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[Synoptic-L] average linkage cluster analysis

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  • Brian E. Wilson
    Brian Wilson wrote -- ... David Gentile replied -- ... Dave, Above, I have wrongly shown the category 121 twice, and omitted 102. The second 121 (in finger 5)
    Message 1 of 9 , Jan 3, 2002
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      Brian Wilson wrote --
      >
      >David Gentile (some time ago) posted the graph of the result of applying
      >the TREE Procedure. It shows six fingers representing six clusters of
      >correlations. The categories (types) associated with each finger are --
      >
      >(1) 222 (also X22, 22X)
      >(2) 220, 221 (also X20, 2X0)
      >(3) 121, 120, 020 (also X21, 12X)
      >(4) 202, 201, 200 (also X02, 20X)
      >(5) 122, 121, 112, 002 (also X12)
      >(6) 211, 210 (also 21X)
      >
      David Gentile replied --
      >
      >Why is 102 in the same "finger" as 200 and 201?
      >
      Dave,
      Above, I have wrongly shown the category 121 twice, and omitted
      102. The second 121 (in finger 5) should have read "102". Sorry about
      that. I have looked carefully at the graph, and in fact 102 is in finger
      5 because it is in line with the column of dots which is closest to
      finger 5 and furthest from finger 4. It is therefore not in the same
      finger as 200 and 201. The corrected version of the above is--
      >
      >(1) 222 (also X22, 22X)
      >(2) 220, 221 (also X20, 2X0)
      >(3) 020, 120, 121 (also X21, 12X)
      >(4) 200, 201, 202 (also X02, 20X)
      >(5) 002, 102, 112, 122 (also X12)
      >(6) 210, 211 (also 21X)
      >
      These can be easily explained on the basis of the new approach, that is
      by assuming that the "same words" indicate that one synoptist has
      redacted the source material, and that "different words" indicate that
      different synoptists have redacted --
      >
      >(1) represents the wording that remains after Mk, Mt and Lk have all
      >redacted the same source material.
      >(2) represents what remains after Mk and Mt, but not Lk, have redacted
      >source material.
      >(3) represents the wording left after Mk, but neither Mt nor Lk, have
      >redacted.
      >(4) represents the remaining wording after Mt and Lk, but not Mk, have
      >both redacted.
      >(5) represents the remaining wording after Lk and Mk, but not Mt, have
      >redacted the wording.
      >(6) represents the wording left after Mt, but neither Mk nor Lk, have
      >redacted.
      >
      Summarizing --
      (1) Mk + Mt + Lk
      (2) Mk + Mt - Lk
      (3) Mk - Mt - Lk
      (4) Mt + Lk - Mk
      (5) Mk + Lk - Mt
      (6) Mt - Mk - Lk

      I would suggest that the TREE Procedure therefore produces results that
      make very good sense on the hypothesis that if different types of
      material show a significant positive correlation, this is consistent
      with the same synoptist having been the redactor, whereas if two
      different types show a significant negative correlation, this is
      consistent with different synoptists having been the redactors.

      Comments would be welcome.

      Best wishes,
      BRIAN WILSON

      >HOMEPAGE http://www.twonh.demon.co.uk/

      Rev B.E.Wilson,10 York Close,Godmanchester,Huntingdon,Cambs,PE29 2EB,UK
      > "What can be said at all can be said clearly; and whereof one cannot
      > speak thereof one must be silent." Ludwig Wittgenstein, "Tractatus".
      _


      Synoptic-L Homepage: http://www.bham.ac.uk/theology/synoptic-l
      List Owner: Synoptic-L-Owner@...
    • dgentil@sears.com
      Hello Brian, Assuming you are looking at this graph linked below, then you re not reading it correctly. The height of the column between the categories
      Message 2 of 9 , Jan 3, 2002
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        Hello Brian,

        Assuming you are looking at this graph linked below, then you're not
        reading it correctly.
        The height of the column between the categories indicates the "strength" of
        their linkage.

        http://groups.yahoo.com/group/synoptic-l/message/7127

        102 is linked more with the 201 group than the "Luke" group.

        The cluster history above the graph gives the order it connects the groups.

        Dave Gentile
        Riverside, Illinois
        M.S. Physics
        Ph.D. management Science candidate








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      • Brian E. Wilson
        Dave Gentile wrote -- ... Dave, Thanks for this. I was reading the graph in Escher reverse . I was seeing it as a black hand with fingers pointing downwards
        Message 3 of 9 , Jan 4, 2002
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          Dave Gentile wrote --
          >
          >Assuming you are looking at this graph linked below, then you're not
          >reading it correctly. 102 is linked more with the 201 group than the
          >"Luke" group.
          >
          Dave,
          Thanks for this. I was reading the graph in "Escher reverse". I was
          seeing it as a black hand with fingers pointing downwards from the axis
          at the top. It has now "flipped" Escher-style, so that I see instead a
          neat histogram with white bars pointing upwards towards the axis.

          Yes. I now agree. I see that 102 belongs to what I call cluster 4.
          However, I would suggest the cluster is not Lukan since it contains two
          non-Lukan Matthean but only one non-Matthean Lukan non-macro categories.
          My re-revised interpretation of this fascinating graph is --

          >
          >(1) 222 (also X22, 22X)
          >(2) 221, 220 (also X20, 2X0)
          >(3) 121. 120, 020 (also X21, 12X)
          >(4) 202, 201, 200, 102 (also X02, 20X)
          >(5) 122, 112, 002 (also X12)
          >(6) 211, 210 (also 21X)
          >
          These can be easily explained on the basis of the new approach, that is
          by assuming that the "same words" indicate that one synoptist has
          redacted the source material, and that "different words" indicate that
          different synoptists have redacted --

          (1) represents the wording that all three synoptists, Mk, Mt and Lk,
          retain after redacting the same source material.
          (2) represents what Mk and Mt retain but Luke does not retain, after
          redacting their common source material.
          (3) represents the wording Mk retains but Mt and Lk do not retain, after
          redacting their common source material.
          (4) represents the wording that either Mt or Lk (or both) retain, but Mk
          does not retain, after redacting their common source material.
          (5) represents the wording Lk retains, but Mt does not, after redacting
          their common source material.
          (6) represents the wording Mt retains, but neither Mk nor Lk retain,
          after they have redacted their common source material.

          Note that the remaining categories are 021, 022, 212, 012.

          Could (6) have also contained 212, so becoming 212, 211, 210 (it is
          designated as with 21X)? And could there have been a (7) consisting of
          022, 021, 012?

          Summarizing (where "W"" means "without 2") --
          (1) 222
          (2) 22W
          (3) W2W
          (4) 2WW + WW2
          (5) WW2
          (6) 2WW
          (7) (2W2 + WW2)??

          I would suggest that the TREE Procedure therefore produces results that
          make very good sense on the hypothesis that if different types of
          material show a significant positive correlation, this is consistent
          with the same synoptist having been the redactor, whereas if two
          different types show a significant negative correlation, this is
          consistent with different synoptists having been the redactors.

          Comments would be welcome.

          Best wishes,
          BRIAN WILSON

          >HOMEPAGE http://www.twonh.demon.co.uk/

          Rev B.E.Wilson,10 York Close,Godmanchester,Huntingdon,Cambs,PE29 2EB,UK
          > "What can be said at all can be said clearly; and whereof one cannot
          > speak thereof one must be silent." Ludwig Wittgenstein, "Tractatus".
          _

          Synoptic-L Homepage: http://www.bham.ac.uk/theology/synoptic-l
          List Owner: Synoptic-L-Owner@...
        • David Inglis
          Brian Wilson wrote: [snip] ... [snip] ... Brian, I completely fail to follow your logic. Cluster (4) includes 202, which can only have been created in one of
          Message 4 of 9 , Jan 6, 2002
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            Brian Wilson wrote:

            [snip]
            > Yes. I now agree. I see that 102 belongs to what I call cluster 4.
            > However, I would suggest the cluster is not Lukan since it contains two
            > non-Lukan Matthean but only one non-Matthean Lukan non-macro categories.
            > My re-revised interpretation of this fascinating graph is --
            >
            > >
            > >(1) 222 (also X22, 22X)
            > >(2) 221, 220 (also X20, 2X0)
            > >(3) 121. 120, 020 (also X21, 12X)
            > >(4) 202, 201, 200, 102 (also X02, 20X)
            > >(5) 122, 112, 002 (also X12)
            > >(6) 211, 210 (also 21X)
            > >
            > These can be easily explained on the basis of the new approach, that is
            > by assuming that the "same words" indicate that one synoptist has
            > redacted the source material, and that "different words" indicate that
            > different synoptists have redacted --
            [snip]
            > (4) represents the wording that either Mt or Lk (or both) retain, but Mk
            > does not retain, after redacting their common source material.

            Brian,

            I completely fail to follow your logic. Cluster (4) includes 202, which can
            only have been created in one of the following ways:

            1 Matthew and Luke copied these identical portions of text from a common
            source (e.g. the LT)
            2 Matthew created the text, which Luke then copied from Matthew
            3 Luke created the text, which Matthew then copied from Luke

            Note that in my case (1) it is IMPOSSIBLE by definition for either Matthew
            or Luke to have 'redacted' this source, since if they did then the text
            would no longer be the same as the other copy, and hence it couldn't be in
            202. In other words, the bits that Matthew redacts become 201, and the bits
            Luke redacts become 102. Therefore it is IMPOSSIBLE for 202 to contain text
            redacted by both Matthew and Luke.

            So, if the 201-202 positive is explained by Matthew redacting 202, then your
            explanation of the 202-102 positive is false because Luke didn't redact 202.
            Conversely, if Luke redacted 202 then your explanation of the 202-201
            positive is false. In other words, your hypothesis cannot explain both the
            202-102 and 202-201 positives at the same time, and is therefore falsified
            as it stands.

            Dave Inglis
            david@...
            3538 O'Connor Drive
            Lafayette, CA, USA




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          • Brian E. Wilson
            Brian Wilson wrote -- ... Dave Inglis replied -- ... Dave, Your argument cannot be valid, since the following shows that what you say is impossible could have
            Message 5 of 9 , Jan 6, 2002
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              Brian Wilson wrote --
              >
              >[snip]
              >Yes. I now agree. I see that 102 belongs to what I call cluster 4.
              >However, I would suggest the cluster is not Lukan since it contains two
              >non-Lukan Matthean but only one non-Matthean Lukan non-macro
              >categories.
              >My re-revised interpretation of this fascinating graph is --
              >
              >(1) 222 (also X22, 22X)
              >(2) 221, 220 (also X20, 2X0)
              >(3) 121. 120, 020 (also X21, 12X)
              >(4) 202, 201, 200, 102 (also X02, 20X)
              >(5) 122, 112, 002 (also X12)
              >(6) 211, 210 (also 21X)
              >
              >These can be easily explained on the basis of the new approach, that is
              >by assuming that the "same words" indicate that one synoptist has
              >redacted the source material, and that "different words" indicate that
              >different synoptists have redacted --
              >[snip]
              >(4) represents the wording that either Mt or Lk (or both) retain, but
              >>Mk does not retain, after redacting their common source material.
              >
              Dave Inglis replied --
              >
              >I completely fail to follow your logic. Cluster (4) includes 202,
              >which can only have been created in one of the following ways:
              >
              >1 Matthew and Luke copied these identical portions of text from a
              >common source (e.g. the LT)
              >2 Matthew created the text, which Luke then copied from Matthew
              >3 Luke created the text, which Matthew then copied from Luke
              >
              >Note that in my case (1) it is IMPOSSIBLE by definition for either
              >Matthew or Luke to have 'redacted' this source, since if they did then
              >the text would no longer be the same as the other copy, and hence it
              >couldn't be in 202. In other words, the bits that Matthew redacts
              >become 201, and the bits Luke redacts become 102. Therefore it is
              >IMPOSSIBLE for 202 to contain text redacted by both Matthew and Luke.
              >
              Dave,
              Your argument cannot be valid, since the following shows that what
              you say is impossible could have happened --

              Matthew LT Luke


              HEY DIDDLE DIDDLE, HEY DIDDLE DIDDLE, HEY DIDDLE DIDDLE,
              THE CAT AND THE THE CAT AND THE THE CAT AND THE
              FIDDLE. AND THE FIDDLE. AND THE FIDDLE.
              THE COW JUMPED THE COW JUMPED THE COW JUMPED
              OVER THE MOON. OVER THE MOON. OVER THE MOON.
              And the little dog And the little dog And the dish ran
              laughed to see such laughed to see such away with the spoon.
              fun. fun,
              And the dish ran
              away with the spoon.


              Matthew has redacted LT, retaining some, but omitting other LT words.
              Luke has also redacted LT, also retaining some, but omitting other LT
              words. We see that 202 material (shown in upper case letters) is formed
              as a result of Mt and Lk having independently redacted LT. This shows
              that it is perfectly possible for LT wording to have been redacted
              independently by both Nt and Lk to produce 202 words that are the same
              in both Mt and Lk. I think the mistake in your argument is in the
              statement --
              >
              >1 Matthew and Luke copied these identical portions of text from a
              >common source (e.g. the LT)
              >
              What you should have written was that Matthew and Luke used the same
              piece of material from the common source (e.g. the LT) with the result
              that *some* of the words they each copied were the same so producing 202
              words in their gospels. On the LTH, each synoptist **edited** the
              wording of the material he selected from the LT. The agreements in
              wording between synoptists are where independently they retained the
              same words of the LT material they selected and edited.
              >
              >So, if the 201-202 positive is explained by Matthew redacting 202,
              >then your explanation of the 202-102 positive is false because Luke
              >didn't redact 202.
              >
              I have just shown that it is perfectly possible that Matthew and Luke
              did redact the same LT material to produce 202 passages so that this,
              and the rest of your argument, collapses.

              By the way, if your argument had been valid, then the Two Document
              Hypothesis would have been sunk without trace, since in your case 1, the
              common source could have been Q as posited by the 2DH!

              Best wishes,
              BRIAN WILSON

              >HOMEPAGE http://www.twonh.demon.co.uk/

              Rev B.E.Wilson,10 York Close,Godmanchester,Huntingdon,Cambs,PE29 2EB,UK
              > "What can be said at all can be said clearly; and whereof one cannot
              > speak thereof one must be silent." Ludwig Wittgenstein, "Tractatus".
              _

              Synoptic-L Homepage: http://www.bham.ac.uk/theology/synoptic-l
              List Owner: Synoptic-L-Owner@...
            • dgentil@sears.com
              Brian Wilson asked: ======== Could (6) have also contained 212, so becoming 212, 211, 210 (it is designated as with 21X)? And could there have been a (7)
              Message 6 of 9 , Jan 8, 2002
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                Brian Wilson asked:
                ========
                Could (6) have also contained 212, so becoming 212, 211, 210 (it is
                designated as with 21X)? And could there have been a (7) consisting of
                022, 021, 012?
                =======

                Because of he low amount of data in these categories, they all form thier
                own cluster if they are included.
                These are called "outliers" in cluster analysis.

                Dave




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                Subject: [Synoptic-L] average linkage cluster analysis


                Dave Gentile wrote --
                >
                >Assuming you are looking at this graph linked below, then you're not
                >reading it correctly. 102 is linked more with the 201 group than the
                >"Luke" group.
                >
                Dave,
                Thanks for this. I was reading the graph in "Escher reverse". I was
                seeing it as a black hand with fingers




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                List Owner: Synoptic-L-Owner@...
              • David Inglis
                ... In the full results 212 does now show some signs of clustering with 211 and 210, but only with low confidence. 022, 021, and 012 are all very clearly in
                Message 7 of 9 , Jan 9, 2002
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                  > Brian Wilson asked:
                  > ========
                  > Could (6) have also contained 212, so becoming 212, 211, 210 (it is
                  > designated as with 21X)? And could there have been a (7) consisting of
                  > 022, 021, 012?
                  > =======
                  >
                  In the full results 212 does now show some signs of clustering with 211 and
                  210, but only with low confidence.
                  022, 021, and 012 are all very clearly in seperate groupings (022-220-222,
                  021-120-121-221, and 012-002-112)

                  Dave Inglis
                  david@...
                  3538 O'Connor Drive
                  Lafayette, CA, USA




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