‘the science of the symbolism of Arabic letters in their ideophonic, ideographic and arithmological dimensions’; the *EI2* article by T. Fahd has valuable references, but for an overall perspective see M. S. Melvin-Koushki, ‘The Quest for a Universal Science: The Occult Philosophy of Ṣā’in al-Dīn Turka Iṣfahānī (1369–1432) and Intellectual Millenarianism in Early Timurid Iran’ (PhD diss., Yale</footnote>
compass),<fnref n="50" /> and the elusive ḥisāb al-nīm (used to predict winners and losers).<fnref n="51" /> In spite
of all this alphanumeric flourishing, however, and rather unlike the case with Greek and
Hebrew scripts, the arithmetical use of the letters was only conceived as an addition to
the writing system which was already functional as a phonographic device.

From a more theoretical point of view, it is interesting to note how the Qur’ān
is doctrinally at the foundation of the letter-number concurrence through the divine
attributes and actions. Among the famous enumeration of the ninety-nine asmā Allāh
al-ḥusnā, the ‘beautiful names of God,’<fnref n="52" /> we find al-Muḥṣī, the Calculator, He Who
Counts, and al-Ḥasīb, the Reckoner, and the roots of these names, ḥ-ṣ-y and ḥ-s-
b, appear repeatedly in the Qur’ān describing God’s qualities. In addition to these
two usual divine names, some of the divine actions involve other forms of counting
and writing. The root for ‘number’, ‘adad, for example, occurs in the interesting
combination, wa-aḥṣā kulla shay’in ‘adadan, ‘he calculates the number of all things’
(72:28),<fnref n="53" /> and in aḥṣāhum wa-‘addahum ‘addan, ‘He has calculated and counted their
number exactly’ (19:94). Ḥasaba is more related to the process of thought in general,
with its cognates sometimes translated as ratio, measure or reason.<fnref n="54" />

Similarly, some of the divine actions or the Qur’ānic images establish a very direct
relation to writing. Because God is said to ‘have prescribed [written] mercy upon
Himself’, kataba ‘alā nafsihi al-raḥma, some have argued that al-Kātib, the Scribe, or the
Writer, can also be considered a divine name.<fnref n="55" /> This is repeatedly confirmed by mentions
of the Qur’ān itself as a kitāb,<fnref n="56" /> and references to books, or writings or records of divine
origin are recurrent in the Qur’ān in the form of the following roots:

• *raqama*— In 83:20, the seventh heaven named ‘Illiyūn is identified with, or said to contain, a *kitābun marqūm*, a ‘numbered book’, a ‘ruled notebook’, practically a ledger for the deeds of the righteous, with its counterpart in the wretched *kitābun marqūm* of Sijjīn, the seventh and lowest of earths (83:7). *Tarqīm* means ‘to add diacritics (*ta‘jīm*) to something written (*kitāb*) in order to make it clear,’ and a *kitāb* is *marqūm* when ‘its

<footnote>University, 2012), 285.</footnote>

<footnote n="50">50. ‘Abd al-Raḥmān Ibn Khaldūn, *Muqaddima*, ed. ‘Abd Allāh Muḥammad al-Darwīsh, 2 vols (Damascus: Dār Ya‘rib, 2004), 1.233–4.</footnote>

<footnote n="51">51. See *ibid.*, 231–233. For a Greek Pythagorean precedent of this technique, see P. Tannery, ‘Les chiffres arabes dans les manuscrits grecs,’ *Revue Archéologique* 7 (1886): 248ff.</footnote>

<footnote n="52">52. The source is a well-known hadith reported by Abū Hurayra, *Sunan Ibn Mājah* 3861; Jāmi‘ al-Tirmidhī 3507.</footnote>

<footnote n="53">53. Ḥaṣāh means pebble, thus making with ḥaṣā a perfect analogue to the Latin pair *calculus/calculare*. From the root ḏ we obtain also miʻdād, abacus.</footnote>

<footnote n="54">54. Cf. Freytag, *Lexicon*, 1.378.</footnote>

<footnote n="55">55. See Muhammad ibn Ibrāhīm Ibn al-Wazīr, *Īthār al-ḥaqq* ‘alā al-khalq, 2 vols (Riyadh: Dār al-ṣumay‘ī, 2016), 106–108 for a thorough application of this reasoning and a very extended list of beautiful names.</footnote>

<footnote n="56">56. E.g. 2:2, 18:1 and *passim*.</footnote>
letters have been made clear by their respective vocalisation signs ('alāmāt al-tanqīṭ). Not only are the roots of muʻjam and nuqṭ found in these definitions, but furthermore, raqama is used for sealing and stamping, and raqm means a numeral.<fnref n="57" /> I hardly need to point out how various aspects of my object of research are found together in this root, to which we shall have occasion to return in later pages.

* saṭara— The aspect of a grid-like or ruled pattern occurs also elsewhere with the root of saṭara: future eschatological events are 'traced (or outlined) in the Book' fī al-kitābin masṭūran (17:58), and the Book itself is called masṭūr (e.g. 52:2), 'drawn in rows', like rows of trees,<fnref n="58" /> or simply 'ruled', like lined paper. One of the most quoted oaths in the Qur'ān is 'by the pen and what they delineate (yasṭurūn)'; the most common explanation to this is that the angels—who incidentally are said to stand in rows (ṣaffāt, 37:1)—do their writing in lines (ṣaff).<fnref n="59" />

* madda— The image of the ink, which I have mentioned above, turns out to be especially interesting due to an ulterior semantic development. In the Qur'ān, the root of madda tends to denote the extension, a spatial or temporal prolongation, as of the earth spread out (13:3, 84:3), or of the life span (19:75), or the ink (midād), with the basic idea of continuity, as if pulling from a string, and also, in some contexts quite inextricably, with the sense of providing help and assistance. We have in this metaphor a complement to the idea of discrete quantity represented by the numerical terms above. In fact, if we unfold the image of the ink, we can see how both aspects of number coalesce in it—as in the Nicomachean distinction between multitudo and magnitudo, discrete and continuous quantity—when the divine writer determines the unlimited extension of the ink with the shapes of the letters (hurūf), and he does this by creating edges (hiraf).<fnref n="60" /> In view of this, it is quite remarkable how in later philosophical developments, although both Hebrew and Arabic made use of adapted forms of the Greek ὕλη (Lat. materia) to name the formless substratum of the world,<fnref n="61" /> both languages also produced native terms which acted mostly as synonyms of the former, namely Heb. *homer*, ‘mud, clay’, and the one that brought us here, Ar. *mādda*, explained by lexicographers as a ‘continuous increase’ (ziyāda muttaṣila).

Later exegesis would explain how the words of God, being continuous with him (*muttaṣila bihi*), ‘assist him in the manner of ink’ (*yumidduhu*) in his overflowing abundance.<fnref n="62" /> This makes it easy to see how the divine words, perhaps specifically in

<footnote n="57">57. *Arqām al-hindiyya* are the ‘Indian’—for us ‘Arabic’—numerals. See Ibn Manẓūr, *Lisān al-‘arab*, 12.248ff.</footnote>

<footnote n="58">58. *ibid.*, 2007a.</footnote>

<footnote n="59">59. Cf. above, Chapter 1, p. 40.</footnote>

<footnote n="60">60. Both *hurūf* and *hiraf* are plurals of the same singular, *harf*.</footnote>

<footnote n="61">61. *היוּלִי hayule* and *היולָי hayūlā*.</footnote>

<footnote n="62">62. See Ebstein, *Mysticism and Philosophy*, 48–9, 113, 153, based mostly on the Ikhwān al-Ṣafā'.</footnote>
their written manifestation, came to be considered as a sort of prime matter (*al-mādda al-ūlā*).<fnref n="63" />

• ratila— Finally, an echo of the same discrete deployment of the divine word mentioned above is found in the terms related to ratila, ‘to be regular and well-ordered’, ‘like healthy teeth’, and which occur solely when speaking of the delivery of the revealed verses. In 25:32, where the subject of the verb is God (*rattalnāhu tartīlan*), ‘We gave it to you in gradual revelation’, with the meaning of a distinct delivery (*bayyinan*), of a ‘harmony and arrangement in proper disposition’ (*ittisāq wa-intiẓām ʿalā istiqāma*).<fnref n="64" /> In 73:4, man is ordered to recite in the same clear and ordered way: *rattili’l-qur’āna tartīlan*, ‘recite the Qur’ān rhythmically and spelling it out distinctly’<fnref n="65" /> or even, simply, ‘with *tartīl*, which is the name of the art of Qur’ānic recitation.

I shall have more to say about some of the above aspects when studying later developments in Islamic thought, but for the time being it is sufficiently clear that the Qur’ān already contains a rich kernel of alphanumeric symbolism. In the following paragraphs I will attempt to trace the unfolding or the branching out of this scriptural kernel into the various manifestations of the science of ‘letters’.

## The Development of the Science of Letters

### ‘Alī: The Common Source

The ‘knowledge of the letters’ (‘ilm al-ḥurūf) started developing in various directions from the time of the Companions of the Prophet, and eventually it branched into at least two lines of study which exhibit various doctrinal refinements and applications. Looking at the Ḥadith literature, it is quite remarkable how the knowledge of the letters seems to have been initially a preserve of the Shī‘a traditions.<fnref n="66" /> This means, concretely speaking, that the traditional wellspring of letter speculation is the person of ‘Alī ibn Abī Tālib, cousin, son-in-law and one of the scribes of Muhammad, whose supporters (*shī’at ‘Alī*, the followers of ‘Alī) accorded him not only the greatest importance as the prolonger of the Prophet’s blood-line (*ahl al-bayt*, the ‘people of the house’), but

<footnote n="63">63. See S. Brentjes, ‘An Exciting New Arabic Version of Euclid’s Elements: MS Mumbai, MULLĀ FĪRŪZ RI 6,’ *Revue d’histoire des mathématiques* 12, no. 2 (2006): 187 for a reference to the other terms used to translate ὕλη.</footnote>

<footnote n="64">64. Samīn, *Umdat al-ḥuffāz*, 2.70.</footnote>

<footnote n="65">65. Al-Ghazālī explains ‘ḥarfan ḥarfan’, ‘letter by letter’, see A. al-Ghazālī, *Kitāb al-arbaʿīn fī uṣūl al-dīn* (Beirut: Dār al-kutub al-‘ilmiyya, 1988), 28.</footnote>

<footnote n="66">66. Cf. P. Lory, ‘La science des lettres en terre d’Islam: le chiffre, la lettre, l’oeuvre,’ in *La contemplation comme action nécessaire*, Cahiers de l’Université Saint Jean de Jérusalem 11 (Berg International Éditeurs, 1985), 91.</footnote>
also an exalted spiritual authority of his own. Imām ‘Alī is not only the first khalīfa or successor of the Prophet recognised by the Shī‘a, but he is also one of the four ‘rightly guided caliphs’ recognised by the Sunnite and other smaller Islamic denominations like the Ibadis. He is directly or indirectly one of the major sources, if not the main source of most Shī‘a hadith literature, and he is also a major transmitter of Sunni hadiths,<fnref n="67" /> in many of which his special nature and relation to the Prophet is unquestionably transmitted. A well known tradition from the Prophet states ‘I am the abode of wisdom (or “the city of knowledge”) and ‘Alī is its gate,’ anā dār al-ḥikma wa-‘Alī bābuhā.<fnref n="68" /> No other of the companions of the Prophet has any comparable authority straddling—and indeed bridging—the Sunni-Shī‘a division.<fnref n="69" /> It is worth remembering not only that Imām ‘Alī is considered the indisputable source of all initiatic sciences, but also that with the exception of one, all Sufi orders count him as the first link of their lineages immediately after the Prophet.<fnref n="70" /> The figure of Imām ‘Alī thus stands in Islamic history as a unique point of intersection between tashayyu‘, the adherence to the Shī‘a, tasannun, following the Sunna, and taṣawwuf, the way of Sufism, or Sunni esoterism.

And it is this figure, admittedly a composite of many elements of varying degrees of historicity, that stands at the origin of the sciences of language and the letters. ‘Alī is acknowledged as the first authority of Arabic grammatical tradition,<fnref n="71" /> as the one who directly instructed Abū al-Aswad al-Du’alī (ca. 603–689), who first put grammar in writing (awwalu man wada‘a al-naḥw);<fnref n="72" /> and he is also at the origin of Arabic calligraphy in its outward and inner aspects.<fnref n="73" /> ‘The Messenger of God made ‘Alī learn a thousand letters (alf ḫarf), each one of which opens a thousand more.’<fnref n="74" />

<footnote n="67">67. M. Z. Siddiqi, *Hadith Literature: Its Origin, Development and Special Features* (Cambridge: Islamic Texts Society, 1993), 18.</footnote>

<footnote n="68">68. Tirmidhī 4089; variations in al-Ḥākim al-Nīshābūrī and Ibn ‘Abd al-Barr.</footnote>

<footnote n="69">69. R. Shah-Kazemi, *Justice and Remembrance: Introducing the Spirituality of Imam ‘Alī* (London & New York: I.B. Tauris / The Institute of Ismaili Studies, 2007), 12ff.</footnote>

<footnote n="70">70. L. Lewisohn, ‘Ali ibn Abi Talib’s Ethics of Mercy in the Mirror of the Persian Sufi Tradition,’ in *The Sacred Foundations of Justice in Islam: The Teachings of ‘Alī ibn Abī Tālib*, ed. M. Lakhani (Bloomington: World Wisdom, Inc, 2006), 112ff.</footnote>

<footnote n="71">71. See Al-Nāṣṣir, ‘Sibawayh the Phonologist,’ 5.</footnote>

<footnote n="72">72. Al-Du’alī is credited with the invention of the first Arabic diacritics, but no work by him has been preserved. Thus, although acknowledged as the first grammarian of Arabic, the first grammar we have access to is that of Sībawayh.</footnote>

<footnote n="73">73. H. Corbin, *Histoire de la philosophie islamique, 2 vols* (Paris: Gallimard, 1986), I, 205.</footnote>

<footnote n="74">74. Muḥammad ibn Ya‘qūb al-Kulaynī, *al-Kāfī*, 15 vols (Qum: Markaz Buḥūth Dār al-Ḥadīth, 1430 [2008/2009]), II, 30 (770).</footnote>
Letters in the Ḥadīth Literature

As mentioned earlier, references to alphanumeric symbolism are notably absent from the major Sunni Hadith collections. A detailed search through the *Kutub al-sitta*, ‘The Six Books’ which form the most accepted canon, with the addition of *Musnad Ahmad* and other collections like the *Riyād al-şāliḥīn*, have yielded the following results.<fnref n="75" />

• *Ḥarf* is used in the Sunni Hadith literature mostly in its meaning of ‘reading variation’, one of the seven canonical *aḥruf* or ‘modes’ of Qur’ānic recitation, and occasionally to refer to any variation as a preference in a way of acting.

• References to **the divine Pen**, *al-qalam*, are perhaps the clearest connections to the written word cosmogony. In most cases the Pen is mentioned as recorder of human destiny, in the fatidic expressions ‘the Pen has dried’ (*jaffa al-qalam*) or ‘the Pen has been lifted’ (*rufiʿa al-qalam*),<fnref n="76" /> but a clearer cosmogonic occurrence speaks of it as ‘the first created being, to whom God said, “Write!” and so it flowed endlessly with every existant,’<fnref n="77" /> in other wordings, there is the significant difference that what is written by the Pen is not the existence itself, but destiny, *al-qadar*.<fnref n="78" /> In the same hadith there is question of the ‘mother of the book’ (*umm al-kitāb*), explained as *kitābun katabahu Allāh qabla an yakhluqa al-samawāt*, ‘a book (writing) He wrote before creating the heavens.’ In other narrations, *umm al-kitāb* refers to the *Fātiḥa*, the first sura of the Qur’ān and main obligatory part of the canonical prayer.

• Most uses of **kataba and cognates**, aside from *kitāb* to refer to the Qur’ān, have to do either with predestination, with ritual prescriptions, or with the divine recording of good and bad deeds; indeed, the ‘recording angels’ assigned to every person are called ‘the scribes’, *al-kuttāb*.<fnref n="79" /> One cosmological example in *Ṣaḥīḥ Muslim*<fnref n="80" /> shows the direct relation between the doctrine of predestination and the divine reckoning and writing: ‘God wrote (*kataba*) the measures (*maqādīr*, related to *qadar*, predestination) of created beings before creating the heavens and the earth.’ In one variation of the above referred tradition, when the Pen is created, it is charged with writing specifically the same *maqādīr*, the ‘measures’.<fnref n="81" /> This semantic

<footnote n="75">75. Digital concordances and indices now made available online allow for recursive searches both in Arabic and English translation. I have relied mostly on *Mawsūʿa al-ḥadīth al-sharīf* (Encyclopaedia of Hadith), 18 vols (Vaduz: Thesaurus Islamicus Foundation, 2000) (hereafter cited as EH), the bilingual collection at sunnah.com, and A. J. Wensinck, *A Handbook of Early Muhammadan Tradition* (Leiden: Brill, 1927). I follow the Arabic EH numbering throughout.</footnote>

<footnote n="76">76. E.g. *Sunan Abī Dāwūd* 4398.</footnote>

<footnote n="77">77. Tirmidhī 3637.</footnote>

<footnote n="78">78. Tirmidhī 2308.</footnote>

<footnote n="79">79. *Muwaṭṭa’ Mālik* 1822.</footnote>

<footnote n="80">80. Hadith 6919.</footnote>

<footnote n="81">81. *Sunan Abī Dāwūd* 4702.</footnote>
field which combines fate with measuring, and with the notion of power and control
intrinsic to this root, is represented by three of the most common divine names, *al-Qadīr*, *al-Qādir*, and *al-Muqtadir*, which express with differing degrees of emphasis the
various aspects of determination.<fnref n="82" /> Among the traditional definitions of *miqdār* is found
simply *mawt*, ‘death’, for ‘when the servant reaches the term, he dies.’<fnref n="83" />

• **Number and counting:** although the important Qur’ānic image of the ink is far from prominent in the Hadith, we find in Tirmidhī and other collections the following litany, given when the Prophet instructs a woman who was counting the praises ‘with pebbles’:<fnref n="84" /> *subḥāna Allāh ‘adada khalqihi [...] subḥāna Allāh midāda kalimātihi* ‘Glory to God according to the number of His creation [...] *Glory to God according to the extension of His Words’ or ‘according to the ink of His words.’<fnref n="85" />

I have little doubt that more in-depth examination of the Hadith literature would
yield more such internal correspondences, which are most often based on the structure
of the Arabic language, hence all too easy to be lost in translation, while at the same time
inseparable from any traditional Arabic exegesis, even when the correspondences are
not brought to light explicitly. What I have tried to show in the previous paragraphs is,
primarily, that what underlies the exegetical principle of *al-Qur'ān yufassiru ba'duhu
ba'dan* (different parts of the Qur'ān explain one another), is extensible to the wider
corpus of Sunni Islamic traditional sciences, which is based on a strict exegetical
hierarchy.<fnref n="86" /> After the Qur'ān, the second source is the Sunnah, the Hadith of the
Prophet, which includes the often overlooked commentaries on the Hadith,<fnref n="87" /> and only
later the *tafsīr* literature, which in some cases actually includes commentary on both
the Qur'ān and the Hadith.

At the junction between the Sunni and Shī‘ī exegetical traditions we find, in addition
to ‘Alī, a few other personalities who seem to be of special relevance in the transmission
of the esoterism of language: ‘Abd Allāh ibn ‘Abbās, ‘Abd Allāh ibn Mas‘ūd, and most
notably, through a direct line from ‘Alī through his son al-Ḥusayn, the towering figure
of Ja‘far al-Ṣādiq (d. 765).<fnref n="88" /> Ja‘far, the sixth Shī‘ī Imam, is also, through his mother’s

<footnote n="82">82. One is reminded of the Greek triple personification of the Fates: Clotho, Lachesis and Atropos—the spinner, the measurer and the decider.</footnote>

<footnote n="83">83. Ibn Manẓūr, *Lisān al-‘arab*, 5.79a.</footnote>

<footnote n="84">84. That is, she was ‘calculating’ her prayers; Abū Dāwūd 1502.</footnote>

<footnote n="85">85. Tirmidhi 3903, al-Nasā’ī 1360, Muslim 7089.</footnote>

<footnote n="86">86. See A. Habil, ‘Traditional Esoteric Commentaries on the Qur’an,’ in *Islamic Spirituality: Foundations*, ed. S. H. Nasr (London & New York: Routledge, 1989), 91–97.</footnote>

<footnote n="87">87. ‘These commentaries find in the Ḥadīth, in addition to direct interpretations of Quranic verses, the very principles of symbolism found in the Quran and applied in later Quranic commentaries,’ *ibid.*, 94. See Abdal Hakim Murad, *Selections from the Fath al-Bārī by Ibn Hajar al-‘Asqalānī* (Bartlow, Cambridge: Muslim Academic Trust, 2000), 1, for a brief introduction to the genre.</footnote>

<footnote n="88">88. See M. A. Amir-Moezzi, *The Divine Guide in Early Shi‘ism: The Sources of Esotericism in Islam*, trans.</footnote>
lineage, a descendant of the caliph Abū Bakr al-Ṣiddīq, thus uniting, like ‘Alī, the two main lines of Prophetic succession. He is also a prominent link in most Sufi initiatic chains (*salāsil*), and a source *par excellence* of Islamic occult sciences.<fnref n="89" /> I shall have occasion to mention him again when discussing the origin of Islamic alchemy.

## The Two Branches

The two major lines of study of the Islamic ‘science of letters’ refer respectively to ① the symbolism of the alphabet and ② to the symbolism of a subset of fourteen letters known as the *muqaṭṭa‘āt* or ‘cut-off’, ‘isolated’ letters, found at the beginning of twenty-nine Qur’ānic suras, alone or in unsemantic combinations of up to five letters. Some suras derive their names from these opening letters, like *Qāf* (50), or *Ṭā Hā* (20) and *Yā Sīn* (36) which have even become personal names.<fnref n="90" />

Two complementary Shī‘ī hadiths illustrate and sanction these two main branches of letter speculation:

> ‘God Most High has a choicest part (*ṣafwa*) in every book, and the choicest part of this book are the letters of the alphabet (*hurūf al-tahajjī*).’<fnref n="91" />

> ‘God Most High has a secret (*sirr*) in every book, and his secret in the Qur’ān is in the isolated initial letters of the suras (*awā’il al-suwar*).’<fnref n="92" />

Leaving aside the possible implications of the distinction between *ṣafwa* and *sirr*, which might prove too subtle for this context, we can observe that the first group, the ‘spelling letters’, resembles that comprehensive set of alphanumeric principles called in Greek the twenty-four στοιχεία. Because of their inclusiveness—they comprise all letters—and as I had had occasion to mention when speaking of the Gnostic concept of the pleroma,<fnref n="93" /> they are primarily *cosmological*, that is related to the constitution of the universe as it stands—or as it stands in the divine blueprint—, formed by all the elements, and this is why they are related to wisdom, to the comprehension of reality.

On the other hand, the sub-set of fourteen might be compared to one of the alphabetic subsets we had encountered among the Greek grammarians, with the difference that

<footnote>D. Streight (Albany, NY: SUNY Press, 1994), 64; Habil, *‘Traditional Esoteric Commentaries on the Qur’an,’* 95–96.</footnote>

<footnote n="89">89. Ibn Khallikān, *Wafayāt al-a‘yān wa-anbā’ abnā’ al-zamān*, 8 vols (Beirut: Dār Ṣādir, 1972), 327; M. Hodgson, ‘Dja‘far al-Ṣādik,’ *Encyclopaedia of Islam, Second Edition* (consulted online on 8 January 2018).</footnote>

<footnote n="90">90. They are also called *awā’il* and *fawātiḥ al-suwar*, the ‘first ones’ or ‘the openers’ of the suras. A succinct and well rounded characterisation is found in P. Garrido Clemente, ‘Ibn Masarra a través de las fuentes: obras halladas y escritos desconocidos,’ *Estudios Humanísticos. Filología*, no. 31 (2009): 95–6.</footnote>

<footnote n="91">91. *Bihar al-anwār*, vol. 88, p. 9, cited in Mir-Kasimov, *Words of Power*, 469.</footnote>

<footnote n="92">92. *Ibid*.</footnote>

<footnote n="93">93. See above p. 145.</footnote>
this time what sets the fourteen letters apart is not a phonetic trait, but an inscrutable
divine design. The isolated letters are primarily related to cosmogony, insofar as they
are selected instruments used by the demiurgic God, and this explains why they are so
important in magic and other related disciplines where their creative energy is brought
into play. I will call this type of speculation ‘restricted’ letter cosmology, in contrast
to the full-alphabet ‘comprehensive’ type.<fnref n="94" />

In line with the object of this research, I shall refrain from studying in any detail
the attributes and powers of particular groups of letters, in order to focus instead on
the cosmological meaning of the alphanumeric system as a whole. Nonetheless, I must
take note of the following dictionary definition of muqaṭṭaʻāt, which comes as close as
possible to our elemental enquiry:

ومقطعات الشيء طرائقه التي يتحلل إليها ويتركب عنها كمقطعات الكلام ومقطعات
الشعر ومقاطيعه ما تحلل إليه وتركب عنه من أجزائه التي يسميها عروضيّو العرب
الأسفّاب والأوتاد

The elements (*muqaṭṭaʻāt*) of something are those modes (*tarāʾiq*) into
which it decomposes and from which it is composed, like the elements of an
utterance. The elements of poetry and its rhythmic divisions (*maqātīʿ*) are
those parts (*ajzāʾ*) into which it decomposes and from which it is composed,
and which the Arab prosodists call syllables and feet.<fnref n="95" />

This brief passage is remarkable for more than one reason: in the context of this work,
the similarity with the definition of στοιχείον given by Aristotle is striking enough, but
when we realise that the terminology used belongs to prosody and metrics as the most
musical aspects of language,<fnref n="96" /> then we cannot but be reminded of Balázs’ theory about
the meaning of στοιχεία,<fnref n="97" /> and how he relates the term to metrics and prosody. There
is also a clear parallel to the *Philebus* description of how the phonetic continuum was
cut asunder by Thoth in order to produce the phonemes.<fnref n="98" /> The word *tarāʾiq*, ‘ways,
pathways’, agrees neatly with the etymology proposed by Balázs, whereby στοιχείον
derives from στείχω, ‘to walk’, as if each of the elements is a pattern, as the tracks left
on a path, which is not far at all from the actual way of drawing letters on different

<footnote n="94">94. I wonder if it might be useful to introduce in this context the rare distinction between ‘ulūm al-ḥarf, the ‘sciences of the letter’, as the more metaphysical and cosmological, in contrast to the well known ‘ilm al-ḥurūf. I am currently tracking the usage of ‘ulūm al-ḥarf, which seems to go back to at least the fourteenth century.</footnote>

<footnote n="95">95. Ibn Manẓūr, *Lisān al-‘arab*, 8.279.</footnote>

<footnote n="96">96. Cf. A. Shiloah, 'The Origin of Language and its Link with Music according to the Theory of Jābir ibn Hayyān,' *Al-Masāq* 21, no. 2 (2009): 159.</footnote>

<footnote n="97">97. Above, p. 29.</footnote>

<footnote n="98">98. See above p. 138.</footnote>
media, and which brings us close once again to the term paleographers use to describe
the tracing pattern of a letter, the *ductus*, that is, the movement pattern of the writing
instrument. Needless to say, the fact that these elementary letters are related to metrics
and prosody has doctrinal implications regarding the cosmogonic role of poetry and
song. In this regard, it must also be noted that the three *matres lectionis*, the semivowels
*alif*, *wāw*, *yā* ('glides', in linguistic terminology) are called in the grammatical tradition
*iturūf al-madd*, 'letters of extension',<sup>99</sup> with the same root of *midād*, the ink, and *mādda*,
matter, as explained above. An alternative name is *iturūf al-ʿilal*, 'causal letters' or
'letters of affliction', because as in Greek grammar, words with 'accidents' are viewed
as afflicted, ill, in opposition to 'healthy' words without accidents.<sup>100</sup>

Returning to our two branches, I should mention two other existing classifications
or typologies of the Islamic ‘science of letters’:

1) For Denis Gril<sup>101</sup> there is one first aspect he characterizes as ‘cosmological and Hellenic in origin’, present especially in the Jābirian corpus and in the *Epistles* of Ikhwān al-Ṣafā’; and a second aspect ‘metaphysical, spiritual, eschatological, inspired by the Qur’ān,’ and ‘represented by esoteric Shī‘ism and taṣawwuf.’

2) Sara Sviri and Michael Ebstein propose,<sup>102</sup> after a ‘comparative and analytical study’, two types designated by Greek letters: ‘the most familiar, *type α*’, is found in orthodox Islamic literature and in classical Sufi texts, and it reflects a ‘symbolic and etymological approach to the Arabic alphabet’ and especially to the *fawātiḥ*,<sup>103</sup> while notably eschewing any conception of letters as building blocks of creation in cosmogonic and cosmological contexts. The second ‘*type β*’ reflects an approach which views language, and in particular letters, as the primordial building blocks of the cosmos. This type is found in the Shī‘ī-Isma‘ili tradition and in Andalusian letter mysticism, for example in the writings of Ibn Masarra and Ibn ‘Arabī.

The first typology is more historical, based on demarcation between two distinct
doctrinal traditions: the Greek heritage and the original Islamic material. The second
typology is more idiographic, based on the premise of a distinct duality within the
Islamic tradition between ‘orthodox Sunni and classical Sufi’, and ‘Shi‘ī-Isma‘ili’.

Needless to say, both classifications have their usefulness, and this is not the place to
examine their aptitude in any detail. In any case, I shall not be making use of either of

<footnote n="99">99. See EALL, 2.308–10. *Al-madd iṭāla al-ṣawt*, ‘*al-madd* is an prolongation of the utterance.’ The many symbolic associations of the Arabic *matres lectionis* are explored in J. Canteins, *Phonèmes et archétypes: contextes autour d’une structure trinitaire*; AIU (Paris: G.-P. Maisonneuve et Larose, 1972).</footnote>

<footnote n="100">100. See EALL, 2.309.</footnote>

<footnote n="101">101. Gril, *The Science of Letters*, 146; adopted in Melvin-Koushki, *The Quest*, see p. 171.</footnote>

<footnote n="102">102. M. Ebstein and S. Sviri, ‘The So-called *Risālat al-iturūf* (*Epistle on Letters*) Ascribed to Sahl al-Tustarī and Letter Mysticism in al-Andalus,’ *Journal Asiatique* 1, no. 299 (2011): 230–32.</footnote>

<footnote n="103">103. The ‘openers of the suras’; see above 90.</footnote>
them, and I trust that the reader will have noted why I remain rather unconvinced on both accounts. The intricacy of the exchanges between the Greek heritage and simultaneous and subsequent traditions is simply too bewildering and opaque to allow for clear categorisations; and similarly, deciding to what extent we can consider the Islamic tradition a continuum or a clear-cut mosaic, and deciding where to set the boundaries between the different strands of Islamic esoterism is without doubt an uncertain task. Naturally, I remain perhaps just as unconvinced by the classification in ‘two branches’ posited above, since a clear demarcation between the two types of letter speculation I mentioned is not only elusive but it may prove eventually cumbersome. Hence I shall try to continue presenting the relevant evidence in forensic fashion, and only occasionally sum up the findings rather than trying to draw too many conclusions.

## Some Key Texts

Adding to the verses and other passages cited above, and to give a more rounded perspective of the sources of Islamic alphanumeric esoterism before moving on to other sources not directly religious, I shall present in the following paragraphs a few key passages taken from hadith and *tafsīr* literature. As in previous chapters, I will add my own commentaries to bring out the relevance of the citations to the present enquiry.

**Jawāmi‘ al-kalim** • There are a number of hadiths<fnref n="104" /> in which there is mention of the *jawāmi‘ al-kalim*, the ‘comprehensive plenitude of expressions’, as one of the Prophetic gifts. An oft-cited commentary introduces a reference to the nature of the letters,

> In the hadith ‘I was given the comprehensive plenitude of expressions (*jawāmi‘ al-kalim*),’ is meant the Noble Qur’ān, because God has comprehended in a small number of His words (*alfāẓ*) a multitude of meanings, so much so that it has been narrated: ‘there is no letter of the Qur’ān which does not contain seventy-thousand meanings.’<fnref n="105" />

In relation to this inexhaustibility of each particular element, and while commenting on the ‘verses of the ink’ (Q. 18:111 and 31:28) much later in Islamic history, Mulla Ṣadra Shirāzī would add the following: ‘And as His existential script (*kitābuhu takwīnī*) is endless, so His recorded script (*kitābuhu tadwīnī*), I mean the Noble Qur’ān, is also endless, because it is fashioned after its emitter (*qā’iluhu*).’<fnref n="106" /> We can appreciate how he

<footnote n="104">104. E.g. Bukhārī 7099; Muslim 1195; Tirmidhī 1640.</footnote>

<footnote n="105">105. Fakhr al-Dīn al-Ṭurayḥī, *Majma‘ al-baḥrayn*, 3 vols (Qum: Mu’assasa al-Bi‘thah, 1415 AH), 312, s.v. *j-m-‘*.</footnote>

<footnote n="106">106. Mullā Ṣadrā Shīrāzī, *al-Ḥikma al-muta‘ālīya fī al-asfār al-‘aqlīya al-arba‘a*, 6 vols (Tehran: Ministry of Culture / Islamic Guidance, 1386 HS), 5.322.</footnote>
is speaking of the ‘two Qur’āns’ or the ‘two books’, the *kitāb takwīnī* or cosmic book and the *kitāb tadwīnī* or ‘records’ book, exactly along the lines of the ‘two books’ or the *duplex liber*, the *liber mundi* or *liber creaturarum* and the *liber sacrae doctrinae* of the European middle ages.<fnref n="107" /> In the thirteenth century, ‘Azīz al-Dīn al-Nasafī had also spoken of the *Qur’ān-i tadwīnī* and *Qur’ān-i takwīnī*,<fnref n="108" /> but what is most important from our point of view is the ‘endlessness’ of the book. It is not based on the idea of incalculability, as if there were too many letters to be counted, but rather on the idea that every letter opens onto an innumerable quantity, hence constituting what has been called an ‘intensive magnitude’,<fnref n="109" /> analogue to the ‘density’ of the real numbers, and most importantly, since we are looking into the physical/cosmological correspondences, clearly distinct from an atomistic understanding of matter.<fnref n="110" /> This is a topic I shall have occasion to return to in later pages.

**A limit and a summit •** The following tradition, found in slightly different forms in various sources,<fnref n="111" /> is important as a source for the traditional multi-layered exegesis of the Qur’ān. I quote here the section, with minor comment, where it is shown how the multiple meanings depend partly on the nature of the letters.<fnref n="112" />

> في ذكر القرآن لكل حرف منه حدّ ولكل حدّ مطلع قيل معناه لكل حدّ مضعد يصعد
> إليه يعني في معرفة علمه

> ‘About the recitation (*dhikr*) of the Qur’ān: every one of its letters has a
> limit/terminus (*hadd*), and every limit has its place of ascent/departure
> point (*muṭṭala*).’ The meaning of ‘every limit’ is a summit towards which
> one ascends, that is, in the experiential comprehension of its knowledge (*fī
> ma’rifat ‘ilmihi*).<fnref n="113" />

<footnote n="107">107. Cf. Curtius, *European Literature and the Latin Middle Ages*, 321; C. Bradatan, ‘Berkeley and Liber Mundi,’ *Minerva* 3 (1999).</footnote>

<footnote n="108">108. See O. Safi, ‘Qur’an of Nature: Cosmos as Divine Manifestation in Qur’an and Islamic Spirituality,’ *Religions*, no. 2012 (2012): 127.</footnote>

<footnote n="109">109. L. de Freitas, ‘The Mathematical Continuum: A Haunting Problematic,’ *The Mathematics Enthusiast* 15, no. 1 (2018): 151.</footnote>

<footnote n="110">110. This is the ‘synechist’ position; see J. L. Bell, *The Continuous and the Infinitesimal in Mathematics and Philosophy* (Monza: Polimetrica, 2005), 57–9.</footnote>

<footnote n="111">111. References, which include Ṭabarī, Suyūṭī and Tustarī, in T. Mayer, ‘Traditions of Esoteric and Sapiential Quranic Commentary,’ in *The Study Quran: A New Translation and Commentary*, ed. S. H. Nasr (Harper Collins, 2015), 1661.</footnote>

<footnote n="112">112. See *ibid*. for a comparison with the rabbinic *pardes* acrostic and the scholastic hermeneutical *quadriga*.</footnote>

<footnote n="113">113. Abū ‘Ubayd al-Harawī, *Kitāb gharīb al-ḥadīth*, 6 vols (Cairo: al-Maṭābi‘ al-Amīrīya, 1984). Cf. R. Todd, ‘Qūnawī’s Scriptural Hermeneutics,’ chap. 7 in *The Spirit and the Letter: Approaches to the Esoteric Interpretation of the Qur’an*, ed. A. Keeler, S. H. Rizvi, and M. Nguyen (Oxford University Press, 2016), 308–309.</footnote>
The image of the ‘mountain summit of a letter’ is a striking one to convey the depth, in this case height (Lat. *altitudo*), of every element of the sacred text. It is easy to imagine the readers, when having access to the real knowledge (*maʿrifat ʿilmihī*) of the letters, as mountaineers walking along the summits of a vast range. This image of immensity expresses in a more graphic way the same ‘endless’ nature of each letter that we found in the previous passage.

**Beyond utterance •** In *Al-Kāfī*, ‘the Shīʿī Bukhārī’, that is, the most authoritative of the Shīʿī hadith collections, is found the following,

> خلق اسمًا بالحروف غير متصوّت وباللفظ غير منطق، وبالشخص غير مجدد، والتشبيه غير موصوف، وباللون غير مصبوغ...

He created names with letters without uttering a sound (*mutaṣawwit*), and with a word without speaking (*munṭiq*),114 with individuality without embodying (*mujassid*), with a similarity beyond qualities, with colour without hue...115

There is a rich textual tradition on the different kinds of divine names, at times strikingly similar to some passages of the Jewish *hekhalot* literature, with names of different lengths, cosmic attributes and functions. Some Muslim communities, small in numbers but large in doctrinal influence, like the Ismāʿīlīs and the Ghulat movements,116 developed complex cosmological schemes based on these names in combination with Qur’ānic material, like the speculations based on the ‘myth of Kūnī-Qadar’. This is based on the Qur’ānic cosmogonic imperative *kun* (‘Be!’) and the doctrine of *qadar* or predetermination, for ‘God brought all things into existence by means of kūnī, and predetermined them by means of *qadar*’ (*fa-bi-kūnī kawwana Allāh jamīʿ al-ashyāʾ wa-bi-qadar qadarahā Allāh*).117 In general, this and similar theories belong under the restricted letter speculation, and as such, in spite of their interest, I shall only be referring to them when they shed light on the comprehensive letter speculation.

What is to be noticed particularly in this hadith is the mention of an ‘un-linguistic language’ *in divinis*, with letters beyond utterance and with a word beyond language, in short, an intermediary realm (‘ālam mutawassīt), a *barzakh* where opposites are not

<footnote n="114">114. I follow Muḥammad Ṣāliḥ Māzandarānī, *Sharḥ Uṣūl al-Kāfī*, ed. ‘Alī ‘Āshūr, 12 vols (Beirut: Dār Iḥyā’ al-Turāth al-‘Arabī, 2000), 3.285 for the syntax. As the foremost commentator of the most authoritative hadith collection, Māzandarānī is often considered the Shī‘a equivalent of al-‘Asqalānī.</footnote>

<footnote n="115">115. Hadith 305, ch. 15,1.</footnote>

<footnote n="116">116. See, for the latter, M. Asatryan, *Controversies in Formative Shi‘i Islam: The Ghulat Muslims and Their Beliefs*, Shi‘i Heritage Studies 4 (London: I.B. Tauris, 2017), 5ff. with special attention to the mention of *Silsilat al-turāth al-‘Alawī*, a major collection of Ghulat sources published 2006–2013.</footnote>

<footnote n="117">117. See Ebstein, *Mysticism and Philosophy*, 41ff.</footnote>
necessarily dissociated. In the ‘world’ of the *barzakh*, forms are described as ‘measures devoid of matter’ (*maqādīr mujarrad ‘an al-mādda*),<fnref n="118" /> ‘unlike the forms of this material world and also unlike the forms of the spiritual world.’<fnref n="119" /> Another passage in the same commentary mentions ‘the mimetic and intermediary shapes or bodies’, *al-ashbāḥ ayy al-ajsām al-mithāliyya wa-al-barzakhiyya*, thus making clear that these intermediary forms are conceived as metaphysical models or patterns.<fnref n="120" />

## Back to Basics: Philosophy & Physics

Before moving forward in history, and taking advantage of the mention of the metaphysical dimension of the letters, we need to complete the Arabic picture of the semantic field we are studying. Following what we did in the initial pages of this enquiry, where I introduced the Greek concept of element citing Aristotle, it is now time to see what the Arabic scholars made of the polysemy of στοιχεῖον.

### The Metaphysics

With the passing of time, the study we now know as ‘metaphysics’ came to be known in Arabic under two different names: one very literal from the Greek, *mā ba‘d al-ṭabī‘a*, ‘what is beyond nature,’ and one more theological, *al-ilāhiyyāt*, ‘divine matters.’ As expected, Aristotle’s book has been known under these two names through history. This makes it more remarkable that the earliest name for the *Metaphysics* was *Kitāb al-Ḥurūf*, ‘The Book of Letters.’<fnref n="121" /> The name was due, it was explained, to the fact that the chapters were named sequentially after the Greek letters, starting with *Metaphysics Alpha*, and so on. This was of course the usual Greek practice to enumerate sections of a literary work. The prime example is the Homeric epics, but in philosophy it is noticeably the case of the books of Plato’s *Republic*, and of Aristotle’s *Physics*. Why would these others not be called also *Kitāb al-Ḥurūf*? It is certainly not my intention to start speculating, but in the context of the present work, after we have seen how the order and other features of the Greek alphanumeric series made of it a model for any system of principles, it would be hard to miss the possible implications of the title.<fnref n="122" /> In fact, it has been noted that another famous *Kitāb al-Ḥurūf*, by al-Fārābī, owes its

<footnote n="118">118. Note that *maqādīr* is also a technical term in prosody, meaning ‘metres’.</footnote>

<footnote n="119">119. Māzandarānī, *Sharḥ*, 1.129.</footnote>

<footnote n="120">120. *ibid.*, 3.52.</footnote>

<footnote n="121">121. Ibn Nadīm (tenth century) gives it as the title, with *al-ilāhiyyāt* as an alternative; see A. Bertolacci, ‘On the Arabic Translations of Aristotle’s *Metaphysics*, *Arabic Sciences and Philosophy* 15, no. 2 (2005): 244ff.</footnote>

<footnote n="122">122. Cf. D. Abercrombie, ‘What is a “Letter?”,’ *Lingua* 2 (1949): 54–63, on the ancient and medieval meaning of ‘letter’ in general.</footnote>
title not only to Aristotle’s work, but also to the understanding that Greek ‘particles’ (‘particle’ is one of the important grammatical meanings of ḫarf) are ‘comparable to the logical constants of an ideal language’ and ‘demarcate the domain of metaphysics.’<sup>123</sup> It is worth noting that al-Fārābī himself refers to Aristotle’s work as ‘al-kitāb al-mawsūm bi-al-ḥurūf’, ‘the book known by letters,’ i.e. the book known by the letter-names of its chapters.

Let us now turn our attention to the ‘Glossary’ in book Δ, where this thesis started. I follow the text as found in Averroes’ *Tafsīr*,<sup>124</sup> ‘a fundamental witness to the different versions of the Arabic *Metaphysics*,’<sup>125</sup> and I shall bring in for comparison the Hebrew version.<sup>126</sup>

The Arabic word used in *Tafsīr* Δ3, and in general most frequently to translate
στοιχείον, is a calque from the Greek, *usṭuqus* ἀστάξ (pl. *usṭuqusāt*), found with
numerous alternate spellings and vocalisations<sup>127</sup> which are testimony to the instability
of the foreign word. Other indigenous Arabic terms are occasionally used, like ‘unṣūr
(pl. ‘anāṣir), a ‘race, lineage’, i.e. conveying the meaning of origin, or *rukn* (pl. *arkān*), a
‘pillar, cornerstone’, i.e. a structural support, but in metaphysical terminology, *usṭuquss*
tends to be prevalent. Whereas Arabic translators decided to use this calque, which
would be fleshed out with meaning through the centuries of literature, it is notable
that Hebrew translators decided to use native words like *yesod*, ‘fundament’, ‘etsem,
‘bone, gist’, *shoresh*, ‘root’, and even *em*, ‘mother’, or *av*, ‘father’,<sup>128</sup> thus displaying in
the different contexts the many aspects of the concept. It is as if the Arabic authors,
recognising the untranslatable semantic complexity—precisely what we have been

<footnote n="123">123. S. Menn, ‘Al-Fārābī’s *Kitāb al-Ḥurūf* and his Analysis of the Senses of Being,’ *Arabic Sciences and Philosophy* 18, no. 1 (March 2008): 59; this article gives a fine treatment of al-Fārābī’s scope and intention. Cf. above, p. 86, my reference to ‘prepositional cosmology,’ especially to Dörrie, ‘Präpositionen und Metaphysik.’</footnote>

<footnote n="124">124. Ibn Rushd, *Tafsīr Mā baʻd al-ṭabīʻa*, ed. M. Bouyges, 3 vols, Bibliotheca Arabica Scholasticorum, Série Arabe, V, 2 (Beirut: Imprimérie Catholique, 1938), 499ff. See also Halper, ‘Averroes on Metaphysical Terminology,’ especially the glossary tables, 436ff.</footnote>

<footnote n="125">125. Bertolacci, *On the Arabic Translations*, 250.</footnote>

<footnote n="126">126. While the concept relevant to this research does not presently warrant a wider survey, I would like to draw attention to the valuable philosophical glossaries in the Arabic tradition which, though varying in scope and extension, could be considered successors of *Metaphysics* Δ. K. Kennedy-Day, *Books of Definition in Islamic Philosophy: The Limits of Words* (London & New York: RoutledgeCurzon, 2003) gives a good introduction. Al-Kindī, Ibn Sīnā and Isaac Israeli authored each a *Kitāb al-ḥudūd, Book of Definitions*; al-Fārābī wrote his *Alfāẓ al-musta‘mala fī al-manṭiq, Terms Used in Logic*, similar to al-Ghazālī’s glossary in his logic treatise *Mi‘yār al-‘ilm*; Jurjānī (d. 1078 AD) wrote a *Compendium of Definitions, Mu‘jam al-ta‘rifāt*.</footnote>

<footnote n="127">127. Including *isṭaqis, asṭaqis* and others, see *Munjid*, 11.</footnote>

<footnote n="128">128. *Thesaurus philosophicus linguae hebraicae* (Otsar ha-munahim ha-filosofiyyim) (Berlin: Eshkol, 1928) (hereafter cited as Klatzkin), ss.vv.</footnote>
studying—realised that they had no equivalent that could do justice to the original and decided to use the Greek word which acted as an empty semantic container.<fnref n="129" />

On some occasions, when the grammatical meaning is clear, the Arabic translators have also used *harf*, and the Hebrew *ot*.<fnref n="130" /> There is not much of immediate interest for us in the detailed comparison between the texts of the *Metaphysics*, since the translators have used different words when necessary, bringing out the aspects of the concept according to the context. Other major works of philosophy, like Ibn Sīnā’s section on metaphysics in his *Shifā*’ follow the same flexible usage, and I shall cite some of them in the coming pages, but only specially relevant passages.<fnref n="131" />

In the wider philosophical and scientific literature, a recurrent device which highlights the difficulty of the translation is the use of a hendiadys (two joint nouns expressing the one source term) to translate *usłuquiss*. In Aristotle’s *Rhetoric* (II, 26, 1403a18 and elsewhere), the combination *hurūf wa-uṣūl*, ‘letters and principles’ is used to translate στοιχεῖα; alternative combinations include *hurūf ayy usłuquussāt*, ‘letters, i.e. “elements”’, or also ‘*anāṣir wa-uṣūl*, ‘elements and principles.’<fnref n="132" />

It is also worth noting, and again an indicator of the early semantic instability of *usłuquuss*, how the original Greek expression τὰ καλούμενα στοιχεῖα, ‘the so-called elements,’<fnref n="133" /> was occasionally translated literally in Arabic in spite of losing its meaning in a new language: *allatī tusammā usłuquussāt*, ‘the ones called “elements”’,<fnref n="134" /> does no longer convey the implicit lexical objection read by most interpreters of the Greek text, because *usłuquuss* is already a foreign term and an empty vessel in Arabic, with no previous meaning to play upon. In contrast to this, we find also the variant *allatī tusammā al-uṣūl*, ‘the ones called principles,’ which makes better sense in translation.<fnref n="135" />

Galen, notably, wrote a treatise entitled Περὶ τῶν καθ' Ἱπποκράτην στοιχείων, *On the*

<footnote n="129">129. The ending in *sin of usłuquuss* has been considered evidence that the word comes from στοῖχος, ‘row’ instead of στοιχεῖον. Even though this sounds plausible and might give rise to interesting morphological precisions, I doubt that it would have much impact on the semantics of the term.</footnote>

<footnote n="130">130. See Halper, *Averroes on Metaphysical Terminology*, 2,80; 24,8.</footnote>

<footnote n="131">131. For a number of examples, see G. Endress and D. Gutas, *A Greek and Arabic lexicon: Materials for a Dictionary of the Mediaeval Translations from Greek into Arabic*, Handbuch der Orientalistik. Erste Abteilung, der Nahe und Mittlere Osten (Leiden: Brill, 2013) (hereafter cited as GALex), s.v. *usłuquuss*, and see in particular the still unpublished filecards made available online at Glossarium Graeco-Arabicum ([http://telota.bbw.de/glossga/](http://telota.bbw.de/glossga/)).</footnote>

<footnote n="132">132. Cf. above, p. 100, my reference to the use of ‘*unşur* in Nicomachus *De Arith.*, 2, 1. Kraus’ assertion that *usłuquuss* was never used in the sense of ‘letter’ could only be true of a restricted alchemical corpus; see P. Kraus, *Jābir ibn Hayyān. Contribution à l’histoire des idées scientifiques dans l’Islam II: Jābir et la science grecque*, Mémoires de l’Institut d’Egypte 45 (Cairo: Institut français d’archéologie orientale, 1943), 237.</footnote>

<footnote n="133">133. See above p. 14; Diels, *Elementum*, 25.</footnote>

<footnote n="134">134. Arist. *Gener. anim.* I, 1, 715a11; see GALex, 218.</footnote>

<footnote n="135">135. Artem. *Onirocr.* 5.21.</footnote>
*Elements according to Hippocrates*, in which he compares ἀρχαί to στοιχεῖα, discussing the meanings of these terms according to several schools. It was partially translated into Arabic and commented by Ḥunayn ibn Isḥāq (*Kitāb Jālīnūs fī al-usṭuqussāt alā ra’y Abuqrāt*), who tries to shed some light on the confusion regarding the different translations of *usṭuquss*.136 This ‘element’ ‘differs from *unṣur* in that, unlike the latter, it possesses qualities,’ and from *ibtidā* because the *usṭuqussāt* ‘are “parts of the generated thing, existing in potentia”’.137 I shall not enter into the discussion, but only point out that the fact that *usṭuqussāt* was the term used for the title would seem to agree with the undecided status of the elements in this treatise, halfway between material reflection of the elemental qualities and corporeal *minima*, or sometimes considered minimal in respect of size, and others as minimal in respect of quality.138

A valuable contrast is here furnished by the translation of the most famous of the related titles, namely Euclid’s *Στοιχεῖα*, which became in Arabic the unequivocal *Uṣūl* or *Uṣūl al-handasah, Principles of Geometrical Construction*<fnref n="139" /> (and in Hebrew *Ha-Yesodot, The Foundations*). Whereas the meaning of *στοιχεῖα* in a medical or chemical context was elusive and hard to define, it seems to have been clear in the logical, mathematical sense. On a similar note, Euclid is known to have also written, following Pythagorean teachings, a treatise on the elements of music, and it is reported that Proclus, together with his disciple Marinus, pointed to a rapprochement between Euclid’s *Elements* and the elements of alchemy. Though sadly not extant, the musical treatise was related to an anonymous text dealing with the *στοιχεῖα* of music and alchemy, and attributed to an unidentified Zosimus.<fnref n="140" /> The underlying common ground here is the study of harmonics, the theoretical arithmetic basis for the tuning of musical instruments, through which mathematical proportions are in a way transmuted and made tangible in sound.<fnref n="141" />

All these chemical, medicinal, musical and alchemical tangents of the science of the elements set the scene for an important landmark in the development of our concept in Arabic tradition, the works of Jābir ibn Ḥayyān, with which we shall bring this chapter to an end.

<footnote n="136">136. See G. Bos and Y. T. Langermann, ‘An Epitome of Galen’s on the Elements Ascribed to Ḥunayn ibn Isḥāq,’ *Arabic Sciences and Philosophy* 25 (2015): 36.</footnote>

<footnote n="137">137. *Ibid*., 36–7.</footnote>

<footnote n="138">138. R. J. Hankinson, ‘Substance, Element, Quality, Mixture: Galen’s Physics and His Hippocratic Inheritance,’ consulted on 21 June 2018, *Aitia (online)* 7, no. 2 (2017): 11.</footnote>

<footnote n="139">139. Also, rarely, *al-Usṭuqussāt*; see W. Fischer and H. Gätje, *Grundriss der arabischen Philologie*, 3 vols (Reichert Verlag, 1987), III.62.</footnote>

<footnote n="140">140. See A. Barbera, *The Euclidean Division of the Canon: Greek and Latin Sources*, vol. 8 (Lincoln and London: University of Nebraska Press, 1991), 11, for a thorough study of the Κατατομὴ κανόνος.</footnote>

<footnote n="141">141. See Shiloah, *The Origin of Language*, 154, for the corresponding phonetic-alchemical correspondence.</footnote>
## Jābir and ‘The Element’

Alchemical works began to enter Islamic lands from Alexandria as early as the seventh century, even before the time of Jābir ibn Hayyan, a legendary figure of the eighth and early ninth centuries—a disciple of Ja‘far al-Ṣādiq—who is often viewed as the founder of Arabic alchemy, and whose image would be enormously influential in later European alchemical literature under the name of Geber. The authorship and Arabic provenance of the Latin writings ascribed to him have been the object of the ‘Geber problem’,<fnref n="142" /> but I shall not be dealing with these works, as there is an earlier and large Arabic corpus of works in which the different terms used to translate στοιχεῖον coexist in remarkable ways.

It is generally agreed that the name ‘Jābir’ stands more *Homericο* for a collective rather than a single author, and it is established that the chronology of ‘his’ life does not quite agree with the possible dates of large part of his works. I shall be referring to the person and the received chronology<fnref n="143" /> with the understanding that they may still correspond to a significant part of a historical Jābir, and that in any case they correspond to a part of the conceptual story I am narrating here.

Just as in Jābir’s works are blended the Greek philosophical influence that came from Ḩarrān, and the Shī‘ī heritage in doctrines of Ismaili and Qarmatian character, we find within the corpus a remarkable doctrine of the *usṭuquiss* and also a very developed isopsephic technique under the name of the ‘balance of the letters’ (*mīzān al-ḥurūf*).<fnref n="144" />

## The ‘Element’ of the Foundation

*Kitāb al-usṭuquiss al-uss* is the title of the exposition presented in the first four treatises of the *112 Books*, the first of the four groups of writings in the Jābirian corpus.<fnref n="145" /> It consists of three numbered treatises and a fourth one which acts as a *tafsīr* of the previous three. The title, *The Element of the Foundation*, has a remarkable Milesian ring to it,<fnref n="146" /> echoing early ‘one element’ cosmologies, like ‘All is water’ and ‘All is fire,’ as

<footnote n="142">142. For a summary of the debate, see A. Y. Al-Hassan, ‘The Arabic Origin of the *Summa* and Geber Latin Works: A Refutation of Berthelot, Ruska and Newman on the Basis of Arabic Sources,’ in *History of Science and Technology in Islam*, now published also as chapter 3 of his *Studies in al-Kimya* (Georg Olms, 2009).</footnote>

<footnote n="143">143. Muḥammad ibn Isḥāq Al-Nadīm, *Al-Fihrist*, ed. Gustav Flügel (Leipzig: F. C. W. Vogel, 1872), 354.</footnote>

<footnote n="144">144. See the extensive annotated bibliography in P. Kraus, *Jābir ibn Hayyān. Contribution à l'histoire des idées scientifiques dans l'Islam I: Le corpus des écrits jabiriens*, Mémoires de l'Institut d'Egypte 44 (Cairo: Institut français d'archéologie orientale, 1942).</footnote>

<footnote n="145">145. The four groups are: *The 112* (sc. treatises), *The 70*, the *Books of the Balances* (*Kutub al-mawāzīn*), and *The 500*; see P. Zirnis, ‘The *Kitab Ustuqus al-Uss* of Jabir ibn Hayyan’ (PhD diss., New York University, 1979), 22.</footnote>

<footnote n="146">146. Bos and Langermann, ‘*An Epitome of Galen’s*,’ 38.</footnote>
they were characterised by Aristotle. *Al-uss* (pl. *asās*) has strong building connotations in an architectural sense,<fnref n="147" /> and it is often used to translate Gr. θεμέλια, foundation stones. In combination with *usṭuquss*, the reference is clearly to ‘foundation’ in a sense close to matter, and in any case not of the more abstract metaphysical level, and this agrees with the alchemical context, with the liminal science and art of transmutation.

Due to the alchemical practice of ‘scattering of knowledge’ (*tabdīd al-‘ilm*), whereby no topic is treated in linear form, but rather as if in a mosaic, with strands of a single discourse occurring and recurring in seemingly haphazard fashion, it takes some pages for Jābir to begin to explain what is meant by the title of the book, then it takes longer to develop the explanation, and the definitions pile up as so many facets of the concept: the first definition of ‘element’ follows Aristotle, ‘something into which all things dissolve and of which they are composed,’ but shortly after there is a sharp turn into the alchemical proper, ‘the philosophers’ stone of virtuous colour... this is the “element” of this Art.’<fnref n="148" /> Further down the text, the ‘four pillars’ (*arkān*), referring to the four elemental bodies, are said to be, each one, an *usṭuquss* too, and thereafter the title of the treatise is made clear: it is called ‘*The Element of the Foundation*’, because it sums up the dissolution and composition of the parts of the elixir,’ while *al-uss* indicates the fundamental role of this particular treatise within the *112 Books*.<fnref n="149" />

Later in the book, in the second part, a direct reference is made to the Galenic discussion mentioned above, where ‘*unṣur* is given as a synonym of element.<fnref n="150" /> The discussion goes along the lines of philosophical discourse and several opinions are given from different sources: the ‘Element’ is identified successively with the ‘receptive matter’ (*mādda al-mawḍū‘a*), with a ‘religious idea’ (*ma‘nā diyānī*), and with ‘guidance itself’, and ‘the art and the practice’ (*al-ṣanā‘a wa-al-‘amal*), in a way that reminds of Sufi pious practices; finally, the ‘Element’ is identified to the Prophet and the ‘Foundation’ (*al-uss*) to a legatee (*waṣī*), who would most likely refer to ‘Alī.<fnref n="151" /> The fourfold introduction to the *112 Books* is thus, from our point of view, an extraordinary catalogue of the potential meanings of the ‘Element’, ranging from the Hellenistic philosophical to the Islamic Imāmī. But perhaps, and more simply, it was that the semantically malleable and high-born term was a perfect candidate to be the centre of a cosmological and alchemical discourse.

<footnote n="147">147. It is defined as *așl al-bină*, see Ibn Manẓūr, *Lisān al-‘arab*, 6.6.</footnote>

<footnote n="148">148. K. *Uṣṭuquss al-uss I*, in Jābir ibn Hayyān, *Muṣannafāt fī ‘ilm al-kīmīyā* (*The Arabic Works of Jābir ibn Hayyān*), ed. E. J. Holmyard (Paris: Geuthner, 1928), 72.</footnote>

<footnote n="149">149. *ibid.*, 73; Zirnis, ‘*The Kitab Ustuqus*,’ 41.</footnote>

<footnote n="150">150. Jābir ibn Hayyān, *Muṣannafāt*, 79ff.</footnote>

<footnote n="151">151. *ibid.*, 82; Zirnis, ‘*The Kitab Ustuqus*,’ 120.</footnote>
The Balance of the Letters

In Jābir’s historical context—either the seventh or the ninth century in an Islamic
environment—any mention of the mīzān would have evoked an immediate association
with Sura al-Raḥmān (Qur’ān 55:7–9), ‘He has set the balance (mīzān) so that you may
not exceed in the balance: And establish weight (wazn) in justice and do not fall short
in the balance.’ Jābir’s balance, just as in this Qur’ānic context, was meant to measure
all of creation; the entire universe could be deciphered through its laws.<fnref n="152" /> In keeping
with the customary ‘scattering’, the ideas on the Balance are scattered throughout the
144 treatises of the Kutub al-mawāzīn, but the practical gist is that it is a method
of letter manipulation, called the ‘balance of the letters’ (mīzān al-ḥurūf), and based
completely on the numerical values of the letters. These values allowed the alchemist
to calculate or decipher the intrinsic properties of animals, plants, minerals and all
creatures, thus acquiring knowledge with a view to the obtention of the alchemical
elixir. The relation to the transformative power of alchemy is established on several
levels: this manifestation of the operative science of letters and words (sīmiyā) is a
science of the transmutation of language just as al-kīmiyā deals with the transmutation
of matter.<fnref n="153" /> If we recall the patronage of Hermes, god of alchemy, upon language, it
is easy to see the shared characteristics between the two realms: the mobility, the ever
shifting bearings, the uninterrupted flow of movement, either as a phonetic stream of
sounds or a graphical sequence of characters which metamorphose into each other
incessantly, like snakes.<fnref n="154" />

The principle underlying Jābir’s Balance is ‘the coordination between the letters forming the words and the Natures or elements constituting the things named.’<fnref n="155" /> It is not only a manifestation of the seminal idea explored in the *Cratylus*, of language as a direct prolongation of reality and a doorway to reality, but it is also the clearest manifestation we have found so far of the total identification between letter, number and concept; it is the science of *names as alphanumeric realities*. It can naturally be viewed as a kind of particle physics, and this is why it has often been compared to the atomism of Democritus and to that of the *Timaeus*.<fnref n="156" /> In fact, the lineage proposed for the precedents of Jābir’s Balance retraces closely some stages of the previous pages of this work: the association with the Pythagorean tradition is there, as is the affinity with Philo’s cosmology.

More specifically into the Balance theory, it is through the four elements—or more

<footnote n="152">152. Zirnis, *The Kitab Ustuqus*, 20.</footnote>

<footnote n="153">153. P. Lory, *La Science des lettres en Islam* (Paris: Dervy, 2004).</footnote>

<footnote n="154">154. See above, p. 49.</footnote>

<footnote n="155">155. Kraus, *Jābir et la science grecque*, 236.</footnote>

<footnote n="156">156. *ibid.*, 237.</footnote>
precisely the elemental qualities—that beings relate to their numeric values. The isopsephic analysis of the words allows the alchemist to determine the quality of the particular mixtures and their deficiencies or excesses, and so to bring them closer to the perfection of the elixir.<fnref n="157" /> Jābir expresses forcefully the interpenetration between the ‘natures’ (ṭabā’i‘) (sc. of the four elements or the qualities) and the letters (ḥurūf): anẓur ilā al-ḥurūf kayfa wuḍi‘at ‘alā al-ṭabā’i‘ wa-ilā al-ṭabā’i‘ kayfa wuḍi‘at ‘alā al-ḥurūf, ‘See how the letters are imposed (wuḍi‘at) on the Natures, and how the Natures are imposed on the letters,’ and later ‘how they transform into (tantaqal) each other…’<fnref n="158" /> As could be expected, the relation between the Jābirian writings and the Arabic grammatical tradition is strongly apparent in some of the treatises and in the terminology.<fnref n="159" /> Similarly evident is the connection to the Greek arithmological tradition, running through a line of Pythagorean references. But what is characteristic here is the accomplished synthesis. In later times, a comparable, if less comprehensive, doctrine developed in a Jewish milieu, invoking as a forerunner Bezalel ‘the prototype of alchemists’, whom we had encountered in previous pages as the divinely inspired craftsman ‘who knew how to combine the letters by which heaven and earth were created.’<fnref n="160" />

<figure><img src="image_16.png" /></figure>

In these two doctrines from the Jābirian corpus we find expressed in more than one way the intrinsic dualities of the concept of στοιχεῖον: one deals with the more philosophical sense and the other with the more grammatical; but also it is as if one of them had to do mostly with the singular στοιχεῖον, the one universal ‘element of foundation’, while the other has to do with the multiplicity manifest in the alphabetic series, στοιχεῖα. What is common to both is the *Alchemy*, meaning by this the power attributed to the ‘element’ and the ‘letters’, and also their liminal, transformative, properly *alchemical* character.

<figure><img src="image_17.png" /></figure>

More generally now, trying to take stock of the previous chapters before moving on to the last part, a similar pattern can be discerned in the different stories of the στοιχεῖα in the Abrahamic scriptural and in the Hellenistic traditions: it is a pattern of incorporation, of embodiment of the doctrine of the letter-numbers, moving from lofty cosmological

<footnote n="157">157. I am very grateful to Sébastien Moureau for sharing his Jābirian knowledge. Cf. Ebstein, *Mysticism and Philosophy*, 97.</footnote>

<footnote n="158">158. Kraus, *Jābir et la science grecque*, 239.</footnote>

<footnote n="159">159. The key name of the ‘balance’, mīzān, is directly related to wazn, one of the most fundamental terms of Arabic grammar, meaning originally ‘weight’, but used to denote a morphological ‘pattern’ or ‘template’, and in prosody a ‘metre’; see EALL, 2.448–50.</footnote>

<footnote n="160">160. Patai, *The Jewish Alchemists*, 296.</footnote>
and theological speculations to a more humanly accessible reality, either through the
soteriological and ascetic religious developments or through the transformation of
alchemical techniques. It is not a complete process, and this is why I shall directly
continue to explore the developments as if in a second historical stage, when every
particular tradition had continued to evolve and to subtly interpenetrate each other in
countless ways around the Mediterranean.
# Part III

## World Construction:
Systems of Cosmic Design
Introduction: System Building

After having scratched the surface of the ‘scriptural’ **foundations** of the alphanumeric
identity in Late Antiquity and the early Middle Ages, I shall employ the following
three chapters to illustrate with a few significant examples the **elaborations** that
signal the transformation of the concept we follow. This transformation is manifest
in doctrinal **crystallization**, as in **systematic** expositions of previously unconnected
or dimly connected aspects, and it is a transformation which can be seen at once
as an indication of a mature sophistication, and as the heralding of the end of an
‘alphanumeric age’ *stricto sensu*.<fnref n="1" />

As in Part 2, I will again devote one chapter to each of the three Abrahamic faiths,
more for methodological ease than to emphasise very clear doctrinal distinctions.
Rather, as shown variously by the amalgamation of the Hermetic tradition into the
Jewish, Christian and Muslim doctrinal corpora, the High Middle Ages present us again
and again with the inspiring evidence of a fully shared intellectual life among scholars
of the three faith communities. My exposition will be centred, with a few necessary
complements and asides, on key passages from the *Sefer Yetsirah*, certain doctrinal
developments from Aquinas’ *Summa Theologiae* and some passages from Ibn ‘Arabī’s
works.

<footnote n="1">1. More details about this below, p. 251.</footnote>
# Chapter 7

## *Sefer Yetsirah: The Bright Jewel of Alphanumeric Cosmopoiesis*

The *Sefer Yetsirah* (henceforth *SY*) would surely rank among the very first of a list of works whose size is out of proportion with their cultural impact; even the longest of its various versions is just above two thousand words,<fnref n="1" /> and the shortest of its versions retains perfect readability even when set on one single page, as in the illustration on the following page which contains the text in full. The *SY* would also rank very high among books whose obscurity of origin is in contrast to the brightness of their influence. It is like a precious stone: we know next to nothing about its origin, with only guesses about its authorship and date of origin, and yet, like a brilliant<fnref n="2" /> with a structure based on a pattern of thirty-two, it seems to have gathered and refracted within its symmetry the light received from previous centuries of alphanumeric wisdom literature, and then to have reflected it with renewed force and charm for later generations.

<figure><img src="image_18.png" /><figcaption>PATTERN OF THE CUT OF A BRILLIANT, TOP VIEW</figcaption></figure>

<footnote n="1">1. See D. Karr, 'Notes on Editions of *Sefer Yetzirah* in English,' 1; this most useful bibliographic survey has been kept up-to-date since 1991 and gives a comprehensive overview of the available literature in English, with a few references to secondary literature in other languages too.</footnote>

<footnote n="2">2. 'Brilliant', used as a noun, refers here expressly to the diamond cut designed in the early twentieth century to optimise the light return of the gemstone.</footnote>
שלשים ושתיים נתיבות פלאות חכמה חקק יה יהוה
צבאות בשלש ספרים בספר וספר וספור. עשר ספרירות
בלי מה מספר עשר אצבעות חמש כנגד חמש וברית
יחיד מכוונה באמצע במילה ולשון ופה. עשר ספרירות בלי
מה עשר ולא תשע, עשר ולא אחת עשרה הבן בחכמה
וחכם בבינה בחון בהם וחקור מהם והעמד דבר על בריו
והשב יוצר על מכונו. עשר ספרירות בלי מה בלום פיך
מלדבר בלום לבך מלהרהר ואם רץ ליבך שוב למקום
שכך נאמר רצוא ושוב ועל דבר זה נכרתה ברית. עשר
ספרירות בלי מה נעוץ סופן בתחילתן ותחילתן בסופו
כשלהבת בגחלת שהיוצר אחד ואין לו שיני ולפני אחד
מה אתה סופר. עשר ספרירות בלי מה ומידתן עשר שאין
להן סוף עומק ראשית ועומק אחרת עומק טוב ועומק
רע עומק רום ועומק תחת עומק מזרח ועומק מערב
עומק צפון ועומק דרום ואדון יחיד אל מלך נאמן מושל
בכולן ממעון קדשו ועד עדי עד. עשר ספרירות בלי מה
צפתית כמראה הבזק ותכליתם אין להן קץ ודברו בהן
כרצוא ושוב ולמאמרו כסופה ירדופו ולפני כסאו הם
משתחוים. עשר ספרירות בלי מה אחת רוח אלהים חיים
זו היא רוח הקודש. שתים רוח מרוח חקק וחצב בה
אDom מרחות השמים. שלש מים מרוח חקק וחצב בהם
תוהו ווהבו רפש וטייט חקק כמין ערגה הציבן כמין
חומה סיכן כמין מעזיה. ארבע אש ממים חקק וחצב
בה כסא כבוד וכל צבא מרום שכך כתוב עשה מלאכיו
רוחות. חמש חתם רום פנה למעלה וחתמו ביהו שש
חתם תחת פנה לrima וחתמו ביהו שבע חתם מזרח פנה
לפנינו וחתמו בהוי שמנה חתם מערב פנה לאחריו וחתמו
בהיו תשע חתם דרום פנה לימינו וחתמו בויה עשר חתם
צפון פנה לשמאלן וחתמו בוהי. אילו עשר ספרירות בלי
מה רוח אלהים חיים ורוח מים אש. ממעלה מטה מזרח
مערב צפון ודרום. עשרים ושתים אותיות יסוד שלש
אמות שבע כפולות ושתים עשרה פשוטות. עשרים
ושתים אותיות חקוקות בקול חצובות ברוח קבועות בפה
בבחמש מקומות אח העו בו מף גי כק דט לנת זש שרץ.
עשרים ושתים אותיות קבועות בגלגל חזר גלגל פנים
ואחור סימן לדבר אין בטובה למעלה מעונג ואם ברעה
לrima בנגנ. עשרים ושתים אותיות חקקן תצף שקלהn והמירין כיצד שקלהn והמירין אלף עם כלן, וכלן עם
אלף בית עם כלן וכלן עם בית וכלן חוזרות חילה נמצאו
יוצאות במאתים ושלשים ואחד שערים נמצא כל היצור
وכל הדבור יוצא בשם אחד. יצר מתוהו ממש ועשאו
באש וישנו וחצב עמודים גדולים מאויר שאינו נתפש.
שלוש אימות אמש יסודן כו זכות וכף חובה ולשון חק
מכרזע בינתיים. שלוש אמות אמש סוד גדול מכוסה
ומפולא וחתום בשש תבעות ומנו יוצאין אש מים ורוח
ומחותל בזכר ונקבה. שלש אמות אמש למעלה מים לrima
ורוח חק מכרזע בנתיים. שלש אימות אמש מם דוממת
שין שורקת אלף רוח חק מכרזע בנתים. המליך את אלף

ברוח וקשר לו כתר וחתם בו אויר בעולם רויה בשנה
וגיה בנפש. המליך את מם במים וקשר לו כתר וחתם בו
ארץ בעולם וקור בשנה ובטן בנפש. המליך את שין באש
וקשר לו כתר וחתם בו שמים בעולם וחשום בשנה וראש
בנפש. שבע כפולות בגד כפרת מתנהגות בשתי לשונות
חיים ושלום וחכמה ועושר חן זרע ממשלה ומתנהגות
בשתי לשונות בי בי גימל גימל דלת דלת כך כך פי פי
ריש ריש תיו תיו רק וקשה גיבור וחלש. שבע כפולות
בגד כפרת משתמשות בשני לשונות בֵּי בֵי גימל גָּמָל דֶּלֶת
דֶּלֶת כָּף כָּף פִּי פִּי הַיִּשׁ הַיָּהִיו תְּהוּךְ רַך וקשה תבנית גבור
וחלש כפולות שהן תמורות תמורת חיים מות תמורת
שלום רע תממה תמורת חכמה אולת תמורת עושר עוני תמורת
זרע שממה תמורת חן כיאור תמורת ממשלה עבדות.
שבע כפולות בגד כפרת שבע קצוות והיכל קדוש מוכן
באמצע ואינו נושא את כולם. שבע כפולות בגד כפרת
חקקן חצבן צרפן וצר בהן כוכבים ימים ושערים. כאיזה
צד צרפן שתי אבנים בונות שני בתים שלוש בונות ששה
בתים ארבע בונות עשרים וארבע בתים חמש בונות מאה
ועשרים בתים שש בונות שבע מאות ועשרים בתים שבע
בונות חמשת אלפים וארבעים בתים מיכאן ואילך צא
וחשוב מה שאין הפה יכול להדבר ומה שאין האוזן יולח
לשמוע. חיצה את העדים והgehיד אחה אחד לבדו עולם
לבדו, שנה לבדה נפש לבדה. שתים עשרה פשותות
הוזיטלןסchaft יסודן ראיה שמיעה ריחה שיחה לעיטה
תשמיש מעשה הילוך רוגז שחק הרהור שינה. שנים
ערבי אלכסון גבול מזרחית צפונית גבול מזרחית
דרומית גבול מזרחית רומית גבול מזרחית תחתית גבול
צפונית תחתית גבול צפונית מערבית גבול צפונית רומית
ערבית רומית גבול דרומית תחתית גבול דרומית
רומית. שתים עשרה פשוטות חקקן צרפן חצן שקלהn
והמירין וצר בהם מזלות וחדשים ומניגים. אילו עשרים
ושתים אותיות שהבן יסד יה' יה' צבאות אלהים חיים
אלחי ישראל רם ונשא שוכן עד וקדוש שמו. שלשה
אבות ותולדותיהן ושבעה כבשים וצבאותיהן ושנים עשר
גבולי אכלוס וראיה לדבר עדים נאמנים עולם שנה
ונפש. חק עשרה שלשה ושבעה ושנים עשר פקודין בתלי
ונגלג ולב. תלי בעולם כמלך על כסאו גלגל בשנה כמלך
במדינה לב בנפש כמלך במלחמה. גם כל חפץ זה לעומת
זה עשה אלהים טוב לעומת רע רע מרע וטוב מטוב טוב
מבחין את רע ורע מבחין את טוב טובה גנוזה לטובים.
עשאן כמין מריבה וערכן כמין מלחמה גם את זה לעמת
זה עשה האלהים. שלשה אחד אחד לבדו עומד שבעה
שלשה חלוקין על שלשה ואחד חוק מכרזע בנתיים שנים
ערש עומדין במלחמה שלשה אויבים ושלשה אוהבים
שלשה מחיים ושלשה ממיתים וכולן אדוקין זה בזוה.
כשהבין אברהם אבינו וצר וצרף וחקר וחשב ועלתה בידו
ניגלה עליו יי
Thanks to Hayman's and Gruenwald's works,<fnref n="3" /> effectively the two most significant landmarks in the textual history of SY, and unless new manuscripts are discovered, we are nowadays probably as close as we can be to a comprehensive vision of the three main recensions in which SY appears from the earliest evidence.<fnref n="4" /> The earliest evidence of the existence of SY is given by one of its commentaries,<fnref n="5" /> the one authored in Arabic by Saʻadyā Gaon and dated 931, which is our *terminus ante quem*.<fnref n="6" /> Because by the time of Saʻadyā's commentary the textual tradition already exhibits three well attested strands, it seems obvious that the origin must be found before the ninth century, and in fact, it is the quest for the earliest possible date of existence of the text that has been occupying the experts for decades, with arguments ranging from the second century AD to the ninth century.<fnref n="7" /> Because most arguments for an earlier dating are based on doctrinal parallels, I shall leave for later further references to them.

It has become almost fashionable to elaborate on the 'fluidity' of the textual state of SY, which, according to Wolfson, 'should be seen rather as a composite of distinct literary strands,'<fnref n="8" /> instead of being considered a text in any modern sense. I shall not enter into textual discussions other than in the few passages related to this research, but what could be observed is that the textual confusion, for all its bewildering abundance, was never enough to obscure a doctrinal core of the SY which is what evidently has attracted readers through the ages. Regardless of how many authors contributed to the 'mythical' or 'illusory' 'original text',<fnref n="9" /> it is clear that at some point in the history of the book, a number of paragraphs encapsulated a discernible doctrine which was worth the while of many of the greatest Jewish scholars who commented on it. I quite agree with Segol's intuition that a great part of the text's 'meaning' has to do with its structure, that there is 'a discernible pattern in its organization that is key to understanding its

<footnote n="3">3. A. P. Hayman, *Sefer Yeşira, Texts and Studies in Ancient Judaism* 104 (Tübingen: Mohr Siebeck, 2004); I. Gruenwald, ‘A Preliminary Critical Edition of Sefer Yezira,’ *Israel Oriental Studies* 1 (1971): 132–177.</footnote>

<footnote n="4">4. Hayman himself refers to Gruenwald's edition to complement his own vis-à-vis the inclusion of some manuscripts and readings (p. 9ff.), so in fact, regarding all philological points, they may be treated as a two-volume work.</footnote>

<footnote n="5">5. It has been said that aside from the *Tanakh*, no other Jewish work has been commented as extensively as the *SY*. Cf. also Wasserstrom, ‘Sefer Yesira and Early Islam: A Reappraisal,’ for dating matters.</footnote>

<footnote n="6">6. Hayman, *SY*, 18.</footnote>

<footnote n="7">7. See M. Segol, *Word and Image in Medieval Kabbalah*, The New Middle Ages (New York: Palgrave MacMillan, 2012), 25ff.; note particularly in Hayman, *SY*, 41, 95, how a detailed analysis of the textual evidence impacts the complex dating question.</footnote>

<footnote n="8">8. E. Wolfson, ‘Text, Context, and Pretext: Review Essay of Yehuda Liebes’s *Ars Poetica in Sefer Yetsira*,’ *The Studia Philonica Annual* 16 (2004): 218.</footnote>

<footnote n="9">9. See *ibid*., 222.</footnote>
meaning and function.’<fnref n="10" /> I would add that the other essential factor constituting the core of the book is a small constellation of key concepts, like *sefirah* and *ot yesod* ('letter of foundation').<fnref n="11" /> It is in no small measure due to the symbolic power of these key concepts, and to the subtle web of their linguistic interplay—like glints within a gem—that *SY* had and continues to have such unabating influence.

In the following pages I will examine some particular passages of the book and its commentary tradition in the light of our alphanumeric quest, focusing on some of the Hebrew terms and their place in the history I have been drawing in previous pages. Before introducing some reflections on the title and authorship of the book, it will be better to start by presenting directly those verses of *SY* which are most relevant to this work, to comment on them, and then to introduce as needed other notable passages.

## Selections from the Text

1 שלשים ושתים נתיבות פליאות חכמה חקק יהוה צבאות בשלש ספרים בספר וספור 2 עשר ספירות בלי מה ועשרים ושתים אותיות יסוד שלש אמות ושבע כפולות ושתים עשרה פשוטות

19a עשרים ושתים אותיות חקקן חצבן צרפן שקלן והימירן 59 חק עשרה שלשה ושבעה ושנים עשר פקודין בתלי וגלגל ולב 48a ישאן כמין מריבה וערכן כמין מלחמה גם את זה לעמת זה עשה האלהים

61 כשהבין אברהם אבינו וצר וצרף וחקר וחשב ועלתה בידיו ניגלה עליו יי קרא עליו המקרא הזה בטרס אצורך אצורך בבטן ידעתיך וגווי

1) Yah, Lord of Hosts, carved (*haaqaq*) thirty-two wondrous paths of wisdom in three count-modes (*sefarim*): in writing (*sefer*), in number (*sefar*), and in speech (*sippur*). 2) They are ten absolute numerations (*sefirot beli mah*) and twenty-two elemental letters: three mothers, seven doubles and twelve simples.

19a) Twenty-two letters: he carved them out, he hewed them, he combined them, he weighed them and he exchanged them. 59) Law of ten, three, seven, and twelve, they are present in the heavenly axis (*teli*),<fnref n="12" /> in the

<footnote n="10">10. Segol, *Word and Image*, 16.</footnote>

<footnote n="11">11. Segol speaks of ‘letterforms’ along similar lines, see *ibid*., 143.</footnote>

<footnote n="12">12. For the translation of *teli*, see A. Kaplan, *Sefer Yetzirah: The Book of Creation in Theory and Practice*, revised edition (Boston, MA: Weiser Books, 2004), 231–39; see also P. Mancuso, ‘Cosmological Traditions in Judeo-Byzantine South Italy: A Preliminary Analysis,’ in *From Māshā’allāh to Kepler: Theory and Practice in Medieval and Renaissance Astrology*, ed. C. Burnett and D. G. Greenbaum (Sophia Centre Press, 2015), 320–24.</footnote>
sphere and in the heart. 48a) He made them as if in strife, he arranged them as in battle array, ‘God made the one side by side with the other.’<fnref n="13" />

61) When Abraham our father understood and formed and combined and investigated and pondered, and the matter came into his possession, the Lord was revealed to him, and He recited over him this scripture: ‘Before I formed you in the womb I knew you; and before you came forth out of the womb I sanctified you, and I ordained you a prophet unto the nations.’<fnref n="14" />

The *SY* presents itself from the outset as a compendium of cosmogony and cosmology based on the Hebrew language.<fnref n="15" /> There are thirty-two paths of wisdom which comprise the ten primordial numbers (*sefirot*) and the twenty-two Hebrew letters. So from the very start we seem to encounter here a set of ‘elements’ (the ‘paths’) which comprises numbers and letters, just as the *στοιχεῖα*, but in this case they no longer coalesce, but appear to be clearly distinguished. I insist quite deliberately on the *appearance* of numbers and letters, because the text does not actually speak of them, but rather uses two very unusual expressions, as I have tried to reflect in my translation above: *sefirah* is not the same as *mispar*, number, just as *ot-**yesod* is not the same as a simple letter, *ot*.<fnref n="16" /> In order to better appreciate their qualities and how they relate to this research, let us now dwell individually on each of these three sets of elements: the paths, the numerations and the letter-elements.

## The Thirty-Two Wondrous Paths of Wisdom

Quite remarkably and in direct relation to our main concern, Leo Baeck had already suggested that ‘the word *n’tivot* (“paths”) might be a *transference* of the Greek *στοιχεῖα*,

<footnote n="13">13. Ecc. 7:14.</footnote>

<footnote n="14">14. Jer. 1:5. Aside from specific minor variations which I shall indicate, I follow Hayman’s ‘earliest recoverable text’, that is his attempt at reconstructing the common ground of the three accepted recensions; see Hayman, *SY*, 33ff., 49–51.|| Following Gruenwald, ‘A Preliminary Critical Edition,’ 484, I take here verse 2 as a gloss of the thirty-two ‘paths’.</footnote>

<footnote n="15">15. As such, Wolfson has related it to the esoteric rabbinic tradition known as *ma‘aseh bere’shit*, the ‘work of creation’, noting also that some parts of it belong to the *ma‘aseh merkavah*, the ‘work of the chariot’; see E. Wolfson, ‘Jewish Mysticism: A Philosophical Overview,’ in *The Routledge History of Jewish Philosophy*, ed. D. Frank and O. Leaman (New York and London: Routledge, 1997), 450–498.</footnote>

<footnote n="16">16. Unlike Hayman, who treats *otiyot yesod* as a nominal clause, ‘the elements are the foundation,’ I read it consistently as a compound name, not only on conceptual grounds as I shall explain, but also based on stylistic reasons: as noted in Y. Liebes, *The Publication of the Kabbalah* (Ars Poetica in Sefer Yetsira) (Tel Aviv: Schocken, 2000), ch. 2, every section of the text is punctuated by the repetition of such compounds: ‘ten absolute numerations’, ‘twenty-two elemental letters’, ‘three mothers’ and so on. See also J. Dan, ‘A Kabbalistic Commentary on the Book of Numbers,’ *Daat: A Journal of Jewish Philosophy & Kabbalah*, no. 34 (Winter AM5755 / 1995CE): 5.</footnote>
which depicts the *Urprinzipien* [primary or first principles] as well as the *letters* and the signs of the *zodiac*. According to his interpretation, the root word στοΐχος, ‘line’ and its verb form στοιχεῖν, or ‘to advance in a row,’ could have meant the same to some Greek and Hebrew readers as the word *n'tivot*.<fnref n="17" /> In his recent monograph, Yehuda Liebes suggests that the central theme of *SY* is not the universe itself in its construction, but rather the ‘stones’ themselves used to build it, namely the thirty-two paths, which he calls *ha-yesodot ha-nistarim shel hokhmat mevinah ha-yaqum*, ‘the hidden elements of the intelligent wisdom of the universe.’<fnref n="18" />

Such emphasis on the importance of the ‘paths’ is at odds with some contemporary arguments for two separate original textual strands, one for numbers and one for letters, which were made into a single discourse by means of this first introductory paragraph,<fnref n="19" /> as if a misguided late author had come up with the invention of a sort of genus, the ‘wondrous paths’, that encompass ‘number’ and ‘letter’.<fnref n="20" /> Considering the fact that §1, with all 32 paths, is attested in all the available textual witnesses,<fnref n="21" /> this attempt may seem hasty. And for us, from the vantage point of the alphanumeric elements in this work, the unitary concept under suspicion presents no problem. In the *SY* itself, this is the particular interest of §§59 and 48a,<fnref n="22" /> for in them number and letter are once again subsumed within the same group: after the description of the cosmic correspondences between *sefirot* and *otiyot yesod* which take up most of the book, §59 sums up saying, ‘this is the law of 10, 3, 7 and 12.’ The relation to the first paragraph is underlined by the relation between *haqaq*, ‘to carve’, the action whereby God creates the thirty-two paths, and the word for law, *hoq*.

Like in the Arabic cognate *haqq*, the original meaning of this root, as in the Heb. verb *haqaq*, has to do with etching, inscribing and tracing.<fnref n="23" /> The thirty-two are ‘inscribed’ and thus sanctioned as law by God in the universe in a manner comparable to that of the great legal inscriptions, the Mosaic Decalogue or the Roman Twelve Tables. I would also note here the important relation to the tracing of the characters, the *ductus*, considered as the *path* of the pen or the stylus. This correspondence is reinforced when we realise that the adjective applied to the paths, *peli'ot* comes from the root *p-l*–, ‘to

<footnote n="17">17. L. Baeck, ‘Zum Sepher Jezira,’ *Monatsschrift für Geschichte und Wissenschaft des Judentums* 70 (1926): 371.</footnote>

<footnote n="18">18. Liebes, *Torat ha-yetsira*, 12.</footnote>

<footnote n="19">19. See Wolfson, 'Text, Context, and Pretext: Review Essay of Yehuda Liebes's *Ars Poetica in Sefer Yetsira*,' 227–8, for discussion and references.</footnote>

<footnote n="20">20. G. Busi, *Qabbalah visiva* (Torino: Einaudi, 2005), 35, speaks of a ‘strong conceptual imbalance’ between the two concepts.</footnote>

<footnote n="21">21. Hayman, *SY*, 64.</footnote>

<footnote n="22">22. The order in our selection follows Hayman's 'earliest' text proposal.</footnote>

<footnote n="23">23. E. Klein, *A Comprehensive Etymological Dictionary of the Hebrew Language for Readers of English* (Jerusalem: Carta, 1987), s.v. *h-q-q*.</footnote>
set apart, to split.' Considering the cosmogonic context, and what appears to be the
primordial bringing into being of a set of elements by separation, we are reminded of
the story of Thoth in the *Philebus*, discerning the στοιχεῖα from the formless acoustic
continuum.

There is a noteworthy textual variation at the very beginning of the text, which in
many manuscripts, and certainly in most modern editions, begins with a locative or
instrumental preposition, *bi-shloshim ushtayim*..., i.e. God carved ‘in the thirty-two’
or ‘by means of the thirty-two.’ Most commentators interpret that the 32 are then
*instruments* of the formation of the universe, which echoes the letters being called
‘helpers’ of the Divine Maker, and also reminds of Philo explaining that the λόγος is
the instrument used by God. However, as has been observed by Hayman, this initial
preposition brings unsolvable syntactic problems. It is much preferable to read the 32
paths as the object of *haqaq*, which then has an adverbial complement in *be-shalosh
sefarim*.

The Three Modes of Inscribing

According to Jospe,<fnref n="24" /> Saʻadyā established a tradition of interpreting the three *sefarim* as *sefer* (writing), *sefar* (number), and *sippur* (speech),<fnref n="25" /> a tradition followed by all the early philosophical commentators: Dunash, Donnolo and Judah ben Barzillai al-Bargeloni (eleventh/twelfth cent.). It was Halevi’s *Kuzari*, not particularly dedicated to the *SY*, which ‘interpreted the three *sefarim* innovatively in Aristotelian terms of the identity of the subject, act, and object of intellection.’<fnref n="26" /> Jospe also gives a summary of Judah ben Barzillai’s commentary with regard to the three *sefarim*. ‘*Sefar* is calculation, which is number’ (*s’far heshbon ve-hu mispar*)—‘*sippur* is language, which is uterance’ (*sippur ha-dibur ve-hu ha-ma’amar*)—‘*sefer* is writing, which is script’ (*sefer hu kitabah she-hu miktab*). In addition to these of his own, al-Bargelloni reports several other interpretations by unknown commentators who equate the three *sefarim* to different triads: ‘wisdom, understanding and knowledge (*hokhmah, tevunah, daʻat*)’, ‘God’s creative word, command and act (*ma’amar, tsivuy, ʻasiyah*)’, or the three sections of the Tanakh, *Torah, Nevi’im, Ketuvim*.

<footnote n="24">24. R. Jospe, ‘Early Philosophical Commentaries on the Sefer Yezirah: Some Comments,’ *Revue des études juives* 149, no. 4 (1990): 372.</footnote>

<footnote n="25">25. In Saʻadyā's Arabic, 'three things: *khaṭṭ wa-'adad wa-nuṭq.'</footnote>

<footnote n="26">26. The relevant section is 4:25, Judah Halevi, *Kitāb al-radd wa-'l-dalīl fī'l-dīn al-dhalīl* (al-Kitāb al-Khazarī), ed. David H. Baneth and Haggai Ben-Shammai (Jerusalem: The Magnes Press, The Hebrew University, The Israel Academy of Sciences / Humanities, 1977), 174; Judah Halevi, *Le Kuzari. Apologie de la religion méprisée*, ed. Charles Touati, Collection de la Revue des Études juives, Traduit sur le texte original arabe confronté avec la version hébraïque et accompagné d'une introduction et de notes (Paris-Louvain: Peeters, 2006), 415.</footnote>
Although not along the Aristotelian lines proposed by Jospe, I find that the commentary found in the *Kuzari* is one of the most insightful, and especially useful for this comparative work because it was written in Judaeo-Arabic. Here are some passages relating to the *sefarim*:

In the reality of God, *S'far*, *Sippur*, and *Sefer* are a unity, whilst they are three in the reality of man. For man reckons with his mind (*dhihn*), speaks with his mouth, and writes with his hand, referring with all three to one among the creatures of the Creator. Man's reckoning, his writing, and his **word** (*lafẓ*) are thus signs which refer to a thing but are not the thing itself. Whereas the reckoning of God and his speech are the thing in its essence, and at the same time His writing (...) So the three *sefarim*: *S'far*, *Sippur*, and *Sefer* are conjoined into one thing, and this product of reckoning comes to be as if one of unmixed self (*dhū al-nafs al-khāliṣa*) had calculated it (*qaddarahu*), uttered it (*naṭaqahu*) and written it. And thus this book says that God Most-High: 'created His world with three *sefarim*: *S'far*, *Sippur*, and *Sefer*,' which are all one in the reality of God. This is the one principle (*mabda*) of the 'thirty-two marvellous ways of wisdom,' which are the ten Sefirot and the twenty-two letters.

Apart from approaching the passage from what appears to be a deeply monotheistic position, it is further clear evidence for the understanding that the 32 paths are the sum of the *sefirot* and the 'letters'. Some similar comprehension might be behind the Arabic title given by Saʻadyā to his translation of *SY, Kitāb al-mabādi*, the *Book of Principles*.

Returning to the metaphysical notion of principle, it is important to establish a remarkable parallelism between this idea of the three 'count-modes' and the passage of Aristotle's *Metaphysics* I have repeatedly discussed earlier, where we find the definition of στοιχεῖον.<fnref n="27" /> When the definition is given, the following three examples of composites are used: φωνή, the voice, διαγράμματα, as the graphic aspect, and ἀποδείξεις as the logical aspect of geometrical demonstrations. Suffice to say that the three examples match quite closely the threefold aspect of the root *s-f-r* as presented in *sefarim: sippur*, the spoken word, *sefer*, the written word, and *s'far* the numeric/logic aspect. The comparison is particularly apropos given that the context in both cases is about the definition of very similar principles.

There are two other triads which also may shed light on the range of meanings of the *sefarim*, one from the field of grammar, and the other from the field of arithmetic. The attributes of *litera* common among medieval Latin grammarians were three: *nomen*, which identified the letter for discussion; *figura*, the written shape; and *potestas*, the

<footnote n="27">27. Δ3, 1014a26ff.</footnote>
sound.<fnref n="28" /> The last two may be seen to correspond with *sefer* and *sippur* respectively, but because in the Latin tradition the alphabet was not used to write numbers, a correspondence with *s'far* is not easily discernible.

Finally, Merlan considers that the three *sefarim* correspond to the three kinds of number found in Plotinus:<fnref n="29" /> ἀριθμοί, the ‘first and true numbers’, ἀριθμοί ἀριθμητοί, numbers in countable beings, and ἀριθμοί ἀριθμοῦντες, things used to count, like a standard of measure. Once again, but now from the numeric aspect, a clear correspondence with the *sefarim* seems precarious, but in any case, I shall soon have an opportunity to return to late Platonic associations.

<figure><img src="image_19.png" /></figure>

I have chosen to translate *sefarim* as ‘count-modes’ thinking of the various meanings of ‘counting’: the arithmetical one, as in enumerating, and also the narrative one, as in recounting a story. In fact, the word ‘account’ would also be a very suitable alternative, since it can mean: 1) a written account (*sefer*), 2) a tally (*s'far*), and 3) a narration (*sippur*). The basic structure of the paragraph would then read, ‘God formed the thirty-two wondrous paths of wisdom in three accounts: writ, number and narrative.’

## The Absolute Numerations—Sefirot

Much has been made of this word, and there are frequent claims of it being introduced to Jewish literature through the *SY*. For Baeck, who calls it a neologism, it replaces the customary *mispar* (number) in order to indicate that the numbers meant are not the numbers of mathematics.<fnref n="30" /> According to Saʻadyā, the ten *sefirot* correspond to the ten Aristotelian categories (*maʻlūmāt*) and also to the ten commandments.<fnref n="31" />

If it is true that the concept of *sefirah* in the text is not limited to what we know as a number, the word itself is used in the Long Recension (§58b) with the meaning of ‘count’: ‘the count (*sefirah*) of the universe is ten; the count of the year is ten…’<fnref n="32" /> As observed by Vajda, it is a common term in the Talmud with the same meaning, and used notably as a singular only.<fnref n="33" /> What the *SY* does is employ the term in a completely new

<footnote n="28">28. Abercrombie, 'What is a "Letter?]', 59. These were an adaptation from the Greek Stoic triad: ὅνομα, χαράκτηρ, στοιχεῖον, see Robins, *The Byzantine Grammarians*, 54.</footnote>

<footnote n="29">29. VI. 6, 15. See Merlan, 'Zahlenlehre,' 169.</footnote>

<footnote n="30">30. L. Baeck, 'Die zehn Sephirot im Sepher Jezira,' *Monatsschrift für Geschichte und Wissenschaft des Judentums* 78 (1934): 448–455; cf. Liebes, *Torat ha-yetsira*, 13–14.</footnote>

<footnote n="31">31. Saʻadia ben Yosef Gaon, *Commentaire sur le Séfer Yesira ou Livre de la création par le Gaon Saadya de Fayyoum*, ed. C. Mopsik, Partial reprint of the 1891 edn. (Alençon: Editions Bibliophane, 1986), 20–21.</footnote>

<footnote n="32">32. See Liebes, *Torat ha-yetsira*, 15; Hayman, *SY*, 173–4.</footnote>

<footnote n="33">33. G. Vajda, 'Recherches sur les commentaires du Livre de la Création,' in *La consolation de l'expatrié spirituel: un commentaire sur le Livre de la Création (Sefer yeşîrâh)*, ed. P. Fenton (Paris: Éditions de l'éclat, 2008), 24.</footnote>
way, to designate the first ten of the 32 'paths', called more specifically *sefirot beli mah*,<fnref n="34" /> literally 'numerations without anything'. Saʻadyā translates as *aʻdād al-maḥzurah*, 'enclosed numbers' or 'forbidden numbers', thus obviating any ambiguity inherent in the Hebrew term in favour of an 'arithmetical' reading. For Baeck and Merlan, once again, there is a clear relation here, also because they are ten, with later Greek metaphysics, and specifically with Proclus. *Sefirot beli mah* would accordingly refer to the ἀριθμοί ψιλοί or ἀριθμοί ἄνευ πραγμάτων, the 'unalloyed numbers' or 'numbers without things', or perhaps to the αὐτοτελεῖς ἑνάδες, the 'self-perfecting monads' located between the primal essence [*Urwesen*] and the Intelligible, mediating the transition from the original unity to multiplicity; *beli mah* corresponds quite literally to ἀμιγεῖς, 'pure' or 'unmixed'. Regarding the numbers as cosmic building blocks, Merlan refers to a quotation by Syrianus describing number as κριτικὸν κοσμουργοῦ θεοῦ ὅργανον, the 'decisive instrument of the world-creating deity.'

According to these German scholars, the high cosmological status of numbers can
only be explained by the influence of Platonism and Neoplatonism, namely of Proclus
and his immediate circle. Merlan observes that there is a possible Jewish connection,
because Domininus, Marinus, Zeno of Alexandria and other close associates of the main
later Neoplatonists were either of Jewish origin or were related to Jews.

Another notable reference to Greek sources is the suggestion by Liebes that the
number of the *sefirot* can, in their close relation to the letters, be compared to the
existence of ten Greek diacritic marks. It is perhaps due to this association that Liebes
speaks of the ten *sefirot* as the ‘inner aspect of the 22 letters.’<fnref n="35" /> Now, any direct bearing
of the Alexandrian prosodic marks on the origin of *SY* would make for a very early
dating, but the farther back we move from the tenth century, the harder it is to justify
the lack of mentions of the book in the intervening centuries.

There are certainly doctrinal parallelisms of various solidity along the lines
mentioned above, but perhaps the most interesting effect of establishing the relation to
Proclus is that it suggests a new possible *terminus a quo* for a treatise like the *SY*, i.e.,
the fifth century CE.<fnref n="36" />

This derivation of our book is also significant in terms of intellectual history. At the
waning of the ancient world, and casting his shadow far into the distance, stands the
figure of Proclus. By way of the writings of Dionysius the Areopagite, Proclus had an
influence on the Christian Middle Ages, and through the *Sefer Yetsirah* he would also
have made an enormous impact on later Jewish literature.

<footnote n="34">34. See Hayman, *SY*, 65–6, for the alternative *belimah* and possible provenance.</footnote>

<footnote n="35">35. Liebes, *Torat ha-yetsira*, 14.</footnote>

<footnote n="36">36. This is close to Vajda's suggestion of an approximate origin between 450 and 700; see Vajda, *Recherches*, 40.</footnote>
◆

Once again, a sufficient characterisation of the *sefirot* is given by the *SY* itself. In §7 they are described as ‘*eser she eyn lahen sof*’, ‘ten that have no end’—they are ten endless valleys or chasms;<fnref n="37" /> and in §16 the ten are named, they are, first, the Spirit of the Living God (*Ruaḥ Elohim Hayyim*); then the three elements wind, water, fire; and to complete the decad, the six directions of space: above, below, east, west, north, and south. Hayman sums up calling them ‘pre-conditions for creation.’ They seem to constitute a numeric middle realm upon which, as Plotinus says of numbers, ‘beings have their “foundation, source, root and principle” (βάσιν δὲ ἔχει τὰ ὄντα ἐν αὐτῶι καὶ πηγὴν καὶ ῥίζαν καὶ ἀρχήν).’<fnref n="38" />

It may seem crucial for our enquiry to establish how numeric, just how arithmetical, the *sefirot* really are,<fnref n="39" /> but this manner of asking is rather anachronistic, especially in the light of Chapter Two above, where we have seen that ‘number’ itself was not in Antiquity quite the same as we understand today as number. So, in asking the above question, what we really want to know is just how close to the medieval concept of number was the concept of the *sefirot*. Saʻadyā for one identified them very clearly.<fnref n="40" /> When it is said that ‘*SY* does not speak of the *sefirot* as of numbers in the full sense of the word,’<fnref n="41" /> the answer should be that it actually does, but in the full ancient Pythagorean sense of the word. That is, unless we decide that Platonist and Pythagorean philosophers who elaborated on the cosmic function of numbers were not speaking of numbers either. The *SY* has to do with arithmetic somehow like the *Theologoumena arithmetica* does, that is, insofar as the metaphysical decad can be considered anything arithmetical. This is why I have translated *sefirot beli mah* as ‘absolute numerations’ and thus avoided rendering *sefirah* as plain ‘number’, but rather opted for an English word which is a clear cognate and yet unusual enough to be imbued with an altogether abstract meaning. A useful alternative to render *sefirot* would be a word related to ‘counting’, perhaps ‘ten absolute counts,’ thinking also of the Indo-European cognates, all derived from Lat. *computare*, as mentioned in a previous chapter.<fnref n="42" />

## The Twenty-Two Elemental Letters

It is a commonly held view that from the *SY* description of how the elemental letters interact within creation, arose the notion that ‘the letters are not merely the tools of

<footnote n="37">37. Cf. above, p. 156, the notion that every letter is a potential infinite.</footnote>

<footnote n="38">38. *Enneads* VI. 6, 9.</footnote>

<footnote n="39">39. Busi, *Qabbalah visiva*, 36, argues for a non-numerical meaning altogether.</footnote>

<footnote n="40">40. For an interesting Gnostic association, see M. Marcovich, *Studies in Graeco-Roman Religions and Gnosticism*, Studies in Greek and Roman Religion 4 (Leiden: Brill, 1988), 171–72.</footnote>

<footnote n="41">41. Dan, *The Concept of Number*, 13.</footnote>

<footnote n="42">42. See above, p. 113.</footnote>
<figure><img src="image_20.png" /><figcaption>FOUR-ALPHABETS WHEEL. PARIS, BNF, HÉBREU 825, 214R</figcaption></figure>

These elemental letters transform into each other, exchange places with one another, and in so doing they act like *signatures* of the three elements, the seven planets and the twelve universal divisions on every being. The wheel reproduced above is thought to be related to the four alphabetic wheels described by Judah ben Nissim (thirteenth century) as ‘cosmic entities on whose movement depend both intelligible reality and the material world.’<fnref n="46" />

<figure><img src="image_21.png" /></figure>

I had already had the opportunity to present a number of examples of the cosmogonic role of the letters of the alphabet in the Hebrew tradition, mostly from the rabbinic literature. A plausible historical development is that at some point in late antiquity, between the death of Proclus (485) and some decades before the publication of Saʻadyāʼs *Commentary* (931), the Jewish tradition which assigned to the Torah a key role in the creation of the world merged with insights from Platonic sources into the earliest form

<footnote n="46">46. See Busi, *Qabbalah visiva*, 45, 138.</footnote>
of SY.

## The Title: ‘Creation’ or ‘Formation’?

A question directly related to the nature of the 32 paths is the title of the book, why *yetsirah*? What sort of ‘creation’ is the one treated in this work?

The basic root *tsur* is very close to the Greek idea of ποίησις, a creation related to the arts, to forming and shaping,<fnref n="47" /> like its Ar. cognate ṣūra. Maimonides, in his *Dalālat al-ḥā’irīn*, the *Guide for the Perplexed*, on occasion of distinguishing between *awwal* and *mabda’*—the ‘principle’ in its sequential or temporal meaning and its metaphysical meaning—<fnref n="48" /> examines the various biblical verbs for creation and concludes that ‘the word *yetsirah* corresponds to shaping and delineating’ (*al-YETSIRAH innamā taqa‘u ‘alā tashkīl wa-takhṭīṭ*). I need hardly observe that the two words *tashkīl* and *takhṭīṭ* are common terms in the art of lettering, referring to the addition of diacritics and to the basic tracing of the letters.<fnref n="49" /> To complete his explanation, Maimonides gives as a first example the expression *Yotser Or*, the ‘Shaper of Light,’ as the well-known epithet of God and the title of the prayer we have already discussed.<fnref n="50" />

Just as God is called in Hebrew *Yotser*, the divine Potter or Giver of Form, so in Arabic we find as one of the divine names *al-Muṣawwir*, ‘He who gives form.’ *Yetsirah* refers to a demiurgic creation for which a design with parameters and calculations and tools are needed.<fnref n="51" /> In the Talmud we find the clearest association in *tsayyar*, ‘the Designer’, a divine name derived from the same root as *Yetsirah*,

### מאי אין צור כאלהינו אין צייר כאלהינו

What is the meaning of there is no rock [*tsur*] like our God? There is no designer [*tsayyar*] like our God.<fnref n="52" />

<footnote n="47">47. See above pp. 112 and 114. In Genesis Rabba 1:9, God is called an ‘artist’, *tsayyar*, with the same root.</footnote>

<footnote n="48">48. II.30, M. Maimonides, *Dalālah al-ḥā’irīn*, ed. S. Munk, Sifriyah Filosofit, Text in Judaeo-Arabic (Jerusalem: J. Junovitch, 5691 (1929)), 230–55.</footnote>

<footnote n="49">49. Let us also retain for the time being that *takhṭiṭ* is also used in land surveying (‘*ilm al-misāḥa*), where *takhṭiṭ bi-al-taqāṭiʿ* means the ‘tracing of the intersections,’ referring to the initial laying of a square grid.</footnote>

<footnote n="50">50. See above, p. 114.</footnote>

<footnote n="51">51. Cf. Sa‘adia, *Commentaire sur le Séfer Yesira ou Livre de la création par le Gaon Saadya de Fayyoum*, 13, ‘A partir de dix nombres primordiaux sans limite et des vingt-deux lettres de l’alphabet hébraïque aux combinaisons non moins illimitées, le Créateur—ou plutôt le Potier (*yotser*)—construit comme à partir de briques, l’univers entier.’</footnote>

<footnote n="52">52. *bBerakhot* 10a:22; cf. *bMegillah*, 14a:20; see Busi, *Qabbalah visiva*, 3.</footnote>
A less common version of the title is more specific, *Sefer Yetsirah Otiyot*, the *Book of Formation of Letters*—where the ambiguity in the preposition of is an attempt to reflect the original double entendre: it can mean ‘the book where the letters are formed,’ or ‘the book describing how to give form with the letters.’<fnref n="53" />

It is worth keeping in mind, as a crucial cosmogonic reference in Genesis, that throughout the Hexameron only the verbs *ברא bara* and *עשה asah* are used, including the creation of man and woman on the sixth day. It is only after the seventh day that the verb *יצר* appears: Adam is ‘fashioned’ (Gen. 2:7). The Septuagint keeps the distinction, using ἐποίησεν and ἦρξατο, and then in 2:7, ἔπλασεν for *יצר*. The Vulgata has *creavit*, *fecit* and *formavit* respectively.

An often mentioned variation of the title of the book is *Hilkhot Yetsirah*, the ‘Laws of Formation,’<fnref n="54" /> with the plural of *halakhah*, ‘method’, something to walk by, mirroring the etymology of Ar. *sharīʿa* and *sunna*. This alternative title is notably mentioned in bSanhedrin 67b, speaking of forbidden magic and sorcery practices: ‘What is permitted *ab initio* is to act like Rav Ḥanina and Rav Oshaya: Every Shabbat eve they would engage in the study of the *halakhot* of creation, and a third-born calf would be created for them, and they would eat it in honor of Shabbat.’ Even though this reference has been questioned,<fnref n="55" /> it is important in that it opens a view onto the field of magic which has very often been associated with *SY*. This relation is only to be expected for the same reason that in Hermes are fused the patronage of language and of magic and occult arts. Magic as an art of *transmutation* of the immaterial will into material effects, has always something alchemical about it. In fact, in this light it is not difficult to see how the procedures applied by God to the letters sound very much like alchemical and magical operations with all that etching and weighing. Segol draws attention also to the architectural metaphors and the conceptions of creation by the creation of boundaries, particularly as occurring in Job 38, a very important biblical reference for the *SY* and its commentators.<fnref n="56" />

Finally, yet another title of the book, *Sod ha-‘Ibur*, the *Secret of Intercalation*, or of *Hebraization*, ‘on which the whole world depends,’ gives prominence to a procedure

<footnote n="53">53. Hayman, *SY*, 193.</footnote>

<footnote n="54">54. *ibid.*, 193–5.</footnote>

<footnote n="55">55. See J. Dan, *The ‘Unique Cherub’ Circle: A School of Mystics and Esoterics in Medieval Germany*, vol. 15 (Mohr Siebeck, 1999), 39–40.</footnote>

<footnote n="56">56. See Segol, *Word and Image*, 174.</footnote>
which is obviously related to the letter manipulations mentioned above.

Authorship and Conclusion

When thinking about the authorship, we refer again to §61, where Abraham appears as the adept who attains mastery of the book and thereby is rewarded. One first question that poses itself is ‘why Abraham?’ One powerful reason may be, always from the particular perspective of this work, that the three Abrahamic religions are called in Islamic tradition the ‘religions of the book’ or, perhaps more accurately, ‘religions of the writing.’ We have already seen in the second part of this work how intricately related are the alphanumeric doctrines of the Abrahamic religions, and they in turn with the Greek tradition. Abraham is a watershed figure for the religions of the Early and High Middle Ages, and the ascription of the book to him refers the reader to a very fundamental doctrinal core, properly esoteric, where theological differences are less urgent.

The closing scriptural citation from Jeremiah, is remarkable on various grounds,

‘Before I formed you in the womb I knew you; and before you came forth
out of the womb I sanctified you, and I ordained you a prophet unto the
nations.’

The verse starts by using the root verb that gives title to the book, *tsur*, and making clear, after displaying all the rules of creation, that His giving form is not like man’s, and it ends on a note related to the considerations just above, proclaiming the mission of Abraham *le-goyim*, for all the nations, not only for the Jews.

Let me conclude with a story which gives an idea of the reverence shown to the *SY*
in the Jewish tradition.<fnref n="57" />

> When Abraham was born, God consulted with the Sefer Yetsirah which said,
> 'Give (me to him).' So God handed it over to Abraham, who sat alone and
> meditated on Sefer Yetsirah, but he could not understand it at all until there
> came a heavenly voice and said to him, 'Do you seek to compare anything
> with me? I am One and I created Sefer Yetsirah and investigated it and made
> everything which is written in it. You cannot understand it on your own. Go to
> Shem and look at it together and understand it.' Immediately Abraham went
> to Shem his teacher, and sat down with him for three years, and they found
> out how to create the world. (fol. 26r)

<footnote n="57">57. Cited in A. P. Hayman, 'Sefer Yetsira (The Book of Creation),' *Shadow, The Newsletter of the Traditional Cosmology Society* 3 (1986): 20–38, from BL Add MS 15299 (the Ms is now available online).</footnote>
## Chapter 8

# Alphabetic Consecration & Metaphysical Foundation

The ecumenical presence of Abraham as a patron figure of alphanumeric science is found, together with other aspects of the ‘thirty-two paths of wisdom’, in a most remarkable rite belonging to the liturgy for the dedication of a new church. The metaphysical associations of this rite, and in particular their relation to architectural imagery, will be explored in the following pages.

### The Abecedarium in Church Dedication

The oldest known mention of this rite is found in *Ordo XLI* of the *Ordines Romani*, the early medieval Roman liturgical guidelines.<fnref n="1" /> Here is this original succinct description from a seventh century manuscript:

> Deinde incipit pontifex de sinistro angulo ab oriente, scribens per pavimentum cum cambuta sua abcdurium, usque in dextro angulo occidentalis; incipiens iterum similiter de dextro angulo orientalis abcdurium, scribens usque in sinistro angulo basilicae occidentalis.

> Then the priest starts from the left eastern corner, writing the alphabet on the floor with his staff, until he reaches the right hand western corner, and then he starts again from the right hand corner on the east, writing the alphabet in the same way until he reaches the left corner of the western end of the church.

<footnote n="1">1. M. Andrieu, *Les Ordines romani du haut moyen âge*, 5 vols, Études et documents 28 (Spicilegium sacrum lovaniense, 1956), 340-41.</footnote>
In later liturgical literature,<fnref n="2" /> other details are added, like the fact that the letters are traced on two previously laid stripes of ashes, or that one of the alphabets is the Greek alphabet,<fnref n="3" /> and in some manuals there are graphic aids for the officiants, like the following diagram,

<figure><img src="image_22.png" /><figcaption>FROM AN 1859 PONTIFICAL<fnref n="4" /></figcaption></figure>

In general, it is clearer in the later descriptions that, as in the illustration, the tracing of the two alphabets is done in *modum crucis*, and more specifically in the form of a decussate crux (*crux decussata*). The origin of the word *decussis*, meaning the decad, or simply ‘ten’, is particularly significant in our context. It comes from the compound *decem* and *as*, ‘ten units’. Vitruvius (3, 1) explains: *ex singularibus rebus, quae μονάδες apud Graecos dicuntur, perficitur decussis*, ‘the decad is brought to completion by the

<footnote n="2">2. See K. Schreiner, ‘Abecedarium. Die Symbolik des Alphabets in der Liturgie der mittelalterlichen und frühneuzeitlichen Kirchweihe,’ in ‘Das Haus Gottes, das seid ihr selbst’: mittelalterliches und barockes Kirchenverständnis im Spiegel der Kirchweihe, ed. R. M. Stammberger, A. Warnke, and C. Sticher, Erudiri Sapientia 6 (Walter de Gruyter, 2007), 143ff. for the most recent and exhaustive treatment and references.</footnote>

<footnote n="3">3. See W. Berschin, *Griechisch-lateinisches Mittelalter: Von Hieronymus zu Nikolaus von Kues* (Bern/München: Francke Verlag, 1980), 37, who calls this ‘most significant testimony of the medieval keenness to relate the Greek language to the Latin liturgy,’ and who suggests a direct relation to the ‘ancient doctrine of the στοιχεία.’</footnote>

<footnote n="4">4. *Pontificale Romanum Clementis VIII ac Urbani VIII jussu editum et a Benedicto XIV recognitum et castigatum* (Paris: A. Jouby, 1859), 217. Cf. also G. De Rossi, ‘Degli alfabeti, che il vescovo scrive sulla croce decussata nel consecrare le chiese,’ *Bullettino di Archeologia Cristiana* (Roma), 3rd ser., 6, no. 4 (1881): 140–146.</footnote>
single entities called μονάδες in Greek.' Because ten was represented by the crossing lines, the symbol X came to be another meaning of *decussis*, whence St Andrew's *crux decussata*.

In the dedication rite there is thus a convergence between the alphabet and the decad, the twenty-something letters and the ten first numbers, very much like the thirty-two paths of wisdom mentioned in *Sefer Yetsirah*. This combination summarises the form of the rite: the two alphabets—that is the elements—written on the pattern of a cross or a Greek uppercase *chi*, X. This form is still in use today with some simplifications,<fnref n="5" /> but the origin and meaning of the rite have long been a subject of speculation.

The shape of the *chi* has been associated, even from the early Church Fathers, with the important cosmological mention of this same pattern in *Timaeus* (36b), with all its Pythagorean echoes, where the two circles of the World Soul are said to rotate on crossing orbits, similar to the way in which the ecliptic and the celestial equator cross in the sky.<fnref n="6" />

A meaning ascribed repeatedly to the bilingual alphabetic cross over the centuries is the union of different peoples under the Christian faith, like the two Testaments of the Bible, or like the Eastern and Western churches.<fnref n="7" /> It is following this same reading that the layer of ashes (or often sand and ashes) upon which the alphabets are inscribed is identified to Abraham, the biblical Prophet who says ‘I am nothing but dust and ashes’ (Gen. 18:27). Once again, it is as if, in his intimate association with the letter-elements and, in this strange rite, the decadic sign, represented a fundamental layer shared between Abrahamic faiths.

Regarding its provenance, it is to be noted first that this ceremony does not form part of the Byzantine dedication rites, and that it only appears in the Roman record from around the eighth century. Some authors have established interesting parallels with the rich Roman literature and practice of land surveying,

## The Roman Gromatici

De Rossi gives references to the strikingly similar consecratory rites performed by Greek and Roman augurs when they were establishing a τέμενος, practices later reproduced by the Roman *agrimensores* or *gromatici*<fnref n="8" /> upon the foundation of cities and any establishment of boundaries, sacred or profane.<fnref n="9" />

<footnote n="5">5. See A.-G. Martinort, ‘Le nouveau rite de la dedicace des eglises,’ *La Maison-Dieu* 70 (1962): 15–16.</footnote>

<footnote n="6">6. Cf. Schreiner, ‘Abecedarium,’ 152–3. It will be remembered that one of the meaning of στοιχεία is the constellations of the zodiac.</footnote>

<footnote n="7">7. *ibid.*, 160, 171–2.</footnote>

<footnote n="8">8. So called after the main instrument of their craft, the *groma*, used for triangulation.</footnote>

<footnote n="9">9. De Rossi, ‘Degli alfabeti,’ 142.</footnote>
<figure><img src="image_23.png" /><figcaption>DEPICTION OF A GROMA ON A TOMBSTONE<fnref n="10" /></figcaption></figure>

The drawing of the two fundamental axes, *cardo maximus* and *decumanus maximus* naturally formed the decussate cross,<fnref n="11" /> which is of course the same Greek capital X of Χριστός. In this context and in view of my further observations below, the striking resemblance between the groma and the labarum should not be left unmentioned.

<figure><img src="image_24.png" /><figcaption>FROM HYGINUS GROMATICUS<fnref n="12" /></figcaption></figure>

The measures and other terrain features established by the land surveyors were marked and codified with special signs called *casae litterarum*, which comprised the

<footnote n="10">10. G. Chouquer and F. Favory, *L'arpentage romain: histoire des textes, droit, techniques* (Paris: Errance, 2001), 67.</footnote>

<footnote n="11">11. The word *decumanus* itself comes from *decem*, because the *decumanus* forms a figure of ten, X, with the *cardo*. This etymology is enough to disprove claims against a relation between the *abecedarium* and the surveyors' work based on the narrow angle at the crossing of the lines.</footnote>

<footnote n="12">12. M. Clavel-Lévêque et al., trans., *Corpus Agrimensorum Romanorum IV. 1. Hygin l'arpenteur. L'établissement des limites* (Luxembourg: Office des publications officielles des communautés européennes, 1996), 96.</footnote>
entire Greek and Latin alphabetic series.<fnref n="13" /> The relation between language and temple consecration is firmly attested, with several examples, among which this by Servius:

*loca sacra, id est ab auguribus inaugurata, effata dicuntur.*

Sacred places, that is those inaugurated by the augurs, are said to be ‘uttered’.<fnref n="14" />

This certainly is in line with the basic Hermetic task of signposting and dividing the land,<fnref n="15" /> and thus taking possession of it, and with his patronage of language. In fact, the act of the dedication has been explained as an apotropaic ritual, given the conjuring power of the alphabet, followed by *dedicatio*, a ‘spelling’, and *possessio*.<fnref n="16" /> This ‘inaugural’ aspect of the rite has well-documented parallels in catechetical and baptismal rites, in which the importance of the ‘first letters’, sometimes resumed as AΩ, is a constant.<fnref n="17" />

## Christening the Land: mensuratio/γεωδαισία

Even further on the Hermetic association, the establishment of *limites* was considered as the most important among all the rites or actions related to measures (*inter omnes mensurarum ritus sive actus eminentissima traditur limitum constitutio*),<fnref n="18" /> but these ‘limits’ are said to be of a liminal nature (*limites autem ab liminibus vocabula acceperunt*), and they are identified with the concept of *signum*, which ‘has no parts’ and is the ‘beginning and end of every observation of measures.’<fnref n="19" /> These ‘signs’ were laid out on the terrain by centuriation (in Latin *centuriatio* or, more usually, *limitatio*) a method of land measurement used by the Romans,<fnref n="20" /> consisting of the regular division of the surveyed land in a square grid pattern, *stoichedon* style.

<footnote n="13">13. See, J. B. Campbell, *The Writings of the Roman Land Surveyors* (London: Society for the Promotion of Roman Studies, 2000), 232ff. A remarkable contemporary analogue is found in the ‘corner stakes’ which to this day are marked by builders using letters and numbers.</footnote>

<footnote n="14">14. *Ad Aeneid.*, III, 463.</footnote>

<footnote n="15">15. See above, p. 137.</footnote>

<footnote n="16">16. Martimort, ‘*Le nouveau rite de la dedicace des eglises*,’ 20. For the apotropaic aspect, see also Schreiner, ‘*Abecedarium*,’ 155ff.</footnote>

<footnote n="17">17. Cf. G. De Rossi, ‘Dell’alfabeto nei monumenti cristiani,’ *Bullettino di Archeologia Cristiana* (Roma), 3rd ser., 6, no. 4 (1881): 135, ‘until the eleventh century it was customary to solemnly show the catechumens the monogram with the two letters AΩ, to begin their instruction in the elements of the catechism.’</footnote>

<footnote n="18">18. Clavel-Lévêque et al., *Corpus Agrimensorum Romanorum IV.* 1, 112; Campbell, *Writings of the Roman Land Surveyors*, 135.</footnote>

<footnote n="19">19. *ibid.*, 208. The liminality of this craft is already evident in its being used by Aristotle as one of the examples when discussing the existence of ‘intermediaries’; *Metaph.* 997b27.</footnote>

<footnote n="20">20. Apparently of Etruscan origin, see O. Dilke, *Greek and Roman Maps: Aspects of Greek and Roman Life* (London: Thames / Hudson, 1985), 18.</footnote>
<figure><img src="image_25.png" /><figcaption>FROM HYGINUS GROMATICUS<fnref n="21" /></figcaption></figure>

Rabanus Maurus

Coming back to the church dedication and an early medieval Christian association, an immediate striking visual parallel is found in the lattice-work of Rabanus Maurus' *Liber sanctae crucis*, where letters, rhythm, Christic motifs and a rigorous grid pattern combine in what must count as one of the summits of alphanumeric art.<fnref n="22" />

<footnote n="21">21. Clavel-Lévêque et al., *Corpus Agrimensorum Romanorum IV. 1*, 97.</footnote>

<footnote n="22">22. For the title and a 'theological' appraisal, see G. d'Onofrio, 'La teologia della croce in epoca carolingia,' in *La croce, Iconografia e interpretazione, Atti del Convegno Internazionale di Studi*, ed. B. Ulianich, vol. 2 (Napoli: D'Auria, 2007), 271-320, who calls the *Liber* 'a series of symbolic-religious meditations.'</footnote>
<figure><img src="image_26.png" /></figure>

All the above makes it quite easy, in the context of this work, to see how some aspects of the Roman surveying tradition could have been assimilated into this rite of the early church, in a process comparable to the assimilation of the patterns of Roman law into canon law. In fact, it may have been during the times of Rabanus, by the end of the eighth century, when the *abecedarium* rite was first performed, but regarding its origin, and in spite of any Greek, Etruscan or classical Roman associations, the decisive argument is a linguistic one.

## The Celtic Connections

Going back to the earliest textual occurrence of the *abecedarium* rite, and as pointed out by Andrieu,<fnref n="23" /> there are two key terms used in *Ordo XLI* which are of clear Celtic origin: the officiant is said to trace the *abcedurium* (or *abcturium*, instead of the usual

<footnote n="23">23. Andrieu, *Ordines romani*, 319–20.</footnote>
*abecedarium*) with his *cambuta* (instead of *baculus* for the bishop's crozier). A more recent study has confirmed, upon examination of a manuscript dating from the end of the ninth century,<fnref n="24" /> the similarities and Gallican origin of the rite, and its 'baptismal' character, including exorcisms, aspersion, unction, and thus also confirming an ancient interpretation of the rite as being related to the catechetical teaching of the *initia et rudimenta doctrinae sacrae*, the 'principles and rudiments of sacred doctrine' symbolised by the letters.<fnref n="25" /> This is in fact directly related to the text of Heb. 5:12, where the faithful are said to need instruction in τὰ στοιχεῖα τῆς ἀρχῆς τῶν λογίων τοῦ Θεοῦ 'the letter-elements of the principle of the oracles of God.'

## Eriugena

It is in the light of this specifically Irish connection that the figure of John Scotus Eriugena comes to our attention. Eriugena (c. 815-c. 877) is known as the first since Saint Augustine to introduce the ideas of Neoplatonism from the Greek into the Western European intellectual tradition, where they were to have a strong influence on Christian theology. His *Periphyseon* or *Division of Nature*, a work which 'synthesizes the philosophical accomplishments of fifteen centuries,' has been called the final achievement of ancient philosophy.<fnref n="26" />

In a general way, the *logos* in the works of Eriugena has been characterised as 'the unitary conglomerate of the universe in its *causae primordiales*,'<fnref n="27" /> but even more particularly, his doctrine of the elements in their cosmogonic role has been studied minutely by Frances Yates in the context of another major representative of an alphanumeric cosmology, that of Ramon Llull (c. 1232-c. 1315).

Llull's diagrams (remarkably similar to some Kabbalistic devices) where the letters of the alphabet symbolise the divine attributes and encompass in their combinations all possible knowledge, appear at first sight like a perfect representation of the combinatorial 'skill' (the *ars*) whereby the Artist of the *Sefer Yetsirah* makes the world. However, one searches his works in vain for a cosmological doctrine that corresponds to this visual impression, and the use of the letters seems restricted to that of a conventional code to be deciphered. Given Llull's background, and especially his acquaintance with Jewish and Muslim doctrines, I find hard to believe that some kind of real alphanumeric cosmology does not underpin his diagrams, but a thorough

<footnote n="24">24. D. Barbet-Massin, 'The Rite of Church Dedication in Early Medieval Ireland and the Dedication Scheme in the Angers Manuscript 477,' *Peritia* 27 (2016): 11-30.</footnote>

<footnote n="25">25. See C. Vogel and R. Elze, *Le Pontifical romano-germanique du dizième siècle*, 2 vols, *Studi e testi* 226 (Biblioteca apostolica vaticana, 1963), 97-8.</footnote>

<footnote n="26">26. G. B. Burch, *Early Medieval Philosophy* (New York: King's Crown Press, 1951), 5.</footnote>

<footnote n="27">27. G. Buchwald, *Der Logosbegriff des Johannes Scotus Erigena* (Leipzig: J. Drescher, 1884), 18.</footnote>
examination of this topic exceeds the boundaries of my current research.<fnref n="28" />

<figure><img src="image_27.png" /><figcaption>FROM LLULL'S ARS COMBINATORIA</figcaption></figure>

As suggested by Yates, there is a Neoplatonic influence clearly at play under Llull's 'natural logic', based as it is on the elemental structure of the created world. This influence is as it were revealed in the role assigned by Eriugena to what he calls the 'universal elements,' *universalia elementa quae Graeci catholica στοιχεία vocant*.<fnref n="29" /> These 'elements', immediate effects of the primordial causes, are the four elements, though not in any corporeal form or as the four elemental qualities, but existing *per se*, universally diffused in a mysterious and incomprehensible way, and they correspond to the *firmament* of Genesis in that they *separate*, create a boundary, between the supernal waters (the primordial causes) and the lower waters (elemental qualities).<fnref n="30" /> The universal elements, *καθολικὰ στοιχεία*, are a sort of mediator, *medietas quadam*, between the primordial causes and the composite bodies. They come together and accord with one another, *conveniunt et concinunt*, and Eriugena explains how this is so because the meaning of *στοιχείωσις* is *διατύπωσις*, *hoc est, conformatio*—the 'elementation' is a setting into forms, a kind of 'typing' of reality—in what can be

<footnote n="28">28. Notably, Idel and Djebbar have argued respectively for Jewish and Islamic sources of Llull's combinatorial art, see M. Idel, *'Dignitates and Kavod: Two Theological Concepts in Catalan Mysticism,' Studia lulliana* 36, no. 92 (1996): 69; and A. Djebbar, 'Las prácticas combinatorias en el Magreb en la época de Ramon Llull,' *Quaderns de la Mediterrània*, no. 9 (2008): 322–3. See also D. Urvoy, '¿En qué medida se vio influido el pensamiento de Ramon Llull por su relación con el islam?,' *Quaderns de la Mediterrània*, no. 9 (2008): 287–295, who points out significant connections with the *Budd al-ʻārif* (*The Object of Worship of the Gnostic*) of Ibn Sabʻīn.</footnote>

<footnote n="29">29. F. A. Yates, 'Ramon Lull and John Scotus Erigena,' *Journal of the Warburg and Courtauld Institutes* 23, nos. 1/2 (1960): 5, 9.</footnote>

<footnote n="30">30. *ibid.*, 9.</footnote>
easily read in a typographic sense.<fnref n="31" /> Not surprisingly, we are finding here again the images of dance and acoustic harmony that we had encountered in the first chapter of this research.<fnref n="32" /> And echoing even more the attributes of the στοιχεία discerned by the grammarians, Eriugena explains that these elements must be affirmed to be luminous, or indeed, light itself, in that through their mediation all bodies are made visible.<fnref n="33" /> Of particular interest is his insistence on the reality of this imagery: no allegory is meant in these, but ‘only a direct physical regard’ (*nuda solummodo physica consideratio*).<fnref n="34" />

To return to the opening lines of this section, it should be noted that in this metaphysical continuum of elements of various degrees, one can discern the profound imprint of a worldview found in other manifestations of the Celtic mentality. It is well known in theological studies that one of the hallmarks of Celtic Christianity is its emphasis on the metaphysical continuity between heaven and earth; what has been called, significantly in our context, the ‘St John tradition.’ The doctrines of Pelagius, like the convoluted patterns of Celtic graphic arts, have long been considered representatives of a theology in which the emphasis is on the immediacy of God in all created life.<fnref n="35" /> Eriugena’s metaphysics, according to which the divine goodness is not only the essence, but also the substance of creation,<fnref n="36" /> fits neatly into this doctrinal line, and it is little wonder that the interplay of the elements in his expositions has been likened to the sinuous patterns of the masterpieces of Celtic illumination.<fnref n="37" />

<figure><img src="image_28.png" /><figcaption>FROM THE LINDISFARNE GOSPELS, EARLY EIGHTH CENTURY</figcaption></figure>

<footnote n="31">31. *Periphyseon*, 3, 706c; page numbers follow the *Patrologia*, the text is Jeauneau’s as in Gorlani’s edition.</footnote>

<footnote n="32">32. See above, p. 29.</footnote>

<footnote n="33">33. *Ibid*.</footnote>

<footnote n="34">34. *Periphyseon*, 3, 707b.</footnote>

<footnote n="35">35. J. P. Newell, *Listening for the Heartbeat of God: A Celtic Spirituality* (London: SPCK, 1997), 32–3, 36.</footnote>

<footnote n="36">36. *Periphyseon*, 681D.</footnote>

<footnote n="37">37. Yates, ‘Ramon Lull and John Scotus,’ 10.</footnote>
Psellos: Letters and Matter

As I bring to completion the account of Christian alphanumeric literature in the high middle ages, the examination of the most important related work in the Byzantine tradition brings me to an unexpected passage echoing the Celtic doctrine just mentioned, and shedding light on a new aspect of the intermediary elemental realm.

The Byzantine work is the Ἐρμηνεία περὶ τῶν εἰκοσιτεσσάρων στοιχείων, *Interpretation of the twenty-four letters*, by Michael Psellos (d. 1078).<fnref n="38" /> In spite of the title, there is not much of interest for us in the treatise itself, since it is devoted to a letter by letter elucidation rather than discussing the nature of the alphabet as a whole,<fnref n="39" /> but following immediately after this treatise there is the following four-line *Fragmentum de materia*,

Η ὕλη μήτηρ τῶν εἰδῶν καὶ τιθηνὸς λέγεται· καὶ γὰρ καὶ αἱ τῶν
ζώων μητέρες κατὰ τὸν λόγον τὸν τὸ ‘τί ἦν εἶναι’ σημαίνοντα τοὺς
λόγους ἅπαντας ἔχουσι τῆς γενέσεως διὰ τῶν παρὰ τῶν ἀρρένων
καταβαλλομένων γονῶν ἐν τοῖς κατὰ τὰς μήτρας ὑγροῖς.

Matter is called the mother and nurse of forms, because just like it,
the mothers of living beings too contain all the analogies (λόγους)
of generation, according to that analogy which betokens the essential
quiddity and by means of the male sperm cast in the humidity of the womb.

I shall try to make this clear by paraphrasing and explicating the condensed meaning:

1—Matter (which is in Greek something similar to timber, and also like the living wood from where the timber is extracted) is like a mother and a nurse, meaning that it not only originates but also nourishes and sustains.

2—Why is this comparison valid? Because there is something in which matter resembles a mother: mothers have in them all the ‘words’ (the term is *logos*) of generation. But the best translation here may be ‘patterns’—mothers hold in themselves all the patterns of their future progeny, just as matter contains the patterns, words, ratios, analogies of the future beings. Obviously, the matter referred to here is not a primordial chaotic substratum but some sort of in-formed primary constituent.

3—Each being has a quiddity, an essential what-ness which is revealed or signified (σημαίνεται) by a pattern or word. When we say that the mothers, like matter, hold the patterns of every future progeny, it is understood that these patterns refer to every

<footnote n="38">38. Treatise 36 in M. Psellus, *Philosophica minora*, ed. J. Duffy (Leipzig: Teubner, 1992), 120–41.</footnote>

<footnote n="39">39. There is a useful overview in K. Ierodiakonou, 'The Greek Concept of Sympatheia and Its Byzantine Appropriation in Michael Psellos,' in *The Occult Sciences in Byzantium*, ed. P. Magdalino and M. Mavroudi (Geneva: La Pomme d'or, 2006), 110–17.</footnote>
individual pattern which signifies the essence of a being. Matter is thus conceived as a semantic repository.

4–Finally, it is made clear that mothers perform their ‘metaphysical’ task of individuation by the ordinary means of animal reproduction between male and female.

It is well known that the Latin word *materia* itself derives from *mater*, mother,<fnref n="40" /> as if prefiguring in its derivation the understanding laid bare by Psellos, and there is a wealth of literature, especially in mythical narratives, where the original cosmic substance is conceived as a benign motherly figure; what is of special note here is the fact that this compressed passage appears almost as a coda to the treatise on the twenty-four letters. Indeed, the last lines of the *Interpretation* are about intellectual motherhood: ‘I have engendered many times many other discourses (λόγους), but I never begot one son like this one, for which I endured birth-pains and whom I gave birth to in one single night... And we shall hold onto our own progeny...’<fnref n="41" /> And immediately after that follow the lines on the universal motherhood of matter, where the λόγος plays such a crucial *defining* role. Our final witness to the doctrinal alphanumeric developments is in fact related to the numerical aspect of the λόγος.

## Aquinas and the Second ‘Signified’ Matter

The *locus classicus* for the maternal aspect of matter as the receptive pole of creation is *Timaeus* 50d3, προσεικάσαι πρέπει τὸ μὲν δεχόμενον μητρί—‘it behoves to compare the receptive to a mother.’ This passage and other related epithets found in *Timaeus* were translated and commented upon by Calcidius, who gives a list of various alternative names for the same reality,

quam modo matrem, alias nutriculam, interdum totius generationis gremium,
non numquam locum appellat quamque iuniores hylen, nos silvam vocamus

What he now calls ‘mother’, in other places ‘nurse’, and sometimes the
‘womb of all generation’, or even ‘place’, and what later thinkers call *hyle*,
we call ‘wood’.<fnref n="42" />

The bewildering semantic shifts of the terms for matter through the middle ages have
been well charted and need no retelling. Charlton gives a pithy account,<fnref n="43" /> including

<footnote n="40">40. Originally, the trunk of a tree which gives birth to offspring.</footnote>

<footnote n="41">41. 36.637–42.</footnote>

<footnote n="42">42. Calcidius, *On Plato's Timaeus*, ed. J. Magee, Dumbarton Oaks Medieval Library (Harvard University Press, 2016), 273; the references are scattered through *Timaeus* 49a–52b. Cf. also L. Brisson, *Le même et l'autre dans la structure ontologique du Timée de Platon: un commentaire systématique du Timée de Platon*, 3rd ed., International Plato studies 2 (Sankt Augustin: Academia Verlag, 1998), 208ff.</footnote>

<footnote n="43">43. W. Charlton, *Aristotle's Physics: Books I and II* (Oxford University Press, 1983), 142.</footnote>
the importance of the role played by Calcidius' work until the second half of the twelfth century, when the translations of the Aristotelian physical and metaphysical texts started circulating in Europe.<fnref n="44" /> By examining the text of the *Timaeus* and its commentaries, Brisson has shown in every detail how the aspects of the primordial substrate include always a tension between the constitutive (mother, nurse, wood) and the spatial (place, receptacle—ἐκμαγεῖον), and he argues for the necessity to preserve this tension and ambiguity within the expression, to try to honestly grasp 'that something whose existence we must postulate, but whose ontological nature is so difficult to determine.'<fnref n="45" />

It is no wonder that Aristotle's writings are particularly abstruse on this point, and just as he posited two kinds of matter, a sensorial one and an intellectual one (ὑλη νοητή—*Metaph.* 1036a9)<fnref n="46" /> there were many others who developed alternative nomenclature. Iamblichus, for instance, speaks of three kinds of matter: sensorial, mathematical and intellectual.<fnref n="47" /> Proclus reaches the summit of elaboration of this doctrine with ten hierarchical levels according to the interplay between the Limited (Form) and the Illimited (Matter). What all doctrines of matter have in common through the centuries is that they are always forced to fill a primordial gap between the intelligible forms and the spatial receptacle, and to do it by positing some sort of intelligible matter in whose image the sensorial world will be modelled.<fnref n="48" />

In the thirteenth century, when Aquinas was writing his *Summa Theologiae* (ca. 1265–1274), his preferred solution to the same conundrum was to explain first that *materia est duplex*, ‘matter is dual’: *communis, et signata vel individualis*, ‘common’ and ‘delimited/demarcated/designed’ or ‘individual.’<fnref n="49" /> Then he speaks also of two kinds of *materia*: *sensibilis aut corporalis* and *materia intelligibilis*, which is said to be ‘substance inasmuch as it is subject to quantity.’<fnref n="50" />

So we have four kinds of matter, *communis, signata, sensibilis* and *intelligibilis*, which are paired up in an increasingly subtle scheme of common sensible, signate sensible, common intelligible and signate intelligible,<fnref n="51" /> but we want to dispense with the subtleties now, and to focus on the signate intelligible matter.

<footnote n="44">44. See *Encyclopedia of Medieval Philosophy: Philosophy Between 500 and 1500*, ed. H. Lagerlund (Springer, 2010), s.v. ‘Form and Matter’.</footnote>

<footnote n="45">45. Brisson, *Le même et l'autre*, 218.</footnote>

<footnote n="46">46. Cf. Annas, *Metaphysics Mu and Nu*, 33, who calls this an ‘oddity in Aristotle’s thought.’</footnote>

<footnote n="47">47. Brisson, *Le même et l'autre*, 241.</footnote>

<footnote n="48">48. *Ibid.*, 243.</footnote>

<footnote n="49">49. The translation variations are meant as references to the Hermetic and Roman surveying texts discussed in previous pages.</footnote>

<footnote n="50">50. *Summa*, Iª q. 85 a. 1 ad 2.</footnote>

<footnote n="51">51. Cf. R. Pasnau, ‘Abstract Truth in Thomas Aquinas,’ chap. 3 in *Representation and Objects of Thought in Medieval Philosophy*, ed. H. Lagerlund, Studies in Medieval Philosophy (Ashgate, 2007), 40.</footnote>
This ‘dimensioned’ or ‘designated matter’, called elsewhere *materia sub quantitate
determinata*,<fnref n="52" /> is the *principium individuationis*, the principle of individuation in which
there is a clear analogue of that λόγος ὁ ‘τί ἦν εἶναι’ σημαίνων, that ‘ratio signifying the
quiddity’ of a future being, which dwells in the motherly womb of universal matter.<fnref n="53" /> It
is also the intermediate level, the interface which makes possible the total reciprocity
of the encounter between intelligible and sensorial matter.<fnref n="54" /> One way of realising the
various ways in which it has to do with this current enquiry is afforded us by the
explanation, from a leading Thomist philosopher, that: ‘intelligibility is *the ground of
possibility*, and possibility is the possibility of being.’<fnref n="55" /> It is easy and seemingly natural
to conceive of intelligence, in its relation to existence, as a net cast from above, but
perhaps what we encounter in this basic notion of the ‘measure of the land’ is the
complementary image from below, the laying of a grid in preparation for the building
of existence.

Dante and Hildegard

To conclude this chapter, I would like to observe how the imagery explored in all these
authors is always not only orbiting, as it were, the central alphanumeric concept of
λόγος in most of its aspects, but also in particular, and as we had found in the previous
chapter, its intermediary and *crucial* function in the cosmopoiesis, the making of the
universe. This constructive function seems to be strictly liminal in a very practical sense:
it is not so much architectural as cadastral, i.e. related to the land surveying needed
to lay the foundations of a new building—it is a strictly intermediary stage, like the
transference of a design to the terrain, which partakes necessarily of a logical, creative
process, and also of practical, material actions (often involving real timber). But rather
than continue to establish the many correspondences which the reader may already be
discerning between the previous sections, I should like to finish with examples taken
from two of the most important Christian literary monuments of this age.

The first is from Dante's *Commedia*, significantly called 'the *Summa* in verse' in
relation to Aquinas,<fnref n="56" /> as a literary representative of the same tendency of the age to

<footnote n="52">52. *De Principio Individuationis*, Textum Taurini, 1954. This work is now attributed to the fourteenth century Dominican Thomas of Sutton.</footnote>

<footnote n="53">53. An important caveat regarding the concept of quantity is given in W. Smith, *The Wisdom of Ancient Cosmology: Contemporary Science in Light of Tradition* (Oakton, VA: Foundation for Traditional Studies, 2004), 28–9, where this doctrine is approached from the point of view of contemporary physics.</footnote>

<footnote n="54">54. Brisson, *Le même et l'autre*, 265.</footnote>

<footnote n="55">55. B. Lonergan, *Verbum: Word and idea in Aquinas*, vol. 2, Collected Works of Bernard Lonergan (University of Toronto Press, 1997), 57, my italics.</footnote>

<footnote n="56">56. H. S. Bowden, *Dante* (London: Catholic Truth Society, 1901), 30, reports this saying, perhaps</footnote>
bring together many tributaries from different traditions into a single coherent and comprehensive whole. Among the verses of its last chant, we have a vision of the world as a book:<fnref n="57" />

Nel suo profondo vidi che s'interna,
legato con amore in un volume,
ciò che per l'universo si squaderna:
sustanze e accidenti e lor costume
quasi conflati insieme, per tal modo
che ciò ch'i' dico è un semplice lume.

In its profundity I saw how is recollected
and bound with love into one single volume
what is scattered through the universe:
substances, accidents, and their dispositions
as if conjoined, in such a way that what
I can tell is only a faint reflection.

It has to be noted that the chant begins with an invocation to the Virgin Mary, in which she is addressed as *Vergine Madre, figlia del tuo figlio, / umile e alta più che creatura, / termine fisso d'etterno consiglio*, 'Virgin Mother, daughter of your son, / more humble and yet higher than any creature, / fixed limit of the eternal counsel.' That is, she reunites the polarities in a dumbfounding unity, so much so that perhaps 'we could say of her, without lying, that she is some sort of form beyond vision or shape, that she is all-receptive, and that she shares in the intellectual in the most perplexing way.'<fnref n="58" />

The second example is from *O splendidissima gemma*, one of the hymns of Hildegard of Bingen (1098–1179), who furthers the identification between the Virgin and the attributes of the intermediary undefinable matter which encloses all the definitions:

Hoc Verbum effabricavit tibi Pater hominem,
et ob hoc es tu illa lucida materia
per quam hoc ipsum Verbum exspiravit omnes virtutes,
ut eduxit in prima materia
omnes creaturas.

The Father crafted for you this Word into a man,
and so you are that luminous matter
through which this Word breathed forth all virtues,
when in the primal matter
he brought forth all creatures.<fnref n="59" />

<footnote>referring in general to A.-F. Ozanam, *Dante et la philosophie catholique au treizième siècle* (Paris: Lecoffre fils et Cie., 1872).</footnote>

<footnote n="57">57. *Paradiso* XXXIII, 85–90; transl. Mandelbaum with a few changes.</footnote>

<footnote n="58">58. This is the description of the ‘mother and receptacle of the sensorial’, αἰσθητοῦ μήτηρ καὶ ὑποδοχή, in *Timaeus* 51a.</footnote>

<footnote n="59">59. Hildegard of Bingen, *Symphonia: A Critical Edition of the Symphonia Armonie Celestium Revelationum*, ed. Barbara Newman, Cornell Paperbacks (Cornell University Press, 1998), 114–15; transl. Newman with minor modifications.</footnote>
The epithet *lucida materia*, adding the aspect of light to the 'second matter', is found in another hymn as *aurea materia*, 'golden matter'. In this little sample of Mariology, outlining Mary's essential role in the process of creation,<fnref n="60" /> we have the fully Christian expression of a very developed alphanumeric cosmology:<fnref n="61" /> it is only the luminous matter, Mary,<fnref n="62" /> as only the alphanumeric series of designating universal elements, which can make the perfection of creation possible.

<footnote n="60">60. See P. Schäfer, *Mirror of his Beauty: Feminine Images of God from the Bible to the Early Kabbalah* (Princeton University Press, 2018), 165.</footnote>

<footnote n="61">61. An interesting comparison between the Jewish doctrine of the *shekhinah* and the Marian attributes is found in *ibid*., 169.</footnote>

<footnote n="62">62. Or the 'matrix of light' as in the alternative translation in Hildegard of Bingen, *Symphonia*, 115.</footnote>
Chapter 9

Islamic Systematisation and the Sublime
Letters That We Were

The three witnesses in this final chapter retrace the trajectory of our concept along lines which have become familiar—as they reoccur in varying degrees and ways since late antiquity—and with a sophistication and an encyclopedic push which are at once Islamic and also very universal.

This historic trajectory of the *stoicheia* draws a path from the East to the West—like the Phoenician and Ephesian letters came to Greece, and like the Indian numerals came to the Arabs, and then again westward into Europe, or like the religions of Abraham spread from the East. Then there is also the semantic trajectory of the *stoicheia*, from ancient Greek doctrines and techniques—from Greek philosophy, science and magic—to Abrahamic religions in their many salvific dimensions.

In the following pages I shall examine, always from the same alphanumeric vantage
point, the works of the *Ikhwān al-Ṣafāʾ* or *Brethren of Purity* (active around the early
tenth century), the works on magic and esoteric lore attributed to Aḥmad al-Būnī
(d. 1225), and the works of the Andalusian scholar and mystic Muḥyī al-Dīn Ibn ʿArabī
(d. 1240). As will be appreciated, this selection retraces once again a path from Basra in
the East to the farthest western reaches of the Islamic polity. By way of transition and
as a sort of preamble, and given its interest from the point of view of letter cosmology,
I shall first introduce a passage from the *Kitāb al-zīna* (*Book of the Ornament*, on the
superiority of the Arabic language) of Abū Ḥātim al-Rāzī, an Ismāʿīlī scholar of the early
tenth century.

Abū Ḥātim’s Letter Cosmogony

The following text<fnref n="1" /> comes naturally into our timeline not only because of its subject, but because it is introduced as a tradition reported from Ja‘far al-Ṣadiq, and because it has been related for obvious reasons to the *Sefer Yetsirah*.<fnref n="2" /> The word used for letters is the usual *hurūf*, but it is clear from a later passage that their phonetic meaning is primarily intended.

كان أوّل ما توهم الله عزّ وجلّ شيئا متوهّما
وأراد مرادا وشاء مشيئا فكان توهمه ومشيئته
وإرادته الحروف التي جعلها عزّ وجلّ أصلا
لكل شيء ودليلًا على كل مدرك وفاصلا لكل
مشكل ومن تلك الحروف يعرف كل شيء
[...] وعليها اجتمعت الأمور كلّها ولم يجعل
الحروف عند توهمه لها شيئا غير أنفسها بتناء
ولا وجود لأنها متوهّمة بالتوهم والتوهّم في هذا
الموضوع أوّل فعل الله عزّ وجلّ الذي هو نور
السموات والأرض والحروف هي مفعولة لذلك
الفعل وهي الحروف التي عليها بني الكلام
كلّه والعبارات واللغات كلّه من الله عزّ وجلّ
ومن خلقه وهي ثلاثة وثلاثون حروفا [...]

The first thing imagined, willed and desired
by God, Mighty and Majestic, was something
imaginal, an object of will, and an object of
desire; this imagined, desired and willed by
Him was the letter-sounds, which He, Mighty
and Majestic, made the root for every thing,
the sign for every object of perception and
the criterion of every difficulty. All things
are known through these letter-sounds ...
and all phaenomena are joined to them.
And when He imagined them, He did not
make them anything but themselves in their
delimitation without existence, since they
were something imagined in the imagination.
'Imagination' at this stage was the first action
of God, Mighty and Majestic, who is the light
of heavens and earth, and the letter-sounds
are the act of this action. These are the letter-
sounds upon which is built all speech: and
all manners of speaking and languages come
from God, Mighty and Majestic, and from
his creating, and they are thirty-three letter-
sounds.

The first thing to note about this text is the liminal status of these primordial letters, which are not yet the Arabic letters but the phonemes of every language: they are

<footnote n="1">1. Abū Ḥātim al-Rāzī, *Kitāb al-zīna fī al-kalimāt al-islāmiyya al-‘arabiyya*, ed. Ḩusayn ibn Fayd Allāh al-Hamadānī (Sanaa: Markaz al-dirāsāt wa-al-buḥūth al-yamanī, 1994), 77–8; G. Vajda, ‘Les lettres et les sons de la langue arabe d’après Abū Ḥātim al-Rāzī,’ *Arabica* 8, no. 2 (1961): 119–21.</footnote>

<footnote n="2">2. See Vajda, *Les lettres et les sons*, 124ff.</footnote>
‘imagined’<fnref n="3" /> and they have a ‘limit’ (*tanāhin*) but no existence; this is not unexpected perhaps, since they are precisely a border, an edge (*harf*). *Tanāhā*, as a form of the root *n-h-y*, is said of the water when it reaches a pond and becomes still,<fnref n="4" /> a very apt image for the delimitation of the flow of air divided into phonemes, as in the familiar passage in the *Philebus*.

Let me also note how we had in previous pages found the Arabic hendiadys ḫurūf wa-uṣūl and ʿanāṣir wa-uṣūl used to translate στοιχεῖα, and now here we encounter the metaphysical phonemes being called ‘the așl’, the root-foundation of all things. Lastly, here we seem to have again, though in an indirect way, the relation between the divine light and the metaphysical letters: the mention of God as nūr al-samawāt wa-al-arḍ (Qur’ān, 24:35) occurs in such a way that it is unavoidable to relate it to the making of the letters.

Further down the text, Rāzī explains that twenty-eight of these letters are used by the Arabic language, while the remaining five are used by other languages. And then, still on Jaʻfar's authority, he proceeds to explain the 'three creations':

فالخلق الأوَّل التوَهَّم لا وزن له ولا لون ولا حركة
ولا يسمع ولا يحسّ

والخلق الثاني الحروف لاوزن لها ولا لون وهي
مسموعة بالآذان موصوفة بالأحسن غير منظور إليها
والخلق الثالث كلّ ما كان بالحروف موصوفا في
الأنواع كلّها وهو ملموس ذو وزن منظور إليه

The first creation is imagination (*tawah-
hum*), which has no weight, colour or
movement, and is inaudible and imper-
ceptible.

The second creation is the letter-sounds, which have no weight or colour, are heard by the ears and articulated by the tongues, but are not visible.

The third creation is everything that is articulated by the letters in every possible kind, what is tangible and perceptible, having weight and being visible.

It is quite remarkable that in this cosmology, the ‘letters’ are limited to their phonetic reality, ignoring the Qur’ānic imagery of the ink, related, as we have seen, to the concepts of matter and measure. One of the recurring traits of the concept of stoicheia is the ambiguity between their phonetic and graphic aspects, manifest from the earliest grammatical evidence in the unstable lexical distinction between στοιχεῖον and γράμμα.

<footnote n="3">3. The translation of *wahm* and related terms is something of a *cause célèbre*, with alternatives varying according to the fields of study: ‘estimative faculty’, ‘compositive imagination’, ‘magical imagination’, ‘conjectural faculty’... Cf. Vajda, *Les lettres et les sons*, 245; C. W. Ernst, *Refractions of Islam in India: Situating Sufism and Yoga* (SAGE Publications India, 2016), 397; ‘Abd-al-Karīm al-Jīlī, *De l’homme universel: Extraits du livre* Al-insān al-kāmil, trans. Titus Burckhardt, Mystiques et religions (Paris: Dervy-Livres, 1986), 26, 92; and T. Kukkonen, ‘Imagination in philosophy,’ *Encyclopaedia of Islam, THREE*, 2018.</footnote>

<footnote n="4">4. Ibn Manẓūr, *Lisān al-‘arab*, 4565b.</footnote>
This strictly aural cosmogony will perhaps serve as a guiding thread for future research
into the source of this striking report by Rāzī.

A Pure Brotherhood

The Ikhwān al-Ṣafā’ or Brethren of Purity, an enigmatic group of scholars active around Basra in the early tenth century,<fnref n="5" /> produced an encyclopedic collection of 52 treatises or *Epistles*, the *Rasā’il Ikhwān al-Ṣafā’, which have been rightly considered unique in every way, both inside and outside the Muslim world.<fnref n="6" /> Indeed, the tendency to merge into a doctrinal synthesis the accumulated treasury of late Hellenistic and Abrahamic scriptural scholarship comes to the fore in the *Rasā’il* again and again in many ways, and it is hardly surprising that they have been called ‘the Pythagoreans of Islam’,<fnref n="7" /> or ‘Muslim Neoplatonists’,<fnref n="8" /> and even a ‘Masonic brotherhood of the eleventh century’.<fnref n="9" /> Their work was greatly influential in many direct and indirect, acknowledged and unacknowledged ways over the centuries, on authors of very different disciplines who were all able to draw from the overflowing source of the Ikhwān. The *Rasā’il* were translated into Persian, and some excerpts of it into Hebrew, Turkish, Hindustani and Latin.<fnref n="10" />

The variety and extension of the collection will inevitably force me to be uneven and limited in my treatment of their doctrines, as I shall, more than in other cases, try to restrict myself to the points which are immediately relevant to this research. The

<footnote n="5">5. See G. De Callataÿ, ‘Brethren of Purity (Ikhwān al-Ṣafā’), *Encyclopaedia of Islam, THREE*, 2013 for attribution issues; regarding the earlier dating, see G. De Callataÿ, ‘Philosophy and Bāṭinism in al-Andalus: Ibn Masarra’s *Risālat al-I‘tibār* and the *Rasā’il Ikhwān al-ṣafā’, *Jerusalem Studies in Arabic and Islam* 41 (2014): 298–9, and S. Stroumsa, ‘Wondrous Paths: The Ismā‘īlī Context of Saadya’s ‘Commentary on *Sefer Yeşira*’, *Bochumer Philosophisches Jahrbuch für Antike und Mittelalter* 18, no. 1 (2015): 85. L. Saif, ‘Ikhwān Al-Ṣafā’s Religious Reform and Magic: Beyond the Isma‘ili Hypothesis,’ *Journal of Islamic Studies*, March 2018 is an important recent contribution regarding the Ismā‘īlī affiliation of the Ikhwān.</footnote>

<footnote n="6">6. See G. De Callataÿ, ‘The Classification of the Sciences according to the Rasa’il Ikhwan al-Safa’’, (lecture), (The Institute of Ismaili Studies, London), 2003: 1.</footnote>

<footnote n="7">7. Y. Marquet, ‘Les Frères de la pureté, pythagoriciens de l’Islam,’ *SEHA, Édidit*, 2006.</footnote>

<footnote n="8">8. I. R. Netton, *Muslim Neoplatonists: An Introduction to the Thought of the Brethren of Purity (Ikhwān Al-Ṣafā)* (Psychology Press, 2002).</footnote>

<footnote n="9">9. M. Steinschneider, ‘Die lautern Brüder, ein Freimaurerorden des XI. Jahrhunderts,’ *Hebräische Bibliographie 2* (1859): 91–92, (republished in F. Sezgin (ed.), *Rasā’il Ikhwān aș-Șafā’. Texts and Studies. Frankfurt: IGAIW, 1999).</footnote>

<footnote n="10">10. See De Callataÿ, ‘Brethren of Purity—EI3’; G. De Callataÿ, *Ikhwan al-Safa’: a Brotherhood of Idealists on the Fringe of Orthodox Islam*, Makers of the Muslim World (Oneworld Publications, 2005), 16; G. Flügel, ‘Ueber Inhalt und Verfasser der arabischen Encyclopädie :رسائل اخوان الصفاء وخلان الوفاء die Abhandlung der aufrichtigen Brüder und treuen Freunde. Nebst Andeutungen über die Einrichtungen des Bundes der Verbrüderten,’ *Zeitschrift der Deutschen Morgenländischen Gesellschaft* 13 (1859): 2–3.</footnote>
Rasā’il make for fascinating reading—al-Qifṭī calls them maqālāt mushāwwiqāt ghayr mustaqṣāt, ‘thrilling, unfathomable treatises’—<fnref n="11" /> and it is easy to be carried away in the train of thought of the Ikhwān from one interesting topic to another. In fact, the Rasā’il delve into all the different aspects of alphanumeric cosmology that we have been studying this far, and what I will try to do is to single out a few more important instances that make a significant addition to this chapter.

## How Pythagorean are the Ikhwān?

A full identification of the Ikhwān as Pythagorean can only give rise to complications, given that the definition of what is Pythagorean is itself subject to discussion, as we have seen in Chapter 2, and Marquet’s attempt to make the doctrines of the *Epistles* fit neatly into a Pythagorean scheme have met with valuable criticism.<fnref n="12" /> Nonetheless, from our alphanumeric point of view which leaves aside the more soteriological and ascetic aspects of Pythagoreanism, there would seem to be hardly any question regarding this identification: the primal role of number in cosmology is evident throughout the *Epistles*, where it is ‘the ultimate foundation of every truth’,<fnref n="13" /> conceived as order and correspondence, and inseparable from the ideas of cosmos and order.<fnref n="14" />

This all-important place of number in the cosmology of the Ikhwān is already made clear in an example from the introduction to the whole collection, which illustrates just how daunting their usage of the terminology can be, and which presents one of the handful of occurrences of the word *usṭuqus*,

> إن علم العدد جذر العلوم وعنصر الحكمة ومبدأ المعارف وأسطقس المعاني

> The science of number is the root of the sciences, the stock (‘unṣur) of
> wisdom, the principle (mabda’) of the subtle comprehensions, and the
> primal element (usṭuqus) of meanings.<fnref n="15" />

In *Epistle* 32, ‘On the Essential Intellectual Principles according to the View of the Pythagoreans’, Pythagoras is introduced again as the great arithmetic authority who affirmed:

<footnote n="11">11. Flügel, ‘Ueber Inhalt und Verfasser,’ 38.</footnote>

<footnote n="12">12. See P. Lory, review of *Les « Frères de la pureté », pythagoriciens de l’Islam*, by Y. Marquet, *Bulletin critique des Annales islamologiques* 23 (2007): 27–28; Izdebska, ‘The Attitudes of Medieval Arabic Intellectuals towards Pythagorean Philosophy: different approaches and ways of influence,’ 33–4.</footnote>

<footnote n="13">13. P. Lory, ‘La philosophie du nombre chez les Ikhwân al-Safâ’, *Annuaire de l’École pratique des hautes études. Ve section, Sciences religieuses* 101 (1992): 211.</footnote>

<footnote n="14">14. For these topics above in Chapter 2, see pp. 72 and 70.</footnote>

<footnote n="15">15. Ikhwān al-Ṣafā’, *Rasā’il Ikhwān al-Ṣafā’ wa Khullān al-Wafā’*, 4 vols. (Beirut: Dār Ṣadir, n.d.), 1.22 (hereafter cited as RIS-Beirut); I quote from the Beirut edition, with references to the IIS/OUP editions when possible.</footnote>
إن طبيعة الموجودات بحسب طبيعة العدد

*The nature of existing beings accords with the nature of number.*<fnref n="16" />

This characterisation of the relation between beings and number is rather flat when we recall the expressions used by Nicomachus and conveyed by Thābit, speaking of participation, lineage, marriage (μετουσία, translated as Ar. *mushāraka*), between numbers and reality.<fnref n="17" /> It would seem that the Ikhwān follow a sort of ‘soft’ number Pythagoreanism. Number would thus remain an epistemological ‘category’ to be applied to things—quite far from the *Timaeus*, Nicomachus, Iamblichus and Proclus. The word *bi-ḥasabi* is key, as it defines a relation which has to do with reckoning, enumeration, mental processes.

But in truly Pythagorean fashion, because it has to do with harmony, with music, and with more than a hint of reticence, it turns out that the deepest understanding of number in the *Rasā’il* is found in relation to squared numbers—what we know nowadays as ‘magic squares’—and with music.

## Magic Squares in the *Epistles*

It is currently accepted that the figurate numbers or ‘harmonic dispositions of numbers’ (*awfāq al-a‘dād*), as they came to be called in later Arabic literature,<fnref n="18" /> were dubbed ‘magic’ because they were transmitted to Europe in the fourteenth century through astrological and magical texts.<fnref n="19" /> This explanation is a little simplistic, given that from the most ancient occurrences in China, the squares were already part of rituals that we would call magic, just as long before getting their European name, they were used to bring about ‘special’ effects. But this may be, once again, a matter of labelling—we needed a word to identify something which could no longer be explained within a new cosmology, one in which quantity and quality where no longer inextricably united. As we shall see immediately, this was far from being the case in the *Rasā’il*.

<footnote n="16">16. Ikhwān al-Ṣafā’, *On Arithmetic and Geometry: an Arabic critical Edition and English Translation of Epistles 1-2*, trans. N. El-Bizri, Epistles of the Brethren of Purity (Oxford: Oxford University Press in association with The Institute of Ismaili Studies, 2012), 32a.1, emphasis mine. Due to complexities of the manuscript tradition, the editors of the IIS edition have decided to publish *Ep*. 32 in two versions. Version 32a is only a brief tract introducing and sketching subjects developed in *Ep*. 32b.</footnote>

<footnote n="17">17. See above, p. 86.</footnote>

<footnote n="18">18. B. Hallum, ‘New Light on Early Arabic *Awfāq* Literature,’ (forthcoming), (London), 2018: 2. I am most grateful to Bink Hallum for sharing his knowledge on magic squares so generously every week at the Warburg Institute, and for allowing me to cite his forthcoming publication.</footnote>

<footnote n="19">19. See J. Sesiano, ‘Les Carrés magiques de Manuel Moschopoulos,’ *Archive for History of Exact Sciences* 53, no. 5 (1998): 379.</footnote>
One of the main appeals of figurate numbers has always been the mathematical combinatorial one: how to develop methods to construct new arrays of increasing complexity. This partly justifies why, towards the end of the *Epistle on Geometry*, the Brethren introduce them explaining that, after having shown some of the special properties (*khawāṣṣ*) of numbers and of geometrical shapes, they will now speak about some of the properties of their conjunctions, for through them ‘are made evident some of their particular properties which are not visible when they are separated.’<fnref n="20" /> Then follow in ascending order the first seven regular squares, called at first simply *ashkāl*, ‘shapes’, but finally identified to talismans, and then a little more explanation: why do they have such ‘special properties’? It is because ‘there is no entity, either mathematical, natural or divine, which is devoid of an exclusive property. And so their combinations (*majmūʻāt*) too have special properties’ which do not manifest in isolation.<fnref n="21" /> This applies to numbers, shapes, forms, times, places, flavours, colours, utterances, letters, etc., and so, ‘when you join them symmetrically (‘*alā al-nisab al-taʼlīfiyya*),<fnref n="22" /> then their special properties and their effects become evident.’

After the previous chapters of this enquiry, it will not be difficult to appreciate how this conjunction of shape and number echoes the nature of the alphanumeric elements, which were each of them precisely such a conjunction (with the third acoustic level added to it) and which had their own ‘personality’, their ‘character’ as listed in the many works devoted to restricted letter cosmology. But actually, the Ikhwān do still inch closer to some of our previous findings.

## Music: Prosody: Grammar

It is quite significant that the *Epistle on Music* includes lengthy tracts on prosody and on writing (*kitāba*), the ‘noblest of arts’.<fnref n="23" /> From music the transition is seamless, since music is based, like prosody and metrics, on the contrast between sound and silence, like vowels and consonants, long and short syllables. Regarding writing, the shapes of the letters are explained to derive also from a binary, the straight and curved lines, and so put in relation with the art of geometry (1.219)—the letter-shapes are explicitly here the geometrical aspect of language.<fnref n="24" />

<footnote n="20">20. II.1.109; Ikhwān al-Ṣafā', *On Arithmetic and Geometry*, 2.26.</footnote>

<footnote n="21">21. II.1.113.</footnote>

<footnote n="22">22. Literally, ‘following the proportions of composition.’ The original meaning of *συμμετρία* is very apt here, implying commensurability, due proportion and suitability, all more intellectual than aesthetic. See Tatarkiewicz, *History of Six Ideas*, 90–91, which includes a comparison with the closely related concept of eurhythmy. Cf. Hallum, ‘New Light,’ 33.</footnote>

<footnote n="23">23. RIS-Beirut, V.1.196ff.</footnote>

<footnote n="24">24. See also VI.1.252, where the letters are said to ‘differ in their shapes, and to be distinct in their forms’, *mukhtalifa al-ashkāl mutabayyina al-șuwar*.</footnote>