Chapter 12 Placing the Fragments on the Canvas Using the Stegemann Method

In: Material and Digital Reconstruction of Fragmentary Dead Sea Scrolls
Jonathan Ben-Dov
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Asaf Gayer
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Eshbal Ratzon
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In the previous chapter we established the way to determine the order of fragments in the scroll and their height in the column. This chapter will focus on the last stage of the Stegemann Method, namely, finding the precise distance between fragments that were identified as part of the same wad. The final purpose of this step is to estimate the amount of missing text between fragments on the canvas. This task was described in detail by Stegemann in his seminal article and later by others, and is summarized here.1 Some of Stegemann’s premises have been contested in subsequent scholarship. We address the reservations in this chapter, but will expand on the method’s margin of error in Appendix 3.

In order to find the distance between fragments, the first step is to find out the circumference of at least one turn of the scroll through either measurement or reconstruction. Measurement is possible in cases when a long fragment preserves at least two, preferably three points of damage, which would indicate the circumference of the scroll at those points (figure 42). If no such fragment exists, one can reconstruct the circumference of the scroll at an area where at least two fragments, textually overlapping a long enough section from other copies, are preserved. In this case it is possible to apply the methods for the reconstruction of column and intercolumnar width described in chapter 9. The known circumference is in fact the distance between two layers that will serve as the anchor of the reconstruction. The fragment or fragments from which we begin our reconstruction are named in this book the “anchor fragment(s).”

Figure 42
Figure 42

Columns 8–11 in 1QS. The distance between two adjacent damages at the bottom of the scroll indicates the circumference of the scroll at this point.

© Shrine of the Book, Israel Museum. Ardon Bar Hama

From the first known circumference one has to measure the distances to other layers of the scroll. It is easier to find these distances in the case of documented wads, or when other material indications exist, with the relevant fragments representing consecutive turns of the scroll. The distance between fragments increases toward the outer part of the scroll and decreases toward its inner part. Thus, if one knows the circumference of the scroll at a certain point, one should be able to place the rest of the fragments, which originated in other – inner or outer – turns.

Instead of conceiving the scroll as a spiral, the Stegemann Method approximates its shape to concentric cylinders, assuming that the circumference of succeeding turns of the scroll changes linearly, i.e., that the increase and decrease of the distances between every layer of the wad is constant throughout each scroll. This assumption is not realistic. The growth is affected primarily by the thickness of the skin and the tightness of the rolling, which are uneven throughout a scroll.2 But since we have no way of knowing these variations for every layer, one has to estimate the average difference, keeping in mind that the actual difference can vary, as will be specified in Appendix 3. Thus, we take the known circumference at a certain point, and add or reduce a constant number for every turn or layer. If all fragments are extant, we can place them one by one according to the calculation.

Finding the average difference for a specific scroll is not always possible. The thickness of the skin is not regularly indicated in publications, and the IAA has just recently acquired the instrumentation to measure it without damaging the skin. Moreover, gelatinization has changed the skin’s original thickness.3 In addition it is not always possible to know how tightly the scroll was rolled. Thus, since no better option is available, it is advised to rely on Stegemann’s dataset which is based on earlier computations. According to Stegemann, the minimum increase per turn in a very thin scroll such as 11QTa (11Q19) may be 1 mm, while the maximum can reach up to 5 mm in the rather thick scroll 11QPsa (11Q5).4 Comparing the thickness of the skin under discussion to these two scrolls may help.

After establishing the increase or decrease between 1–5 mm, one can proceed to placing the next layers. 4Q511 is a good example, where three consecutive circumferences were measured. The constant difference is 3 mm, thus the circumference is growing from the inner turn to the outer turn, beginning with 4.6 cm, continuing to 4.9 cm, and ending with 5.2 cm (figure 43).

Figure 43
Figure 43

Corresponding Damage points on 4Q511 fragments 63 iii–iv. Angel, “Material Reconstruction,” 32.

Photographer: Najib Anton Albina. Illustration courtesy of Joseph L. Angel

1 Columns and Margins in the Material Reconstruction

After the fragments are placed in a certain position based on their decay pattern, it is time to divide the rest of the canvas into columns. The first step is to mark on the digital canvas all the column borders and intercolumnar margins preserved on the actual fragments (see chapter 9). These data constitute anchors for the subsequent procedure. We digitally attach these borders to their respective fragments, so that if the fragment moves the borders will move accordingly.

The next step is to determine the widths of all other columns and margins, both those known from the large fragments and those reconstructed based on line width (which are, in turn, known from textual parallels). Since the width of columns and margins can vary within one scroll, one should follow the general limit for the narrowest and widest possible widths (see chapter 9). Deviating from these limits is possible when necessary, but it is best to keep deviations small.

The empty space on the canvas is then divided into columns, in an attempt to place all extant and computed column borders in their right place. The idea is to draw the column borders in such a way that all extant columns, margins, and borders could be placed on the canvas without conflict (see figure 44).

Figure 44
Figure 44

4Q418a cols. XVXVII. The end of col. XVII was set by the left margin preserved on frag. 5. The text of frag. 7 parallels the text of 4Q415 6, which suggests some limitations for the reconstruction (see chapters 15 and 16). The rest of the space between frags. 5 and 7 does not include any clues for the reconstruction. We fill it with two columns based on the remaining space. The fact that these two columns are within the range of the known columns of 4Q418a validates the reconstruction.

© IAA, LLDSSDL, Najib Anton Albina

Drawing the column borders is a crucial move for the verification of the material reconstruction. While the Stegemann method is based on several approximations, and a certain reconstruction can never be proven correct beyond any reasonable doubt, the certainty can be improved by using a process of trial and error. Scholars should try positing various configurations until one of them cannot be contradicted. Recall that the outcome of the method is not a positive reconstruction of the scroll as it really was, but rather one possible reconstruction out of several others within a certain limit, whose main merit is that it does not contradict any other known data.

If the suggested reconstruction is not possible, this proves that one of the previous steps needs to be adjusted. The mistake may result from one small detail, which can be mended by altering that detail and will then make the reconstruction work. If this is not the case, the basic figures may be wrong, such as the stage of reconstructing the first circumference. An easy and common solution, applicable in cases when the known circumference is placed in a column whose text appears in parallel copy, is to change the width of the intercolumnar margin within the reasonable range found among the fragments of the scroll.

After the reconstruction based on the preserved fragments is completed, Stegemann suggests the reconstruction of the length of the rest of the scroll inwards, using the same assumption that the decrease of circumference between every consecutive turn is constant, in addition to the assumption that the core of the scroll has a minimum size. He estimated the error for such a computation as approximately 25%.5 Later, Dirk Stoll suggested another mathematical computation for the length of the scroll. It was more complicated, but eventually equivalent to a simple sum of an arithmetical series.6 Based on Stoll’s computations, Drew Longacre mathematically estimated a larger margin of error (approximately 50%). Longacre claimed that even with this large margin of error, some conclusions can be drawn regarding extra-long scrolls.7 However, Ratzon and Dershowitz empirically estimated the margin of error for such reconstruction, based on the information preserved in the long, comparatively intact scrolls. Their experiment showed an enormous margin of error of several hundreds percent, and sometimes even more.8 This means that, at the bottom line, the Stegemann Method cannot be used for the estimation of the length of the unpreserved part of the scroll.

The present chapter described the creation of a canvas for one given scroll. In chapter 13 we will show how the results of this procedure can be extrapolated for the reconstruction of yet other copies of the same composition (in our case, Instruction). For that purpose, however, it is important to keep track of the margin of error of the original anchor. Thus, while the visual reconstruction of the first scroll must – by definition – contain only one accurately delineated option, this representation must be accompanied by a written account, in which the width of each column should include a range of numbers instead of one specific figure. The entire range should be taken into account when extrapolated. This range may be narrowed down when working on a parallel copy with its own limitations. Trial and error are the main check on the validity of this rolling procedure. One should posit numbers for the next fragments and the next copies while making sure that they do not contradict any other known data.


Stegemann, “Methods for the Reconstruction”; Steudel, “Assembling”; Stökl Ben Ezra, Qumran, 53–55.


For an empirical examination of these variations see Ratzon and Dershowitz, “The Length of a Scroll.” They also claim that the difference in the error caused by a spiral approximation compared to concentric circles is negligible, and is not worth the extra effort of the computations. Another example can be found in Elgvin, “1QSamuel” (284–85), who notes that in 1QSamuel the two innermost columns (= 7 turns) were rolled in a tighter way than the preceding ones.


According to the information given to us by the IAA conservator, Tanya Bitler, in a private conversation.


Ratzon and Dershowitz, “The Length of a Scroll,” measured an average growth of 4 mm in 11QPsa with a standard deviation of 1 mm and a maximum of 6 mm.


Stegemann, “Methods for the Reconstruction,” 199–200.


Dirk Stoll, “Die Schriftrollen vom Toten Meer – mathematisch oder Wie kann man einer Rekonstruktion Gestalt verleihen?” in Qumranstudien: Vorträge und Beiträge der Teilnehmer des Qumranseminars auf dem internationalen Treffen der Society of Biblical Literature, Münster, 25.–26. Juli 1993, ed. Heinz-Josef Fabry et al., Schriften des Insitutum Judaicum Delitzschianum 4 (Göttingen: Vandenhoeck & Ruprecht, 1996), 205–18.


Drew Longacre, “Methods for the Reconstruction of Large Literary (Sc)rolls from Fragmentary Remains,” in The Hebrew Bible Manuscripts: A Millennium, ed. Élodie Attia-Kay and Antony Perrot, Supplements to the Textual History of the Bible 6 (Leiden: Brill, 2021), 110–141.


Ratzon and Dershowitz, “The Length of a Scroll.”

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