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    Re: Benetnasch and Alkaid revisited
    From: Bill B
    Date: 2005 Apr 5, 17:17 -0500

    Peter
    
    Some I know would argue they were little more than bank vaults for the
    ancients work.  That being said, I have no argument to make either way.
    
    The following, found while researching the international date line,
    indicates some progress under their watch.
    
    Bill
    
    The circumnavigator?s paradox
    
    What appears to be the earliest reference to the circumnavigator?s paradox
    is found in the works of the Syrian prince and geographer-historian Isma?il
    ibn ?Ali ibn Mahmud ibn Muhammad ibn Taqi ad-Din ?Umar ibn Shahanshah ibn
    Ayyub al Malik al Mu?ayyad ?Imad ad-Din Abu ?l-Fida (1273 - 1331). In his
    Taqwin al-Buldan (?The ??? of the Lands?), Abu ?l-Fida described how a
    traveller, depending on his dircetion of travel, would either lose or gain a
    day at the completion of his circumnavigation [Rudolf Wolf, Handbuch der
    Astronomie, Ihrer Geschichte und Literatur (Zurich, 1890), vol 1, pp.
    465-466; I still have to check the original source].
    
    Another early reference to the circumnavigator?s paradox is found in the
    works of the French scholar Nicole Oresme (c. 1325 - 1382). In his Traiti?
    de l?espere (which was also translated into Latin as the Tractatus sperae),
    Oresme presented a "remarkable circling of the Earth" by two imaginary
    travellers Jehan and Pierre (Johannes and Petrus in the Latin version) who
    set out to journey around the world along the equator in opposite directions
    at a speed of 30 degrees of longitude per 24-hour day. Jehan, travelling in
    a westward direction, would claim at the completion of his journey that it
    took him only eleven days and nights while Pierre, travelling in an eastward
    direction, maintained that it lasted thirteen days and nights. A third man,
    Robert, who had remained at the starting point, would however point out that
    only twelve days and nights had elapsed since both travellers had set out.
    
    Oresme repeated this argument in his Quaestiones supra speram, a series of
    clarifications of questions based on the popular cosmographical treatise De
    sphaera by Sacrobosco, in which he renamed his travellers Plato and Socrates
    and the ?control? Petrus and allowed both travellers a more leasurely pace
    of 14.4 degrees of longitude per 24-hour day. At the return of the
    philosophers at the starting point, Plato (the westward traveller) would
    have logged twenty-four days, Socrates (the eastward traveller) no less than
    twenty-six days, while Petrus saw the sun rise and set only twenty-five
    times.
    
    Around 1377 Oresme wrote his Traiti? du ciel et du monde, a French
    translation and commentary of Aristotle?s De caelo et mundo, in which he
    again discussed the circumnavigator?s paradox. Here the westward traveller
    is simply named A, the eastward traveller B and the control C. Each of both
    travellers is now assumed to cover 40 degrees of longitude per 24-hour day;
    A counting eight days for his circumnavigation, B ten days, while C only
    marks nine days on his calendar.
    
    In order to resolve the circumnavigator?s paradox for future travellers,
    Oresme concluded his discussion of the imaginary journeys of Plato and
    Socrates in the Quaestiones supra speram with the observation:
    
    "From this it follows that if this [equatorial] zone were everywhere
    habitable, one ought to assign a definite place where a change of the name
    of the day would be made, for otherwise Socrates would have two names for
    the same day and the other [Plato] would have the same name for two days."
    
    
    
    > Why do we have so many stars with Arabic names?
    >
    > Astronomy may be the oldest science, but most knowledge gets lost. While the
    > lights of scientific knowledge were burning particularly dim, during the
    > European dark ages, things were rather different in the Arabic world. Islam
    > had quickly established a vast empire of many very different peoples and
    > cultures that were administered with a rare tolerance and humanity. Schools
    > were established in places as far apart as Spain and Samarqand (central
    > Asia) that specialized in astronomy and mathematics and drew students and
    > scholars from afar. Many were Jewish, some were Christian. Their knowledge
    > base was Arabic and Greek and Babylonian, their lasting contribution was
    > bringing it together and expanding upon it. When the European scientific
    > world stirred from a long sleep during the reformation, the legacy of these
    > schools was a principal source of knowledge that, for example, the
    > Portuguese and Spanish drew upon to build up a new science of scientific
    > navigation.
    
    
    

       
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