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Re: [Synoptic-L] the nature of the data

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  • Stephen C. Carlson
    ... Of course, it reveals the decisions of the editors about the relationship between the synoptic gospels. The main question, however, is whether and to what
    Message 1 of 27 , Dec 1, 2001
      At 08:31 AM 12/1/2001 +0000, Brian E. Wilson wrote:
      >The more I look at the HHB categorization the more I wonder whether
      >analysing the stats reveals the decisions of the editors of the
      >Concordance rather the relationship between the synoptic gospels.

      Of course, it reveals the decisions of the editors about the
      relationship between the synoptic gospels. The main question,
      however, is whether and to what extent the editors' judgment
      is biased to a particular solution to the synoptic problem.

      Stephen Carlson
      --
      Stephen C. Carlson mailto:scarlson@...
      Synoptic Problem Home Page http://www.mindspring.com/~scarlson/synopt/
      "Poetry speaks of aspirations, and songs chant the words." Shujing 2.35


      Synoptic-L Homepage: http://www.bham.ac.uk/theology/synoptic-l
      List Owner: Synoptic-L-Owner@...
    • Ron Price
      Dave, What surprises me about this whole discussion is that you have been trying to make sense of a set of results which represents a small proportion of the
      Message 2 of 27 , Dec 2, 2001
        Dave,
        What surprises me about this whole discussion is that you have been
        trying to make sense of a set of results which represents a small
        proportion of the published data, and apparently (unless I've missed
        something) without any attempt to check for overall consistency.
        Before attempting to explain individual positive and negative
        correlations, I would like to see a consistency check along the
        following lines.
        Divide the words up into three or four groups by first letter, e.g.
        A-D, E-K, L-P, R-W, then carry out the analysis on each group, then
        compare the correlations. Any disagreements among the correlations might
        suggest there is something wrong with the method or with our implicit
        generalization from a subset of the data. If they were all in agreement,
        then we really would feel obliged to try hard to explain them.
        If the whole alphabet is too much to tackle, carry out this procedure
        with a subset of the alphabet divided into groups.

        Ron Price

        Weston-on-Trent, Derby, UK

        e-mail: ron.price@...

        Web site: http://homepage.virgin.net/ron.price/index.htm

        Synoptic-L Homepage: http://www.bham.ac.uk/theology/synoptic-l
        List Owner: Synoptic-L-Owner@...
      • David Gentile
        Hello Ron, Thanks for the suggestion. I was planning to do exactly that, once I got the next batch of data entered. I m not sure how soon that will be. Dave
        Message 3 of 27 , Dec 2, 2001
          Hello Ron,

          Thanks for the suggestion. I was planning to do exactly that, once I got
          the next
          batch of data entered. I'm not sure how soon that will be.

          Dave Gentile
          Riverside, Illinois
          M.S. Physics
          PhD Management Science candidate


          > Dave,
          > What surprises me about this whole discussion is that you have been
          > trying to make sense of a set of results which represents a small
          > proportion of the published data, and apparently (unless I've missed
          > something) without any attempt to check for overall consistency.
          > Before attempting to explain individual positive and negative
          > correlations, I would like to see a consistency check along the
          > following lines.
          > Divide the words up into three or four groups by first letter, e.g.
          > A-D, E-K, L-P, R-W, then carry out the analysis on each group, then
          > compare the correlations. Any disagreements among the correlations might
          > suggest there is something wrong with the method or with our implicit
          > generalization from a subset of the data. If they were all in agreement,
          > then we really would feel obliged to try hard to explain them.
          > If the whole alphabet is too much to tackle, carry out this procedure
          > with a subset of the alphabet divided into groups.
          >
          > Ron Price
          >



          Synoptic-L Homepage: http://www.bham.ac.uk/theology/synoptic-l
          List Owner: Synoptic-L-Owner@...
        • Stephen C. Carlson
          ... In this regard, it occurs to me that the 95% level of assessing significance is far too generous. 95% implies that one in twenty may be wrong, but in our
          Message 4 of 27 , Dec 2, 2001
            At 10:43 AM 12/2/2001 +0000, Ron Price wrote:
            > What surprises me about this whole discussion is that you have been
            >trying to make sense of a set of results which represents a small
            >proportion of the published data, and apparently (unless I've missed
            >something) without any attempt to check for overall consistency.

            In this regard, it occurs to me that the 95% level of assessing
            significance is far too generous. 95% implies that one in twenty
            may be wrong, but in our data set we have 19 total sections (222
            through 002) for a total of 171 different pair-wise comparisons
            (19*18/2). If 1 in 20 is wrong (inherent in the 95% level), then
            about 9 of the "significant" correlations are really just to due
            to random chance.

            This is why in such analyses textbooks recommend using P < 0.05/C,
            which, in this case, works out to P < 0.0003. Thus, only those
            correlations at that level should be considered significant. And
            any attempts to build a theory should only be concerned with
            those correlations.

            Stephen Carlson
            --
            Stephen C. Carlson mailto:scarlson@...
            Synoptic Problem Home Page http://www.mindspring.com/~scarlson/synopt/
            "Poetry speaks of aspirations, and songs chant the words." Shujing 2.35


            Synoptic-L Homepage: http://www.bham.ac.uk/theology/synoptic-l
            List Owner: Synoptic-L-Owner@...
          • David Gentile
            Hello again, I agree 95% is very generous. I used that in reporting Delta because there was little data. With Alpha-Delta I reported 99%. (And lost one
            Message 5 of 27 , Dec 2, 2001
              Hello again,

              I agree 95% is very generous. I used that in reporting "Delta" because there
              was little data.
              With "Alpha-Delta" I reported 99%. (And lost one correlation that showed up
              in the "Delta-only" test.)

              I think P < 0.0003 might be a bit too restrictive at the moment. If I'm not
              mistaken, that would be what we want, if we want to be 95% sure that ALL of
              them are real.

              Actually, I'm looking at the confidence of each one in interpreting it. The
              most information is gained by reporting each one with its confidence level,
              then you know which ones to look at more closely. At 99% I expect 1 or 2 to
              be false, but probably only 1 since a lot are well above 99%. My candidate
              for that is 012 with 210.

              Most of the controversial ones were at high levels.
              222 - 202 > 99.99%
              200 - 202 > 99.99%
              122 - 112 > 99.9%

              Again, I'm glad you understand the results.

              Thanks,

              Dave Gentile
              Riverside, Illinois
              M.S. Physics
              PhD Management Science candidate

              -------------------------------------------------------------------------
              "When you have eliminated the impossible,
              whatever remains, however improbable, must be the truth."
              - Sherlock Holmes,
              in The Sign of Four, by Sir Arthur Conan Doyle.

              "Why sometimes I've believed as many as
              six impossible things before breakfast."
              - The Red Queen,
              in Through the Looking Glass, by Lewis Carroll

              ----- Original Message -----
              From: "Stephen C. Carlson" <scarlson@...>
              To: "Synoptic-L" <Synoptic-L@...>
              Sent: Sunday, December 02, 2001 9:29 AM
              Subject: Re: [Synoptic-L] Some numerical results


              > At 10:43 AM 12/2/2001 +0000, Ron Price wrote:
              > > What surprises me about this whole discussion is that you have been
              > >trying to make sense of a set of results which represents a small
              > >proportion of the published data, and apparently (unless I've missed
              > >something) without any attempt to check for overall consistency.
              >
              > In this regard, it occurs to me that the 95% level of assessing
              > significance is far too generous. 95% implies that one in twenty
              > may be wrong, but in our data set we have 19 total sections (222
              > through 002) for a total of 171 different pair-wise comparisons
              > (19*18/2). If 1 in 20 is wrong (inherent in the 95% level), then
              > about 9 of the "significant" correlations are really just to due
              > to random chance.
              >
              > This is why in such analyses textbooks recommend using P < 0.05/C,
              > which, in this case, works out to P < 0.0003. Thus, only those
              > correlations at that level should be considered significant. And
              > any attempts to build a theory should only be concerned with
              > those correlations.
              >
              > Stephen Carlson
              > --
              > Stephen C. Carlson mailto:scarlson@...
              > Synoptic Problem Home Page http://www.mindspring.com/~scarlson/synopt/
              > "Poetry speaks of aspirations, and songs chant the words." Shujing 2.35
              >
              >
              > Synoptic-L Homepage: http://www.bham.ac.uk/theology/synoptic-l
              > List Owner: Synoptic-L-Owner@...


              Synoptic-L Homepage: http://www.bham.ac.uk/theology/synoptic-l
              List Owner: Synoptic-L-Owner@...
            • Brian E. Wilson
              Brian Wilson wrote -- ... Stephen Carlson replied -- ... Stephen, But the aim of the game is to discover the relationship between the synoptic gospels, not the
              Message 6 of 27 , Dec 2, 2001
                Brian Wilson wrote --
                >
                >The more I look at the HHB categorization the more I wonder whether
                >analysing the stats reveals the decisions of the editors of the
                >Concordance rather than the relationship between the synoptic gospels.
                >
                Stephen Carlson replied --
                >
                >Of course, it reveals the decisions of the editors about the
                >relationship between the synoptic gospels.
                >
                Stephen,
                But the aim of the game is to discover the relationship between
                the synoptic gospels, not the editors' decisions.

                I would suggest that a computer could be programmed to categorize every
                word of the synoptic gospels into 222, 221, 220, and so on, without
                assuming the Two Document Hypothesis (as do the editors of the HHB
                Concordance), or any other supposed documentary relationship between the
                synoptic gospels. The program might be designed first to search for
                strings of words in one synoptic gospel containing at least a stated
                number of words (or word-roots) in the same order as strings of words of
                the same size in another synoptic gospel. This could be extended to find
                similarities of wording in the same order in all three synoptic gospels
                within stated parameters. The program would establish triple parallel,
                double parallel, and Sondergut pieces of material. The size of each unit
                of triple, double, or special, could be, say, at least 8 word-roots in
                the same order, though of course a triple, double or special could be
                longer than this minimum. Whatever minimum size is laid down would be
                arbitrary, but at least the procedure using it would be independent of
                any assumed documentary hypothesis. On this basis, the categorization
                into 222, 221, 220 and so on could be carried out without making any
                assumptions of the documentary relationship between the synoptic
                gospels. 222 would represent a word-root present in each synoptic gospel
                in a computer-generated triple parallel, and so on. This would give
                "clean data", to use Dave Gentile's terminology. It would produce
                results that would not be dependent on the decisions of the editors of
                the HHB Concordance. I think that ideally this is where the analysis
                might have started.
                >
                >The main question, however, is whether and to what extent the editors'
                >judgment is biased to a particular solution to the synoptic problem.
                >
                I agree. That is one question I have been asking. The other question I
                have been raising is to what extent the editors' have applied their
                criteria inconsistently.

                What is really needed is computer-produced data that is not dependent on
                any synoptic documentary hypothesis and that applies criteria
                consistently. The HHB Concordance does not provide such data.

                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@...
              • Stephen C. Carlson
                ... If you (or anyone else) could produce such a computer program, I d be very impressed. However, one cannot even identify a parallel without supposing some
                Message 7 of 27 , Dec 2, 2001
                  At 06:07 PM 12/2/2001 +0000, Brian E. Wilson wrote:
                  >I would suggest that a computer could be programmed to categorize every
                  >word of the synoptic gospels into 222, 221, 220, and so on, without
                  >assuming the Two Document Hypothesis (as do the editors of the HHB
                  >Concordance), or any other supposed documentary relationship between the
                  >synoptic gospels.

                  If you (or anyone else) could produce such a computer program,
                  I'd be very impressed. However, one cannot even identify a parallel
                  without supposing some documentary relationship between the synoptic
                  gospels. For example, the decision to identify Mark's healing of
                  the paralytic as a parallel to Matthew's healing of the paralytic --
                  but not to Matthew's genealogy -- supposes that there is a documentary
                  relationship with the former but not the latter. Of course, most
                  decisions about parallelization will not be controversial, but
                  they will be for not only for the so-called Mark-Q overlap texts and
                  for doublets in one gospel where there is only one instance in the
                  others (which of the two in the doublet is "the" parallel?). Even
                  in noncontroversial parallels, there is discretion in deciding which
                  of two KAIs in Mark correspond to the one KAI in Matthew. Frankly,
                  I doubt it can be done objectively, because the theories and hypotheses
                  we hold influence our perception of the data. This extends to the
                  programmer of the computer as well.

                  >>The main question, however, is whether and to what extent the editors'
                  >>judgment is biased to a particular solution to the synoptic problem.
                  >>
                  >I agree. That is one question I have been asking. The other question I
                  >have been raising is to what extent the editors' have applied their
                  >criteria inconsistently.

                  The editors admit their bias on the Mark-Q overlaps, but does that
                  bias extend to other portions? You've pointed out some inconsistencies,
                  but unless one can show they somehow favor the 2ST, it may be better
                  to attribute the inconsistencies to noise rather than bias.

                  >What is really needed is computer-produced data that is not dependent on
                  >any synoptic documentary hypothesis and that applies criteria
                  >consistently.

                  I'm not holding my breath. Perhaps a better approach is to ask
                  the proponents of the various solutions to produce their own
                  "partisan" synopses and concordances that sets forth the data
                  in such a manner that renders their solution in the most favorable
                  light. Then we can compare them to see how well they handle the
                  data. Maybe Dungan was right after all that there is no neutral
                  synopsis.

                  Stephen Carlson
                  --
                  Stephen C. Carlson mailto:scarlson@...
                  Synoptic Problem Home Page http://www.mindspring.com/~scarlson/synopt/
                  "Poetry speaks of aspirations, and songs chant the words." Shujing 2.35


                  Synoptic-L Homepage: http://www.bham.ac.uk/theology/synoptic-l
                  List Owner: Synoptic-L-Owner@...
                • Brian E. Wilson
                  Brian Wilson wrote -- ... Stephen Carlson replied -- ... Stephen, I do not understand your argument here. The occurrence of parallels between Mark s healing of
                  Message 8 of 27 , Dec 3, 2001
                    Brian Wilson wrote --
                    >
                    >I would suggest that a computer could be programmed to categorize every
                    >word of the synoptic gospels into 222, 221, 220, and so on, without
                    >assuming the Two Document Hypothesis (as do the editors of the HHB
                    >Concordance), or any other supposed documentary relationship between
                    >the synoptic gospels. The program might be designed first to search for
                    >strings of words in one synoptic gospel containing at least a stated
                    >number of words (or word-roots) in the same order as strings of words
                    >of the same size in another synoptic gospel. This could be extended to
                    >find similarities of wording in the same order in all three synoptic
                    >gospels within stated parameters. The program would establish triple
                    >parallel, double parallel, and Sondergut pieces of material. The size
                    >of each unit of triple, double, or special, could be, say, at least 8
                    >word-roots in the same order, though of course a triple, double or
                    >special could be longer than this minimum. Whatever minimum size is
                    >laid down would be arbitrary, but at least the procedure using it would
                    >be independent of any assumed documentary hypothesis. On this basis,
                    >the categorization into 222, 221, 220 and so on could be carried out
                    >without making any assumptions of the documentary relationship between
                    >the synoptic gospels. 222 would represent a word-root present in each
                    >synoptic gospel in a computer-generated triple parallel, and so on.
                    >
                    Stephen Carlson replied --
                    >
                    >If you (or anyone else) could produce such a computer program,
                    >I'd be very impressed. However, one cannot even identify a parallel
                    >without supposing some documentary relationship between the synoptic
                    >gospels. For example, the decision to identify Mark's healing of
                    >the paralytic as a parallel to Matthew's healing of the paralytic --
                    >but not to Matthew's genealogy -- supposes that there is a documentary
                    >relationship with the former but not the latter.
                    >
                    Stephen,
                    I do not understand your argument here. The occurrence of
                    parallels between Mark's healing of the paralytic and Matthew's healing
                    of the paralytic but not between Matthew's healing of the paralytic and
                    his Genealogy, is precisely the sort of result such a computer program
                    would produce without assuming a documentary hypothesis such as the 2DH,
                    FH or GH. There are many instances of strings of, say, no more than 20
                    words in the Markan healing that contain at least 8 word-roots the same,
                    and in the same order, in a string of no more than 20 words in the
                    Matthean healing. On the other hand, there is no string of no more than
                    20 words in the Matthaean healing that contains at least 8 word-roots
                    the same and in the same order in a corresponding string of no more than
                    20 words in the Genealogy in Matthew. The criterion would establish that
                    the two healing stories include parallels in the sense of having many
                    word roots the same and in the same order within strings of specified
                    lengths, but that the Matthaean healing and the Genealogy in Matthew do
                    not include parallels in this sense. It would be easy to set up a
                    computer program to show this.

                    Indeed, we could carry out such a check by hand, without using a
                    computer program to spot parallels. I have just done this. There are no
                    pairs of strings that meet the criteria above between the healing of the
                    paralytic in Mt and the Genealogy in Mt. However, the following string
                    of 20 words is found in the Matthaean healing of the paralytic --

                    KAI IDWN O IHSOUJ THN PISTIN AUTWN EIPEN TW PARALUTIKW QARSEI TEKNON
                    AFIENTAI SOU AI AMARTIAI KAI IDOU TINEJ TWN

                    And it has 17 word roots the same and in the same order as the string of
                    words in the Markan healing of the paralytic --

                    KAI IDWN O IHSOUJ THN PISTIN AUTWN LEGEI TW PARALUTIKW TEKNON AFI/ENTAI
                    SOU AI AMARTIAI HSAN DE TINEJ TWN

                    Similarly, in the same two passages, the following are pairs of strings,
                    one string from each passage, of no more than 20 words each such that in
                    each pair there are at least 8 word roots the same and in the same order
                    as in a string of no more than 20 words the same and in the same order
                    in the other member of the pair --

                    EN TAIJ KARDIAIJ UMWN TI GAR ESTIN EUKOPWTERON EIPEIN AFIENTAI SOU AI
                    AMARTIAI H EIPEIN EGEIRE KAI

                    EN TAIJ KARDIAIJ UMWN TI ESTIN EUKOPWTERON EIPEI=N TW PARALUTIKW
                    AFI/ENTAI SOU AI AMARTIAI H EIPEIN EGEIRE KAI

                    ===

                    PERIPATEI INA DE EIDHTE OTI ECOUSIAN EXEI O UIOJ TOU ANQRWPOU EPI THJ
                    GHJ AFIENAI AMARTIAJ TOTE LEGEI TW PARALUTIKW

                    PERIPATEI INA DE EIDHTE OTI ECOUSIAN EXEI O UIOJ TOU ANQRWPOU AFIENAI
                    AMARTIAJ EPI THJ GHJ LEGEI TW PARALUTIKW

                    ===

                    EGERQEIJ ARON SOU THN KLINHN KAI UPAGE EIJ TON OIKON SOU KAI EGERQEIJ

                    EGEIRE ARON TON KRABATTON SOU KAI UPAGE EIJ TON OIKON SOU KAI HGERQH

                    ===

                    Each of these strings is a pair of parallels between Mt and Mk, and many
                    words within these strings (after doing the same sort of comparison with
                    Lk) could be categorized 220, 221, and so on. These are by no means all
                    the parallels of this type that can be listed. These parallels, and
                    others, between Mt and Mk could have been spotted by a computer
                    systematically comparing every string of 20 words in Mt with every
                    string of 20 words in Mk, and looking for at least 8 word-roots the same
                    and in the same order in each pair of strings compared.

                    The point is that it is totally unnecessary to assume a synoptic
                    documentary hypothesis such as the 2DH, FH or GH, to establish that two
                    pieces of material, one in Mt and the other in Mk, are parallels, or
                    that two pieces of material in Mt are not parallels.

                    You also wrote --
                    >
                    >Maybe Dungan was right after all that there is no neutral synopsis.
                    >
                    I am sure he was right. The HHB Concordance, however, is not a synopsis,
                    and the question is whether such a Concordance can be produced without
                    assuming a documentary hypothesis such as the 2DH, FH or GH. The answer
                    is that it can.

                    In the same way, a colour-coded text showing similarities of wording
                    between the synoptic gospels, like W. R. Farmer's SYNOPTICON, is not a
                    synopsis. Such a colour-coded text of the synoptic gospels can be
                    constructed without assuming any particular solution to the synoptic
                    problem, and without using any synopsis.

                    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@...
                  • Emmanuel Fritsch
                    ... I see some different biases in an automatic process : - Brian pointed out that a gospel may be selected, and the priority of this gospel (typicallly :
                    Message 9 of 27 , Dec 4, 2001
                      "Stephen C. Carlson" wrote :
                      >
                      > Brian E. Wilson wrote:
                      > >I would suggest that a computer could be programmed to categorize every
                      > >word of the synoptic gospels into 222, 221, 220, and so on, without
                      > >assuming the Two Document Hypothesis (as do the editors of the HHB
                      > >Concordance), or any other supposed documentary relationship between the
                      > >synoptic gospels.
                      >
                      > If you (or anyone else) could produce such a computer program,
                      > I'd be very impressed. However, one cannot even identify a parallel
                      > without supposing some documentary relationship between the synoptic
                      > gospels. [...] Even
                      > in noncontroversial parallels, there is discretion in deciding which
                      > of two KAIs in Mark correspond to the one KAI in Matthew. Frankly,
                      > I doubt it can be done objectively, because the theories and hypotheses
                      > we hold influence our perception of the data. This extends to the
                      > programmer of the computer as well.

                      I see some different biases in an automatic process :
                      - Brian pointed out that a gospel may be selected, and the priority
                      of this gospel (typicallly : Mark) is assumed, biasing the result.
                      In fact, in the treatment, the input gospels should be processed
                      with equity.
                      - Even if synoptic gospels are processed in equity, some a priori
                      may influence the result. I mean particularly to the pattern
                      of redaction process that will be seen as most probable : a
                      first small document that is step by step increased, or a large
                      first document that as been cut toward our gospel. the balance
                      between deletion and completion in synoptic process is a global
                      a priori in synoptic study.
                      - Then, an automatic process would hardly integrate all the other
                      information, particularly the links between Luke and John.


                      > >What is really needed is computer-produced data that is not dependent on
                      > >any synoptic documentary hypothesis and that applies criteria
                      > >consistently.
                      >
                      > I'm not holding my breath. Perhaps a better approach is to ask
                      > the proponents of the various solutions to produce their own
                      > "partisan" synopses and concordances that sets forth the data
                      > in such a manner that renders their solution in the most favorable
                      > light. Then we can compare them to see how well they handle the
                      > data. Maybe Dungan was right after all that there is no neutral
                      > synopsis.

                      Are there any referenced biases in Boismard's Synopse ?
                      Do you know about a comparison of different existing synopses ?

                      a+
                      manu

                      Synoptic-L Homepage: http://www.bham.ac.uk/theology/synoptic-l
                      List Owner: Synoptic-L-Owner@...
                    • David Inglis
                      ... Dave, did you actually mean: why does 221 look like both 121 and 211, but 122 look only like 121 and not 112 , or have I actually got the wrong data? In
                      Message 10 of 27 , Dec 19, 2001
                        Way back on Dec 1 Dave Gentile wrote:

                        > But perhaps the real question is, why does
                        > 122 look like both 121 and 112, but 221 look only like 121 and not 211?

                        Dave, did you actually mean: "why does 221 look like both 121 and 211, but
                        122 look only like 121 and not 112", or have I actually got the wrong data?
                        In any case, have you decided why?

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



                        Synoptic-L Homepage: http://www.bham.ac.uk/theology/synoptic-l
                        List Owner: Synoptic-L-Owner@...
                      • David Gentile
                        Hi Dave, The case reversed itself with more data. It was 121 - 122 now its 121 - 221 . These appear to be redactor effects / chance , they vanish in the macro
                        Message 11 of 27 , Dec 20, 2001
                          Hi Dave,

                          The case reversed itself with more data. It was 121 - 122 now its 121 - 221
                          . These appear to be redactor effects / chance , they vanish in the macro
                          categories.

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

                          ----- Original Message -----
                          From: "David Inglis" <david@...>
                          To: <Synoptic-L@...>
                          Sent: Thursday, December 20, 2001 12:54 AM
                          Subject: Re: [Synoptic-L] Some numerical results


                          > Way back on Dec 1 Dave Gentile wrote:
                          >
                          > > But perhaps the real question is, why does
                          > > 122 look like both 121 and 112, but 221 look only like 121 and not 211?
                          >
                          > Dave, did you actually mean: "why does 221 look like both 121 and 211, but
                          > 122 look only like 121 and not 112", or have I actually got the wrong
                          data?
                          > In any case, have you decided why?
                          >
                          > Dave Inglis



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