In spite of this common ground between music and writing, music is said not to have
the clarity of language, because melodies and rhythms do not have an alphabet (*laysa
lahā ḫurūf al-mu‘jam*),<fnref n="25" /> a remark made elsewhere to signal similar shortcomings of
other disciplines.

Several pages are devoted to the geometry of calligraphy, culminating with the
geometry of the human body, and all this geometry depends on

ما كانت تركيب بنيته وتَأْلِيف أجزائه على النسبة الأفضل
... that the arrangement of the structure and the composition of the parts
are based on the noblest proportion.

The building vocabulary, with all the terms referring to structure and composition is
essential to the worldview of the Ikhwān which is completely demiurgic, in line with
the doctrines of the *Timaeus*. I shall leave for later further comments on this.

‘Letters’ in the Rasā’il

Further down, even closer to our subject, the most important identification between
letters and numbers occurs in Epistle XXXI *On the Difference between Languages*, where
in order to name the newly created beings, Adam is said to have been taught the nine
‘signs’ (‘alāmāt) or ‘letters’ (ḥurūf) which turn out to be the nine numbers from one to
nine, ‘which the people of India use in this form ۱۲۳٤٥٦٧٨٩’.<fnref n="26" />

In an echo of the triple nature of the στοιχεῖα we have studied before, the letters
are mentioned at the beginning of the logical treatise *On the Isagoge*,<fnref n="27" /> because they
make up utterances and convey logical meaning in three ways: intellective (*fikriyya*),
by giving form (*muşawwira*) in their essences; linguistic (*lafẓiyya*), as utterances; and
graphic (*khaṭṭiyya*).

الحروف الخطية إنما وضعت سمات ليستدلّ بها على الحروف اللَّفظية، والحروف اللَّفظية وضعت سمات ليستدلّ بها على الحروف الفكرية، والحروف الفكرية هي الأصل

<footnote n="25">25. RIS-Beirut, V 1.235; see Ikhwān al-Ṣafā’, *On Music: an Arabic Critical Edition and English Translation of Epistle* 5, trans. O. Wright, Epistles of the Brethren of Purity (Oxford: Oxford University Press in association with The Institute of Ismaili Studies, 2010), 164, 166; see esp. n. 323.</footnote>

<footnote n="26">26. RIS-Beirut, XXXI.3.141–2. For numerals as the ‘letters of Adam’, see S. H. Nasr, *An Introduction to Islamic Cosmological Doctrines* (New York: State University of New York Press, 1993), 211. Also commented in R. F. Albert Reyna, ‘El concepto de lenguaje en las Epístolas de los Hermanos de la Pureza,’ *Anaquel de estudios árabes* 20 (2009): 14; and F. Dieterici, *Die Philosophie der Araber im IX. und X. Jahrhundert n. Chr. aus der Theologie des Aristoteles, den Abhandlungen Alfārābīs und den Schriften der Lautern Brüder*, 2 vols (Leipzig: J. C. Hinrichs’sche Buchhandlung, 1876), 2.116–7.</footnote>

<footnote n="27">27. RIS-Beirut, X.1.392–3.</footnote>
The graphic ‘letters’ denote by signs the linguistic ‘letters’, the linguistic ‘letters’ denote by signs the intellective ‘letters’, and the intellective letters are the foundation.<fnref n="28" />

Once again, the letters in their highest level are the root-foundation, the *așl*.

Later, in chapter 7 of the same epistle,<fnref n="29" /> when this discussion is reprised, the letters are no longer mentioned, as had been promised, but ‘the foundation’ (sc. of intellective letters) is explained, in what seems to me to be the closest to a metaphysics of ‘letters’, saying,

> إن الأشياء كلها بأجمعها صور وأعيان غيرَيَّات أفاضها الباري

> All things in their totality are different forms and selves (aʻyān) emanated
> by the Creator.

Given the context, I think it is clear that by ‘the forms and selves’, or essences, are meant those same that had been called *hurūf* some pages before, and that they are thus said to be emanated by the creator.

Studying in detail the architecture of this emanation, and how it comes about through the setting of metaphysical ‘limits’, and how if forms part of different levels of divine craftsmanship would exceed the limits of this work, but indicating some basics of their cosmogony will doubtlessly be relevant.<fnref n="30" />

Epistle XV is devoted, among other concepts, to explaining what ‘matter’ (*hayūlā*) is, or rather what the four different levels of matter are. It is in their third level, ascending, in what they call the *hayūlā al-kull*, the universal matter, also known as the absolute body (*al-jism al-muțlaq*),<fnref n="31" /> that I seem to find a correspondence to the intermediary level of the ‘universal elements’ or the ‘materia quantitate signata’ of the previous chapter. In Epistle VIII, ‘On the Practical Arts’,<fnref n="32" /> there is similarly a question of the psychic craftworks (*al-mașnū‘āt al-nafsāniyya*), also the third degree on the ascent, which are compared to ‘a system of the centres of the elements’ (*nizām marākiz al-arkān*), and also to ‘a system of the forms of the universe in their totality’ (*nizām șuwar al-‘ālam bi-al-jumla*).

<footnote n="28">28. Ikhwān al-Safā', On Logic: An Arabic Critical Edition and English Translation of Epistles 10-14, ed. C. Baffioni, Epistles of the Brethren of Purity (Oxford University Press in association with The Institute of Ismaili Studies, 2010), 68.</footnote>

<footnote n="29">29. X.1.398/Baffioni 75.</footnote>

<footnote n="30">30. See summaries in De Callataÿ, *Ikhwan al-Safa': a brotherhood*, 17–20; S. Akkach, *Cosmology and Architecture in Premodern Islam: An Architectural Reading of Mystical Ideas* (State University of New York Press, 2012), 36–40; Nasr, *An Introduction*, 51–2.</footnote>

<footnote n="31">31. RIS-Beirut, 6–7.</footnote>

<footnote n="32">32. RIS-Beirut, 1.277.</footnote>
However, because their expositions are not quite free of some contradictions in details, and because they have a system of ten levels of emanation<fnref n="33" /> mingled with the four kinds of matter, and also with the four types of craftworks (*maṣnūʻāt*), what I have is the strong impression of a continuum in which the cutting points do not quite match the notches of other comparable ‘scales’. A close comparison and examination is beyond my competence, but several aspects of their cosmological hierarchy are clearly related to the systems of Plotinus and Proclus, reminding us of Marquet calling their doctrines a ‘syncretism of syncretisms’.<fnref n="34" />

## Risāla al-Ḥāmiʻa

To complete what is necessarily a sketchy examination of the Ikhwān's corpus, I would only like to register two passages from the 'crown' of the *Epistles*, the *Risāla al-Ḥāmiʻa* or *Comprehensive Epistle*,<fnref n="35" /> which in general follows with few divergences the subjects of all the other epistles, but gives more prominence to the doctrine of the divine language.<fnref n="36" />

In the section Fī al-ibdāʻ al-awwal wa-al-qawl bi-anna ʻilm al-ʻadad fayḍ al-ʻaql ʻalā al-nafs, ‘On the first creation and the assertion that the knowledge of number is an effusion of the intellect into the soul’,<fnref n="37" /> practically nothing is said about number, but we find instead a valuable reference to the divine script, drawing on the Qur’ānic images of the Tablet and the grid lines.<fnref n="38" />

### فخط في اللوح الكريم سطور المشيأة واحرف الإرادة

*The script on the Magnificent Tablet is the lines of the Will and the letters of the Volition.*

Later, in the section ‘That numbers precede all sciences in the same way as the intellect precedes all things,’ we find the following lines which are close to what is found in the *Rasā’il*:

سائر العلوم موجودة في علم العدد وصورته مطابقة لصورة الموجودات فكمال الحالين له وهو صورة البسائط

All other knowledges exist within the knowledge of number, as its form corresponds to the form of the existants. So the perfection of both states

<footnote n="33">33. RIS-Beirut, XXXII.3.181ff.</footnote>

<footnote n="34">34. Cited in De Callataÿ, *Ikhwan al-Safa*: *a brotherhood*, 75.</footnote>

<footnote n="35">35. See W. Madelung and T. Mayer, eds, *Avicenna's Allegory on the Soul: an Ismaili Interpretation*. An Arabic Edition and English Translation of ʻAlī b. Muḥammad b. al-Walīd's al-Risāla al-mufīda, Ismaili Texts and Translations 22 (London/New York: IB Tauris / The Institute of Ismaili Studies, 2018), 93n, for a summary and references to the at least equally difficult attribution matters.</footnote>

<footnote n="36">36. See Ebstein, *Mysticism and Philosophy*, 45.</footnote>

<footnote n="37">37. Ikhwān al-Ṣafā', *al-Risālah al-ḥāmiʻah*, ed. M. Ghālib (Beyrut: Dār Ṣadir, 1974/1394), 24.</footnote>

<footnote n="38">38. Cf. a close parallel in *Epistle* XLIX.4.203.</footnote>
بالقوة وصورة التراكب بالفعل
فأما كونه صورة البسائط بالقوة فالقول
بالالفاظ المؤلّفة من الحروف ووضع كل
مرتبة منه في مكانه بالقول في النفس
غير محتاج إلى مكان بالحس ولا معرفة
باللمس لتصوّره في النفس
واما كونه صورة المركبات المحسوسة
والاشياء المركبة الموضوعة في الأمكنة
الكائنة في الأزمنة المشار إليها بالاسماء
التي هي الواحد والاثنان والثلاثة والأربعة
والخمسة والستة والسبعة والثمانية والتسعية
والعشرة وما زاد بالغا ما بلغ فهو بالقوة
مصور في نفس العاد وهو بالفعل صورة
المعدود

belongs to it, since it is the form of the elements
in potency and it is the form of the compounds in
act.

As for its being the form of the elements in
potency: speech is [likewise] in words composed
of letters, and the setting of every rank of number
is to do with its location in the soul by means of
speech, with no need of a sensorial space or tactile
cognition in order to be conceived in the soul.

Now, as regards its being the form of the
perceptible compounds which occupy places and
arise in time—the ones denoted by the names one,
two, three, four, five, six, seven, eight, nine, ten
and so on—it [number] is in potency a fashioner
(muşawwir) in the soul of the one who counts, and
in actuality it is the form of what is counted.<fnref n="39" />

In this fragment we have a complete expression of most aspects of the Ikhwān's
metaphysics of number, accompanied by a curious mention of the letters.

The correspondence in question, *muṭābaqa*,<fnref n="40" /> a conformation or very close concord-
ance, is quite different from the *bi-ḥasabi* found earlier, and more like the relation
between the numbers inside a magic square (*wafq*).

The ‘two states’ refer in this context to those in the section title, the cognitive
of ‘ulūm and the ontological of ashyā’. The ‘simples’ are another name for the four
elements (arkān).<fnref n="41" /> Regarding the two immediate assertions, I am reading the ‘elements
in potency’ as an intermediary level of the elements, as yet immaterial; it would be those
which not only correspond to number, but number is their form. On the lower actual
level, number is the form of the composites too.<fnref n="42" />

The second paragraph expands on the form of number being the elements potentially.
It takes a turn to language—why?—most likely because language and letters belong par
excellence to such level. I read retaining ‘adad as the masculine singular reference: ‘the
disposition (waḍ’) of any order of number (minhu) is to do with its situating it in the

<footnote n="39">39. Ikhwān al-Ṣafā’, Rj, 29.</footnote>

<footnote n="40">40. In Lisān, 2636c it is defined as muwāfaqa, a ‘harmonisation’. Cf. P. Lory, ‘La magie des lettres dans le “Ṣams al-ma‘arif” d’al-Būnī,’ *Bulletin d’études orientales* 39/40 (1987): 109.</footnote>

<footnote n="41">41. RIS-Beirut, XXVI.2.473.</footnote>

<footnote n="42">42. A summary of this topic in context can be found in the section ‘Die Mittelstufen des All’, Dieterici, *Die Philosophie der Araber*, 1.177.</footnote>
soul, abstractly.'

The third paragraph expands on the lower actuality of the form of numbers, and introduces in it a subdivision: when you count, number (here almost personified), as the form of the integers, is in your soul a producer of forms—it *informs* the soul by means of the integers, and as such it is the psychic *formator*. On the other hand, number is, also by means of the integers, the actual form of what is counted; and as such it is the ontological *formator*.

## A ‘Sufi’ Interim

One of the important developments in the Islamic world that go in parallel with the gradual advent of the alphanumeric scission is the consolidation of Sufism (taşawwuf), from the prevailing asceticism of the first centuries, to identifiable groups of masters and disciples, then to a distinct body of literature and associated practices, then, towards the twelfth century, into the arising of the first orders or brotherhoods.<fnref n="43" /> It is remarkable that although both al-Būnī and Ibn ‘Arabī belong by their spiritual lineage to lines of Sufi transmission,<fnref n="44" /> and although they are immediately recognised as mutaşawwifa by Arabic speakers, their writings are not necessarily, or not unanimously, considered typical representatives of Sufi literature; rather, they seem to be each a fountainhead from which later generations of Sufis, philosophers and magicians and others, have drawn and continue to draw.

Now, the lineage of alphanumeric cosmology, as we have seen, does not only run through mystical lineages, but it is also evident in works of grammar and metaphysics, and found often too in theological works that reject any sort of *hurūfī mysticism*. Ibn Sīnā (d. 1037), for instance, aside from his metaphysical writings in Aristotelian style, wrote a brief treatise, the *Risāla al-nayruziyya*, with a cosmogony based on the letters of the alphabet.

Even when there is no question of letters or numbers, the idea of a universal order (nizam), harmonisation (wafq), and of a reckoning (*hisāb*) of God are fundamental in most works of ‘aqīda or articles of faith. The liminal nature of language, necessitated by the status of the Qur’ān and ensuing reflections, make it impossible to always turn a blind eye to the question of the letters, their ontological status, and their special

<footnote n="43">43. For a historical outline, see A. Schimmel, *Mystical Dimensions of Islam* (Chapel Hill: University of North Carolina Press, 1975), esp. 53–85 and 244ff.</footnote>

<footnote n="44">44. J.-C. Coulon, ‘La magie islamique et le « corpus bunianum » au Moyen Âge’ (PhD diss., Sorbonne, Ecole doctorale IV: Civilisations, cultures, littératures et sociétés, 2013), 1.432ff; J. J. Witkam, ‘Gazing at the Sun: Remarks on the Egyptian Magician al-Būnī and his Work,’ in *O Ye Gentlemen: Arabic Studies on Science and Literary Culture (in Honor of Remke Kruk)*, Islamic Philosophy, Theology and Science. Texts and Studies 74 (Brill, 2007), 190–97; Melvin-Koushki, ‘*The Quest*,’ 191–7.</footnote>
properties.

These, and countless such examples, are all testimonies to the underlying coherence and the ubiquity of a cosmology based on the following points:<fnref n="45" />

1. All is number in the universe, from the primordial creative act to the details of earthly phenomena, and the nature of numbers is in full actuality in the divine Word, where number and meaning coalesce as they give form and structure to the world.

2. Hence that the structure of the universe is not only comparable to language: all of it is language indeed. And so alchemy and magic (like prayer and the divinatory arts) are accordingly sub-disciplines of a cosmic linguistics, like cosmic syntax, spelling or morphology.

3. Human language—in its logic, utterance and writing—is the real concretion of universal language; not only is it analogous to it, but it participates in it and in its realisation. When man casts a magic spell or utters a prayer, his speech gives him (literally) a say in the cosmic speech that constitutes the world.

<figure><img src="image_29.png" /></figure>

Down the centuries, these principles are found with varying prominence in the works of authors considered more or less loosely to be philosophers or mystics or esoterists, and all generally related in one way or another to Sufi lineages.<fnref n="46" /> Why? In a process comparable to the Christianization of philosophy in Europe, where monks and anchorites became the *de facto* torch bearers of ancient philosophy,<fnref n="47" /> a gradually institutionalised Sufism tended to include in its fold the likes of Sahl al-Tustarī (d. 896), Ibn Masarra (d. 931), al-Ḥakīm al-Tirmidhī (d. ca. 936), Abū ‘Abd al-Raḥmān al-Sulamī (d. 1021), and Ibn Barrajān (d. 1141),<fnref n="48" /> who were all to a certain extent speculative philosophers, and who in their works dealt with alphanumeric speculation.<fnref n="49" /> Were they Platonising emanationists or straight Ash‘arite creationists? From the point of view of the metaphysical στοιχεία, which synthesize letter, number, phoneme, physical element and zodiac sign, it really is not possible to draw a line between a Platonising doctrine of astral agency and one of divine cosmogonic effusion. We can perhaps take a hint from

<footnote n="45">45. With minor adaptations to the present context, I paraphrase Lory, *La magie des lettres*, 89.</footnote>

<footnote n="46">46. Cf. the account in Saif, *From Ġāyat al-ḥakīm*, 309–17.</footnote>

<footnote n="47">47. Cf. P. Hadot, *Philosophy as a Way of Life: Spiritual Exercises from Socrates to Foucault*, trans. M. Chase (Oxford: Blackwell, 1995), 269–70: ‘If to do philosophy was to live in conformity with the law of reason… the Christian was a philosopher, since he lived in conformity with the law of the Logos—divine reason.’</footnote>

<footnote n="48">48. For concise and balanced historical overviews, I recommend Lory, *La science des lettres en terre d’Islam*,’ and Melvin-Koushki, *The Quest*,’ 183–7.</footnote>

<footnote n="49">49. Cf. T. Mayer, ‘Theology and Sufism,’ chap. 13 in *The Cambridge Companion to Classical Islamic Theology* (Cambridge University Press, 2008), 276: ‘the so-called “School of Ibn Masarra” gave an essentially speculative stamp to the Sufism of the Iberian peninsula.’</footnote>
al-Ghazālī, who provides an elegant, if inconclusive, way out: ‘The truth lies between the masculinity of transcendence (*fuḥūla al-tanzīh*) and the femininity of similarity (*unūtha al-tashbīh*).<fnref n="50" />

Before moving on to my two last authors, who are both heirs to this complex tradition, and through whose works the same cosmology of the divine word and letters manifests in very different ways,<fnref n="51" /> I would concur with Pilar Garrido in that most of our contemporary discussions about whether a given author is ‘Sufi’ or ‘philosopher’, are prolongations of the real vexing question of the definition of philosophy, or for that matter, of a monolithic definition of Sufism.<fnref n="52" /> Even the paradigmatic champion of ‘orthodox’ *taṣawwuf*, Abū Ḥāmid al-Ghazālī (d. 1111), has in his works some passages where a very nuanced doctrine of divine language and of divine causation makes it hard to draw a clear dividing line from late Hellenistic cosmogonies.<fnref n="53" /> In fact, the metaphysical and theological impasse has to do, as mentioned above, with language, ergo, with the ‘letters’: first, the names and the attributes of God, and second, the uncreatedness of the Qur’ān.<fnref n="54" />

Of the three major Sufi summae of the thirteenth century, namely, Rūmī’s *Mathnawī*, al-Būnī’s corpus on magic and esoterica, and Ibn ‘Arabī’s *Futūḥāt*,<fnref n="55" /> the last two are very explicitly based on and pervaded by those theologically risky topics, the Names and the Divine Word, and this is why I shall conclude this chapter with them.

## Al-Būnī and the Sun of Divine Sciences

Alīmad ibn ‘Alī al-Būnī (d. 1225) is the persona of an unknown compiler or a group of authors who produced the greatest and most influential Arabic compilation of magical texts, what we now call the *Corpus Bunianum*, the work of ‘several generations of practising magicians’.<fnref n="56" /> The most famous work of the *Corpus* is the book titled *Shams al-ma‘ārif, The Sun of Divine Sciences*, a ‘true encyclopedia of Islamic, or Islamicised,

<footnote n="50">50. Cited in K. Nakamura, ‘Imām Ghazālī’s Cosmology Reconsidered with Special Reference to the Concept of “Jabarūt”,’ *Studia Islamica* 80 (1994): 34.</footnote>

<footnote n="51">51. Coulon, ‘La magie islamique,’ 438.</footnote>

<footnote n="52">52. P. Garrido Clemente, ‘¿Era Ibn Masarra de Córdoba un filósofo?,’ *Anaquel de Estudios Árabes* 21 (2010): 130.</footnote>

<footnote n="53">53. I am thinking in particular here of the treatise on Divine Names, *al-Maqṣad al-asnā fī sharḥ asmā’ Allāh al-ḥusnā*, and his *Niche of Lights, Mishkāt al-anwār*, which has been the subject of Neoplatonic comparison; cf. Nakamura, ‘Imām Ghazālī’s Cosmology.’</footnote>

<footnote n="54">54. An excellent and concise summary is given in P. Tan, ‘Divine Simplicity in Christianity and Islam: Al-Ghazali, Ibn Rushd, Thomas, and Calvin on the Essence and Attributes of God/Allah’ (PhD diss., Vrije Universiteit Amsterdam, 2016), 37–48.</footnote>

<footnote n="55">55. See Melvin-Koushki, ‘The Quest,’ 183–7 where, in line with the scope of the work, the Persian scholar Sa‘d al-Dīn Ḥamuvayī (d. 1252) is added as a major author.</footnote>

<footnote n="56">56. Witkam, ‘Gazing at the Sun,’ 183.</footnote>
magic.’<fnref n="57" /> As is common in classical Islamic scholarship, and notably as we recently encountered with the *Sefer Yetsirah*, the *Shams al-maʻārif* is extant in three versions of different lengths,<fnref n="58" /> without there being conclusive evidence in favour of the earlier origin of any of the three.<fnref n="59" /> The long version, *Shams al-maʻārif* ‘al-kubrā is by far the most popular version,<fnref n="60" /> the one usually published, and also the one which contains more diagrams and illustrations of later provenance. I shall be using Coullaut’s edited version of the first chapter,<fnref n="61" /> and a contemporary printed edition for the rest of the book.

## The Letter-Elements in al-Būnī

The *Shams al-maʻārif* portends to share knowledge on the disposition of the divine Names, on the qualities and secrets of the letter-numbers (*hurūf*), and on invocations and supplications;<fnref n="62" /> in practice, it includes information on astrology, talismanic magic, alchemy and divination, but underlying all these, or like a refrain running through the whole work, is the concern with the ‘supernatural force contained in the letters and the names.’<fnref n="63" /> It has been considered a perfect example of ‘religious magic’, being all mostly based on an esoteric interpretation of the Qur’ān,<fnref n="64" /> hence that it has also been called ‘Qur’ānic theurgy’.<fnref n="65" />

## The First Paragraph

From the beginning of the first section, the *Shams* is clear about the ‘architectural’ function of the letters:

### The Basics of Letter Cosmology

> أَتَكلَمْ أُولاً عَلَى الْحَرَوفِ الْمَعْجَمَةِ إِذْ هِيَ أُصْولُ الْكَلَامِ وَأَسَاسِهِ وبِهَا يَرْتَفَعُ بِنَبَأِهِ

<footnote n="57">57. Witkam, *‘Gazing at the Sun,’* 185. Regarding the alternative title *Shams al-ma‘ārif wa-lātā’if al-‘awārif* (*The Sun of Divine Sciences and the Subtleties of Those Who Know*) as that of a different work, see Saif, *‘From Gāyat al-ḥakīm,’* 337, based on Gardiner, *‘Forbidden Knowledge?’*</footnote>

<footnote n="58">58. See Witkam, *‘Gazing at the Sun,’* 186.</footnote>

<footnote n="59">59. The shorter version, *al-ṣugrā*, has been edited with a comprehensive treatment of the manuscript tradition in the four-volume thesis by Coulon, *‘La magie islamique’*; see in particular 2.I–III.</footnote>

<footnote n="60">60. J. Coullaut Cordero, *‘El Kitāb Šams al-Ma‘ārif al-Kubrā* (al-ŷuz’ al-awwal) de Aḥmad b. ‘Alī al-Būnī: Sufismo y ciencias ocultas’ (PhD diss., Facultad de filología, Universidad de Salamanca, 2009), xviii–xix.</footnote>

<footnote n="61">61. *ibid.*; see xxxiff. regarding the manuscript tradition.</footnote>

<footnote n="62">62. Aḥmad ibn ‘Alī al-Būnī, *Shams al-ma‘ārif* (Beirut: Mu‘asasa al-nūr al-maṭbū‘āt, 2000), 6.</footnote>

<footnote n="63">63. Lory, *‘La magie des lettres,’* 89.</footnote>

<footnote n="64">64. Coullaut, *‘El Kitāb Šams al-Ma‘ārif,’* xx.</footnote>

<footnote n="65">65. S. N. Ahmad, *Magic and the Occult in Islam: Ahmad al-Buni and his Shams Al-Ma‘arif*, lecture given at the Warburg Institute, May 2013.</footnote>
I shall speak first of the letters of the alphabet, since they are the roots and
the foundation of speech, and upon them is raised its structure.<fnref n="66" />

The terms involved, *așl*, *asās*, *raf’*, *binā’*, belong to the imagery of construction, and three of them are also well-known grammatical terms. A detailed reading of the *Shams* in the light of grammatical terminology remains a desideratum, and may be able to give a more complete understanding of the architectural symbolism. It is remarkable, though surely not surprising, how the three parts of speech in Arabic grammar, *ism*, noun, *fi’l*, verb, and *ħarf*, ‘particle’, are so crucial in the cosmology of Qur’ānic theurgy. The following cosmogonic fragment illustrates another linguistic analogy:

> وأن العالم العلويّ يمدّ العالم السفليّ فعالم العرش يمدّ عالم الكرسي وعالم الكرسي
> يمدّ فلك زحل...

The superior world prolongs itself into the lower world: the world of the
throne prolongs itself into the world of the pedestal, and the world of the
pedestal prolongs itself into the sphere of Saturn...<fnref n="67" />

The descending generative relation between the worlds, or metaphysical stages of manifestation, is one of prolongation (*madd*) in all the senses associated above<fnref n="68" /> with the image of the divine ink, the concept of matter (*mādda*), and the syllabic lengthening (*madd*) as studied in prosody. Quite in line with the Abrahamic doctrines of the divine creative imperative (*amr*), the coming to be of every new level of manifestation occurs in the manner of the prolongation of the syllables in Qur’ānic recitation, and the matter of every new world is a phonetic matter.

## Letter-Number Relation

Also in the first page, it is made clear that ‘numbers have secrets, like letters have effects,’ and soon thereafter an example involving astrology gives a glimpse into the arithmetical workings.

> فلزحل في العلويات حرف الجيم والأعداد الواقعة عليها ثلاثة على الجملة وأما على التفصيل فثلاثة وخمسون هكذا الميم بأربعين والياء بعشرة والجيم بثلاثة وهو أيضا بثلاثة
> أحرف وله من السفليات حرف الصاد وهو في العدد تسعون وله المثلث

<footnote n="66">66. Coullaut, 'El *Kitāb Šams al-Maʻarif*, 1.9; Coulon, 'La magie islamique,' 2.9.</footnote>

<footnote n="67">67. Coullaut, 'El *Kitāb Šams al-Maʻarif*, 1.9; Coulon, 'La magie islamique,' 2.9.</footnote>

<footnote n="68">68. See p. 168. For this translation of *yamuddu*, see Lisān, 4157a; Lane, *LL*, I.22696; the sense is the same as in Qur’ān 31:27, *al-baḥru yamuddu*, ‘the sea is ink/overflows’ with abundance. Cf. also Lory, ‘La magie des lettres,’ 104, n. 34.</footnote>
In the upper realms, Saturn has the letter jīm, and the numbers that correspond to it are three in all: when analysed and added, they total fifty-three in the following way, the mīm is forty, the yā' is ten, and the jīm is three; it also consists of three letters (ahruf); in the lower realms the letter şād belongs to it, which is, in number, ninety; and the order-3 square belongs to it.<fnref n="69" />

The detail of the numerical correspondence escapes me, but it is clear that every number relation is established in various complementing ways, mostly based on isopsephy, but certainly more complex than a mere substitution of abjad values. Further down, more is said about the status of number and its relation to letters:

وللأعداد قوة روحانية لطيفة فالأعداد
من أسرار الأقوال كما أن الحروف
من أسرار الأفعال وللأعداد في عالم
البشرى أسرار ومنافع رتبها الباريء
جلت قدرته كما رتب في الحروف
أسرار النفع كالدعاء والرقى وغير
ذلك... واعلم أن الحروف لا وقت
بحصرها وإنما هي تفعل بالخاصية
لمن شاء والأعداد تفعل بالطبيعات

Numbers have a subtle spiritual power. The numbers
are among the secrets of utterances, like the letters
are among the secrets of actions. In the human
world, numbers have secrets and benefits which
the Creator—majestic is His might—has ordered as
He ordered secrets in the letters for use as in
supplications and charms and others... Know that
the letters are not restricted by certain times, but
rather they work according to each property for
whoever wills, and the numbers work according to
the natures.<fnref n="70" />

The import of these passages is directly at the source of a more forceful expression found in the Dā’irat al-aḥruf al-abjadiyya (The Alphanumeric Circle), an undated treatise within the Būnī tradition, notably attributed to Hermes:<fnref n="71" />

> اذا اردت تعلم قوة كل حرف فانظر ما له من الاعداد وتلك الدرجة المناسبة للحروف
> فтلك قوته في الروحانيات

When you want to know the power of every letter, look at what number it
has: this is the degree that corresponds for the letters, and this is its power
among the spiritual beings.

<footnote n="69">69. Or ‘the triangle’, but cf. J. D. Martin, ‘Theurgy in the Medieval Islamic World: Conceptions of Cosmology in Al-Būnī’s Doctrine of the Divine Names’ (master’s thesis, Dept of Arab and Islamic Civilizations, The American University in Cairo, 2011), 60.</footnote>

<footnote n="70">70. Cf. also translation and commentary in *ibid.*, 59–60.</footnote>

<footnote n="71">71. Edited text in Bonmariage and Moureau, *Le Cercle des lettres*, see 104.</footnote>
Joining the Letters

Finally, a later passage speaks of the operation required to reveal the ‘contents’ of the
letters:

واعلم أن لكل حرف عوالم لا يطلع عليها إلا الذي حظي من الله تعالى وإذا كشف
لك عن عوالم هذه الحروف فإنك متي جمعت الحروف وأضفت لها الأس تمثل لك
ملكا روحانيا مقابلك قضى حاجتك

Know that every letter has sciences to which no one ascends unless
through the graces of God Most High, when He reveals the sciences of these
letters. Indeed, once you have comprehended (or 'combined') the letters
and joined them to the foundation (al-uss), they will seem to you like a
spiritual possession you have received and which fulfills your needs.<fnref n="72" />

This revealing ‘combination’ echoes the ones mentioned above (p. 228) when
discussing the figurate numbers or ‘magic’ squares in the geometrical exposition of
the Ikhwān.

‘Magic’ Squares in the Light of Alphanumeric Cosmology

It is often claimed that the earliest Arabic work devoted to the *awfāq* was written by Thābit ibn Qurra,<fnref n="73" /> and one of the oldest squares is found precisely in a commentary to Nicomachus’ *Introduction*.<fnref n="74" /> Another early treatment of magic squares is due to Ibn Ezra, who introduced the Indian numerals to Hebrew script. In the Greek tradition, the association is between grammar and the squares, through the opuscule by the grammarian Manuel Moschopoulos (fl. end of thirteenth century). Interestingly, his *Libellus de inveniendis quadratis numeris* is part of a codex<fnref n="75" /> including works on metrics, land division (*mensuratio*, γεωδαισία), on astrolabes, and an *Ars calculatoria secundum Indos*.

I draw attention to the subjects of the codex because they illustrate in their variety the very conjunction of many strands of this research that the ‘magic’ squares encapsulate: in them the graphic arrangement of a stoichedon grid, the same pattern of the Roman *centuriatio*, is allied to a sophisticated arithmetic calculation, and all this conjunction is associated to heavenly bodies and their corresponding zodiacal signs (στοιχεῖα)—and even to the alphabetic aspects through the alphanumeric notation.

<footnote n="72">72. al-Būnī, *Shams al-ma‘ārif*, 380.</footnote>

<footnote n="73">73. Ibn al-Qiftī (d. 646/1248) lists an Epistle on Harmonious Numbers (*Risāla fī al-‘adad al-wafq*) among the works attributed to Thābit; Hallum, *New Light*, 46.</footnote>

<footnote n="74">74. Sesiano, *Les Carrés... de Moschopoulos*, 379.</footnote>

<footnote n="75">75. BnF, Supplément grec 652 (ff. 161r–164v).</footnote>
<figure><img src="image_30.png" /><figcaption>SQUARE OF ORDER 3 · PARIS, BNF, SUPPLÉMENT GREC 652, 162R</figcaption></figure>

It is therefore hardly surprising that the construction of magic squares has been called the ‘true purpose’ for al-Būnī’s cosmological expositions, and it is quite befitting that the construction of the *awfāq* is called the ‘building of microcosms.’ In fact, an association between a Socratic/Platonic ancient wisdom and the science of the squared numbers is explicit in al-Būnī, particularly in his *al-Uṣūl wa-al-ḍawābīt*,<fnref n="76" /> a title which from a grammatical angle could be translated as ‘Morphological Patterns and Vocalisations.’

## Ibn ‘Arabī

Muḥyī al-Dīn Ibn ‘Arabī is not only referred to as ‘The Greatest Master’ within the Sufi tradition, but more particularly he has been credited with ‘the most elaborate system of thought which brings God and man together in the context of the creative power inherent in language,’<fnref n="77" /> or, drawing closer to us, as ‘the Muslim thinker who has dealt more thoroughly with the doctrine of the Logos.’<fnref n="78" /> More specifically, the importance of letter speculation in his works has already been the subject of dedicated and thorough works which I can only gratefully cite in the following paragraphs.<fnref n="79" />

<footnote n="76">76. See Martin, *Theurgy in the Medieval Islamic World*, 64–6.</footnote>

<footnote n="77">77. S. Sviri, *The Existence-Bestowing Word in Islamic Mysticism: A Survey of Texts on the Creative Power of Language*, in *The Poetics of Grammar and the Metaphysics of Sound and Sign* (Brill, 2007), 49.</footnote>

<footnote n="78">78. R. Landau, *The Philosophy of Ibn ‘Arabi* (1959; Routledge, 2013), 54–5.</footnote>

<footnote n="79">79. See, in the first place, Gril, *The Science of Letters*'; Ebstein, *Mysticism and Philosophy*, 53–7; and a recent related article, C. Addas and M. Chodkiewicz, 'On Two Books Attributed to Ibn 'Arabî: K. al-mabādī wa l-ghāyāt li ma‘ānī l-ḥurūf and K. māhiyyat al-qalb,' *Journal of the Muhyiddin Ibn 'Arabi Society* 62 (2017). Other relevant studies and useful translations include Chittick, *Sufi Path of Knowledge*, and Muḥyī al-Dīn Ibn 'Arabī, *Le livre du mîm, du wâw et du nûn* (Kitāb al-mīm wa-al-wāw wa-al-nūn), ed. C. A. Gilis, *Héritage Spirituel* (Beirut: Dar Albouraq, 2002). More generally, I find W. C. Chittick, 'Ibn 'Arabī and His School,' chap. 3 in *Islamic Spirituality: Manifestations*, ed. S. H. Nasr (New York: The Crossroad Publishing Company, 1981), 49–79, to be particularly concise.</footnote>
Ibn ʻArabī himself explains that he treated the subject of letters in three works.<fnref n="80" /> Though this count seems to have remained something of an incomplete project, or in any case not quite in agreement with his extant works,<fnref n="81" /> it is noteworthy that one of these works, the only one mentioned by title, is called *Kitāb al-mabādi*, the *Book of Principles*, the same title given by Saʻadyā Gaon to his Arabic translation of *Sefer Yetsirah* centuries earlier.

The most important work mentioned, partly because of its solid textual tradition and also because it deals with letters in all their dimensions—and not just with a restricted set—is chapter two of *al-Futūḥāt al-makkiyya*, entitled ‘On knowledge of the hierarchical degrees of the consonants and vowels in the universe and their counterparts among the Divine Names.’ Aside from it, and from many other scattered passages regarding the ‘letters’, there is also notably chapter 198 of the *Futūḥāt*, ‘On the Breath of the All-Merciful (nafas al-raḥmān)’, where a ‘most famous cosmological scheme’ is built on the divine breathing of twenty-eight primordial letters.<fnref n="82" />

Ibn ʻArabī has been recognised as a synthesizer of many of the aspects of the science of letters as they are found in earlier authors,<fnref n="83" /> combining them into a mystical scheme inextricably integrated, very much ‘to the letter,’ with the Qur'ānic revelation. Particularly relevant to this research is the influence of the Brethren of Purity on the importance of number in his cosmogony,<fnref n="84" /> though I shall not go into details of this.

Ibn ʻArabī appears in some of the lineages of al-Būnī as a transmitter of the science of ‘magic’ squares. These lineages are understood to be more symbolic than historical,<fnref n="85" /> and in this particular case, given that the applications and any comparable detailed treatment about the squares are absent from the Akbarian corpus, they are rather indicative of the shared underlying cosmology. I would also relate this understanding of a shared basic view to the fact that Ibn ʻArabī was sometimes called ‘Ibn Aflaṭūn’, the ‘Platonist’.<fnref n="86" />

<footnote n="80">80. Ibn ʻArabī, *Kitāb al-mīm...*, 40.</footnote>

<footnote n="81">81. Addas and Chodkiewicz, ‘On Two Books,’ 106–12.</footnote>

<footnote n="82">82. See W. C. Chittick, ‘The Wisdom of the Animals,’ *Journal of the Muhyiddin Ibn ‘Arabi Society* 46 (2009): 28.</footnote>

<footnote n="83">83. E.g. his indebtedness to Tustarī (also cited in al-Būnī’s works) to Ibn Masarra, Ibn Barrajān and other Andalusī authors; see Y. A. Casewit, ‘The Forgotten Mystic: Ibn Barrajān (d. 536/1141) and the Andalusian Mu‘tabirūn’ (PhD diss., Yale University, 2014), 2, 44, 230; see also Gril, ‘The Science of Letters,’ 140.</footnote>

<footnote n="84">84. G. De Callataÿ, ‘From Ibn Masarra to Ibn ʻArabī: references, shibboleths and other subtle allusions to the Rasā’il Ikhwān al-Ṣafā’ in the literature of al-Andalus,’ *Studi Magrebini* (Napoli), 2014–2015: 258–61.</footnote>

<footnote n="85">85. Lory, ‘La magie des lettres,’ 98.</footnote>

<footnote n="86">86. Mayer, ‘Theology and Sufism,’ 276.</footnote>
The Place of the Letters

The elaborate and subtle understanding of the intermediary realm of the ‘letters’ in Ibn ‘Arabi’s letter cosmology has been considered one of his most important contributions to the history of world philosophy,<fnref n="87" /> and it is directly related to the science of letters inasmuch as it represents ‘the difficult transition of the inexpressible into that which can be expressed.’<fnref n="88" /> Ibn ‘Arabī uses the Qur’ānic term *barzakh*, the impassable ‘isthmus between two seas,’<fnref n="89" /> to designate a reality that simultaneously divides and unites two poles, like the ‘line’ that separates sunlight and shade. As Chittick explains, ‘he uses the term Supreme Barzakh (*al-barzakh al-a‘lā*) as a synonym for nondelimited Imagination (*al-khayāl al-muṭlaq*—“absolute imagination”).’ It is the cosmos itself and in a way the human faculty as well, ‘the realm of possible things, which in themselves are neither necessary nor impossible, neither infinite nor finite.’ And at the same time, ‘it is the Breath of the All-Merciful, which is neither nondelimited Being nor articulated words.’<fnref n="90" />
Ibn ‘Arabi’s doctrine is remarkable in part for bringing out all the implications of this intermediary realm, and for expressing with Qur’ānic imagery how it is at once invisible, spiritual, and intelligible, and also visible, corporeal, and perceptible. ‘Since the Guarded Tablet or Universal Soul is a spiritual being, born directly from the First Intellect, it is light. But it represents a movement in the direction of Nature, so it embraces the properties of darkness as well. Like any *barzakh*, it brings together the properties of the two sides.’<fnref n="91" /> But as the cosmology goes into detail, complications arise: Ibn ‘Arabī identifies the act of Breathing with that of Imagining, and the world of Absolute Imagination with the Primordial Breath, and also with the Primordial Cloud (‘*amā*’).<fnref n="92" /> I shall not go into further details of the various levels and correspondences, but instead mention some notable aspects.

One of the distinguishing traits of this iteration of the doctrine of the intermediary realm, is the idea of the divine love: ‘He desired to make Himself known, so that they might know Him, and so the Cloud comes to be; it is called the Real Through Whom Creation Takes Place. The Cloud is the substance of the universe (*jawhar al-‘ālam*), so it receives all the forms, spirits, and natures of the universe; it is a boundless receptacle.

<footnote n="87">87. W. C. Chittick, ‘Ibn Arabi,’ in *The Stanford Encyclopedia of Philosophy*, Summer 2018, ed. E. N. Zalta (Metaphysics Research Lab, Stanford University, 2018)</footnote>

<footnote n="88">88. Gril, ‘*The Science of Letters*,’ 107.</footnote>

<footnote n="89">89. Qur’ān 25:53, 55:20.</footnote>

<footnote n="90">90. Chittick, ‘Ibn Arabi (SEP),’ 3.4; S. Akkach, ‘The World of Imagination in Ibn ‘Arabi’s Ontology,’ *British Journal of Middle Eastern Studies* 24 (May 1997): 102.</footnote>

<footnote n="91">91. S. Murata, *The Tao of Islam: A sourcebook on gender relationships in Islamic thought* (SUNY Press, 1992), 163.</footnote>

<footnote n="92">92. Akkach, ‘*The World of Imagination*,’ 109.</footnote>
This is the origin of His love for us.’<fnref n="93" /> And in this it will be noted how once again, like at the end of the previous chapter, we are suddenly involved in a Christic-related imagery, and we may remember Dante’s universal book ‘legato con amore.’ The role of the letters of the logos in the cosmology of Ibn ‘Arabī is in fact remarkably ‘Īsawī, that is, related to Jesus as an Islamic prophet, for ‘the knowledge of Jesus is the knowledge of the letters’ (inna al-‘ilm al-‘īsawī huwa ‘ilm al-ḥurūf).<fnref n="94" /> Regarding the cosmic architecture based on the twenty-eight primordial letters, and thinking of this Christic connection, the tradition of the fourteen stations of the via crucis is an example that stands out as a promising avenue of further research.

All this is naturally inseparable from the divine creative imperative, also taking into account, as with the case of Jesus, the more merciful aspects of the divine: ‘Since God is... the cause of the existence of everything in the world... everything tends towards Love (raḥma), because He created them and brought them into manifestation within the Cloud (‘amā) which is the Breath of the All-Loving (nafas al-raḥmān). They are like the letters in the breath of a speaker in their points of articulation (makhraj)... it is a world ever uttered anew (‘ālam muḥdath)—don’t you see He is called the Arranger (al-Mudabbir), the Differentiator (al-Mufaṣṣil)?<fnref n="95" /> The reference to the phonetic point of articulation brings us back to the linguistic aspect, and indeed, hand in hand with the letter speculation. As could be expected, the writings of Ibn ‘Arabī have a persistent rhythm of allusions to, or rather intimations of, a lughawī dimension, a wealth of linguistic insights in a broad traditional sense. Not the least of the consequences of this tight interplay between the linguistic and the metaphysical, especially in view of the cosmogonic passage just cited, is the understanding that we, on our puny human level, ‘articulate words in our breath just as God articulates words in His All-Merciful Breath.’<fnref n="96" />

## Letters and Numbers

Regarding the intimate relation between number and letter, aside from the isopsephic explanations that abound, and aside from the numerical structure evinced by the cosmology and in which an air of familiarity with the Ikhwānian cosmology is clear, there are specific mentions in the *Futūḥāt* of a common science of the ‘properties of numbers and letters’ (‘ilm khawāṣṣ al-a‘dād wa-al-ḥurūf), or simply ‘of numbers and

<footnote n="93">93. Muḥyī al-Dīn Ibn ‘Arabī, *Al-Futūḥāt al-makkiyya*, 4 vols (Cairo: Dār al-Kutub al-‘Arabiyya al-Kubrā, 1911), II.331.23–4.</footnote>

<footnote n="94">94. *Ibid.*, I.168.5; see also Addas and Chodkiewicz, *On Two Books*,* 110.</footnote>

<footnote n="95">95. Ibn ‘Arabī, *Futūḥāt*, II.465.25–28, discussed in Chittick, *Sufi Path of Knowledge*, 338, with a slightly different interpretation.</footnote>

<footnote n="96">96. Chittick, *The Wisdom of the Animals*, 28.</footnote>
letters,’ as a ‘science of the saints’ and as a prerogative of some of the stations (*manāzil*) of the travelling initiate.<fnref n="97" />

In chapter thirteen of the *Book of the Mīm, Wāw and Nūn* we also have a fine example of the complete integration of the alphabetic symbolism with the arithmetic operations:

> فإذا ضربت «ب» في «ج» كان الخارج «و» فلها أيضا من قوة أبوиها

> If you multiply ب [2] times ج [3], the result is و [6], which shares also in the power of its two parents.<fnref n="98" />

And this is naturally followed by the explanation that the wāw can produce the effect (*yaf'alu al-fi'l*) of six, and it also has the power of two and three.

## The Three Modes

We find also in Ibn 'Arabī an example of the awareness of the three modes of the 'letter-number':

> فاعلم أن الحروف لها خواص وهي على ثلاثة أضرب منها حروف رقمية ولفظية
> ومستحضررة وأعني بالمستحضررة الحروف التي يستحضرها الإنسان في وهمه وخياله
> ويصوّرها

Know that letters have properties, and that they are of three types: written (*raqmiyya*) letters, pronounced (*lafziyya*), and evoked (*mustahdara*); and I mean by ‘evoked’ the letters which a man evokes and makes present in his fancy and imagination, and gives form to them.<fnref n="99" />

In this triple classification we have again with little variation the threefold character of the alphabetic elements: the graphic aspect, the phonetic aspect, and the third mental aspect, which may correspond to the arithmetic, diagrammatic aspect we have found elsewhere and which is related to creativity, as in ‘design’, involving the composition of new images by the form-giving, or ‘in-formative’ faculty (*al-quwwa al-muṣawwira*).<fnref n="100" />

## The Living Letters

There is an aspect of Ibn 'Arabī's alphanumeric science that lies outside the boundaries of my research, but which it is nonetheless fitting to mention, not least because it belongs to a long doctrinal thread with parallels in other traditions. I refer to the relation

<footnote n="97">97. E.g. chapters 354 and 357, Ibn 'Arabī, *Futūḥāt*, III.246.27 and 261.34.</footnote>

<footnote n="98">98. Ibn 'Arabī, *Kitāb al-mīm*..., 62.</footnote>

<footnote n="99">99. Ibn 'Arabī, *Futūḥāt*, I.190; cf. Gril, *The Science of Letters*, 123.</footnote>

<footnote n="100">100. Cf. Akkach, *Cosmology and Architecture*, 40–42.</footnote>
between the divine ‘letters’ of the macrocosmic universe and their intimate relation
with the microcosmic universe represented by the exemplars of human perfection.<fnref n="101" />
When it is said that ‘the science of letters is a science of the saints,’ it does not only
mean that the saints penetrate its mysteries intellectually, but also that they embody the
arcana of the letters. It is in them, par excellence, that the ontological-epistemological
duality of the letters is fully realised, for ‘language and *wilāya* are intrinsecally bound
up.’<fnref n="102" />

Within Islamic prophetology this view of the divine letters belongs primarily in the
Muḥammadan line, where it is related fundamentally to the exalted inner nature of the
Prophet (nūr Muḥammad, ‘the light of Muḥammad’), and thereafter to the Shī‘ī lineage
of the Imams. As could be expected, it had a fruitful history in Ismā‘īlī cosmology.
Secondarily, and as elaborated in great detail by Ibn ‘Arabī, this view relates to the
spiritual heritage of the Prophet, hence to all his ‘friends’ (awliyā’),<fnref n="103" /> and it has to do
with ‘how inextricably linked the science of letters and spiritual realization are.’<fnref n="104" />

Now, instead of devoting more lines to this somewhat peripheral topic, I shall only
illustrate it with two brief poems chosen to represent two major phases. The first is
from one of the many poems attributed to Imām ‘Alī:

وتحسب أنَّك جرمٌ صغير
وفيك انطوى العالم الأكبر
وأنت الكتاب المبين الذي
بأحرفه يظهر المُضمر

Although you think of yourself as a tiny speck,
Within you the great universe is contained;
You are yourself the book that makes things clear
Whose letters reveal what is concealed.<fnref n="105" />

And the following lines are from Ibn ‘Arabī’s poetry collection, *Tarjumān al-ashwāq*:

كنا حروفا عاليات لم نقل
متعلقات في ذرى أعلى القلل

<footnote n="101">101. See Ebstein, *Mysticism and Philosophy*, 108ff.</footnote>

<footnote n="102">102. S. Sviri, 'Words of Power and the Power of Words: Mystical Linguistics in the Works of al-Ḥakīm al-Tirmidhī,' *Jerusalem Studies in Arabic and Islam*, no. 27 (2002): 232. Casewit sees in this 'quasi-incomprehensible ontological in-between-ness of the Universal Servant' 'a solution for the classical philosophical conundrum of how the One relates to multiplicity,' Casewit, *The Forgotten Mystic: Ibn Barrajān* (d. 536/1141) and the Andalusian Muʻtabirūn,' 343.</footnote>

<footnote n="103">103. See Ebstein, *Mysticism and Philosophy*, 123ff., 143, 146–50;</footnote>

<footnote n="104">104. Gril, *The Science of Letters*, 136.</footnote>

<footnote n="105">105. ‘Alī ibn Abī Ṭālib, *Min al-shi’r al-mansūb ilā al-Imām al-Waṣī ‘Alī ibn Abī Ṭālib*, ed. ‘Abd ‘al-‘Azīz Sayyid al-Ahl (Beirut: Dār Bayrūt, 1973), 75. I am grateful to Reza Shah-Kazemi for this reference.</footnote>
أنا أنت فيه ونحْنُ أنت وأنت هو
والكل في هو هو فسل عمَّن وصل

We were letters, exalted! not yet uttered,
Held aloft in the keep of the Highest of Summits,
I Therein am Thou, and we are Thou,
And Thou art He, and All is in He is He—
Ask of any that so far hath reached.<fnref n="106" />

Conclusion to Part III

After having had a glimpse at the beginnings of systematisation of the ‘science of letters and numbers’ in the three Abrahamic traditions, it is important to emphasise how influential all these representatives would be, not only within each tradition, but also in countless exchanges, cross-pollinating each other’s tradition in theology, philosophy and occult sciences.

The *Sefer Yetsirah* is widely considered, with the *Sefer ha-Bahir* (to a lesser extent), the main source of Kabbalistic speculation, or rather, put simply, the precursor and main source material of the Kabbalah as it unfolded through the centuries. It is no exaggeration to say that the defining traits of Kabbalistic doctrines can all be said to pass through the *Sefer Yetsirah*. The single clearest and sufficient example is that this is the text which put into circulation the term *sefirah* with a cosmological meaning.

Eriugena and Aquinas represent each too a historical watershed, a repository and a perennial reference for the Christian tradition in their more contemplative and theological aspects. Something similar happens with the role played by al-Būnī and Ibn 'Arabī in the Islamic tradition, where they have been for centuries the fountainheads of theurgic lore and philosophical Sufism respectively. A major related development in the Islamic world would be the emergence of an openly *Hurūfī* or 'Letterist' movement led by Faḍl Allāh Astarābādī (d. 1394), who with his *Jāvidān-nāma*, the *Book of Eternity*, started a messianic movement of lasting influence. His work is not only related to the teachings of the authors mentioned above, but it cites St John's Gospel and other Christian writings. Moreover, the *Jāvidān-nāma*'s cosmology is based on a set of 28 or 32 'most basic constituent units of the metaphysical language.'<fnref n="107" />

<footnote n="106">106. M. Lings, *Sufi Poems: A Mediaeval Anthology* (Cambridge: Islamic Texts Society, 2004), 64–5; transl. Lings.</footnote>

<footnote n="107">107. See Mir-Kasimov, *Words of Power*, 50–51, 163.</footnote>
# Conclusion

After having walked through so many time doors and after the comparative work that precludes sustained concentration on one single point, there is an inevitable feeling of leaving loose ends. In order to address this, I shall now look at the work done from two perspectives, and in so doing I will be making explicit several conjectures implicit in my earlier deliberations. One perspective is conceptual or philosophical, partly recapitulating some of the main themes and partly commenting on some open avenues of research and further comparative study, also with a view to applications in other scholarly fields. Another perspective, historical, to try to contemplate and make sense of the whole narrative from a broader historical point of view.

## Conceptual Conclusion: Echoes and Ramifications

### Art, Artistry and the Arts

This work is a reflection about art insofar as it never strays from the demiurgic vein shared by the *Timaeus* and the *Sefer Yetsirah*, and this with attention to the two inseparable aspects of the word κόσμος—beauty and order. I have discussed the cosmogony related to them, but I find of great interest too the implications regarding the creative process in general.

Since the *Deus faber* of my account is a geometer and since his creation is based on a *stoichidon* grid pattern, because ‘the world is the field’ of the land-surveying Creator,<fnref n="1" /> how alphanumeric is essentially, or at least should be *de jure*, human creativity? If art is based on μίμησις in the sense of an imitative participation, and if in the words of Lamennais,<fnref n="2" /> ‘*l’art est pour l’homme ce qu’est en Dieu la puissance créatrice*’, just how mathematical or geometrical must human art be to emulate its divine model? And if the demiurge, akin, like Apollo, to a boundary-setting Hermes, is a Magician in his ‘spelling’ and combining in acrostics and pangrams the letters of His word and His

<footnote n="1">1. Cf. E. A. Zaitsev, 'The Meaning of Early Medieval Geometry: From Euclid and Surveyors' Manuals to Christian Philosophy,' *Isis* 90, no. 3 (1999): 546–52.</footnote>

<footnote n="2">2. Cited in Tatarkiewicz, *History of Six Ideas*, 254.</footnote>
world, just how magical is any human creativity called to be? And if creation follows
the logic of a grammar, how logical and grammatical should every human design be?

In relation to the magical view of creation, it must also be remembered that the
divine creation effected in the alphanumeric elements, or through them, seems to be an
immaterial creation, or only material if we understand that it is not quite perceptible
matter that is involved, but an intermediate realm, as is the phonetic reality of language
when compared to the materiality of writing. To what extent does any human art also
belong to an intermediary realm?

Physics and Modern Physics

This work is about physics. Since it is about the elements, it is about the material world, about matter and about atoms, but we saw early on that the στοιχεῖα are understood as minima in a very nuanced way, being material and yet immaterial, ordered and dancing. As seen clearly by Weiss, ‘stoicheion is not simply a name shared in common by two concepts; it also reflects a common understanding of letters and physical elements as components with an atomic character.’<fnref n="3" /> Now, it turns out that this conception of the atoma or ultimate indivisible particles is quite close to contemporary cutting-edge accounts of reality, according to which ‘the fundamental building blocks of matter are not particles, but continuous fluid-like substances known as “quantum fields”’ which dance overlapping with one another.<fnref n="4" />

And this is not far from the furthest reaches of contemporary mathematics, where
some argue for a ‘Platonism on steroids: that external physical reality is not only
described by mathematics, but that it is mathematics,’ asserting that ‘the mathematical
structures in Plato’s realm of ideas or the “mindscape” of mathematicians exist in a
physical sense.’<fnref n="5" />

One striking analogy between these correlated fields of modern physics and ancient alphanumeric cosmology is found in the structural resemblance between the periodic table of elements and the recently elucidated phonological arrangement of the Greek κνάξ pangram: κνὰξ ζβὶ χθύ πτὴς φλεγμὸ δρώψ, in which numerical and phonetic values combine to produce a synthetic arrangement in tabular form, indeed a ‘periodic table’ of Greek *elementa*:<fnref n="6" />

<footnote n="3">3. T. Weiss, ‘On the Matter of Language: The Creation of the World from Letters and Jacques Lacan’s Perception of Letters as Real,’ *The Journal of Jewish Thought and Philosophy* 17, no. 1 (2009): 106.</footnote>

<footnote n="4">4. Cf. D. Tong, *The Real Building Blocks of the Universe*, lecture given at The Royal Institution, London, November 2017.</footnote>

<footnote n="5">5. M. Tegmark, ‘The Mathematical Universe,’ *Foundations of Physics* 38 (2008): 101–150.</footnote>

<footnote n="6">6. Details in Lougovaya, ‘A Perfect Pangram,’ 180–85. This pangram goes back as far as at least 200 AD, with a possible earlier origin.</footnote>
<table><tr><td>K</td><td>Z</td><td>X</td><td>Π</td><td>Φ</td><td>Γ</td><td>Δ</td></tr><tr><td>Ν</td><td>Β</td><td>Θ</td><td>Τ</td><td>Λ</td><td>Μ</td><td>Ρ</td></tr><tr><td>Α</td><td>Ι</td><td>Υ</td><td>Η</td><td>Ε</td><td>Ο</td><td>Ω</td></tr><tr><td>Ξ</td><td></td><td></td><td>Σ</td><td></td><td></td><td>Ψ</td></tr></table>

Without entering into the details, it will be noted, for example, that the third row contains all the vowels, and that the fourth row contains all three sigmatic consonants. This arrangement, including as it does all twenty-four letters, is a graphic representation of an alphabetic pleroma, a totality, and it gives an intimation of the subtleties underlying many similar arrays found in magical literature. This fundamental physical reality, conceived as fields or mathematical structures, is in fact a mediator between what our intellect can comprehend of order and necessity, and what our senses can perceive of beauty and contingency. As Nicomachus puts it, they (these number-letters) are bridges and ladders to the supernal reality.

The intermediary reality they constitute is matter for the lower world, but it is matter in the sense of a 'literary matter';<fnref n="7" /> more precisely, it is the revealed books themselves, which have all a liminal status too: they are the matter for the demiurge to do his craft, writing as a scribe, and they are matter for the lower realities to read from.

## Linguistics, Psychology and Cosmology

This work is about linguistics in a number of its sub-disciplines, as can be seen in my earlier discussions of morphological, prosodic and other such issues, but the crucial linguistic aspect of my research is the twofold segmentation mentioned in Chapter 6.<fnref n="8" /> In linguistics, twofold segmentation refers to the two-layered construction of meaning proper to human language: from the meaningless distinctive elements like letters or phonemes, to the meaningful signs, like words or morphemes. When considered from a cosmological point of view, however, the distinctive elements, our 'letters' are, as we have amply observed, far from meaningless, but rather each one of them considered a 'name' and an 'infinite' of its own. The point of departure of every cosmological understanding of language is based on a modified understanding of the twofold segmentation, *sub specie aeternitatis*, for which the 'distinctive' elements discerned in the second level of segmentation are far from meaningless.<fnref n="9" />

This is also intimately associated with Whorf's conviction that 'science, if it survives the impending darkness, will next take up the consideration of linguistic principles,'

<footnote n="7">7. As when there is question of 'the Matter of Britain' or 'the Matter of Troy.'</footnote>

<footnote n="8">8. See above, p. 161.</footnote>

<footnote n="9">9. This is studied in its historical relation to atomism in F. Hallyn, 'Le Modèle alphabétique de l'atome ancien,' *Alliage* 57-58 (July 2006).</footnote>
and his detailed description of a series of seven initial ontolinguistic planes, from the acoustic to the syntactic, and 'on to further planes still, the full import of which may some day strike and stagger us.'<fnref n="10" /> His reference to an intermediary realm is strikingly close to those mentioned in the previous section:

> the physical world may be an aggregate of quasidiscrete entities... not fully understandable as such, but rather emergent from a field of causes that is itself a manifold of pattern and order... As physics explores into the intra-atomic phenomena, the discrete physical forms and forces are more and more dissolved into relations of pure patternment.

## Metaphysics and Theology

This work is about metaphysics and theology insofar as it is a study of principles, of the foundations of existence and of the constitution of matter in different levels, drawing from the language of philosophers as much as from the language of theologians. As already discussed in Chapter 8 above, our interest here has to do with that 'matter' or 'receptacle' or 'heterogeneous object' 'whose only positive attribute is the necessity by which the hypothesis of its existence imposes itself.'<fnref n="11" />

Characterised as 'difficult and obscure' (*Timaeus* 49a3) or 'invisible and amorphous' (51a7), the matrix of the alphanumeric elements is at once solar and lunar. The στοιχεία are paradoxical in that they are simultaneously luminous and obscure. They are the conglomerate of forms which make possible our *informatio*,<fnref n="12" /> our intellectual discernment through delineation, and at the same time they are in themselves a complex, a *pleroma*, of impenetrable and shifting ambiguity, like snakes, and like ungraspable utterances in the air.

Several aspects of this 'matter' have been discussed sufficiently above, and to close this section I would just like to recall and specify the architectural cosmogonic role of the στοιχεία. In view of their attributes and functions, and after such a long exploration, I find that the most apt image for the letter-numbers are those stakes or pegs used by land surveyors as reference points to *determine* the construction of new buildings. The first step is to extend a measuring tape through the centre of the area, this is called a baseline; then a grid is established, with the grid lines often identified by marking the stakes, alphabetically in one direction, and numerically in the other direction. These stakes are only temporary, they are an intermediate stage between the original blueprint and the actual building.

<footnote n="10">10. Whorf, *Language, Mind, and Reality*, 249, 270.</footnote>

<footnote n="11">11. Brisson, *Le même et l'autre*, 208.</footnote>

<footnote n="12">12. Ar. *tasawwur*; see R. Capurro, *Apud Arabes: Notes on Greek, Latin, Arabic, Persian, and Hebrew Roots of the Concept of Information*, 2014, II.1.</footnote>
איפה היית ביסדי־ארץ הגד אם־ידעת בינה: מי־שם ממדיה כי תדע או
מי־נטה עליה קו

ποῦ ἦς ἐν τῷ θεμελιοῦν με τὴν γῆν; ἀπάγγειλον δέ μοι εἰ ἐπίστη σύνεσιν,
τίς ἔθετο τὰ μέτρα αὐτῆς εἰ οἶδας ἢ τίς ὁ ἐπαγαγὼν σπαρτίον ἐπ’ αὐτῆς;

*Ubi eras quando ponebam fundamenta terræ? indica mihi, si habes intelligen-
tiam. Quis posuit mensuras ejus, si nosti ? vel quis tetendit super eam lineam?*

Where were you when I was ‘elementing’ the earth? Tell me, if you have
understanding! Who determined its measurements—surely you know! Or
who stretched the baseline upon it?<fnref n="13" />

Historical Conclusion: The Alphanumeric End

Around the medieval Mediterranean, and once again spreading from the East, a great wave of change is moving westward from around the eighth century. It is so fundamental in nature and so momentous in its incalculable effect, that I could only liken it to the great shifts of tectonic plates, determining in discreet yet decisive ways the future of the great cultures built upon them. I refer to what might be named ‘the alphanumeric scission’, the separation between letters and numerals which resulted directly from the adoption of the Indian numerals.<fnref n="14" /> Far from happening as if by decree in a once and for all manner, this adoption took place over several centuries, gradually and irregularly. Its landmarks have been charted extensively for the different cultures and their respective writing systems.

The adoption of the numerals into Arabic has an important signalling event in the
visit of a group of scholars from India to Baghdad in 771. 15 Prior to that embassy, there
had been an important mention of the numerals in 662, by the Syrian bishop Severus
Sebokht, giving a strong indication of the importance of Syriac in the transmission
of knowledge across cultures. This famous testimony by Sebokht may indicate not
only an earlier Arabic acquaintance with ‘the nine symbols’, but also, through the
Greek church, a first point of contact with the Byzantine Greek-speaking world, where

<footnote n="13">13. Job 38: 4–5; NRSV, slightly modified.</footnote>

<footnote n="14">14. G. Ifrah, *The Universal History of Numbers: From Prehistory to the Invention of the Computer*, trans. D. Vellos et al. (New York: John Wiley & Sons, 2000), 361, compares their importance to the mastery of fire and the invention of the wheel. Notably, in 2006 Burnett had already started looking into the ‘impact of Indian numerals on the mentality of Western scholars’ in his ‘The Semantics.’</footnote>

<footnote n="15">15. See P. Kunitzsch, 'The Transmission of Hindu-Arabic Numerals Reconsidered,' in *The Enterprise of Science in Islam: New Perspectives*, ed. J. P. Hogendijk and A. I. Sabra (Cambridge, MA: MIT Press, 2003), 3ff. and J. L. Berggren, *Episodes in the Mathematics of Medieval Islam*, 2nd ed. (New York: Springer, 2016), 32–3.</footnote>
otherwise the usage of the numerals was very limited until the thirteenth century. The first Greek work to systematically use the new numerals is the Μεγάλη καὶ Ἱνδικὴ Ψηφιφορία (The Great and Indian Computation) authored by Maximus Planudes in 1252.<fnref n="16" /> Before that there is uncertainty, but we know that the most ancient manuscript of Euclides' Στοιχεῖα, dating from 888, contains glosses with the Indian numerals which predate Planudes' work.<fnref n="17" /> Hebrew scholarly literature was intimately related to Arabic scholarship through the use of the Judeo-Arabic script; the introduction of the positional system is due to Abraham ibn Ezra in the early twelfth century, using initially a hybrid notation with the opening letters of the Hebrew alphabet.<fnref n="18" /> In Latin-speaking Europe, the first preserved example comes from the Codex Vigilanus, dated 976,<fnref n="19" /> but it was much later, in the twelfth and thirteenth centuries, through the scholarly activities based in Sicily and Toledo, that the usage of the new numerals would be consolidated and disseminated.<fnref n="20" /> A remarkable 1153 manuscript from Palermo illustrates the complexity of the situation: it is a trilingual psalter in which numerals appear in alphabetic notation in Greek, in Indian notation in Arabic and in Roman numbers in Latin.<fnref n="21" />

<figure><img src="image_31.png" /><figcaption>HARLEY MS 5786, 14v.</figcaption></figure>

In the light of such a panorama, and craving the conceptual clarity afforded by a time frame, I assume as two significant boundaries of this long process of adoption, first, the publication of al-Khwārizmī's *Kitāb al-jamʻ wa-al-tafrīq bi-ḥisāb al-hind, The Book of Addition and Subtraction According to the Hindu Calculation*, dated sometime after 800;<fnref n="22" /> and, secondly, the publication in 1202, in Florence, of Fibonacci's *Liber Abaci*—<fnref n="23" /> I do so on the understanding that both publications marked, rather than the

<footnote n="16">16. Chrisomalis, 'Re-evaluating Merit,' 2.</footnote>

<footnote n="17">17. See N. Wilson, 'Miscellanea Palaeographica,' *Greek, Roman and Byzantine Studies*, no. 22 (1981): 402–404.</footnote>

<footnote n="18">18. C. Burnett, 'The Transmission of Arabic Astronomy via Antioch and Pisa in the Second Quarter of the Twelfth Century,' in *The Enterprise of Science in Islam: New Perspectives*, ed. J. P. Hogendijk and A. I. Sabra (MIT Press, 2003), 39; N. Ambrosetti, *L'eredità arabo-islamica nelle scienze e nelle arti del calcolo dell'europa medievale* (Milano: LED Edizioni Universitarie di Lettere Economia Diritto, 2008), 110.</footnote>

<footnote n="19">19. Burnett, 'The Transmission,' 29; Ambrosetti, *L'eredità arabo-islamica*, 96.</footnote>

<footnote n="20">20. See Burnett, 'The Transmission,' 29; and also *passim* C. Burnett, *Numerals and Arithmetic in the Middle Ages*, Variorum Collected Studies 967 (Farnham, UK: Ashgate, 2010).</footnote>

<footnote n="21">21. British Library, Harley MS 5786, see Ambrosetti, *L'eredità arabo-islamica*, 102.</footnote>

<footnote n="22">22. Only extant in Latin translations of the twelfth and thirteenth centuries, see Berggren, *Episodes*, 32; Kunitzsch, 'The Transmission,' 3.</footnote>

<footnote n="23">23. For a vernacular, crafts related tradition parallel to the channels that converged in Fibonacci' work, see J. Høyrup, *Jacopo da Firenze's Tractatus Algorismi and Early Italian Abbacus Culture* (Birkhäuser Verlag, 2007).</footnote>
beginning, an advanced stage in the long process of adoption of the Indian numerals in their respective circumstances.

Although it is impossible to ascertain the many consequences brought about by the usage of the new numerals, I would like to observe how on a fundamental level, and in the cases of languages from Semitic and Indo-European stock, this new system of numeric notation lays bare for the first time in graphic fashion the decimality underlying their numerical terminology.<fnref n="24" /> As has been mentioned previously,<fnref n="25" /> when speaking of the difference between *Zahlwort* and *Ziffer*, writing 2, 20 and 200 is as closely descriptive of the underlying decimality as writing β, κ and σ is foreign to it in its arbitrariness. Apart from the obvious and recognised advantages that this brought to all the fields dependent on computation, like accounting and combinatorics, it is not hard to surmise that a long-term cascade effect may also have impacted the most disparate fields of knowledge.

Many major cultural developments took place around the Mediterranean in the High Middle Ages, and there have been attempts to relate them in a grand theory. Focusing on the thirteenth century, the 'age of the summae',<fnref n="26" /> Erwin Panofsky famously drew a detailed analogy between the origins of scholasticism and the flourishing of Gothic architecture, using the term *manifestatio*, in the meaning of 'elucidation of faith by reason,' as the 'first controlling principle of Early and High Scholasticism.'<fnref n="27" /> The requirements of the classic High Medieval *Summa* were three: *totality* (sufficient enumeration), *systematic arrangement* (sufficient articulation), and *distinctness and cogency* (interrelation). These principles in themselves were hardly new, but the scholastics, in contrast to the thinkers of previous centuries, 'felt compelled to make the orderliness and logic of their thought palpably explicit.'<fnref n="28" /> And I wonder, could not a similar observation be made in the sister traditions, considering for instance the works of Maimonides, and setting the Ikhwān's *Rasā'il* as a comparable edifice? My time frame is wide, or perhaps simply and avowedly, loose, because it is given by the undecidable dates of the alphanumeric scission.

It is said that through various chains of transmission, there was a rebirth of mathematics in Europe in the twelfth century.<fnref n="29" /> These are the times of the rise of the

<footnote n="24">24. 'In fact, a great majority of the world's number systems, across all of its roughly 7,000 languages, reveal decimality in one form or another'; see C. Everett, *Numbers and the Making of Us: Counting and the Course of Human Cultures* (Cambridge (MA): Harvard University Press, 2017), 65.</footnote>

<footnote n="25">25. Above, p. 54.</footnote>

<footnote n="26">26. A. Hyman, J. J. Walsh, and T. Williams, *Philosophy in the Middle Ages: The Christian, Islamic, and Jewish traditions* (Hackett Publishing, 2010), 409.</footnote>

<footnote n="27">27. E. Panofsky, *Gothic Architecture and Scholasticism* (New York: Meridian Books, 1957), 30.</footnote>

<footnote n="28">28. *Ibid*., 34.</footnote>

<footnote n="29">29. J. Sesiano, *The Liber Mahameleth: A 12th-century mathematical treatise* (Springer, 2014), xiii.</footnote>
universities and the renovated reception of Aristotle.<fnref n="30" /> In the field of music, which in the guise of grammar and arithmetic is completely central to this enquiry, it was the Paris school of the thirteenth century which introduced the mensural notation still used today, articulating music through an exact and systematic division of time.<fnref n="31" /> In a story with a remarkable ‘Pythagorean’ echo, it is said that also in the thirteenth century, upon hearing the rhythmic hammering of the smiths, Jalāl ad-Dīn Rūmī was inspired to devise the music and the dance of the Mevlevi sema, still practiced today, and this brings us to the other important related field of the contemplative orders and mystical movements.

Just as the Kabbalah was becoming a distinct movement, we observe how a number of Christian monastic orders began to be defined. Carthusians, Cistercians, Franciscans and Dominicans, all originate or crystallise within a span of less than two centuries. Something similar took place in the Islamic world with the consolidation of the Qādirī, Shādhilī, Naqshbandī, Kubrawī and Mevlevī Sufi orders.

<figure><img src="image_32.png" /></figure>

Willing to make sense of all those developments, and in numerous others which it would be out of place to mention, and all in the light of the alphanumeric scission, I go back to the basic observation of a division: as the previously united aspects of the alphanumeric element broke, so must have broken something in many fields of human endeavour. As number and letter were gradually being revealed as separate entities, so in many other fields, what was previously a cryptocrystalline harmony became an explicit harmony, a shining crystal.

Similar and complementary observations could be made about the beginning of the alphanumeric age: I am left to wonder how inscrutably related may be the incipient letter-number conjunction and the momentous developments experienced by Greek culture after the sixth century BC. Closer to parts of this research, for instance, is Luz's observation that the middle of the third century BC may be considered a time of special flourishing of the *technopaignia* in their many dimensions.<fnref n="32" />

At the closing of this era of sorts, over the centuries-long period during which the letter-numeral separation was effected, it is as if number was laid bare, no longer clothed in the same way as words. Naturally, everything had to change and, naturally, it is impossible to trace all the concomitants of this change. These pages, therefore, and the statements made here, cannot be, and do not mean to be in any way categorical, but they are rather meant as an invitation to a wide and incisively interdisciplinary

<footnote n="30">30. Hyman, Walsh, and Williams, *Philosophy in the Middle Ages*, 409.</footnote>

<footnote n="31">31. Panofsky, *Gothic Architecture and Scholasticism*, 39.</footnote>

<footnote n="32">32. See Lougovaya, *‘A Perfect Pangram,’* 184.</footnote>
approach to many major cultural shifts in the Mediterranean international High Middle
Ages.
Appendix A: Latin Grammarians

*unde incipere debet grammatica?*
quidam grammatica a voce coeperunt,
alii a litteris, alii a syllabis, alii a casi-
bus, nos a definitione.

**qui tamen coeperunt melius? uti-**
que qui a definitione vel a litteris. nam
vox naturalis est et sine grammatica
communis cum imperitis. illi autem
qui a litteris coeperunt hac videlicet usi
sunt ratione, quod grammaticae artis
initia a voce oriantur, quae elementis
constat.

*elementum quid est? unius cuiusque*
*rei initium, a quo sumitur incremen-*
*tum et in quod resolvitur. vox igitur,*
*ut diximus, litteris nititur, litterae syl-*
*labis clauduntur, syllabae in dictionem*
*conveniunt, dictio orationem auget,*
*oratio partibus divisa in virtutes vitia-*
*que descendit.*

Where should a grammar start? Some have
started their grammar treating of the sound
[vox], others the letters, others the syllables
and others the cases; we will do so treating
of the definition. Who were right then? Those
who started from either the definition or the
letters, because the sound is common to all,
including the laymen without any need for
grammar. And so, those who started from
the letters obviously reasoned this way: the
beginnings [initia] of the art of grammar
originate from the sound, which is formed
of elements. And what is an element? The
beginning of any single thing, from which
it grows and into which it is resolved. The
sound [vox] then, as we said, has the letters as
support; the letters come together in syllables,
the syllables gather in words, the word gives
rise to sentences, and the sentence, divided in
parts, goes down to the level of virtues or vices.

[Audacis de Scauri et Palladii libris excerpta (2nd century AD, Keil VII)]

The Aristotelian definition of the element as *a quo sumitur incrementum et in quod resolvitur*, is found over and over with little variation in grammarians from the second to the tenth century, including the famous Donatus. Here is Diomedes (c. 375), *De arte grammatica* (Keil I), with some interesting lines about our subject.

II, ‘de littera’

L. est pars minima vocis articulatae ab
elemento incipiens una figura notabilis
[...] l. est vocis eius quae scribi potest

A letter is the smallest part of an articulated
sound, originating from an element and rep-
resented by one sign [...] A letter is the form
of that sound which can be written [...] An ele-
forma [...] elementum est minima vis et
indivisibilis materia vocis articulatae vel
uniuscuiusque rei initium a quo sumi-
tur incrementum et in quod resolvitur.
huius figura littera vocatur; et sunt om-
nes figurae litterarum numero XXIII. sed
harum potestates, quas elementa nomi-
namus, plurimae intelleguntur. litteras
etiam ueteres elementa dixerunt, quod
orationem velut quaedam semina con-
struant atque dissoluant. etenim differt
utrum quis dicat elementum an litteram
an per se, quia elementum quidem est vis
ipsa et potestas, littera autem figura est
potestatis, a vero nomen est et potestatis
et figurae. igitur elementum intellegitur,
littera scribitur, a nominatur.

ment is the smallest force and the indivisible
matter of articulated sound, or else the begin-
ning of every single thing, from which it arises
and into which it resolves. The sign of such
 element] is called ‘letter’, and the signs of
the letters are in total twenty-three. But their
powers [ potestates ], which we call ‘elements’,
are understood in various ways. The people of
old called the letters elements, because they
bring the sentence about as some sort of seeds,
and then dissolve. There is also a difference
depending on whether people refer to the ele-
ment as a letter or in itself, for the element is a
force itself and a power, while the letter is the
sign of a power. ‘A’ for instance is the name
of both a power and a sign: as element it is un-
derstood, as letter it is written, and it is named
‘a’.

In an attempt to clarify several such terms found in this grammatical tradition, Martin Irvine sums up:

The common doctrine on *litterae*, therefore, included the following
assumptions: a ‘letter’ is a minimal phonic/graphic unit (*elementum*)
of ‘scriptible utterance’ (*vox litterata*); the concept of ‘letter’ entails
distinctions by ‘properties’ [...] In the grammatical model of language,
every level of discourse ‘is resolved’ (*solvatur*) [...] into the parts of the
level immediately below it, and all discourse is ultimately resolvable into
‘letters’, the ‘elements’ or ‘atoms’ of writing.<fnref n="33" />

Or in the words of Sergius (c. 450),<fnref n="34" />

omnis oratio solvatur in verba, verba denuo solvantur in syllabas, rursum syllabae solvantur in litteras, littera sola non habet quo solvatur. ideo a philosophis atomos dicitur.

Every sentence is resolved in words; words resolve in syllables; syllables resolve in letters, but the letter alone has nothing to resolve into. This is why it is called *atomos* by the philosophers.

<footnote n="33">33. Irvine, *Making of Textual Culture*, 100.</footnote>

<footnote n="34">34. *GLK*, 4, 475.</footnote>
## Mundi elementa

In the following lines, Priscian (6th century)<fnref n="35" /> gives the Latin equivalent of the cosmological association with the elements.

literas autem etiam elementorum vocábulo nuncupaverunt ad similitudinem mundi elementorum [...] litera igitur est nota elementi [...] abusive tamen et elementa pro literis et literae pro elementis vocantur.

They called the letters with the name of the elements because of their resemblance to the elements of the cosmos [...] The letter is the sign [nota] of the element [...] It is a misuse when they call the elements letters and the letters elements.

Finally, here is a lively dialogue from the grammar by Iulianus Toletanus (c. 680)<fnref n="36" /> introducing some aspects not found previously.

**littera quid est?** pars minima vocis articulatae [...] **quomodo?** si adsumas unum nomen, ut puta Honorius, dividas illud per syllabas, ultima syllaba quae remanserit dividas illam per litteras, littera quae remanserit dividi non potest et est pars minima. **quomodo vocis articulatae?** duae sunt voces, una articulata et altera confusa. **quae est confusa?** quae scribi non potest, ut puta ovium balatus, equi hinnitus, mugitus bovis, et cetera. **item quare dicta confusa?** quia ex aere verberato, nullo modo sono exiliente, vis sermo-nis exprimitur. **quae est articulata?** quae articulo scribentis conprehendi potest. **quare dicta articulata?** artus dicuntur membra maiora hominum, et articuli membra minora, ut sunt digiti, et quidquid per istos articulos scribentis conprehendi potest ipsa est vox articulata. **item quare dicta littera?** quasi legitera. **quomodo?** eo quod legentibus

**What is a letter?** The smallest part of an articulate sound. **How is that?** If you take a noun, say 'Honorius', and you divide it in syllables, then you divide the last remaining syllable in letters, then you can no further divide the remaining letter: that is the smallest part. **How so an articulate sound?** There are two types of sound, articulate and confused. **What is the confused one?** The one which cannot be put in writing, like the bleating of sheep, the horses' neigh, the cows' moo etc. **And why are they called confused?** Because the voice (*sermo*) is expelled with the vibration of the air but the sound has no measure. **And what is the articulate one?** The one that can be grasped thanks to the articulation of the writer. **Why is it called articulate?** The major limbs of man are called *artus*, and the minor ones articulations, such as the fingers, and whatever can be grasped thanks to these articulations of a writer is called articulate sound. **And why is it called littera?** As if we said *legitera*. **How is that?** Because it provides a way (*iter*)

<footnote n="35">35. *Institutionum Gramaticarum* (Keil vol. II).</footnote>

<footnote n="36">36. Iulianus Toletanus, *Ars Iuliani Toletani episcopi: una gramática latina de la España visigoda*, ed. M. Maestre Yenes (Toledo: Instituto Provincial de Investigaciones y Estudios Toledanos, 1973), II.1.</footnote>
iter praebeat, vel quod in legendo iteretur. **Latinas quis adinuenit litteras?**
Nicostrata, Evandri mater, in Italia non quia ipsa eas invenisset, sed quia de Graeco in Latinum illas transtulisset. **quo nomine post adinventionem litterarum vocata est?** Carmentis nympha. **quomodo?** eo quod carmini-bus suis futura caneret [...] **quot sunt genera litterarum?** septem. **quae?**
Hebraeae, Atticae, Latinae, Syrae, Chaldaicae, Aegyptiae, et Geticae. **quis quales adinvenit litteras?** Moyses Hebraeas, Phoenices Atticas, Nicostrata Latinas, Abraham Syras et Chaldaicas, Isis Aegyptias, Gulfila Geticas.

for those who read, or because it is repeated (iteretur) during the reading. **Who invented the Latin letters?** Nicostrata, Evander's mother, but not because she invented them in Italy, but because she brought them over from Greece. **By what name was she called after this invention?** The nymph Carmentis. **Why so?** Because through her prophetic songs (carmina) she would sing of things to come. **How many are the different kinds of letters?**
Seven. **Which?** Hebrew, Attic, Latin, Syrian, Chaldean, Egyptian and Getan. **Who invented each of the letters?** Moses the Hebrew, the Phoenicians the Attic ones, Nicostrata the Latin ones, Abraham the Syrian and Chaldean, Isis the Egyptian ones and Gulfila the Getan.
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