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Jesus the Mathematician

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  • Jan Sammer
    My interest in the mathematical issue involved in the Mk 8:17-21, which I have raised on this list several times over the years, was sparked by a fragmentary
    Message 1 of 39 , Mar 28, 2002
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      My interest in the mathematical issue involved in the Mk 8:17-21, which I
      have raised on this list several times over the years, was sparked by a
      fragmentary manuscript by the late Livio C. Stecchini, an authority in
      historical metrology, that I came across in 1980 when examining the
      Stecchini archive. I hope list members will bear with me if I begin by
      quoting the introductory paragraphs from this manuscript, as an introduction
      to a series of posts in which I would like to present the findings from my
      metrological researches on the two types of volumetric units mentioned in
      the narrative of the feedings.

      begin Stecchini quote ----------------------------------------

      "They Have Eyes and Do Not See"

      In the history of man there is no piece of writing on which more
      commentaries have been compiled than the gospels. Many of these commentaries
      are intended to explain or analyze the gospels not only verse by verse, but
      sentence by sentence. One could say more than this, namely, that there is
      not a single word in the gospels that has not been elucidated, interpreted,
      defined, translated, collated, compared, and construed, both in terms of
      literal and of figurative meaning. Nevertheless, there is a specific group
      of statements in the gospels that through the centuries have been passed
      over in silence. We shall see that these statements do not deal with a minor
      issue, but relate to the very core of the message that the gospels are
      intended to convey.

      This astonishing fact came to my attention by incident, if not by accident.
      Since the study of the history of measures has been a steady concern of mine
      through all my adult life, there came a day when in the gradual unfolding of
      my investigation I undertook to canvass the evidence provided by the New
      Testament. I began by using a concordance in order to make a list of all
      verses that contain technical terms relating to measurement. So I came to
      the word kophinos, which in the Greek of the New Testament refers to a
      special kind of basket. In all cultures of the ancient world the amount of
      grain (which was the essential element of nutrition) consumed in a day was a
      fixed unit of measure (called choinix in Greece), as there was a fixed unit
      for the monthly quantity (basically the talent). The contents of this unit
      varied somewhat according to the system of measures used in the particular
      area and in the particular period of time and was adjusted by fixed rules
      according to the kind of grain used as bread stuff. Among the Jews the
      matter of the container for the daily ration of grain food presented
      specific aspects because, at least in the period around the beginning of our
      era, in order to conform with the rules for ritual cleanliness, they carried
      around their daily supply of bread in a special wicker-work container called
      kophinos in the Greek of the New Testament.

      The term kophinos is given prominence in two famous episodes of Jesus' life,
      the so-called Feeding of the Five Thousand and the so-called Feeding of the
      Four Thousand. According to the narrative of the gospels, an essential point
      in these two miracles of multiplication of breads is that, at the end of the
      first multiplication and consequent feeding of the crowd, there were left
      twelve kophinoi of crumbs, whereas at the end of the similar second
      multiplication and feeding there remained seven baskets of a different type,
      called the spyris. Therefore I asked myself the question why such figures
      should occur and what was their meaning according to the mathematics of
      measurement. I consulted all the standard authoritative commentaries without
      finding a single explanation, comment, or even mention of the figures. This
      alerted my attention by suggesting that some problem existed; hence, my
      search through the commentaries became more systematic. No human being could
      claim that he has consulted all of the existing commentaries on these two
      episodes of the gospels, since a life would not afford adequate time; but I
      have scoured the libraries of some of the best endowed divinity schools, and
      I can also add that I have almost half a century of experience in making
      rapid and effective use of the resources of information provided by
      libraries: but the result has been zero. I have not found one work which
      dealt in any way with the figures of these miracles. Commentaries which are
      intended to explain the Gospels line by line suddenly skip over entire
      verses when they come to the miracles of the multiplication of bread and
      fish. I wish my readers better luck than I have had in finding a commentator
      who does not forget to expound this episode of Jesus' teaching.

      Not only the gospels, but Paul's letters, make clear that the multiplication
      of bread is fundamental to the Christian faith: it is the foundation of the
      Eucharist. The gospels make clear also that the multiplication of breads was
      a turning point in Jesus' career: it is at that moment that crowds begin to
      address him as king and from that moment that the march on Jerusalem and the
      passion become inevitable.

      Mark not only reports two multiplications of breads, but includes a third
      event in which Jesus refers to the two multiplications and compares the
      figures in each of them.

      Mark 8:16-21
      And they were arguing among themselves about having no bread. Knowing what
      was in their minds, he said to them, "Why do you argue about having no
      bread? Have you no inkling yet? Do you still not understand? Have your
      brains turned into stone? You have eyes and do not see. You have ears and do
      not hear. Have you forgotten? When I broke the five loaves for the five
      thousand, how many kophinoi full of crumbs did you pick up?" "Twelve," they
      said. "And when I broke the seven loaves for the four thousand, how many
      spyrides full of crumbs did you pick up ?" They answered, "Seven." And he
      said: "Do you still not understand?"

      Any person who reads the text can recognize that the figures are the
      essential point of the accounts. The wording of the gospels could not have
      been more explicit in conveying that here we have come to the crux of Jesus'
      message, to the foundations of the New Kingdom. But the readers of the
      gospels kept their minds closed. They have eyes but do not see; they have
      ears but do not hear, as Jesus said, quoting Isaiah.

      Ever since the feedings, the followers of Jesus have reenacted the event
      daily by partaking of the Eucharist, but they tell us that the Eucharist is
      a mystery, which is to say that they refuse to answer the question that
      Jesus posed to his disciples.

      end Stecchini quote--------------------

      The end of the manuscript is missing, and I do not know how exactly
      Stecchini derived his own solution, which was "The analysis by Jesus of the
      metrology of the two miracles of the multiplication of breads has the
      purpose of pointing out that whether the bread was made of barley or of
      wheat, he had given the corresponding right measure." Although I do not
      consider this solution as being correct, Stecchini's statement of the
      problem launched my own search for a metrological solution. My library
      researches were not quite as fruitless as Stecchini's. I found that numerous
      commentators do discuss the figures, but almost always assign them a
      symbolic value of some kind. In other words, they do not understand them as
      quantities of given units, but rather as symbols. Most often the twelve
      kophinoi are understood to represent the twelve apostles and the seven
      spyrides the seven deacons. In my study I rule out all such allegorical
      explanations a priori and consider the issue purely in terms of the
      information presented by Mark: the given numbers of containers and their
      respective volumes.

      Jan

      Jan Sammer
      sammer@...
      Prague, Czech Republic
    • Jan Sammer
      From: ... ideas of ... Homer ... the ... Of course the imagery of a ruler as shepherd is one that could occur independently in any
      Message 39 of 39 , Apr 10, 2002
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        From: <LeeEdgarTyler@...>


        TonyBuglass@... writes:

        >
        >> Jan - why is it so unlikely? Both ancient Greece and ancient Israel were
        > >agricultural societies; both had sheep; both had shepherds who care for
        > >their sheep. Is it impossible that both independently developed similar
        ideas of
        > pastoral care by the appropriate divinity from such an obvious everyday
        > >picture?
        >
        > >The problem with sophistication - sometimes it obscures the simple and
        > >obvious! Or does that mean I'm being unsophisticated and thick, like the
        > >disciples Mark portrays...? <G>
        >
        >> Cheers,
        >> Rev Tony Buglass
        > >Pickering Methodist Circuit
        >
        >

        >I meant to post this earlier, but it got lost in the midterm shuffle:
        Homer
        >frequently calls Agamemnon the "shepherd" (poimĂȘn) of the Greeks, and
        >Sophocles uses the term "shepherd of the people" for several different
        >leaders. Pindar and Aeschylus use it to denote a master. And of course
        the
        >term Jerome employs to translate poimĂȘn is "pastor."

        >So there's no doubt that the Greeks had, independently of the Hebrews,
        >developed this metaphorical use of the term "shepherd." I have found no
        >cases in which it is applied to a deity, however; although one of Pindar's
        >odes has a preternatural connotation to it in its use of "shepherds of the
        >Loves" for the sprites attending Aphrodite.

        >best,

        >Ed Tyler

        Of course the imagery of a ruler as shepherd is one that could occur
        independently in any pastoral society. That is the imagery used by Homer and
        other poets; it is also imagery alluded to in Plato's dialogue, The
        Statesman; but there the imagery is developed in a peculiar way that goes
        way beyond a simple allegory of the ruler as the shepherd of his people.
        Plato indeed argues that the statesman should be the shepherd of his people,
        but to justify this proposition he refers back to a myth, narrated by the
        Eleatic Stranger, in which the rulers of the present age are but imperfect
        stand-ins for the true shepherd who had the human flock in his charge in a
        former age. In the present age the divine shepherd's role is emulated,
        albeit imperfectly, by human rulers. In a future age the divine shepherd
        will return to resume control over the human flock. It is this apocalyptic
        myth that I had in mind when I referred to the uncanny correspondence
        between the myth of the Statesman and Hebrew traditions and expectations.

        In the Hebrew tradition as it developed particularly in post-Exilic times,
        there was an age in which man, created out of the earth, lived in a garden,
        needing no clothes, feeding on the fruit that its trees produced by
        themselves. Only after being expelled from the garden did man start having
        to till the soil and produce his own sustenance. He also became mortal,
        began to marry and beget children.

        There was also an age to come, (according to the Markan Jesus) in which a
        men and women will not marry but will live like angels. They will be
        nurtured directly by their divine shepherd. This expectation goes back to
        Isaiah and Ezekiel ("I will set up one Shepherd over them, and He shall feed
        them").

        In the Statesman the Stranger from Elea describes the once and future age of
        divine control as follows: "Over every herd of living creatures throughout
        all their tribes was set a heavenly daemon to be its shepherd. Each of them
        was all in all ot his flock--providing for the needs of all his charges....
        a god was their shepherd and had charge of them and fed them.. When God was
        shepherd there were no political constitutions and no taking of wives and
        begetting of children. For all men rose up anew into life our of the
        earth...they had fruits without stint from trees and bushes; these needed no
        cultivation but sprang up of themselves out of the ground without man's
        toil. For the most part they disported themsleves in the open needing
        neither clothing nor couch, for the seasons were blended evenly so as to
        work them no hurt, and the grass which sprang out of the earth in abundance
        made a soft bed for them."

        In between the former and future age of divine control is the present age in
        which the divinity has left the world to its own devices. But there will
        come a day when the divine shepherd will once more take charge of his flock.

        The feedings of the multitudes are premonitions of this future age. Mark
        indicates this in 6:34: "... he saw this large crowd and his heart was
        filled with pity for them, because they looked like sheep without a
        shepherd." Jesus then proceeds to feed them, proving himself to be their
        shepherd, the sustainer of humanity in the age to come. It is this that the
        disciples are taken to task for failing to understand, though Peter's
        testimony on the road to Caesarea Philippi shows that he has figured it out.
        The ability of Jesus to feed the multitudes is the key to his true identity
        as the divine shepherd of the age to come.

        This idea is almost identical with the idea of the Statesman. It is the
        image of the shepherd as the divine sustainer of humanity in the age to come
        that is so distinctive of the Hebrew tradition and of the Statesman, and
        which raises questions as to whether such concepts could have arisen
        independently of one another. I am currently looking at the possibility that
        both concepts go back to Zoroastrian ideas.

        Regards,

        Jan

        Jan Sammer
        sammer@...
        Prague, Czech Republic
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