Henry Sadovsky and I have both been suggesting that some simple statistical studies be done as tests of the hypotheses before us. I've done a very small one, and present the results here.

The only group of "internal elems" that I considered is the ones that are defined by visually obvious lines (or chains of not-too-separated motifs)extending across most or all the way from one side border to the other. This makes their identification pretty unambiguous, so anyone repeating the same study will probably get the same results. It also allows me to identify the feature almost a a glance when it is present, and is obvious in photos.

My source of rugs for the study is Atlantic Collections. I did not include any pieces that lack side borders (i.e., striped designs like kyzyl juvals or Shahsavan bagfaces); these would simply confound the results. Likewise, I did not include Turkmen ensis, which are compartmented and would also confuse more than enlighten.

I found 8 examples in the book. The data I collected are the positions of the centers of the horizontal lines expressed as a percentage of the distance from the lower to the upper edge of the field. Here are the results;

Plate 34 = 19%
Plate 42 = 32%
Plate 43 = 66%
Plate 61 = 68%
Plate 69 = 18%
Plate 104 = 18%
Plate 264 = 40%
Plate 305 = 2% (one line) and 51% (second line)

There is nothing in this to support the notion that the kind of "internal elem" included here occurs a one specific spot, although the fact that none of the 8 specimens had such a feature in the upper 30% may be significant. Obviously, this is a small sample and, equally obviously, it applies to only one category of the phenomena before us. But it certainly provides no evidence supporting the notion that it is a manifestation of a practice of putting such things in the lower part of a rug, usually in the same place.

I don't want to overinterpret this, but I would encourage anyone with the time and energy to define some kind of easily recognizable "internal elem" and get more data.

Regards,

Steve Price

Even playing by your rather restrictive ground rules, a very cursory glance through a section of the book also shows 266. 299, 300, and 306 with very clearly articulated lines in the bottom half.

Regards, Yon

Ther reason I used fairly restrictive rules was to make the process objective rather than subjective. I will look at the additional examples you mention when I get home tonight; my intention was not to arbitrarily include or exclude any at all. I evidently miscalculated the position on Plate 43; I apologize and stand corrected. I used what I thought were unambiguous criteria and posted the results in detail (rather than in summary) precisely so they could be reviewed by others and modified if need be. I did no formal statistical analysis because the sample is so small (9 internal elem demarcations on 8 rugs) that unless the results were pretty dramatic (they aren't) there would be little to gain from doing one.

As for the ratio of 6.5 to 1 for lines appearing in the lower half versus the upper half, I offer two comments:
1. It has been asserted repeatedly that the hypothesis is supported by the appearance of the demarcation at precisely the same place. Up to now, that precise place has been anywhere in the lower one-third of the rug. I expressed the opinion that I didn't think that was very precise, while allowing as how someone else might think differently. Since I don't think the lower third is a very precise location, I don't think the lower half is a precise location. I guess it really depends on what meaning we attach to the word "precise".
2. The convention in biological sciences is that a probability below 95% is considered to be within chance levels. For things that are really important - that have serious consequences to being incorrect - it is curtomary to demand 99% and, often, 99.9% or more as demonstrating truth. The ratio of 6.5 to 1 translates into an 87% occurrence in the lower half, a 13% occurrence in the upper half.
3. I stress that this little study applies to only one of what I believe to be a number of subcategories of the phenomenon we have been addressing, and has no bearing whatsoever on the still unknown distribution of other subcategories.

Regards,

Steve Price

To be as precise as possible, please consider whethre the following might work as potential criteria or catagories:

1.) The internal elem must appear in the bottom third of the rug. Quantify all such rugs separately within the sample. Divide all rugs matching as below.

2.) Separate matching rugs by design into three subgroups. Repeating designs, central medallions and other.

3.) In rugs with a repeat design differentiate between rugs in which an elem appears at or just above the second row of major/minor motifs and those where it appears higher, but within the bottom third. Quantify both sums.

4.) In rugs with a central medallion differentiate between rugs where it appears at or just above the second major repeated border element and those where it appears higher but within the bottom third. Quantify both sums.

5.) In rugs with other designs record as in 4.

6.) Record separately rugs in each group where an elem appears in the bottom third but at or below the first row of design motifs.

7.) Record separately rugs in which there is a possible marker but where that same marker also appears elsewhere in the rug.

Markers include color changes, unique design elements, inversion, distortion, points and anything else that tends to create or demarcate the upper perimeter line of the rectangle.

Subject to your thoughts and refinements.

Best, Michael

I'll need a little time to digest the list, but I believe that the more categories there are, and the more specific they are, the more likely it is that any underlying generalities will be revealed.

One point about including within the definition of the phenomenon that the demarcation occurs in the lower third of the rug. It would require that the argument that it often occurs in a precise spot (usually defined as anywhere in the lower third of the rug) be abandoned. That is, you can't say "We will only consider it real if it is within the lower third of the rug", and then say "Look! It only occurs in the lower thirds of the rugs!".

I see no great loss in defining the phenomenon as you suggest, since I don't think "anywhere in the lower third" is restricted enough to warrant being called precise, but Yon may see things differently.

Regards,

Steve Price

After a little more rumination, I suggest a much less ambiguous definition of "markers". Your suggestion is Markers include color changes, unique design elements, inversion, distortion, points and anything else that tends to create or demarcate the upper perimeter line of the rectangle. I think people will be able to debate whether individual rugs have such markers forever, and in the absence of some definition that allows different people to identify it whether they want to or not, no conclusions will be possible.

I realize that making the marker definition unambiguous means leaving lots of specimens outside the realm of investigation. On the other hand, if the definitions are ambiguous there is no way any investigation can give persuasive results. Just look at the very simple study I used as the opener for this thread. I set up what I thought was an unambiguous definition for the marker, and found it occurring 9 times (in 8 rugs) in the book I used as my rugs database. Yon, using nominally the same criterion, finds another 4 rugs in the same book! I can't really comment on those until I get home and see what they look like, but I'm sure Yon didn't just invent the claim that they exist.

Defining the phenomenon unambiguously is the key to testing every hypothesis about it. That principle isn't unique to the "internal elem", by the way.

Regards,

Steve Price

Regards, Yon

There is no question that the results of my little survey are consistent with a claim that most examples occur in the lower half of the rug. But you have repeatedly used phrases like "exact" and "precise" location. I've just gone through a bunch of the threads and am horrified by the number of messages that are gone (I've contacted the software developer for fixes to this problem), but did find an earlier post you put up that says,

...I had made it clear in my introduction that I used 'internal elem' purely as a label for any irregularity occurring about one fourth to one third of the way up from the bottom of the field...

If you want to modify your position, that is your privilege, and modification of hypotheses is the usual path toward new knowledge. But the position expressed in the quotation above (and repeated several times in various postings) is the one I was addressing. It doesn't say that most of the markers are in the lower half of the rug. It says that all of them are one fourth to one third of the way up from the bottom. That not only excludes the top half, it excludes everyplace below 25% and above 33%, which is where 8 of the 9 markers in my survey lie. I'd say that the data, however limited, is inconsistent with the hypothesis in that form. Again, I reiterate that the data applies to only one specific subclass of phenomena.

Regards,

Steve Price

Regards, Yon

Now I'm more confused than ever, and was pretty confused before. The problem, I believe, relates to use and interpretation of language.

Your statement, ...I had made it clear in my introduction that I used 'internal elem' purely as a label for any irregularity occurring about one fourth to one third of the way up from the bottom of the field... is one source of my confusion. I originally thought you meant this to include anywhere in the lower third, perhaps anywhere in the lower fourth of the rug, and that kind of fixed itself into my brain.

Your have, in several places, used the argument that one of the reasons for taking the "internal elem" seriously is that it always occurs at the same place. At least one of those messages described it as a precise location, and I believe (but am not 100% certain) that other messages referred to the location as exact. The contexts I'm thinking of were responses to Marla's attributing them to things like the weaver being interrupted. I have, in several places, been critical of referring to the whole lower third (or fourth) of a rug as an exact or precise location.

When I re-read the italicized text, I thought I finally understood. No, I said to myself, Yon doesn't think the entire lower third of a rug is a precise location any more than I do; obviously, the meaning of the text is that the precise location is between the lower third and the lower fourth, a spread of less than 10% of the rug's height.

Would you kindly clarify this matter for me? Do you mean within an 8% range or within a 33% range? In view of the fact that the marker can occur anywhere within the range, if you mean the latter, how large would the range have to be before you would consider it not a precise or exact location?

I'm not trying to be facetious here. I am truly confused and this confusion is probably the reason I have had the perception that the hypotheses were being modified "on the fly" and without explicit statements of having occurred.

Regards,

Steve Price

I have no had a chance to look at "Atlantic Collections" again, so I can comment on your response to my first posting. I have a feeling that we are going to be like the folks who try to decide voter intent from unpunctured ballots in Florida.

1. Plate 43: I called the location of the line 66%, you say it's 44%. The difference is obvious when I look at the rug. This is a prayer rug with an upper border that is (in my view) interrupted by the mihrab or (in Yon's) extended by the mihrab. I don't know any iron rule to resolve this one, so let's just leave it as a difference of opinion.

2. Plate 266: I did not include it because my criterion was ...the ones that are defined by visually obvious lines (or chains of not-too-separated motifs)extending across most or all the way from one side border to the other... This rug has 4 palmettes that are arranged horizontally at a level 44% up from the bottom. They are small and evenly spaced, and collectively make up only about 5% of the width of the rug. None comes very close to a side border. No matter how I stretch things, that isn't a chain of not-too-separated motifs extending across most or all the way from one side border to another.

3. Plate 299: The closest thing to meeting my limited criterion that I can see is two branches extending to the sides from a fairly wide vertical tree. Furthermore, since this is a Belouch prayer rug we would surely disagree about whether the field extends to the top of the mihrab, although it is clearly in the lower half no matter what.

4. Plate 306: A Belouch rug in which horizontal lines can be defined by almost any of the 9 registers of floral devices that cross the field width. Every register is different, and I am reluctant to extend the criterion to include something like "the most different of somewhat related lines".

I don't know if this clarifies anything at all. It certainly emphasizes the necessity for defining things very clearly in order to discuss them sensibly.

Regards,

Steve Price

To return to my four examples:

266. The line is pretty clear, you spotted it right away. It is at least as well articulated as your upper line in 305 (which, by the way, has the clearest line of all at 25%.
299 has a clear delineated area below the start of the repetitive motif. The same theme repeats in modified form higher up, so maybe it's not clear cut.
300 has a very clear area before the start of the main pattern, which includes the inward ponting rows of triangles abutting the borders.
306 ditto. The main pattern consists of the grid defined by the serrated leaves.

305, by the way

As I was about to look up these items in the book it accidentally fell open to no. 111, another clear example with the line at 24%.

Regards, Yon

I don't want to turn this into a debate about who's eye is reliable. That is pointless. I truly tried to do what I did as objectively as I am able, and I'm sure you did the same. Yet, looking at the same database of about 310 rugs, what we saw was quite different. And that's just the two of us, if many more observers were to enter it we could expect a wider range of results.

What we have demonstrated is that the criteria I adopted are not truly objective, and need to be sharper still. That is the big challenge that must be overcome in order to collect meaningful data on the issues. In the absence of criteria that permit reasonably reproducible results when different people look at the same thing, it is not possible to get beyond anecdotal evidence.

Regards,

Steve Price