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Computer Arithmetic, parallel architectures & processing, history of numbers and computation, computistics, lunar and solar cycles, astronomy, chronology, the chronicles of Eusebius, Jerome, Sulpicius Severus, Prosper, Bede and the Irish annals, the Paschal controversy.
Recent publications - click for abstracts:
List of Abstracts -
Abstract. In 1666 John Aubrey remarked on the fifty-six pits spaced around the main monument of Stonehenge, and in 1978 Alexander Thom surveyed these and showed that they form a very regular fifty-six sided polygon of mean radius 141.8 feet. This note shows that the number 56 provides two good, decimally convenient, approximations to pi, namely 562/1000 < pi < 562/1000 + 56/10000, with differences respectively of 5.6×10-3 and 7.3×10-6.
Abstract. The Paschal controversy
in the British Isles centred on the use of an 84-year Easter table, which was
The computational principles underlying the Paschal table, or latercus, found
in the manuscript Padua, Bibl. Antoniana I.27 f. 76r–77v, are closely analysed
and the details of the mechansims of its embolism, bissextile and saltus are
resolved as closely as possible. With this information it is possible to
eliminate all of the scribal errors from the table and, thus restored, the
table is presented in full. From this can be seen that the
This paper demonstrates that the chronological framework of the Annals of
Ulster is a combination of two different systems: one based on January AD
dating (nativity era), the other based on March AD dating (incarnation era).
This discovery explains the discrepancies in the dates, and vindicates Ussher's
analysis of the dating criteria against Bartholomew Mac Carthy's later
critique. The introduction of March AD dating is pinpointed to the eleventh
century, and is related to contemporary political and ecclesiastical
developments. The original chronological apparatus is restored and some of the
literary sources are also identified. The date and place of compilation for the
original are identified as
Abstract. The Chinese and Japanese records are our primary evidence of the supernova of 1054. But their evidence is not entirely consistent, and recent scholarly discussion of them has not yielded clear-cut results. We have therefore re-examined the original sources in some detail in order to determine their relative historical value and to arrive at as close a determination as possible of the appearance of the event itself. We have established from the Chinese sources that, on the authority of the Chief of the Astronomical Bureau at K'ai-feng, a guest star was first sighted between 9 June and 7 July 1054 to the north-west of Zeta Tauri; it became as bright as Venus, was visible in daylight for 23 days and did not disappear from sight until just before 17 April 1056. All this location, duration and brightness data points to this guest star as the supernova progenitor of the Crab nebula. When the Japanese texts are considered the date 4 July 1054 emerges as the most likely date for the first sighting of this supernova. Recent claims for both Middle-Eastern and Western European records are evaluated in the light of this result.
The lunar and Paschal tables in the text De ratione paschali have been
critically discussed by numerous authors over the last 100 years without their
inter-relationship ever being considered or understood. Now, as a result of the
discovery of the
Interest in James Ussher and his chronological work saw a re-awakening as the
date of the 22nd October 1996 approached and it was realised that we
were commencing the six thousandth year from Archbishop Ussher’s estimated date
of Creation, viz. the beginning of the night of the 22nd October
4004 BC. In the popular press some, playing on the inherent uncertainty of our
existence, suggested that Ussher had predicted that the world would end on the
evening of 22nd October 1996; thus the Irish Times headline of this date ‘An early tea would be advisable
as the world may end at 6 p.m.’. However, examination of Ussher’s published
works and manuscripts shows that while he strongly reflected the millenarian
beliefs of his own time that significant events fell at intervals of one
thousand years, he provided no precise time of day for Creation and no
prediction of the time and date of the Last Day. In fact the precise time of
Creation of 6 p.m. represents an interpolation made by the
The astronomical entries scattered through the Irish annals have been examined
in a serious astronomical context by R.R. Newton as part of his research into
the accelerations of the earth and moon, and by D. Schove and A. Fletcher, as
part of the Spectrum of Time project. They have never, however, been fully
collated and examined as a whole as this paper undertakes to do. What emerges
is a body of records from 442 to 1133 documenting eclipses, comets, aurorae,
volcanic dust clouds and possibly a supernova; from 627 to 1133 all of these
records are of observations made in or near Ireland, and most of them are
accurate in their chronological and descriptive details. Analysis of the
details of these records implies that, at least from the seventh to the eleventh
centuries, careful and sustained observation and recording of astronomical
phenomena were conducted in some Irish monasteries, and it is clear that the
underlying motive was religious and specifically eschatological, i.e. to detect
the first signs of the end of time as prognosticated in the Book of Revelation.
Critical examination of this data allows us to throw new light on the
circumstances of the Synod of Whitby in 664, to identify the date of the
eruption of the volcano Eldgjá in
Abstract. This paper presents the same material as is presented in An Evaluation of Astronomical Observations in the Irish Annals, but it concentrates on the textual and historical issues relating to the material. Thus the original texts of all the entries are reproduced and a much more detailed textual treatment is given of the entry found under 1054 and the historical background to the Synod of Whitby and its relationship to the solar eclipse of 664.
Abstract. The chronology of much of the Irish annals has hitherto been most uncertain, particularly from the fifth to the eighth centuries, which has seriously hindered their use as historical sources. This paper demonstrates that the oldest chronological apparatus preserved in these annals is the kalend-plus-ferial and, further, that the ferial data recorded in the Annals of Tigernach and Chronicon Scotorum may be restored and constitutes a cogent sequence from the Incarnation up to the middle of the seventh century. When this chronology is calibrated using events for which we have indepedendent chronological information it emerges that thirteen kalends were removed from the Iona Chronicle between the AD years 424-664, and thus we may recover the nearly all of the original chronology of that chronicle. Collation of this chronology with those of the Annals of Ulster and Inishfallen shows that both preserve derivative and corrupted chronologies; this collation has been made available on the Web at -
A copy of this paper is available as a PDF file for down-loading from the Royal Irish Academy website.
Abstract. This paper investigates the question of the sources and dates of the pre-Patrician material found in the annals of Tigernach and Inisfallen, firstly by reviewing all the contributions which have been made over the last century. From this it emerges that whereas analysis of the non-Irish material has resulted in significant progress, exploration of the Irish material has proven both difficult and singularly unproductive. Consequently a careful examination of the chronological structure and textual details of part of the Roman imperial succession has been made, which discloses that it had been compiled by conflating Eutropius’ Breviarium ab urbe condita with Jerome’s Chronicle. Next, textual collation with Bede’s Chron. Mai. shows that, rather than the annals having been derived from Bede, as has been generally assumed, in fact both pre-Patrician AT and AI, and Bede, all derive from a common source. The evidence shows that, while Bede’s text is generally less textually corrupt, the annals preserve both more of the content of the original source, and its chronological apparatus as well. Next, examination of the Alexandrian episcopal succession found in AT shows that it had been derived directly from Rufinus’ Ecclesiastical History, and details of the errors suggest that it was he himself who constructed it. Finally, examination of the Hebrew succession in Bede and AI reveals divergences from Jerome’s chronology that could not plausibly be the work of Bede, but are all appropriate to Rufinus. Hence, as a working hypothesis it has been proposed that Rufinus compiled a chronicle in the first decade of the fifth century, which travelled to Ireland with the 84-year Paschal table of Sulpicius Severus, whence it was used in Iona in the mid-sixth century as the basis for the Iona Chronicle. Tables of both the Roman imperial reigns and the Hebrew succession are available at:
This is essentially a translation to French of the paper published in 1997 as An Evaluation of Astronomical Observations in the Irish Annals in Vistas in Astronomy, vol 41, no. 1 (1997), 117–38.
Abstract. This paper undertakes a critical chronological and textual analysis of all the annalistic entries bearing on the life of S. Brigit of Kildare. From this it emerges that AT and CS have best preserved the chronology originally given to Brigit in the Iona Chronicle which placed her death at AD 524 aged 86 years, whereas AU and AI transmit a later tradition subsequently interpolated into the Iona Chronicle that she died aged 70 years. It is argued that the author of the original Iona Chronicle entries was S. Columba, a competent computist and near-contemporary of Brigit, and hence that his chronology of Brigit is trustworthy. To check this, a chronological evaluation of the earliest surviving Vitae S. Brigitae reveals that the chronology of all the individuals found jointly in the Vita I and the annals is consistent, implying that both sources have transmitted a chronology which is essentially correct, a result which supports the historical priority of Vita I over Vita II. Finally examination of the context of Cogitosus’ date for Brigit’s death shows that he aligned it to correspond with existing non-Christian celebrations already held in Kildare.
Abstract. The two oldest lives of St. Brigit of Kildare are the anonymous Vita I and Cogitosus’ Vita II, but scholars have disagreed as to which is the oldest. However evaluation of all of Vita I’s topographical references reveals that it maintains a virtually continuous location for her entire active adult life. It thus mirrors topographically the chronological consistency with annals already demonstrated for Vita I. Since these topographical and chronological elements are evidently independent they must derive from a common tradition which is earlier than that of the annals, that is, the later sixth century. On the other hand Vita II is topographically blank but when Vita I is used to locate Vita II’s parallel episodes, all but three are located in Laigin or in Kildare, in conformity with Cogitosus’ emphasis upon the priority of the church in Kildare. Examination of the episodes given in the time-frame of Cogitosus himself shows that he was deeply involved in technical and practical matters concerning the monastery in Kildare, of which he was most likely both prior and master craftsman. When the Vita II episodes which are more detailed than the parallel Vita I episodes are examined, it clearly emerges that the additions are all appropriate to Cogitosus’ style of composition, namely, enhancing his source with a combination of imagined technical details and pious interpretations. This leads to the conclusion that Cogitosus based Vita II directly and solely on Vita I. Finally consideration of Donatus’ account of the Vita Brigitae by Animosus suggests that Gregory’s Dialogues lib. I,7 inspired both of the names Cogitosus and Animosus as pseudonyms for the author of Vita II. These results substantially support the conclusion that Vita I was composed by Ailerán of Clonard, and it is an abridgement of an earlier, now lost, Vita by Ultán of Ardbraccan.
Chronological divergence between the different early Irish annals has hampered
use of their many unique records of events in
Abstract. The view represented by Mac Airt and Mac Niocaill in their 1983 edition of AU that the annals of ff. 12–14 of TCD 1282 are indeed part of the Annals of Ulster has recently been vindicated. Analysis of the chronological apparatus of ff. 12–14 reveals that their author was responsible for the introduction of Dionysiac epacts and continuous Anno Domini into the Irish annals. He accomplished this by an extraordinary series of interpolations into the pre-Palladian section of the Iona Chronicle that he used as source, demonstrating both his computistical skill and profound indifference to historical chronology. By AD 431 his apparatus was accurately synchronised with all the Dionysiac chronological criteria, and he continued with it, re-ordering many events through the fifth and sixth centuries. In the seventh century he omitted a single kalend, which put all his subsequent apparatus in arrears by one year. Collation of AU with the other annals indicates that his compilation continued to c. 1019 and was completed shortly after 1022. This compilation is identified with AU’s Liber Cuanach, and Cuan hua Lothcháin (†1024) is proposed as the author.
Christian Pasch: De ratione paschali
– The Paschal tract of Anatolius,
Very little contemporary evidence for the diversity of Christian Paschal
practice that preceded the Council of Niceae has survived. A unique exception,
however, is the Paschal tract of Anatolius, bishop of
Abstract. This paper demonstrates that the influential ninth century astronomical tract of Ibn Musa al-Khwarizmi incorporated two sine tables, one to norm R=150 at fifteen degree intervals reproduced from an Indian source, and a second to norm R=60 at one degree intervals derived directly from the chord table included by Ptolemy in his Almagest. Consequently it concludes that the norm R=60 sine table preserved in the twelfth century Latin translation of al-Khwarizmi by Adelard of Bath is indeed the work of al-Khwarizmi, and is not an interpolation as recent scholarship had maintained. An analysis of the one-second errors in the R=150 table preserved in the Toledan tables shows that it was derived by scaling and truncating an R=60 sine table, and the details suggest this to be the work of al-Zarquali of Cordoba, and that he used an edition of al-Battani’s sine table as his source.
Abstract. In 1639 bishop James Ussher reviewed all of the evidence relating to the tonsure worn by clerics belonging to the British, Scottish, Pictish and Irish churches from the fifth to the ninth century, and concluded that it was semicircular in shape. In 1703 the Benedictine scholar Mabillon, citing only a portrait of uncertain provenance found in a St. Amand manuscript proposed that the Insular tonsure consisted of entirely denuding of hair the front part of the head, while the back was unshorn. Whilst Mabillon’s hypothesis was unsupported by any evidence and in complete conflict with all of the sixth, seventh and eighth century evidence, some coming from eye-witnesses, nevertheless it has largely prevailed in modern times. This paper carefully reviews the early medieval evidence and proposes that the tonsure was triangular in shape, resembling a Greek delta. This hypothesis is tested against graphic portrayals of tonsures found in some Insular Gospel texts and it emerges that texts associated with Columban monasteries, where the tonsure is known to have been worn, do indeed confirm this triangular shape.
Abstract. Brief accounts of the Irish annals and of the basis for the chronology of Irish history.
Since at least the eighth century the system of counting calendar years from
the supposed year of the birth of Christ (ab Anno Domini) has been
attributed to Dionysius Exiguus, a Scythian monk in
Abstract. Ever since 1861 when in his Manuscript Materials Eoghan O’Curry published James H. Todd’s opinion that the first three folios of the TCD manuscript of the Annals of Ulster (AU), i.e. TCD 1282 ff. 12–14, represented ‘a fragment of an ancient copy of Tigernach’, the virtual consensus amongst scholars has been that these folios were interpolated and hence that AU commenced at AD 431. However this paper undertakes a critical examination of the paleographical and codicological evidence and demonstrates that these folios were in fact written by Ruaidhrí Ua Luinín, the principal scribe of the MS, and they were bound to the following gatherings in the first stitching of the codex. Furthermore their foliation by James Ware in the earlier seventeenth century implies that there were then eleven folios preceding f. 12, which itself commences at AD 82. This then implies that when originally compiled TCD 1282 commenced either at or near Creation, as do the closely related Annals of Boyle. Moreover critical comparison of the annals transcribed by Ruaidhrí Ua Caiside from TCD 1282 to Rawlinson B. 489 ff. 1–32ra, with the numerous interpolations into TCD 1282 in the hand identified as H2 in the edition of Mac Airt and Mac Niocaill, shows this to be the hand of Ua Caiside and not that of Cathal Mac Maghnusa as has been repeatedly asserted. Finally, examination of the concluding folios of TCD 1282, viz. ff 130r–143v, shows that these were also written by Ua Caiside, as James Ware had asserted in 1639, and in them Ua Caiside developed a steadily improving imitation of the hand of Ua Luinín. Hence the conclusion that this MS is complete at the end and that it was written as far as 1504 by Ua Caiside in approximately that year.
‘Irish chronicles and their chronology’, the present edition online since 2005 at www.scss.tcd.ie/misc/kronos/chronology/synchronisms/annals-chron.htm
Abstract. This article provides a short introduction to the two important chronological traditions employed in medieval Ireland. The earlier was the kalend tradition, which was the original Annalistic chronological apparatus, employing the kalends of January (1 January) to identify the commencement of each successive chronicle year. The later was the regnal canon tradition, which employed a table of the regnal years of the supposed successive kings ruling in Ireland. The article provides links to a substantial account of the kalend tradition and to the year-by-year synchronisation over AD 1–1590 of its best witnesses, namely, the Annals of Tigernach, Chronicum Scotorum, the Annals of Roscrea, Ulster, Inisfallen, Boyle, Connacht, Loch Cé, and Mageoghagan’s Book (alias Annals of Clonmacnoise). Links are also provided to a substantial account of the regnal canon tradition, and to a parallel collation of the regnal years of its significant witnesses; these include synchronisms, chronological poems, various editions of Lebor Gabála, Michéal Ó Clérigh’s Seanchas Riogh Ereann and Annala Rioghachta Eireann (alias Annals of the Four Masters), Seathrún Céitinn’s Foras Feasa ar Éirinn, and Ruaidhrí O’Flaherty’s Ogygia.
‘Chronological Synchronisation of the Irish Annals’, the present edition online since 2005 at www.scss.tcd.ie/misc/kronos/chronology/synchronisms/Edition_4/K_trad/K_synch.htm
Abstract. This article briefly outlines the early use of the kalends of January to sequence a chronicle by Rufinus of Aquiliea (†410), and its subsequent continuation in Iona, Clonmacnoise, Armagh, Derry, and along the river Shannon. It provides an extensive discussion of the significant features of the principal collated sources, namely, the Annals of Tigernach, Chronicum Scotorum, the Annals of Ulster, Inisfallen, and Mageoghagan’s Book (alias Annals of Clonmacnoise), and brief discussions of the Annals of Boyle, Roscrea, the Fragmentary Annals, Bede’s Chronica maiora, and the Annales Cambriae. It examines the problem of seven kalends missing at AD 425–431, and a further six kalends missing over AD 612–664, and proposes a restoration of these. From this is derived the synchronised chronology from them over AD 1–1590 based upon the chronological criteria of the Annals of Tigernach, Chronicum Scotorum, and the Annals of Ulster, Connacht, and Loch Cé. Over AD 1–1590 tokens of the annalistic entries are collated in parallel, sometimes comprehensively, at other times using sampling. A chronological survey of Michéal Ó Clérigh’s Annals of the Four Masters is presented demonstrating that its chronology is chaotic relative to all of the older annalistic sources, and for this reason it has not been included in the collation.
‘Collation of the Irish regnal canon’, the present edition online since 2005 at: www.scss.tcd.ie/misc/kronos/chronology/synchronisms/Edition_4/RC_trad/RC_collation.htm
Abstract. This article describes the ten principal witnesses to the regnal canon, namely the Laud synchronisms, chronological poems by Flann Mainistreach, Gilla Cóemáin and Gilla mo Dubda Ó Casaide, various editions of Lebor Gabála, Michéal Ó Clérigh’s Seanchas Riogh Ereann and Annala Rioghachta Eireann (alias Annals of the Four Masters), Seathrún Céitinn’s Foras Feasa ar Éirinn, and Ruaidhrí O’Flaherty’s Ogygia. It describes and provides a parallel collation of these regnal years for each reign, and discusses their significant correspondences and differences. Where possible it identifies the location chosen by each source for the year of the Incarnation.
This is the first book to
systematically survey the manuscripts of the Irish Annals, the unique mediaeval
Christian chronicles which were maintained in
Thomas M. Charles-Edwards The Chronicle of
‘Bede’s primary source for the Vulgate chronology in his chronicles in De temporibus and De temporum ratione’, in Immo Warntjes and Dáibhí Ó Cróinín (edd) Computus and its cultural context in the Latin West – Proceedings of the 1st International conference on the Science of Computus in Ireland and Europe, Galway, 14–16 July, 2006 (Brepols, Turnhout 2010), 159–89.
Abstract. Mommsen’s 1898 assumption that
Bede had compiled the Vulgate chronology of his chronicles in De temporibus (DT) and De temporum ratione (DTR) has been
simply reiterated by scholars ever since. But critical collation of Bede’s
chronicles with the Irish Annals leads to the conclusion that their common features,
including their Vulgate chronology, derive from a common source that originated
in a chronicle compiled by Rufinus of Aquileia †410. By the year 538 Rufinus’
chronicle was being continued in
Abstract. The presence in the manuscripts of early Christian
Ireland of sophisticated geometrical constructions, complex numerical
structures embedded within texts, and computistical works discussing the
different computations of the date of Easter, all attest to a refined interest
and capability in numbers and their uses in early Irish monasteries. The Latercus, compiled in circa 410 by
Sulpicius Severus in southern Gaul, is the earliest of these Paschal traditions
‘A facsimile edition of the Annals of Roscrea’, Bart Jaski & Daniel Mc Carthy available online at www.scss.tcd.ie/misc/kronos/editions/AR_portal.htm
Abstract. The Irish chronicle known to
modern scholarship as the ‘Annals of Roscrea’ is found only in the manuscript
Abstract. The Irish chronicle known to modern scholarship as the ‘Annals
of Roscrea’ is found only in the manuscript
This edition is based upon the online edition, ‘A facsimile edition of the Annals of Roscrea’, see above, and it was published in a limited edition of seventy-five copies with the generous assistance of the Roscrea People, Roscrea Heritage Society, and George Cunningham of Parkmore, Roscrea.
the arrival of the Latercus in
Abstract. The hypotheses published in 1733 by van der Hagen regarding
the supposed computistical parameters and Roman origin of the Latercus, the 84-year Paschal
tradition followed by the early Insular churches, and the alleged forged status
of Paschal tracts cited by Insular authors are profoundly mistaken when viewed
beside the evidence of the copy of the Latercus discovered by Dáibhí Ó Cróinín
in Padua MS I 27. Furthermore, the computistical features of this
‘Ruaidhrí Ó Casaide’s contribution to the Annals of Ulster’ in Seán Duffy (ed.) Princes, Prelates and Poets in Medieval Ireland - Essays in honour of Katharine Simms (Dublin: Four Courts Press, 2013), 444-59.
Abstract. Ruaidhrí Ó Casaide, †1541, a member of a Fermanagh medical family and vicar of Clogher, made three major scribal contributions to the compilatiion of the two principal manuscripts of the Annals of Ulster, Trinity College, Dublin, MS 1282 (MS H), and Oxford, Bodleian, Rawl. B. 489 (MS R). Namely, he wrote numerous marginal and interlinear additions to MS H, he wrote the years AD 1489–1504 in concluding folios 130r–143v of MS H, and he transcribed from MS H the years AD 431–952 in folios 1–32r of MS R. However, a comprehensive survey of the occurrence of Arabic numerals, alternative entries with contrasting chronology, and temporal emphatics such as ‘hoc anno’ and ‘in bliadhain-si’, discloses that Ó Casaide was also the editor of the exemplar used by Ó Luinín to write folios 12–130r of MS H. Consideration of the various temporal horizons in MS H and MS R shows that MS H was written by Ó Luinín and Ó Casaide between circa 1495–1505, while MS H was transcribed to MS R by Ó Casaide and Ó Luinín in circa 1505–7, and the entries were then continued by Ó Casaide until his death in 1541, the additional entries being written for him by twelve different amanuenses.
Abstract. A short essay reviewing the contributions of both Ruaidhrí Ó Casaide and Ruaidhrí Ó Luinín to the writing and compilation of the two principal manuscripts of the Annals of Ulster, namely Trinity College, Dublin, MS 1282 (MS H), and Oxford, Bodleian, Rawl. B. 489 (MS R). This shows that when transcribing MS H into MS R Ó Casaide introduced textual and orthographical changes to the entries. A summary account is also given of the publication of various editions of these annals, starting with Rev. Charles O’Connor in 1826, through to the edition of Seán Mac Airt and Gearóid Mac Niocaill in 1983.
‘The illustration and text on the Book of Kells folio 114rv’, Studies in Iconography 35 (2014), 1 38.
Abstract. This paper presents
the evidence that the illustration on folio 114r of the Book of Kells showing
two similar figures flanking Jesus, and supporting his arms, represents the
disciples James and John watching with him during his Agony in the
It is further shown that this is one of a number of instances in the Book of Kells where warmth is expressed towards John, and ambivalence towards Peter, an attitude found in the Paschal tract De ratione paschali which provided the authority to the early Insular churches for celebrating Easter on luna fourteen. Moreover, it is shown that on folio 32v Jesus is portrayed with the triangular Insular tonsure imposed. These heterodox identifications rule out as possible provenances for the Book of Kells all those Insular churches that had adopted the Paschal and tonsurial traditions followed by the Roman church, which rejected luna fourteen and prescribed the coronal tonsure. This effectively leaves only Kells, whose foundation is described in the Annals at 807 as ‘the new monastery of Colum Cille’, as the only plausible location for the compilation of the Book. The magnificence of the Book suggests that it was commissioned for the church of this new monastery at Kells, which was completed in 814.
book is a selection of the papers presented at the Fifth International Early
Railways conference in Carnarvon,
Abstract. An account of the horse-drawn tramway and funicular system constructed 1816–17 at the instigation of the Scottish engineer, John Rennie, to transport granite from the quarry at Dalkey, county Dublin, to face the piers for the harbour designed by Rennie at Dún Laoghaire, about two miles away. The tramway was very robustly designed and constructed, and continued in service until the middle of the nineteenth century.
‘The contribution of
This paper examines specifically the contributions of
‘The Chronology of Saint Columba's Life’, in Pádraic Moran & Immo
Warntjes (eds), Early Medieval
Abstract. Between Adomnán’s Vita Columbae and Bede’s account in his Historia Ecclesiastica, Saint Columba’s
life and missionary career are the best recorded of all early Irish ecclesiastics.
Further, and in great contrast to his fifth-century British missionary
predecessor, Saint Patrick, Columba’s chronology has not been the subject of
controversy in modern times. At least from the seventeenth century scholarship
has been almost unanimous that Columba died in 597, a date that derives from
Adomnán’s assertion that he died on Sunday, and that he left
Exposition. In 2013 the journal Early Medieval Europe published Roy Flechner’s article, ‘The Chronicle of Ireland: then and now’, in which he endorsed Kathleen Hughes’ 1972 hypothesis of a ‘Chronicle of Ireland’, and added a number of his own hypotheses. In this he found it necessary to reiterate and approve dismissive criticism of my own published analysis of the origin and evolution of the Irish Annals. As I considered that both Hughes’ and Flechner’s hypotheses rest upon mistaken assumptions and that I was entitled to a right of reply to his criticism, I submitted an article entitled ‘On reconstructing medieval Irish chronicles’ to Early Medieval Europe on 27 August, 2015. On 26 November, 2015, the Editors notified me by email that Reviewer 1 disputed my right of reply, with which view they concurred, and so they rejected my submission. Here is the link for the pdf of my submission of ‘On reconstructing medieval Irish chronicles’. A postscript is suffixed to this submission dated 6 July, 2016, which reproduces the Editors’ email, including the Reviewers’ ‘Comments to the Author’, so that scholars may judge the situation for themselves.
Abstract. Examination of Kathleen Hughes’ 1972 hypothesis of a ‘Chronicle of Ireland’ reveals that her primary assumption that the Annals of Ulster represent ‘the most complete version of the Irish annals’ was mistaken. This assumption has strongly influenced the understanding of early Irish annals by most subsequent scholarship. However, this article contends that the kalend and ferial structure of the Clonmacnoise group of annals embodies the earliest surviving witness to the early annals. The methodology of Roy Flechner’s recent analysis of the compilation, motivation, and classification of the ‘Chronicle of Ireland’ is also examined and found to be misjudged.
Exposition. This paper was submitted to the IEEE Annals of the History of Computing on 14 September 2016. On 31 October 2016 an email from the Chief Editor, Dr Nathan Ensmenger, included two reviews, the first recommending publication and the second recommending rejection. Dr Ensmenger concurred with the second reviewer so that the article was not published. Here is the link to a pdf of my submission Offprints_of_Ada_Lovelace’s_translation. In this pdf a postscript has been suffixed to the submission reproducing Dr Ensmenger’s email, including the two reviews, so that scholars may judge the situation for themselves.
This article examines textual and bibliographical aspects of Ada Lovelace’s
article translating and annotating Luigi Menabrea’s account of Charles
Babbage’s Analytical Engine, published in the Scientific Memoirs of 1843. Textually it concludes that the preface
to her translation, although apparently attributed to the ‘Editor’, was
actually compiled by Babbage himself, and in it he reviewed the history of both
his Difference Engine and Analytical Engine. However, as published the account
of the Analytical Engine is incomplete because the concluding section dealing
with Babbage’s conflict with the British Government was refused by the editor
of the Scientific Memoirs.
Consequently, Babbage published this concluding section soon afterwards in the Philosophical Magazine of 1843. For the
remainder of his life Babbage regarded this publication as his ‘defense’, and
he placed it first in his un-published ‘History of the Analytical Engine’.
Bibliographically it is shown that offprints of both publications circulated
amongst friends and contemporaries of both
‘Analysing and Restoring the Chronology of the Irish Annals’, in Ralph Kenna, Máirín MacCarron & Pádraig MacCarron (eds), Maths Meets Myths: Quantitative Approaches to Ancient Narratives, (Switzerland: Springer International Publishing, 2017), 177–194.
Abstract. Substantial annalistic chronicles of Irish affairs exist in a number of medieval versions, but they exhibit considerable variation both in the sequences of events and the chronological apparatus used to link each year to the Julian calendar. Of these, the Anno Domini years of the Annals of Ulster have been principally relied upon by historians. However, these are demonstrably incorrect from the seventh to the eleventh centuries. Moreover, its remaining chronological data of ferials and lunar epacts at the kalends of January, that is, the day of the week and the age of the moon on 1 January, are almost all interpolations by a later scribe. On the other hand, the Annals of Tigernach and the Chronicum Scotorum have only kalends and ferials marking the commencement of each year from the Incarnation up until the mid-seventh century. Because these kalends and ferials are susceptible to scribal miscopying they were dismissed by historians and textual scholars as “hopelessly confused”. However, analysis of the 28 year cycle of the ferials reveals that they possess a powerful error-correction property. Exploitation of this property has enabled the restoration of all the missing kalends and erroneous ferials of the Annals of Tigernach and Chronicum Scotorum, as well as of the closely related Annals of Roscrea, known collectively as the Clonmacnoise group. Using computer table structures, the kalends and ferials and events of these three have been synchronized with the Anno Domini years over the range AD 1–1178, and this tabulation, with cross-references to the other Irish medieval annals, has been made available online at www.irish-annals.cs.tcd.ie. In this chapter the process of analysis, correction, and synchronization is illustrated, taking the year of the death of St Patrick as an example.
‘Representations of tonsure in the Book of Kells’, Studia Celtica 51 (2017), 89–103.
Abstract Four Insular documents from the seventh and eighth centuries show that a major controversy took place amongst the Insular churches regarding the shape of the tonsure worn by clerics. Those who followed the customs of the Roman church wore a coronal tonsures, oval or circular in plan, while those belonging to some earlier Irish and British churches wore a delta tonsure, triangular in plan. This paper critically examines six figures in the Book of Kells proposed to have been illustrated with tonsures. Three of these at ff. 32v, 34r and 273r all show Jesus with the delta tonsure. The haloed figure above the second Canon table at f. 2v is likewise shown with the delta tonsure. On the other hand, the mounted figure at f. 255v is shown with a coronal tonsure and is explicitly coupled to the words ‘unum’ and ‘peccauerat’ of Luke 17:1 and 17:3 respectively. In Luke 17:1–3 Jesus censures all those who give cause for temptation to sin, saying it would be better that they were cast into the sea with a mill-stone about their neck. Consequently, by this graphic presentation of the coronal tonsure the compilers of Kells expressed their strong disapproval of it. A sixth figure at f. 182r proposed by James McIlwain in 2008 to be illustrated with the coronal tonsure is shown in fact to represent Pontius Pilate wearing an oval cap. Thus the five illustrations of tonsure in the Book of Kells represent a graphic polemic, exalting those who wore the delta tonsure, but directed against those who wore the Roman coronal tonsure.
‘The Paschal cycle of St Patrick’ in Immo Warntjes & Dáibhí Ó Cróinín (edd) Late Antique Calendrical Thought in the Early Middle Ages – Proceedings of the 3rd International Conference on the Science of Computus in Ireland and Europe – Galway, 16–18 July, 2010 (Brepols: Turnhout, 2017), 94–137.
Abstract. Notwithstanding the substantial corpus of early mediaeval
references to St Patrick and his works, the only account we have of a paschal
cycle associated with him is that provided by Cummian in his letter to Ségéne
of Iona and Bécán the hermit in c. AD
633. In this letter Cummian identified himself and his community with Patrick,
but he furnished only limited technical details for both Patrick’s cycle and
the cycle he indicated that he and his community had recently adopted. However,
critical examination of Cummian’s account shows that Patrick had adapted the
532-year paschal cycle compiled by Victorius of Aquitaine in AD 457, and that
this was the cycle that Cummian’s community and other influential southern
Irish churches had resolved to adopt at the synod of Mag Léne in c. AD 630.
Consequently, Cummian’s account of Patrick’s cycle, the earliest attested
reference to him, holds significant implications for both the chronology of
Patrick’s mission to
Abstract. This article gives an account for a
general audience of the two Irish annals employing the same sequencing
mechanism as the
Abstract. The ten major compilations of Irish
Annals collectively present thousands of entries from Creation to AD 1616.
These are preserved in manuscripts from the eleventh to the seventeenth
centuries and, with virtually no contemporaneous documentation on their
compilation, they pose a complex challenge to deduce their origin and
evolution. Mac Neill published the first hypothesis in 1913, and this was
further developed by O’Rahilly in 1946. In 1972 Hughes essentially reiterated
O’Rahilly’s hypothesis, entitling it the ‘Chronicle of Ireland’, which she envisaged
as a recompilation of earlier Irish regional annals in c. 913. Since then her hypothesis
has been endorsed and developed by other scholars from
‘The Council of Nicaea and the Celebration of the Christian Pasch’, in Kim, Young Richard (ed.), The Cambridge Companion to the Council of Nicaea, (Cambridge University Press: Cambridge, 2021), 177 – 201.
Abstract. In 525 Dionysius Exiguus in Rome compiled his 95-year continuation of the Alexandrian Paschal table and this table came eventually to schedule the celebration of Pasch for the entire western Church. In an accompanying letter Dionysius stated that the Council of Nicaea had authorized the 19-year cycle of Paschal full moons of the Alexandrian table, and that this cycle had been subsequently maintained by the Alexandrian bishops Athanasius († 373), Theophilus († 412), and Cyril († 444). These statements were accepted and reiterated for almost twelve centuries until 1718 when Johann Wilhelm Jan challenged them. Since then some scholars have endorsed Jan’s conclusion, while others have disputed the matter and insisted that some element of Nicaean authority indeed lies behind the Alexandrian Paschal table. This article re-examines the matter by first considering the Evangelistic authority for the celebration of Pasch and showing that while the Synoptic Gospels agree that the Crucifixion took place on the day after the Jewish Passover, John’s Gospel places it on the day of the Passover and hence on the fourteenth day of the spring moon. Thus there is serious chronological conflict inherent in the Evangelistic accounts of Jesus’ Crucifixion. At Nicaea the emperor Constantine sought to resolve this conflict and all the contemporaneous accounts agree that by a substantial majority the Council decreed that celebration of Pasch be allowed only on Sunday, and that celebration on the fourteenth day of the moon was to be rejected. There is no contemporaneous evidence that the Council’s decision went beyond this. Nevertheless, scholars who have believed that the Alexandrian Paschal table derived from Anatolius’ 19-year Paschal table compiled in the mid-third century have preferred to assume that an Alexandrian continuation of this cycle was in some way endorsed by the Council. However, this paper presents the argument that in fact the origin of the Alexandrian Paschal table lies rather with bishop Theophilus in the last decades of the fourth century, about sixty years after the Council of Nicaea. Consequently, Dionysius’ claim that Athanasius had maintained a 19-year cycle of Paschal moons authorized by the Council of Nicaea is unsustainable.
Page updated 31 March 2021