INTRODUCTION
In a series of books and articles I have considered a tradition of thought and a mode of composition in which accounts of the Creation provided models for human artistic creations.[1] In this tradition God is imagined as having created the universe as a mathematical and musical act in seven days, mathematical because everything was counted -- in the words of Wisdom 11.21 'You have disposed all things by measure and number and weight' -- and musical because everything was harmonious - in the words of Job 38.7 'the morning stars sang together and all the sons of God shouted for joy'. God made seven 'planets' or wandering stars, each of which gave its name to and governed one day of the week, Sunday, Moonday, Mars > Martis dies = Tiw's day, Mercurius > Mercurii dies = Woden's day, Jupiter > Jouis dies = Thor's day, Venus > Veneris dies = Frey's day, Saturnday, and while these planets circled the earth in their crystal spheres they made music, the music of the spheres, there being coincidentally seven notes in the gamut. Because in ancient Hebrew and Greek and Latin alike there was a single notational system, letters of the alphabet, for recording letters and numbers and musical notes, this latter a phenomenon that survives among us as the notes ABCDEFG, every word exhibited a semantic meaning and a numerical value and a harmonic value.

This tradition was fully developed in the Hebrew text of the Old Testament and in the Greek text of the New Testament, and it was perfectly represented in the Latin text of the Biblia Vulgata published by Jerome in response to a commission by Pope Damasus in A.D. 382. The principles of composition are preserved in Plato's Timaeus, a dialogue never lost in the West, where it was read in the Latin translation by Calcidius. The principles of composition are explicitly discussed in the Talmud and in the basic texts of Latin rhetoric, the Rhetorica ad Herennium and Cicero De Oratore. The practice of reckoning numerical values is exhibited in the Book of Judges, in the Gospel according to Saint John the Evangelist, in the Apocalypse of Saint John the Divine, and in Martianus Capella's De Nuptiis Mercurii et Philologiae Book II, all known in the Latin West long before the thirteenth century.

The fully developed tradition is exhibited in inscriptions on stone and in literary and diplomatic texts from the beginning of the Roman Conquest of Britain, in every language written in these islands -- Latin, Greek, Hebrew, Aramaic, Arabic, Old Welsh, Old Irish, Old English, Old Norse, and Old French -- in chains of transmission so tight that there is not a gap as long as twenty-five years among texts from Roman times to the modern period. This literary, mathematical, and musical tradition is also abundantly illustrated in the plastic arts of these islands, in manuscript illumination, in stone sculpture, in metalwork, on coinage, and in architecture.[2]

Conspicuously beautiful monuments in this tradition are the Cosmati pavements in Westminster Abbey, considered in a conference at the Warburg Institute and the Abbey in November 1998, the proceedings of which were published in 2002 [3] in a book reviewed in this journal in 2003 (vol. 5 no. 2) by John Sharp, who considered that my contribution to that conference and book 'sticks out like a sore thumb amongst other scholarship'.

Sharp wrote:

For instance, if I take the title of his paper with its eight words [The Inscriptions in the Sanctuary Pavement at Westminster] the fifth word in the title, Sanctuary, should be significant, because it holds roughly the Golden Section position in the title (the ratio 8:5 is Golden Section). I am sure that Howlett did not employ this technique in his title; if I were deliberately employing this technique, I would have made pavement the prominent word).

This is the first of many things about which Mr Sharp was sure. The Golden Section is called 'division by extreme and mean ratio' because it affords a rule, easily applied, by which to draw attention to important words and ideas in aesthetically pleasing positions, in this case, 8 dividing by extreme and mean ratio at 5 and 3, at Sanctuary | Pavement, five words from the beginning and three from the end of my title.

Sharp went on:

I am sceptical of anyone playing such games with numbers … . It is easy to be mislead [sic] and shocked or surprised, and this makes it possible to play on the superstitions of others and/or deceive oneself. … The type of games [Howlett] plays with the Biblical text … is juggling with Fibonacci numbers in the way I described at the beginning of the review of this paper.

Someone who composes in this tradition does not need to juggle. He knows beforehand where things belong, and he puts them there, by deliberate design that can be confirmed by the coordination of many rules. Someone who analyses texts composed in this tradition cannot mistake whether a composer intended a structure, nor can he impose a structure on a text composed without one. Among the hundreds of literary, diplomatic, and epigraphic texts I have analysed in thousands of published pages there are no dubious examples. A text plays either perfectly or not at all. If it plays it conforms not with one rule, but with scores of rules, independent but interlocking and mutually corroborative.

Here follows the text of the Westminster inscription, with the rhyme scheme marked at the right. First the verses round the outer edges.

Second the verses round the surrounding circles.

Third the verse round the inner circle.

I translate thus:

+ In the year of Christ, the thousandth, twice hundredth, twelfth, with the sixtieth, with four subtracted, the third King Henry, [the pope in] the City [of Rome], Odoric, and the Abbot [of Westminster] fixed together these porphyry stones.
If the reader would revolve prudently all the arranged things here he will find the end [i.e. both 'chronological conclusion' and 'purpose'] of the Prime Mover. Should you add hedges three times, dogs and horses and men, stags and ravens, eagles, tremendous sea monsters, the world, each thing following triples the years of the one going before.
The spherical globe here shows the archetypal macrocosm.

Sharp wrote:

There is no clue to why Howlett begins with XPISTI adding three extra characters: can it be only to juggle the numbers? … Apart from adjusting the first word … .

In Antiquity Roman standards bore the inscription S.P.Q.R., which stood for Senatus PopulusQue Romanus 'Senate and People of Rome'. In Christian times the Greek letters IHs crs stood for IHsOus crIsTOs 'Jesus Christ', and the Latin letters IHS stood sometimes for the first three letters of 'Jesus' and sometimes for In Hoc Signo 'In This Sign', referring to the Cross. The letters of the Greek word ICQus, meaning 'fish', were recognized as an anagram of IHsOus crISTOS QEOU UIOS SWTHR 'Jesus Christ, Son of God, Saviour'. At the end of the third century, from 286 or 287 to 293, the Romano-Briton Carausius, who supported his claim to be emperor with a restoration of the coinage to a long-abandoned standard of purity, issued coins and medallions with the inscriptions RSR INPCDA, which represented the initials of Redeunt Saturnia Regna / Iam Noua Progenies Caelo Demittitur Alto 'The Saturnian Realms Return, / Now a New Progeny is Sent down from Lofty Heaven'.[4] The mere initials, to be effective as propaganda, had first to be expanded as parts of two lines of verse, second to be recognized as Vergil's Eclogue 4.6-7, and finally to be understood as implying Carausius's fulfilment of the prophecy of the Messianic Eclogue. Supply of full texts for the abbreviations or initials of any of these inscriptions should be no more suspicious than expansion of D. G. REG. F. D. as Dei Gratia Regina Fidei Defensor 'By the Grace of God Queen, Defender of the Faith' on our coinage. Expansion of crI to crisTI, which Sharp describes as juggling and adjusting, is required for scansion of the verse, a subject over which he blundered.

[Howlett] also chooses to break the second part of the inscription that falls on the circles in a different way from Richard Foster, I assume in an attempt to convert it into verse, something which I don't think it is. All he seems to show is that since it is a continuous text, breaking it into a series of lines can either be an arbitrary act or some skilled analysis of the flow of syllables is required. He has appeared to do the former and then attempt [sic] to analyse the structure by syllables rather than the other way round.

There can be no doubt whatever that the text is composed in Latin verse, dactylic hexameters and elegiac couplets, the commonest verse forms at all periods of the history of Latin. Ignorance of Latin prosody is not a capital offence, but it is a serious disqualification for discussing this inscription, which can be scanned by rules known to schoolboys for more than two millennia.

- - | - - | - - | - - | - u u | - - |
- - | - - | - - | - - | - u u | - - |
- u u | - - | - - | - u u | - u u | - - |
- - | - - | - || - u u | - u u | - |
- - | - u u | - - | - - | - u u | - - |
- - | - - | - || - u u | - u u | - |
- - | - u u | - u u | - u u |- u u | - - |
- - | - - | - u u | - - | - u u | - - |
- - | - u u | - u u | - - | - u u | - - |
- u u | - u u | - u u | - - | - u u | - - |

The only way in which these lines can be scanned reveals a symmetrical pattern of three hexameters, one pentameter, one hexameter, one pentameter, and three hexameters before the final hexameter at the centre of the pavement.

By denying that the inscription is in verse and querying the arrangement in lines, as if it were my imposed construct, as distinct from an authorial structure, Sharp can then ignore the infixed self-referential evidence of the words for numbers. There are two words before bis 'twice' and two words after it, ten letters between bis and deno 'tenth', and six words before sexageno 'sixtieth'. In the second line quatuor 'four' is the fourth word, after which there are four letters. The third line, at the beginning of the third side of the square, begins with the word tertius 'third'. Sharp thus ignores two forms of evidence, one by denial and the other by dismissal as 'word games'.

What Sharp means by my breaking 'the second part of the inscription … in a different way from Richard Foster' is unclear to me, unless he refers to my indentation of the second lines of elegiac couplets, intended to aid recognition of the verse forms. The only real variant is that some of the medieval scribes recorded the form trima and others the form trina, hardly a problem for comprehension, as the meaning of both forms is identical.

I had written 'italics suggest rhymes. Bold type suggests alliteration within lines and between adjacent lines.' Sharp wrote:

I see no alliteration, but occasional spurious similar pairs of letters or ones which are not even related and not even at the beginning of words in some cases. This adds a whole new meaning to alliteration, even allowing that we do not even know how the letters were sounded so long ago.

There are reliable ways of inferring exactly the ways in which letters were pronounced in thirteenth-century England. Francophone scribes from the period after the Norman Conquest often wrote cum as quum, the noun economus as equonomus and conversely the noun equus as ecus, and the thirteenth-century surname Neckam as Nequam, from which contemporary evidence one infers that the suggested alliteration between cum and quatuor is not 'spurious'. As the simplex verb ducere underlies the compound verb subducere, both stressed on the syllable du, one may suggest alliteration between duodeno and subductis, even though the latter is not at the beginning of the word. For the rest it requires more boldness than judgement to deny alliteration between sexageno and subductus, urbs Odoricus et abbas (all vowels alliterating on the glottal catch), porphyreos and posita, prudenter and primi, hic and inueniet, et equos hominesque (h and vowels alliterating), sepes and subaddas, ceruos et coruos aquilas immania cete, mundum and monstrat, sequens and spericus.

Sharp erred even more grotesquely about rhyme.

Also given that Latin has endings that are similar, the same or a similar ending does not make a rhyme. In the marked rhyming I was going to say that selection has been undertaken in order to make a point, but I don't see any point having been made. … I would also read the third line with rhyming stress on

tertius Henricus rex urbs Odoricus et abbas.

A post-Roman Briton, Faustus, fourth son of Vortigern, Abbot of Lérins and Bishop of Riez (†c490), was the earliest known writer of comprehensively rhyming Latin prose. Another Briton, Samson of Dol, son of a Demetian father and a Gwentian mother, educated at the school of Saint Illtut at Llanilltud Fawr in Glamorgan, signed the acts of the Synod of Paris in A.D. 562 with a rhyming leonine hexameter, Samson subscripsi et consensi in nomine Xpisti 'I Samson have subscribed and consented in the name of Christ'. Thereafter rhyming leonine hexameters recur frequently in Insular Latin poetry, as in this inscription. The form of this verse suggests that the third syllable of tertius and the fourth syllable of Odoricus, being short, cannot bear the stresses Sharp would give them. No one with either an eye or an ear should deny the rhymes of milleno - duodeno - sexageno - anno; compegere - cete; reuoluat - inueniet; Henricus - abbas - lapides - canes - subaddas - coruos - sequens - annos; archetipum - macrocosmum.

As a response to a coherent analysis of a text Sharp's review is a comprehensive and humiliating failure. It ends even worse than it began: 'the saying 'cobblers should stick to their lasts' springs to mind and non-mathematicians should not play games with numbers'.

The advice may be directed with more purpose to the reviewer than to the writer, who is guilty of none of the incompetence imputed to him. Nor is the writer guilty of the gratuitous rudeness in which the reviewer tries to disguise breathtaking ignorance as honest scepticism.

Sharp concludes his review of the entire book thus:

The geometry is neglected, although Richard Foster has made some inroads to this in his book. Partly this is because scholars feel intimidated by the tainting of the study of such geometry by the 'sacred geometers', and partly by the unease with [sic] which many inthe humanities feel about mathematics in general. It is not just the unease, but a naivete as well, as indicated by the inclusion of a paper on number games which by contrast seems acceptable when it has less content than might be seen to be mixed up in fringe geometry.

To dismiss the analyses in my paper as 'number games' is to imply that the reviewer has not read the syllabus for study of arithmetic, music, geometry, and astronomy, which remained stable from Antiquity to the thirteenth century, notably texts by Plato, Euclid, Ptolemy, Boethius, and Martianus Capella, in which he will find explicit justification for every technique I have employed. He will be hard pressed to discover and cite a single authority from long before or long after the thirteenth century who regarded these phenomena as 'fringe geometry'. When he will have begun to acquire some of the elementary learning that might make him fit to judge what he has reviewed, he might consider withdrawal of the charge of naivete levelled against the editors who included 'a paper on number games'.

NOTES
[1] David Robert Howlett, Liber Epistolarum Sancti Patricii Episcopi: The Book of Letters of Saint Patrick the Bishop (Dublin: Four Courts Press, 1994); The Celtic Latin Tradition of Biblical Style (Dublin: Four Courts Press, 1995); The English Origins of Old French Literature (Dublin: Four Courts Press, 1996); British Books in Biblical Style Dublin: Four Courts Press, 1997); Cambro-Latin Compositions: Their Competence and Craftsmanship (Dublin: Four Courts Press, 1998); Sealed from Within: Self-Authenticating Insular Charters (Dublin: Four Courts Press, 1999); Caledonian Craftsmanship: The Scottish Latin Tradition Dublin: Four Courts Press, 2000); Insular Inscriptions (Dublin: Four Courts Press, 2005); and articles in Archivum Latinitatis Medii Aevi: Bulletin Du Cange, Cambridge (now Cambrian) Medieval Celtic Studies, Mittellateinisches Jahrbuch, and Peritia from 1992 to 2004; Charles Thomas and David Howlett, 'Vita Sancti Paterni: The Life of Saint Padarn and the Original Miniu', Trivium 33 (2003). return to text

[2] Robert D. Stevick, The Earliest Irish and English Bookarts: Visual and Poetic Forms Before A.D. 1000 (Philadelphia: University of Pennsylvania Press, 1994). return to text

[3] Lindy Grant & Richard Mortimer eds., Westminster Abbey: The Cosmati Pavements, Courtauld Research Papers 3 (Aldershot: Ashgate, 2002). return to text

[4] Guy de la Bédoyère, 'Carausius and the marks RSR and I.N.P.C.D.A.', Numismatic Chronicle 158 (1998) 79-88. return to text

ABOUT THE AUTHOR
David Howlett is a Research Fellow of the Faculty of Classics in the University of Oxford, Editor of the British Academy's Dictionary of Medieval Latin from British Sources, Consultant to the Royal Irish Academy's Dictionary of Medieval Latin from Celtic Sources, and a member of the Comite(acute) de Redaction at the Institut de France responsible for the Novum Glossarium Mediae Latinitatis.

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Copyright ©2005 Kim Williams Books