BOOKREVIEW: The Easter Calculator of the Strasbourg clock

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  1. Fortunat Mueller-Maerki

    Fortunat Mueller-Maerki Registered User
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    BOOKREVIEW by Denis Roegel
    roegel@loria.fr
    Posted with permission of the reviewer


    Joseph Flores, Denis Kleinknecht, Marc Augereau:

    Le comput ecclésiastique de Frédéric Klinghammer,


    Besançon: AFAHA (Association Française des Amateurs d'Horlogerie Ancienne),
    2007, 160 pages and a CD with a 58 minutes movie. 40 euros, shipping
    included to France. Order at AFAHA, BP 33, 25012 Besançon, France, phone:
    (33)3 81 82 26 74. 1700 copies printed, including 1300 offered
    to the AFAHA members.



    The Strasbourg cathedral houses one of the most famous, perhaps even the most famous, astronomical clock in the world. The current clock, which is
    actually the third, was designed by Jean-Baptiste Schwilgué (1776-1856)
    and built from 1838 to 1843. It improved the previous clock from the
    16th century in every possible way, be it on astronomical matters with
    for instance intricate mechanisms for obtaining the real positions
    of the Sun and the Moon, or on calendrical matters with what was
    probably the first perpetual and mechanical Church calendar able to
    compute automatically the date of Easter Sunday.

    Easter has been following an apparently simple rule for almost
    2000 years, namely that Easter is defined as the Sunday following
    the first full moon in the Spring, starting on March 21. If for
    instance there is a full moon on March 26 and this is a Wednesday,
    Easter will take place on March 30. Now, since the motion
    of the Moon is very complex, approximations of its motion have
    been used since the dawn of time. The moon alluded to in the definition
    of Easter is therefore not the real astronomical moon, but some
    approximation which tries to follow the real moon as best as it can,
    but without making things too complex, and in such a way that
    Easter becomes predictible.

    Before 1582, when the Julian calendar was still effective,
    Easter was following a simple pattern, and repeating itself
    after 532 years. The Julian calendar, however, was somewhat defective,
    and it is well known that the Julian year being slightly too long
    with respect to the tropical year (the year of the seasons),
    the error accumulated and amounted to about 10 days in 1582.
    The calendar was modified under Pope Gregory XIII and in addition
    to dropping 10 days, the reform also made the Gregorian year slightly shorter
    than the Julian one, by removing three days out of 400 years:
    years such as 1700, 1800, 1900, which would have been leap years
    in the Julian calendar, were no longer so in the Gregorian calendar.
    This was the most obvious change introduced by the Gregorian
    reform, but there was another change, that went by almost unnoticed,
    and it concerned the cycles of the Moon. In the Julian calendar,
    the approximation used for the Moon was based on the Golden Number,
    a lunar cycle of 19 years known for more than 2000 years. Incidentally,
    the word ``Golden Number'' is much more recent than the cycle itself.

    In the Gregorian calendar, the cycle of the Moon was made more accurate
    and based on the calculation of the Epact, which is approximately
    the age of the Moon (the number of days since last new Moon)
    on December 31st of the previous year. In 2008, for instance,
    the Epact is 22, and this means that there was approximately
    a new moon on December 9, 2007. An examination of ephemerides
    shows that there was indeed one on that day, but there might
    have been a difference of up to two days between the real
    astronomical moon and the ecclesiastical moon.

    Computing Easter is not very difficult using tables, but there are
    a number of tricky issues, like those of the secular leap years,
    and a special case for the Epact 25. One can for instance
    compute the dominical letter (a letter from A to G specifying where
    are the Sundays in the year), and then the Epact. The latter, sometimes
    aided by the Golden Number, provides the position of the first
    full moon of Spring. It is then straightforward to find Easter, by hand,
    that is. But the complexity of the calculation is apparent when
    one considers that the cycle of Easter is now no longer a mere 532 years,
    but 5700000 years!

    The first known mechanization of the Gregorian Easter calculation,
    the so-called ``computus paschalis,'' seems to have been that of
    Jean-Baptiste Schwilgué in 1821, after an idea that first
    occurred to him in 1816. Schwilgué built a small model which was
    able to compute the Solar Cycle (a cycle of 28 years in the Julian
    Calendar), the Dominical Letter, the Epact, the Golden Number,
    the Roman Indiction (a cycle of 15 years unrelated to Easter),
    and finally Easter Sunday, for any year in the Gregorian calendar.
    20 years later, Schwilgué built this mechanism, with only few
    modifications except size, into the Strasbourg astronomical clock.
    The computus is triggered by the clock on New Year's Eve, and
    after a few minutes, it sets Easter (and the associated feasts
    such as Passion Sunday, Pentecost, etc.) on a nearby calendar dial.

    Schwilgué's prototype was unfortunately stolen around 1945 and
    has not been recovered since. In the 1970s, however,
    Frédéric Klinghammer (1908-2006), a former employee of the Ungerer company that used to take care of the Strasbourg clock, and who was instrumental in the construction of the great astronomical clock in Messina (1933), built a new replica of Schwilgué's computus.
    Klinghammer's computus was recently restored by Joseph Flores,
    from the French AFAHA group, and he, together with Denis Kleinknecht
    and Marc Augereau, describe this model in the book which we are
    reviewing.

    We will say little on the mechanism itself, because it would
    obviously take a long time to explain all its details. Flores's
    book is 160 pages long, but still leaves a number of questions
    unanswered. Our purpose, in this review, is not so much to describe
    the computus, than the book on the computus. The computus itself
    is a marvelous little jewel. There is unfortunately scarce
    information in English on how it works, but the most complete
    published sources on the Strasbourg clock so far are the books
    by Alfred and Théodore Ungerer ``L'horloge astronomique
    de la cathédrale de Strasbourg'' (1922) and by
    Henri Bach and Jean-Pierre Rieb ``Les trois horloges astronomiques
    de la cathédrale de Strasbourg'' (1992). The latter was also published
    in German. There is a small booklet written by Théodore
    Ungerer, which has been published in English, and gives
    a technical overview of the clock, including its computus. To my knowledge,
    there isn't anything else.

    Flores's book is a very welcome addition, and I must stress right
    away that even if you don't read French, interest in the Strasbourg
    clock alone makes this a necessary buy. You won't regret it.
    Flores gives a first hand overview of the structure of the computus,
    and the included CD (by Denis Kleinknecht)
    shows you how it works in practice. You can follow
    several year changes and analyze the motion of all the parts
    by slow motion. Although the accompanying text is read in French,
    I believe the images are mostly self sufficient.

    If the book had been perfect, I would probably stop here, and wish
    you a happy reading. Alas, reading the book has left me with very
    mixed feelings. First, the book is obviously concentrating
    too much on the structure of the computus, and is not, in my
    opinion, enough pedagogical. Understanding such a mechanism
    makes it necessary to have first a good understanding of the
    Gregorian calendar, which few readers will have, at least as far
    as the lunar part is concerned. The book contains indeed an introduction
    to the Gregorian calendar, by Denis Kleinknecht, but this introduction
    is more of an appendix than an introduction, and is certainly
    not well interleaved with the study of the mechanism itself, although
    Flores refers here or there to Kleinknecht's part. It is possible
    to understand how the computus works using this book, but the reader
    will have to do a lot of back and forths from Flores's part,
    to Kleinknecht's, and to the CD. How many readers will really complete
    this mission is not clear. Probably not that many!

    The book is supplemented with an appendix by Marc Augereau
    computing various gear ratios, but this part can be totally skipped.
    It is badly typeset, contains mostly irrelevant material
    that seems to have landed here just because this author
    was asked to compute all possible ratios. Actually, only a few of
    the calculations are needed, but they are hidden in a jungle
    of formulae that are not well explained, and probably inscrutable
    for most readers, besides containing a number of typos.
    The main text doesn't make use of Augereau's part at all.

    It would have been nice to find some historical material on
    the mechanical side of things. One wonders, for instance, what other clocks
    have had a computus, before or after Schwilgué's clock, but
    Flores has unfortunately done no historical research at all.
    He therefore does not even seem to know that there are two
    related mechanisms only a few miles from where he lives and
    examined the computus, next to the Swiss border. Such oversights
    are surprising for someone who got a Gaïa prize in the
    historical category. Nor does Flores offer much
    information on the development of Klinghammer's computus itself,
    and he fails to notice that the computus was at some point
    modified, as for instance the examination of the pictures
    published in the 1992 book by Bach and Rieb shows.
    Lack of historical research also leads Flores to attribute
    some features to Klinghammer, when they were actually
    already present in Schwilgué's model.

    Many other problems could be mentionned, among them the rather
    surprising fact that Flores alone appears on the front cover,
    when he basically only dismantled and described the computus,
    but did no historical research, whereas Denis Kleinknecht
    researched on the Gregorian calendar and made the accompanying CD.

    But what I have come to regret most is the too AFAHA-oriented
    documentation. This is a book which was written for the AFAHA members
    and they are probably happy with it. However, when someone has the
    privilege of being able to dismantle and document such a rare
    mechanism, knowing that not many people will have that opportunity,
    I believe there is a duty towards the scientific community,
    which far extends a group such as the AFAHA. Now, how could these
    two aims have been reconciled? The scope of the current book
    could have been kept as it is, provided the author made for instance
    clear that all historical research were to appear elsewhere, as well
    as all details that could not fit in the current work. Among
    the missing details, for instance, are those of the two weight-engines.
    The number of teeth are never given, although some of them can be
    obtained or guessed from the pictures. Why they were not given is
    a mystery, and it would have helped for a more complete comparison
    with Schwilgué's computus. A companion volume, written by Flores,
    or by someone else, should have been planed simultaneously,
    and it could have contained, in a more archivistic manner,
    all the things that would perhaps have bored the casual reader.
    I have for instance in mind the kind of documentation which
    was made in the 1980s by Ludwig Oechslin for the clock of Bernardo
    Facini, or more recently for the clock by Johann Wolfgang Hartich (2007).
    In both cases, Oechslin shows every part in isolation, on graph paper.
    No such thing was made by Flores, at least not in his book.

    Scientific rigor is no waste of time, and it should be the aim
    of every author, whether the author writes for children or
    for scholars. An author should always state why he writes this,
    what are his sources, or, perhaps, state why he doesn't give them.
    He should not be oblivious of his duties towards the scientific
    community, and keep an open mind. An author should not write
    only for him, not write only for his group, he should write for
    all, or start some kind of collaboration to make this possible.
    None of this was attempted by Mr. Flores, and the book eventually
    appears very amateurish. It reminds me of what Anthony Turner
    and Emmanuel Poulle wrote on Baillie, Lloyd, and Ward's ``The Planetarium
    of Giovanni de Dondi'' (1974) which published the translation of
    a 14th century manuscript, but as a collage of several translations
    and drawings coming from at least three different sources,
    the translations being accompanied by no critical commentary and
    being practically useless, at least at the time of publication.
    Poulle wrote that this book made public the amateurism of
    the team that produced it, and turned to their confusion.
    In some way, this is what now happens with Mr. Flores.

    Denis Roegel, January 23, 2008.

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