Warning: file_put_contents(/opt/frankenphp/design.onmedianet.com/storage/proxy/cache/778957660d9741f0395f923d68b1fe98.html): Failed to open stream: No space left on device in /opt/frankenphp/design.onmedianet.com/app/src/Arsae/CacheManager.php on line 36

Warning: http_response_code(): Cannot set response code - headers already sent (output started at /opt/frankenphp/design.onmedianet.com/app/src/Arsae/CacheManager.php:36) in /opt/frankenphp/design.onmedianet.com/app/src/Models/Response.php on line 17

Warning: Cannot modify header information - headers already sent by (output started at /opt/frankenphp/design.onmedianet.com/app/src/Arsae/CacheManager.php:36) in /opt/frankenphp/design.onmedianet.com/app/src/Models/Response.php on line 20
Dating ancient manuscripts using radiocarbon and AI-based writing style analysis - PMC Skip to main content
PLOS One logoLink to PLOS One
. 2025 Jun 4;20(6):e0323185. doi: 10.1371/journal.pone.0323185

Dating ancient manuscripts using radiocarbon and AI-based writing style analysis

Mladen Popović 1,*, Maruf A Dhali 1,2, Lambert Schomaker 2, Johannes van der Plicht 3, Kaare Lund Rasmussen 4, Jacopo La Nasa 5, Ilaria Degano 5, Maria Perla Colombini 5, Eibert Tigchelaar 6
Editor: Carlos P Odriozola7
PMCID: PMC12136314  PMID: 40465545

Abstract

Determining by means of palaeography the chronology of ancient handwritten manuscripts such as the Dead Sea Scrolls is essential for reconstructing the evolution of ideas, but there is an almost complete lack of date-bearing manuscripts. To overcome this problem, we present Enoch, an AI-based date-prediction model, trained on the basis of 24 14C-dated scroll samples. By applying Bayesian ridge regression on angular and allographic writing style feature vectors, Enoch could predict 14C-based dates with varied mean absolute errors (MAEs) of 27.9 to 30.7 years. In order to explore the viability of the character-shape based dating approach, the trained Enoch model then computed date predictions for 135 non-dated scrolls, aligning with 79% in palaeographic post-hoc evaluation. The 14C ranges and Enoch’s style-based predictions are often older than traditionally assumed palaeographic estimates, leading to a new chronology of the scrolls and the re-dating of ancient Jewish key texts that contribute to current debates on Jewish and Christian origins.

1 Introduction

The discovery of the Dead Sea Scrolls from ancient Judaea fundamentally transformed our knowledge of Jewish and Christian origins [1]. Determining the chronology of these handwritten manuscripts, mostly written in Aramaic/Hebrew script, is essential for reconstructing the evolution of ideas. Palaeography—the study of ancient handwriting—is used to date manuscripts on the basis of their handwriting [24] but its subjectivity and the impossibility of measuring the significance of handwriting features poses a problem [5, 6]. The model that was constructed to trace the evolution from the imperial Aramaic script (fifth and fourth centuries BCE) to the Jewish square script (first and second centuries CE) and to date scrolls and religious, cultural, and historical developments [710] is not reliably grounded. For palaeographic comparison, one requires enough date-bearing manuscripts in similar script, but date-bearing documents are hardly available among the scrolls and most scrolls have no stratigraphy in the archaeological record. Only some of the very oldest and the very youngest manuscripts have calendar dates. Inscriptions or historical hypotheses, such as a slow development of the Aramaic/Hebrew script in the third century BCE and the emergence and rapid development of a national script around the mid-second century BCE [8, 9, 11, 12], cannot compensate for the palaeographic scarcity for the centuries in between and do not enable one to reliably date the scrolls (see S1 Appendix).

In this study, we present new 14C dates derived from manuscript samples as reliable time markers to bridge the chronological gap between the fourth century BCE and the second century CE. The 14C dating leads to a list of expected dates for a number of chosen manuscript fragments, though this list cannot be ordered sequentially, independent of 14C. Based on the dating results for the tested samples, Enoch, named after the ancient Jewish science hero, was trained as a machine-learning-based date-prediction model applying Bayesian ridge regression on established handwriting-style descriptors. The corresponding handwritten style features in those tested manuscript images can then be used to estimate the date of undated manuscripts. Thus, Enoch reduces palaeographic subjectivity and the role of implicit knowledge by offering date predictions as probability-based options, grounded in physical (14C) and geometric (shape-based) evidences, that can aid palaeographers and historians in their decision-making and contribute to historical debates.

2 Integration of multiple dating methods

2.1 Radiocarbon dating

We performed 14C dating on 30 manuscripts from 4 sites, spanning an estimated 5 centuries: 25 from the Qumran caves, 1 from Masada, 2 from the Murabba’at at caves, and 2 from the Nah ˙ al H ˙ ever caves (see Sect 2.1 in S2 Appendix). This study is the first to apply to the scrolls, prior to 14C dating, a chemical treatment specifically designed to remove fatty materials, employing solvent extraction (see Sects 2.2 and 2.7.1 in S2 Appendix). Additional specialized analytical chemistry methods were applied before and after sample pretreatment to demonstrate that the total amount of lipid materials is below a threshold that does not significantly skew the 14C date (see Sects 2.7.2–2.7.5 in S2 Appendix). The samples were dated by two Accelerator Mass Spectrometry (AMS) machines (see Sect 2.3 in S2 Appendix). For the relevant time range, the calibrated results are often bimodal, which is an effect of the calibration curve not being monotonous, but this issue can be solved (see Sect 2.4 in S2 Appendix and Sects 5.6–5.7 in S5 Appendix).

The AMS results yielded 27 valid 14C dates (see Sects 2.4–2.6 in S2 Appendix and Tables in S1 Appendix), improving and extending the existing series of 14C-dated Dead Sea Scrolls [13, 14]. In general, the 14C results indicate older date ranges for individual manuscripts as well as for the emergence of the so-called ‘Hasmonaean’ and ‘Herodian’ scripts (see S4 Appendix). Fig 1 shows the comparison between the 2σ accepted calibrated ranges and traditional palaeographic estimates (in blue and red; please note that the accepted range is not the complete calibrated range; for more details, see Sect 4.2 in S4 Appendix and Sect 5.6 in S5 Appendix). Only two manuscripts have date ranges that go in the direction of a younger possible range. The 14C results for most manuscripts confirm the basic distinction between older Hasmonaean-type manuscripts and younger Herodian-style manuscripts, and also between so-called ‘Archaic’ and Hasmonaean-type manuscripts. However, the 14C date ranges for manuscripts traditionally considered Hasmonaean and Herodian are quite differently distributed throughout the timeline. As can be seen in Fig 1 (in blue), Hasmonaean-type manuscripts are all grouped together in a narrower part of the timeline but Herodian-type manuscripts are more spread across the timeline, extending from the second century CE all the way back to the second century BCE (see Sects 4.1.1–4.1.3 in S4 Appendix). The validated 14C results represent a data set that will be used in the next stage.

Fig 1. Overview of date estimations by three information sources and a calendar date.

Fig 1

Blue bars indicate (accepted) 2σ calibrated ranges 14C, green indicates Enoch, red refers to palaeography, and black denotes the historical date. The vertical axis contains the manuscript numbers, and the horizontal axis contains dates: BCE in negative and CE in positive. Broad palaeographic types of the samples are indicated on the right.

Sample 4Q114 is one of the most significant findings of the 14C results. The manuscript preserves Daniel 8–11, which scholars date on literary-historical grounds to the 160s BCE [15, 16]. The accepted 2σ calibrated range for 4Q114, 230–160 BCE, overlaps with the period in which the final part of the biblical book of Daniel was presumably authored (see Sect 4.1.2 in S4 Appendix).

2.2 Date-prediction model

The completed 14C results set the stage for further manuscript dating analysis. The granularity of the 14C dating is coarse due to the limited number of data points but character-shape-based analysis provides an additional information source to tap into the historical development of handwriting styles.

While it is tempting to use modern methods of deep learning, as we have done before [1721], there are several arguments to not currently use such approaches for the proposed style-based date prediction on a very small data set. It was decided to let the available data speak, not depending on a pre-trained model (S6 Appendix). Since a general, large, representative, and labeled data set is not available for the period of the scrolls, we apply dedicated pattern recognition and machine-learning models, only using the relevant scrolls data for training a date-prediction model. Given the topic’s importance, pre-trained deep transfer learning based on extraneous material may be expected to elicit valid concerns among palaeographers about the relation between the scrolls’ target data and training data from a (very) different origin and period.

We used 24 manuscripts from the 14C samples with valid dates as a labeled dataset for the primary training set for Enoch (see Sects 2.4–2.6 in S2 Appendix and Sect 4.2 in S4 Appendix). For the data labels, we used OxCal v4.4.2 [22, 23] to obtain the raw data points for the probability distributions. This is because the 14C results are not single dates, as with date-bearing documents, but represent date ranges with probability distributions. The 14C data input for training Enoch consists of the probability distributions of accepted 2σ calibrated ranges. In the case of bimodal evidence, we used a Bayesian method outside the OxCal program to limit the date ranges produced from each calibration. We did this to prevent propagation of 14C bimodality, which is an effect of the calibration curve not being monotonous (see Sect 2.4 in S2 Appendix), to the next processing stage of training the style-based predictor. Only in the case of bimodal evidence was palaeographic domain knowledge used in training the Enoch model as it allows making a binary split in the OxCal distribution of 2σ ranges using the Heaviside function with the position of the step being placed at an innocuous low-probability point, near zero, on the curve (see Sect 5.6 in S4 Appendix).

In addition to the primary training set, we created different combinations of training data to perform comparative analyses and further check the robustness of the model. These combinations include the tentative addition or omission of 4Q52, some previously tested 14C samples [13, 14], date-bearing documents from the fifth–fourth centuries BCE and the second century CE (see tables in S9 Appendix for complete lists of manuscripts), the Maresha ostracon from 176 BCE (see Sect 1.1 in S1 Appendix). We performed cross-validation in three ways: using a train-validation split, via manuscript-image splitting for train-test sets, and through leave-one-out of the training data points.

2.2.1 Deep neural networks for detection of handwritten ink-trace patterns

For this study, the digital images of the 24 14C-dated manuscripts [24, 25] underwent multiple preprocessing measures to become suitable for pattern recognition-based techniques. It should be noted that the images are extremely difficult to work with (some examples can be seen in illustration 9 in S5 Appendix and illustration 22 in S7 Appendix; see also Sect 7.1 in S7 Appendix). We are not dealing with digitally encoded text but with pixel images of highly degraded manuscripts as input.

We utilize multispectral band images of each fragment and employ BiNet [26], an artificial neural network based on an encoder-decoder U-net architecture designed to binarize the diverse range of scroll images, to generate a three-channel image. The resulting binarized images consist solely of black foreground pixels (ink) against a white background, ensuring that subsequent style analyses focus exclusively on the handwritten patterns while minimizing inadvertent matches due to material-texture attributes. We further correct the rotation of the binarized images and divide them into multiple parts to maintain a balanced distribution of handwritten characters within each new image. No extraneous image material was used to train this binarization method.

Thus, we obtained a data set of 75 images from the 24 14C-dated manuscripts. The image samples typically contain 150–200 characters, which has been shown to be sufficient for the comparable task of writer identification [27].

2.2.2 Extracting features for style attribution

In this study, ‘style’ is not related to textual content or wording. For characterizing the handwritten shapes, small shapes along the ink trace are used, largely uncoupled from the textual content, because we want to avoid spurious matches or date predictions on the basis of textual content. Once the training images were available, we could perform feature extraction techniques to translate handwriting patterns into feature vectors. The feature vectors relate directly to the shape-based evidence of the ink traces in the manuscripts and have a solid basis in writer identification [2830] and document dating [31, 32]. We extract features from both the allographic and textural levels of characters [6]. An overview of machine-learning methods can be found in [33].

The allographic method uses a self-organized character map obtained using a Kohonen neural network. As an example, this allographic codebook feature allows for a 93% (± σ=2.3%) accuracy classification of the scripts ‘Hasmonaean’ vs. ‘Herodian’, using PCA, on 590 labeled manuscripts, results averaged over 32 random odd/even splits for training/testing [34]. The textural method uses statistical pattern recognition on angular information. The ‘hinge’ method for estimating the curvature distribution has been used extensively in writer verification and dating studies [30, 31, 35]. Whereas the allographic feature addresses stylistic elements at the character level, the ‘hinge’ method concerns a micro-level feature directly related to the original writing activity that yielded the curvature of the ink trace. Therefore, we make a weighted combination of textural and allographic features to obtain an adjoined feature vector for each manuscript image. Such a feature vector constitutes the input data to Enoch.

2.2.3 Bayesian ridge regression

Due to the limited size of the data set, we cannot employ high-parametric models like period-specific temporal codebooks [32]. Instead, we utilize conditional modeling with Bayesian ridge regression [36] (see Sect 5.6 in S5 Appendix). This approach applies Bayesian inference to estimate model parameters for date prediction. By placing a prior distribution on the parameters and updating it with observed data using Bayes’ rule, we obtain the posterior distribution of the parameters and predicted dates. The Bayesian approach is chosen because our target output data represents probability curves for 14C dates (i.e., a vector) containing the accepted 2σ calibrated ‘OxCal’ ranges. This probabilistic approach enables us to incorporate all available information while maintaining interpretability. Moreover, instead of producing a single number for the estimated date of a sample, it provides a posterior distribution that allows us to assess the uncertainty associated with the estimated dates. Additionally, Enoch is able to provide error margins for predictions on unseen data. Regarding data balance, we used two methods to compensate for the imbalanced distribution of the training data over different periods (see Sect 5.7 in S5 Appendix).

3 Validating Enoch

We used 62 images of the data set of 75 images from the 24 14C-dated manuscripts to train Enoch. We then validated Enoch in two ways. The remaining 13 images were passed as unseen test data to cross-validate the robustness and reliability of Enoch’s performance. The prediction of these 13 images by Enoch gives an 85.14% overlap to the original 14C probability distributions (see tables in S9 Appendix). We also performed validation by leave-one-out tests (see Sect 5.9.1 in S5 Appendix). Fig 1 (in green) also shows the results of cross-validation and leave-one-out tests for training Enoch. The choice for the bandwidths (2σ date ranges for 14C, 1σ uncertainties of the ridge regression for style-based predictions) is based on the intrinsic reliability of the two information sources. 14C date ranges are evidently superior to style-based predictions.

Regarding the differences between the 14C date ranges and Enoch’s script style-based estimates, the mean absolute error (MAE) is 30.7 years. The MAE drops to 27.9 years when minor peaks are ignored (see illustration 26 in S8 Appendix). Minor peaks concern small secondary peaks in 12 cases, which are mostly smaller than 3.5% of maximum peak value except for two exceptions (5.2% in 4Q2 and 9.4% in 4Q416; see tables in S5 Appendix). In manuscript dating, MAE is commonly used [37] for evaluation of a regression method. The difference with rms error is limited [38]. With the chosen 2σ (14C) and 1σ (AI) bandwidths, the error for the leftmost margin is 6.4 years while for the rightmost margin it equals –38.4 years, indicating that Enoch’s style-based estimate range ends earlier than the 14C range. For each sample, the date ranges of the two information sources have partial to full overlap with an average of 88.8%. For Ithaca [39], AI and epigraphy were similarly used as two heterogeneous information sources to predict dates for ancient Greek inscriptions. Their prediction provides an average distance of 29.3 years from the target dating brackets, with a median distance of 3 years based on the totality of texts. We also aim for date prediction, but, unlike Ithaca, we utilize three information sources: 14C, shape-based writing style analysis (AI), and palaeography, the latter only in the case of bimodal 14C evidence.

Qualitatively, Enoch’s style-based predictions largely follow the 14C results, even though the validation samples (rows) are in no way present in the training data. In the range 300–50 BCE, Enoch’s estimates provide an improved granularity compared to 14C. For samples 5/6Hev1b, Mas1k, and XHev/Se2, the style-based estimate is earlier and more uncertain. However, all of them overlap with 14C estimates. Interestingly, although 5/6Hev1b has the widest predicted range from Enoch, the palaeographic estimate still falls within the overlap region. In addition, 11Q5 shows that in the late date range, a fairly certain style-based date estimate above 100 CE can also be achieved. This may go against historical reconstructions according to which the scrolls were hidden in the Qumran caves before the summer of 68 CE [40]. Yet, we did not impose here a chronological limit on the model, because of the 14C result for 11Q5, and in order to examine the possibility of style continuation after 70 CE.

Fig 1 shows the general result that, on average, 14C date ranges and Enoch’s predictions indicate older dates than traditional palaeographic estimates. Only 4Q201 and 11Q5 have older palaeographic date estimates, although there is an overlap with the 14C results (see Sect 4.1.1 in S4 Appendix).

4 Exploration of style-based dating on unseen manuscripts

The general recipe for Enoch’s analysis of manuscript images is presented in Table 1. Before applying this to other previously undated scrolls, we first tried out a known mediaeval benchmark data set of charters, MPS [32], with success [41]. We then applied the trained Enoch model to a collection of 135 unseen manuscripts from the ca. 1000 Dead Sea Scrolls to explore the viability of style-based dating at this stage (S7 Appendix). Enoch, thus, produces an empirical evaluation which modifies a previously uniform date expectancy distribution to a curvilinear distribution with some dates becoming more likely, others becoming less likely for a sample. Like the OxCal program for 14C, Enoch delivers probabilities on dates as well as the corresponding error estimates. This is advanced in comparison to older, more primitive methods which only provide, e.g., a date point as an answer. In the analysis of our results both the (1) likelihood of a date point and the (2) estimation reliability of that point need to be taken into account. These are the first published results on date estimation for this collection of manuscripts. Future research, with more data and improved images, may be directed at further validation and refinement.

Table 1. Style-based date prediction recipe for Enoch.

1. Select and crop the relevant manuscript images based on scholarly identification criteria;
2. In the images, perform a separation of the ink trace from the material background texture by using a deep-learning-based U-net variant for multispectral image-intensity binarization [26];
3. For each manuscript, compute two shape descriptors: a histogram of allographic fraglet occurrence and a histogram of angular co-occurrence along the ink-trace edges [29, 30];
4. Adjoin the two feature vectors, properly weighted, to a single handwriting-style vector [43];
5. In order to decorrelate the features, avoid collinearity, and minimize the necessary number of parameters in the next stage, perform a strong dimensionality reduction (PCA, 20 dimensions).
6. Take the 14C-dated manuscript-image samples for training Enoch as a style-based Bayesian ridge-regression model with a scalar date estimate as the target output. In this training, augment the image data set by using random elastic morphing to obtain a sufficient and balanced number of examples per 14C-dated reference. This step is an essential, new contribution that allows a merger of 14C-based and style-based information in the date estimation. For validating Enoch, use the leave-one-out approach: each sample that is under evaluation does not occur in the training data;
7. Predict: style-based dates for undated manuscripts.

Table 2 summarizes the palaeographic post-hoc evaluation of Enoch’s date predictions for 135 undated manuscripts. Expert palaeographers among the article’s authors evaluated the style-based date predictions, condensing the prediction into two main categories: realistic and unrealistic, the latter subdivided into too old and too young. As can be seen in Table 2, 107 (79%) of the undated manuscripts were dated realistically and 28 unrealistic predictions (21%) were divided between too old (46%) and too young (39%), according to the palaeographers (S7 Appendix). With this sample size, the confidence margin is 7% at α=0.05. Enoch’s date prediction task is not a 50/50, binary decision task but regressive, with many possible years in the interval 300 BCE–200 CE. Assuming a coarseness of 25 years, as in the MPS project [32], the date range would consist of 20 bins, with a 5% prior-probability hit rate. A success rate of 79% is unlikely to be accidental. A binomial test achieves a p-value of 4.44e–12 so that the observed result is highly unlikely to have occurred by chance alone.

Table 2. Expert evaluation of Enoch’s date predictions.

Prediction is: Subcategory Manuscript count Percentage
Realistic - - 107 79.26%
Unrealistic Indecisive 4 28 20.74%
(r10pt)2-5 Too old 13
(r10pt)2-5 Too young 11
Total manuscripts - - 135 100.00%

Previously, we demonstrated that two scribes were at work in the Great Isaiah Scroll [6]. Now, Enoch shows that there is no temporal difference between the two halves of the manuscript as if one part were written significantly later than the other. On the contrary, both scribes are estimated to have worked on their respective part of the scroll of 1QIsaa in the same period. Fig 2 shows that Enoch dates the two halves consistently between 180–100 BCE.

Fig 2. Enoch’s date prediction plots for 6 of the 54 columns from the two halves of 1QIsaa.

Fig 2

The left 3 columns are from the first half of the manuscript, the right 3 columns are from the second half of the manuscript.

5 The Enoch approach to dating ancient manuscripts

To our knowledge, Enoch is the first complete machine-learning-based model that employs raw image inputs to deliver probabilistic date predictions for handwritten manuscripts utilizing the probability distribution from 14C output, and that is completed by palaeographic input while ensuring transparency and interpretability through its explainable design. Also, Enoch’s integration of multiple dating methods yields a strongly improved value of sources of evidence and allows for a mutual confirmation of evidence from the two sources—physical (material) and geometric (shape-based). As an illustrative example, samples 4Q259 and 4Q319 show that Enoch can accurately find a similar date estimate for the same writing style. The accepted 2σ calibrated range of 4Q259 was used to train Enoch. 4Q259 contains text that is part of the so-called Rule of the Community. 4Q319 contains a calendrical text. Due to perceived generic differences, 4Q319 received a separate classification number but is materially actually part of the same manuscript as 4Q259 [42]. Fig 3 shows that Enoch was able to give a date prediction estimate for 4Q319 that is similar to the accepted 2σ calibrated range of 4Q259 (see Sect 7.5 in S7 Appendix).

Fig 3. Enoch’s date prediction estimate for 4Q319.

Fig 3

(a) from full spectrum colour image to binarized image to 14C plot for 4Q259 that went into the training of Enoch. (b), from full spectrum colour image to binarized image to Enoch’s date prediction plot for 4Q319 (see also illustration 9 in S5 Appendix). Red bars represent the probability of each date bin. The blue curve shows the smoothed distribution. Grey spikes indicate the local uncertainty of the estimate.

This study in style-based date prediction using the Enoch approach is a first step. The advantage of the Enoch model is that it provides quantified objectivity to palaeography, reducing the method’s subjectivity and the role of tacit expert knowledge, by offering a limited number of probability-based options on empirical grounds, both physical (14C) as well as geometric (shape-based analysis) evidence, that can assist palaeographers to substantiate, sharpen, or modify their own estimate for an individual manuscript. Also, the methods underpinning Enoch can be used for date prediction in other partially-dated manuscript collections. Finally, we did not take any model that is already available, but we developed a robust model that can (1) predict dates using only a very small amount of data, i.e., 24 sample or data points, (2) deal with uncertainty, and (3) provide explainability.

It could be argued that the style-based predictions are influenced by the 14C-based training of the model. However, the leave-one-out validation results indicate that unseen samples obtain their interpolated position on the time axis based on the detected handwriting style in the images. The placement of an unseen sample on the time axis is not fundamentally constrained. Any date in the time range of 300 BCE–200 CE could have been reached, looking at all style-based dates empirically covered by the model.

In this study, we have avoided using palaeographic estimates as target values for machine learning because our goal is to provide physical (material) and geometric (shape-based) evidences for manuscript dating. While the use of palaeographic estimates as target values for machine learning is technically possible, we consider it too risky, given the existing uncertainties and lack of consensus associated with the precise dating of individual manuscripts.

In its manuscript analysis, Enoch differs from traditional palaeographic approaches. Enoch emphasizes shared characteristics and similarity matching between trained and test manuscripts, whereas traditional palaeography focuses on subtle differences that are assumed to be indicative for style development. Combining dissimilarity matching and adaptive reinforcement learning can uncover hidden patterns. This interdisciplinary fusion may enrich our understanding of textual content, material properties, and historical context, leading to enhanced interpretations of the past. This remains a task for the future. New 14C evidence or, with new discoveries, a whole range of date-bearing manuscripts can be added to Enoch’s training data for further refinement and precision, continuously improving accuracy. The consequences of each newly added manuscript sample to the Dead Sea Scrolls 14C reference collection can now easily be computed using the Enoch approach.

Although the limited data were insufficient for a full deployment of deep-learning in the prediction task (S6 Appendix), future research needs to address the problems of sparse labeling and high dimensionality. It is to be expected that new solutions will appear here, because these problems are encountered in many application domains. If palaeographers are willing to accept the use of ‘black box’, pre-trained deep-learning models that are based on completely extraneous large image and photograph collections, future research may be directed at adapting the output of such models to the vectorial regression-based date-prediction task that is proposed in the current article.

6 Aramaic/Hebrew script development in ancient Judaea

The results of this study lead to four novel insights into Aramaic/Hebrew script development during the period under consideration and the date of individual manuscripts.

First, 14C date ranges and Enoch’s style-based estimates are overall older than previous palaeographic estimates. These older dates for the scrolls are realistic. Hasmonaean-type manuscripts have accepted 2σ calibrated ranges that allow for older dates in the first half of the second century BCE, and sometimes slightly earlier, instead of only circa 150–50 BCE. There are no compelling palaeographic or historical reasons that preclude these older dates as reliable time markers for the ‘Hasmonaean’ script. This also applies to the accepted 2σ calibrated range for 4Q70 and its ‘Archaic’ script.

Second, ‘Herodian’ script emerged earlier than previously thought. This suggests that the ‘Hasmonaean’ and ‘Herodian’ scripts were not transitioning from the mid-first century BCE onward, but that they existed next to each other at a considerably earlier date.

Third, this novel approach of palaeography leads to a new chronology of the scrolls that impacts our understanding of the history of ancient Judaea and the people behind the scrolls. Hypotheses about whether the movement behind the scrolls originated in the second or first century BCE will need to be reconsidered in light of Enoch’s second-century BCE date predictions for Hasmonaean-type manuscripts such as 1QS and 4Q163 (S7 Appendix), bearing texts that are regarded typical for the movement. Scholars often assume that the rise and expansion of the Hasmonaean kingdom from the mid-second century BCE onward caused a rise in literacy and gave a push to scribal and intellectual culture. Yet, the results of this study attest to the copying of multiple literary manuscripts before this period. One example is 4Q109, a copy of the biblical book of Ecclesiastes, a book which scholars tentatively date to the end of the third century BCE [15], for which Enoch gives a third-century BCE date prediction (S7 Appendix), close to Archaic-type manuscripts such as 4Q52 and 4Q70—copies of the biblical books of Samuel and Jeremiah.

Fourth, this study’s 14C result for 4Q114 and Enoch’s date prediction for 4Q109 now establish these to be the first known fragments of a biblical book from the time of their presumed authors [15].

The results of this study thus dismantle unsubstantiated historical suppositions and chronological limitations, and call into question the validity of the default model’s relative typology. This relative typology can only be maintained with restrictions. The spread of the Hasmonaean-type manuscripts over the timeline does not affect the default relative typology in a major way, but the older, second-century BCE date ranges of the Herodian-type manuscripts challenge the relative typology. More research is needed to solve this issue.

Supporting information

S1 Appendix. The dating problem of the Dead Sea Scrolls.

(PDF)

pone.0323185.s001.pdf (168.3KB, pdf)
S2 Appendix. Radiocarbon dating of the Dead Sea Scrolls.

(PDF)

pone.0323185.s002.pdf (11MB, pdf)
S3 Appendix. 14C determinations and calibrated date plots.

(PDF)

pone.0323185.s003.pdf (289.8KB, pdf)
S4 Appendix. Palaeography and radiocarbon dating of the Dead Sea Scrolls.

(PDF)

pone.0323185.s004.pdf (213.5KB, pdf)
S5 Appendix. Artificial intelligence (AI) in dating the scrolls.

(PDF)

pone.0323185.s005.pdf (23.7MB, pdf)
S6 Appendix. On the use of pre-trained deep learning methods for image-based dating.

(PDF)

pone.0323185.s006.pdf (759.2KB, pdf)
S7 Appendix. Enoch’s date predictions for 135 previously undated manuscripts.

(PDF)

pone.0323185.s007.pdf (4.5MB, pdf)
S8 Appendix. Comparative plots for different information sources.

(PDF)

pone.0323185.s008.pdf (329.5KB, pdf)
S9 Appendix. List of images for different tests.

(PDF)

pone.0323185.s009.pdf (157.4KB, pdf)
S10 Appendix. Radiocarbon sample information.

(PDF)

pone.0323185.s010.pdf (228.2KB, pdf)
S11 Appendix. Data-sheet radiocarbon runs.

(PDF)

pone.0323185.s011.pdf (258.7KB, pdf)
S12 Appendix. Worksheet of comparative data for 2σ 14C dates and traditional palaeographic estimates.

(PDF)

pone.0323185.s012.pdf (182.8KB, pdf)

Acknowledgments

The authors thank P. Shor, J. Uziel, T. Bitler, H. Libman, B. Riestra, O. Rosengarten, and S. Halevi at the Dead Sea Scrolls Unit of the Israel Antiquities Authority (IAA) and E. Boaretto (advisor to the IAA from the Weizmann Institute of Science, Jerusalem) for providing physical samples and multispectral images of the scrolls—courtesy of the Leon Levy Dead Sea Scrolls Digital Library; Brill Publishers for the Dead Sea Scrolls images from the Brill Collection; A. Aerts-Bijma and D. Paul for handling and measuring the 14C samples at the Center for Isotope Research (Groningen); S. Legnaioli for the Raman analyses performed at the CNR-ICCOM (Pisa); A. Krauss and T. van der Werff for their contributions to developing and testing Enoch; L. Bouma for cleaning images; D. Longacre, G. Hayes, A.W. Aksu, H. van der Schoor, C. van der Veer, and M. van Dijk for their contributions to preparing images for training Enoch; M.W. Dee for advising on and inspecting the code and data acquisition process from OxCal to the Enoch model at the Center for Isotope Research (Groningen). All necessary permits were obtained for the described study, which complied with all relevant regulations.

Data Availability

All data, code, and test film associated with this article are publicly available on Zenodo with the following DOIs: - Data and prediction plots (v3): https://doi.org/10.5281/zenodo.10998958. - Code and feature files (v6): https://doi.org/10.5281/zenodo.13319794. - Film (see details in S7 Appendix): https://doi.org/10.5281/zenodo.8167946.

Funding Statement

This project has received funding by the European Research Council under the European Union’s Horizon 2020 research and innovation programme under grant agreement no. 640497 (HandsandBible). The funding was received by M. Popović. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.

References

  • [1].Brooke G, Hempel C. T&T Clark companion to the dead sea scrolls. London: T&T Clark. 2018. [Google Scholar]
  • [2].Nongbri B. Palaeographic analysis of codices from the early christian period: a point of method. J Study New Testament. 2019;42(1):84–97. doi: 10.1177/0142064x19855582 [DOI] [Google Scholar]
  • [3].Orsini P. Introduction. Studies on greek and coptic majuscule scripts and books. Berlin: De Gruyter. 2018. p. VII–XVI. [Google Scholar]
  • [4].Orsini P, Clarysse W. Early new testament manuscripts and their dates: a critique of theological palaeography. Ephemerides Theologicae Lovanienses. 2012;88:443–74. [Google Scholar]
  • [5].Pavlopoulos J, Konstantinidou M, Perdiki E, Marthot-Santaniello I, Essler H, Vardakas G, et al. Explainable dating of greek papyri images. Mach Learn. 2024;113(9):6765–86. doi: 10.1007/s10994-024-06589-w [DOI] [Google Scholar]
  • [6].Popović M, Dhali MA, Schomaker L. Artificial intelligence based writer identification generates new evidence for the unknown scribes of the Dead Sea Scrolls exemplified by the Great Isaiah Scroll (1QIsaa). PLoS One. 2021;16(4):e0249769. doi: 10.1371/journal.pone.0249769 [DOI] [PMC free article] [PubMed] [Google Scholar]
  • [7].Tigchelaar E. Seventy years of palaeographic dating of the dead sea scrolls. Sacred texts and disparate interpretations: qumran manuscripts seventy years later. BRILL. 2020. p. 258–78. doi: 10.1163/9789004432796_014 [DOI] [Google Scholar]
  • [8].Puech E. 6 La paléographie des manuscrits de la mer Morte. The Caves of Qumran. BRILL. 2017. p. 96–105. doi: 10.1163/9789004316508_008 [DOI] [Google Scholar]
  • [9].Cross FM. The development of the Jewish scripts. Leaves from an epigrapher’s notebook: collected papers in Hebrew and West Semitic palaeography and epigraphy. Winona Lake, IN: Eisenbrauns. 2003. p. 1–43. [Google Scholar]
  • [10].Avigad N. The palaeography of the dead sea scrolls and related documents. Scripta Hierosolymitana. Jerusalem: Magness Press. 1965. p. 56–87. [Google Scholar]
  • [11].Yardeni A. Textbook of Aramaic, Hebrew and nabataean documentary texts from the judaean desert and related material. The Hebrew University. 2000. [Google Scholar]
  • [12].Yardeni A. The palaeography of 4QJera – a comparative study. Textus. 1990;15(1):233–68. doi: 10.1163/2589255x-01501012 [DOI] [Google Scholar]
  • [13].Bonani G, Ivy S, Wölfli W, Broshi M, Carmi I, Strugnell J. Radiocarbon dating of fourteen dead sea scrolls. Radiocarbon. 1992;34(3):843–9. doi: 10.1017/s0033822200064158 [DOI] [Google Scholar]
  • [14].Jull AJT, Donahue DJ, Broshi M, Tov E. Radiocarbon dating of scrolls and linen fragments from the judean desert. Radiocarbon. 1995;37(1):11–9. doi: 10.1017/s0033822200014740 [DOI] [Google Scholar]
  • [15].Schmid K, Schröter J. The making of the Bible: from the first fragments to sacred scripture. Cambridge, MA: Belknap Press. 2021. [Google Scholar]
  • [16].Zenger E, Frevel C. Einleitung in das alte Testament. neunte, aktualisierte auflage ed. Stuttgart: Kohlhammer. 2016. [Google Scholar]
  • [17].He S, Schomaker L. Deep adaptive learning for writer identification based on single handwritten word images. Pattern Recognition. 2019;88:64–74. doi: 10.1016/j.patcog.2018.11.003 [DOI] [Google Scholar]
  • [18].He S, Schomaker L. FragNet: writer identification using deep fragment networks. IEEE Trans Inform Forens Secur. 2020;15:3013–22. doi: 10.1109/tifs.2020.2981236 [DOI] [Google Scholar]
  • [19].He S, Schomaker L. GR-RNN: Global-context residual recurrent neural networks for writer identification. Pattern Recognit. 2021;117:107975. doi: 10.1016/j.patcog.2021.107975 [DOI] [Google Scholar]
  • [20].Zhang Z, Schomaker L. DiverGAN: an efficient and effective single-stage framework for diverse text-to-image generation. Neurocomputing. 2022;473:182–98. doi: 10.1016/j.neucom.2021.12.005 [DOI] [Google Scholar]
  • [21].Ameryan M, Schomaker L. How to limit label dissipation in neural-network validation: exploring label-free early-stopping heuristics. J Comput Cult Herit. 2023;16(1):1–20. doi: 10.1145/3587168 [DOI] [Google Scholar]
  • [22].Bronk Ramsey C. Development of the radiocarbon calibration program. Radiocarbon. 2001;43(2A):355–63. doi: 10.1017/s0033822200038212 [DOI] [Google Scholar]
  • [23].Bronk Ramsey C, van der Plicht J, Weninger B. ‘Wiggle matching’ radiocarbon dates. Radiocarbon. 2001;43(2A):381–9. doi: 10.1017/s0033822200038248 [DOI] [Google Scholar]
  • [24].Israel Antiquities Authority. The Leon levy dead sea scrolls digital library. https://www.deadseascrolls.org.il/explore-the-archive
  • [25].Lim T, Alexander P. The Dead Sea Scrolls electronic library (volume 1). 1995. [Google Scholar]
  • [26].Dhali M, de Wit J, Schomaker L. Binet: degraded-manuscript binarization in diverse document textures and layouts using deep encoder-decoder networks. arXiv preprint 2019. https://arxiv.org/abs/1911.07930 [Google Scholar]
  • [27].Brink A, Bulacu M, Schomaker L. How much handwritten text is needed for text-independent writer verification and identification. In: 2008 19th International Conference on Pattern Recognition (ICPR). Piscataway: IEEE. 2008. [Google Scholar]
  • [28].Bulacu M, Schomaker L, Vuurpijl L. Writer identification using edge-based directional features. In: Proceedings of the Seventh International Conference on Document Analysis and Recognition. IEEE Comput. Soc. 2003. [Google Scholar]
  • [29].Schomaker L, Bulacu M. Automatic writer identification using connected-component contours and edge-based features of uppercase Western script. IEEE Trans Pattern Anal Machine Intell. 2004;26(6):787–98. doi: 10.1109/tpami.2004.18 [DOI] [PubMed] [Google Scholar]
  • [30].Bulacu M, Schomaker L. Text-independent writer identification and verification using textural and allographic features. IEEE Trans Pattern Anal Mach Intell. 2007;29(4):701–17. doi: 10.1109/TPAMI.2007.1009 [DOI] [PubMed] [Google Scholar]
  • [31].Dhali MA, Jansen CN, de Wit JW, Schomaker L. Feature-extraction methods for historical manuscript dating based on writing style development. Pattern Recognit Lett. 2020;131:413–20. doi: 10.1016/j.patrec.2020.01.027 [DOI] [Google Scholar]
  • [32].He S, Samara P, Burgers J, Schomaker L. Image-based historical manuscript dating using contour and stroke fragments. Pattern Recognit. 2016;58:159–71. doi: 10.1016/j.patcog.2016.03.032 [DOI] [Google Scholar]
  • [33].Sommerschield T, Assael Y, Pavlopoulos J, Stefanak V, Senior A, Dyer C. Machine learning for ancient languages: a survey. Comput Linguist. 2023;1–45. [Google Scholar]
  • [34].Schomaker L. Monk - search and annotation tools for handwritten manuscripts. http://monk.hpc.rug.nl/. 2023.
  • [35].Adam K, Baig A, Al-Maadeed S, Bouridane A, El-Menshawy S. KERTAS: dataset for automatic dating of ancient Arabic manuscripts. IJDAR. 2018;21(4):283–90. doi: 10.1007/s10032-018-0312-3 [DOI] [Google Scholar]
  • [36].Hoerl AE, Kennard RW. Ridge regression: biased estimation for nonorthogonal problems. Technometrics. 2000;42(1):80–6. doi: 10.1080/00401706.2000.10485983 [DOI] [Google Scholar]
  • [37].Hamid A, Bibi M, Moetesum M, Siddiqi I. Deep learning based approach for historical manuscript dating. In: 2019 International Conference on Document Analysis and Recognition (ICDAR). IEEE. 2019. p. 967–72. doi: 10.1109/icdar.2019.00159 [DOI] [Google Scholar]
  • [38].Hodson TO. Root-mean-square error (RMSE) or mean absolute error (MAE): when to use them or not. Geosci Model Dev. 2022;15(14):5481–7. doi: 10.5194/gmd-15-5481-2022 [DOI] [Google Scholar]
  • [39].Assael Y, Sommerschield T, Shillingford B, Bordbar M, Pavlopoulos J, Chatzipanagiotou M, et al. Restoring and attributing ancient texts using deep neural networks. Nature. 2022;603(7900):280–3. doi: 10.1038/s41586-022-04448-z [DOI] [PMC free article] [PubMed] [Google Scholar]
  • [40].Popović M. Qumran as scroll storehouse in times of crisis? a comparative perspective on judaean desert manuscript collections. J Study Jud. 2012;43(4–5):551–94. doi: 10.1163/15700631-12341239 [DOI] [Google Scholar]
  • [41].Koopmans L, Dhali M, Schomaker L. The effects of character-level data augmentation on style-based dating of historical manuscripts. In: Proceedings of the 12th International Conference on Pattern Recognition Applications and Methods. SCITEPRESS - Science and Technology Publications. 2023. p. 124–35. doi: 10.5220/0011699500003411 [DOI] [Google Scholar]
  • [42].Hempel C. The community rules from Qumran: a commentary. Mohr Siebeck. 2020. [Google Scholar]
  • [43].Bulacu M, Brink A, Zant T van der, Schomaker L. Recognition of handwritten numerical fields in a large single-writer historical collection. In: 2009 10th International Conference on Document Analysis and Recognition. IEEE. 2009. p. 808–12. doi: 10.1109/icdar.2009.8 [DOI] [Google Scholar]

Decision Letter 0

Carlos Odriozola

23 Jan 2025

PONE-D-24-53510Dating ancient manuscripts using radiocarbon and AI-based writing style analysisPLOS ONE

Dear Dr. Popović,

Thank you for submitting your manuscript to PLOS ONE. After careful consideration, we feel that it has merit but does not fully meet PLOS ONE’s publication criteria as it currently stands. Therefore, we invite you to submit a revised version of the manuscript that addresses the points raised during the review process.

**Editor's Response:**

Reviewers appreciate the potential of your innovative approach to dating historical scrolls using AI and radiocarbon data. However, they highlight several areas for improvement before publication. Key concerns include the model's reliance on its training data's chronological range and the unclear integration of palaeography. Reviewers recommend clarifying these points, enhancing reproducibility (e.g., specifying Python versions and providing virtual environment instructions), and addressing minor issues such as missing figures and redundant text.

We find the study scientifically valuable and encourage you to address these revisions to strengthen the manuscript for publication.

Please submit your revised manuscript by Mar 09 2025 11:59PM. If you will need more time than this to complete your revisions, please reply to this message or contact the journal office at plosone@plos.org. When you're ready to submit your revision, log on to https://www.editorialmanager.com/pone/ and select the 'Submissions Needing Revision' folder to locate your manuscript file.

Please include the following items when submitting your revised manuscript:

  • A rebuttal letter that responds to each point raised by the academic editor and reviewer(s). You should upload this letter as a separate file labeled 'Response to Reviewers'.

  • A marked-up copy of your manuscript that highlights changes made to the original version. You should upload this as a separate file labeled 'Revised Manuscript with Track Changes'.

  • An unmarked version of your revised paper without tracked changes. You should upload this as a separate file labeled 'Manuscript'.

If you would like to make changes to your financial disclosure, please include your updated statement in your cover letter. Guidelines for resubmitting your figure files are available below the reviewer comments at the end of this letter.

If applicable, we recommend that you deposit your laboratory protocols in protocols.io to enhance the reproducibility of your results. Protocols.io assigns your protocol its own identifier (DOI) so that it can be cited independently in the future. For instructions see: https://journals.plos.org/plosone/s/submission-guidelines#loc-laboratory-protocols. Additionally, PLOS ONE offers an option for publishing peer-reviewed Lab Protocol articles, which describe protocols hosted on protocols.io. Read more information on sharing protocols at https://plos.org/protocols?utm_medium=editorial-email&utm_source=authorletters&utm_campaign=protocols.

We look forward to receiving your revised manuscript.

Kind regards,

Carlos P. Odriozola, Ph.D

Academic Editor

PLOS ONE

Journal Requirements:

When submitting your revision, we need you to address these additional requirements.

1. Please ensure that your manuscript meets PLOS ONE's style requirements, including those for file naming. The PLOS ONE style templates can be found at

https://journals.plos.org/plosone/s/file?id=wjVg/PLOSOne_formatting_sample_main_body.pdf and

https://journals.plos.org/plosone/s/file?id=ba62/PLOSOne_formatting_sample_title_authors_affiliations.pdf

2. In your manuscript, please provide additional information regarding the specimens used in your study. Ensure that you have reported human remain specimen numbers and complete repository information, including museum name and geographic location.

If permits were required, please ensure that you have provided details for all permits that were obtained, including the full name of the issuing authority, and add the following statement:

'All necessary permits were obtained for the described study, which complied with all relevant regulations.'

If no permits were required, please include the following statement:

'No permits were required for the described study, which complied with all relevant regulations.'

For more information on PLOS ONE's requirements for paleontology and archeology research, see https://journals.plos.org/plosone/s/submission-guidelines#loc-paleontology-and-archaeology-research.

3. Thank you for stating the following financial disclosure:

“This project has received funding by the European Research Council under the European Union’s Horizon 2020 research and innovation programme under grant agreement no. 640497 (HandsandBible). M.Popović and E.Tigchelaar were also supported by NWO, Netherlands Organisation for Scientific Research, and FWO, the Research Foundation - Flanders (SV-15-29).”

Please state what role the funders took in the study. If the funders had no role, please state: "The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript."

If this statement is not correct you must amend it as needed.

Please include this amended Role of Funder statement in your cover letter; we will change the online submission form on your behalf.

4. We note that the grant information you provided in the ‘Funding Information’ and ‘Financial Disclosure’ sections do not match.

When you resubmit, please ensure that you provide the correct grant numbers for the awards you received for your study in the ‘Funding Information’ section.

5. Thank you for stating the following in the Acknowledgments Section of your manuscript:

“This project has received funding by the European Research Council under the European Union’s Horizon 2020 research and innovation programme under grant agreement no. 640497 (HandsandBible). M.P. and E.T. were also supported by NWO, Netherlands Organisation for Scientific Research, and FWO, the Research Foundation - Flanders (SV-15-29).”

We note that you have provided funding information that is not currently declared in your Funding Statement. However, funding information should not appear in the Acknowledgments section or other areas of your manuscript. We will only publish funding information present in the Funding Statement section of the online submission form.

Please remove any funding-related text from the manuscript and let us know how you would like to update your Funding Statement. Currently, your Funding Statement reads as follows:

“This project has received funding by the European Research Council under the European Union’s Horizon 2020 research and innovation programme under grant agreement no. 640497 (HandsandBible). M.Popović and E.Tigchelaar were also supported by NWO, Netherlands Organisation for Scientific Research, and FWO, the Research Foundation - Flanders (SV-15-29).”

Please include your amended statements within your cover letter; we will change the online submission form on your behalf.

6. Please upload a copy of Figure 12, 25 and 29, to which you refer in your text on page 4 and 5. If the figure is no longer to be included as part of the submission please remove all reference to it within the text.

7. Please include a copy of Table 19, 20, 21 and 10 which you refer to in your text on page 3 and 5.

8. Please review your reference list to ensure that it is complete and correct. If you have cited papers that have been retracted, please include the rationale for doing so in the manuscript text or remove these references and replace them with relevant current references. Any changes to the reference list should be mentioned in the rebuttal letter that accompanies your revised manuscript. If you need to cite a retracted article, indicate the article’s retracted status in the References list and also include a citation and full reference for the retraction notice.

[Note: HTML markup is below. Please do not edit.]

Reviewers' comments:

Reviewer's Responses to Questions

Comments to the Author

1. Is the manuscript technically sound, and do the data support the conclusions?

The manuscript must describe a technically sound piece of scientific research with data that supports the conclusions. Experiments must have been conducted rigorously, with appropriate controls, replication, and sample sizes. The conclusions must be drawn appropriately based on the data presented.

Reviewer #1: Yes

Reviewer #2: Yes

**********

2. Has the statistical analysis been performed appropriately and rigorously?

Reviewer #1: Yes

Reviewer #2: Yes

**********

3. Have the authors made all data underlying the findings in their manuscript fully available?

The PLOS Data policy requires authors to make all data underlying the findings described in their manuscript fully available without restriction, with rare exception (please refer to the Data Availability Statement in the manuscript PDF file). The data should be provided as part of the manuscript or its supporting information, or deposited to a public repository. For example, in addition to summary statistics, the data points behind means, medians and variance measures should be available. If there are restrictions on publicly sharing data—e.g. participant privacy or use of data from a third party—those must be specified.

Reviewer #1: Yes

Reviewer #2: Yes

**********

4. Is the manuscript presented in an intelligible fashion and written in standard English?

PLOS ONE does not copyedit accepted manuscripts, so the language in submitted articles must be clear, correct, and unambiguous. Any typographical or grammatical errors should be corrected at revision, so please note any specific errors here.

Reviewer #1: Yes

Reviewer #2: Yes

**********

5. Review Comments to the Author

Please use the space provided to explain your answers to the questions above. You may also include additional comments for the author, including concerns about dual publication, research ethics, or publication ethics. (Please upload your review as an attachment if it exceeds 20,000 characters)

Reviewer #1: The authors' aim has been to use the geometric features derived from the writing style as vectors to construct a regression function that points to a probabilistic range that allows dating scrolls in a specific chronological range.

The training dataset has been constructed from the dating of 30 manuscripts from which 24 valid C14 dates have been obtained for training. The images of the scrolls were binarised using a variant of U-Net and used as input for the model. Of the 75 processed images, 62 were used for training and 13 for evaluation using a leave-one-out strategy, appropriate given the size of the data.

The idea of using features based on the shape of handwriting to train a supervised regression model oriented to a chronological range based on c14 dates is indeed a clever way of looking for patterns in the data using novel computational methods that has the potential to bring a greater objectivity and a higher degree of resolution to the study of historical questions in the specific period and subject under consideration and can therefore be of help to palaeographers and historians in their decision-making and contribute to historical debates.

The model is fully reproducible, resulting in a folder with tabular and graphical outputs that match those presented in the text.

Particularly the contribution of new empirical data (c14 dates) is quite relevant to the problem of accurately reconstructing historical developments from the 4th to the 2nd century BCE and fill the chronological gap between the third century BCE and the second century CE (according to the authors) .

I am not an expert on the particular subject on which the ML techniques have been applied, so my comments are limited to a critical assessment of the methods used on an archaeological problem given my experience in that field.

I have some comments which I will describe below and which lead me to suggest some minor revisions before publication:

My main concern is how much weight the model actually contributes to the conclusions drawn. Let me explain: If the model has been trained with c14 dates in a specific chronological range. Therefore, when making out-of-sample estimates, the model will only be able to give results in the chronological ranges within which it has been trained. Thus, it is possible that some of the undoubtedly interesting conclusions, such as the greater antiquity of some materials (and their historical consequences) are strictly due to the empirical data provided and not to the results of the AI approach. With a larger sample set for training, perhaps these conclusions will change?

This leads me to suggest a consideration of nuancing some of the conclusions drawn in the paper as these observed correlations between chronological ranges and features derived from writing style, while undoubtedly relevant and contributing to reducing uncertainty about the particular problem, have limitations that could be made more explicit and should serve to prevent causal conclusions.

- Line(75) It could be dispensed with as it does not add much to the debate.

- (Line 167) I cant find fig 29.

- (Line 1529-1532 S7). Did the authors of the article perform the post-hoc evaluation? If so, more clarity is needed in the main text on how the assessment has been carried out, as the issue has methodological implications as it is the baseline from which the final reliability of the model is assessed when dealing with out-of-sample data and may be susceptible to confirmation bias.

- (Line 234 Main text) What are the multiple dating methods integrated in the model? As I understand it, the shape-based features derived from the writing style (geometric evidence) have been extracted, binarized and used as input to construct a supervised dataset whose response variable is a date interval (2σ) according to the set of radiocarbon dates (phyisical evidence) presented, and that the results have been validated against the default palaeographic method. It is not clear how other dating methods(palaeography) are integrated into the model. My concern is compounded by the statement in line (258) about avoiding palaeographic estimates as target values and the statement in line (890 S4.2) that says that ‘In this study, we combine palaeography and radiocarbon dating to train our date prediction model’. Just after, in line (924 S 4.2) it is confirmed that ‘To train our artificial intelligence-based date prediction model, we used the accepted 2σ calibrated data from 24 of the 26 valid 14 C results". In Appendix S 4.2, although the problem associated with the qualitative nature of the palaeographic method for estimating the age of the scrolls is explained, it is not made clear how this method has been integrated into the training of the model. Therefore, it seems to me necessary to better explain how palaeography has been used in the model's predictor space, if at all, or to disambiguate the different references to the dating methods used within the model, as well as to rephrase the title of S4.2.

Technical comments:

Although the reproduction of the procedures presented requires a certain level of expertise for which the resources are sufficiently well presented, possible non-technically skilled stakeholders may benefit from having a static version that presents the results alongside the code.

The inclusion of indications for the creation of a virtual environment as well as the specific version of python whitin the README file would benefit the reproducibility of the exercise.

The work therefore presents in a general way novel knowledge that can contribute to advance the knowledge of the specific subject and is of general scientific and historical interest.

Reviewer #2: This manuscript presents a novel use of AI based on radiocarbon dating and handwriting style to determine or correct the dates estimated by the palaeographic studies of the so-called Dead Sea Scrolls. It introduces Enoch, an AI-based prediction model that the authors have trained and tested with these manuscripts, demonstrating its potential, which this reviewer understands to be of significant interest (even to be trained and used in other archaeological/historical contexts where dating based on writing analysis can be corrected).

The study presents results of an original research. With regard to materials and methods, the authors are thorough in describing the manuscript selection processes, sampling, laboratory analysis, and data treatment. Radiocarbon analysis protocols have been adapted to solve the difficulties on dating the fragile samples avoiding contamination.

The main difficulty in dating the scrolls lies in the uncertainty inherent in the two methods used, the discrepancies on writing style analysis and the limitations of the radiocarbon dating method and its calibration. The authors dedicate several pages in the supplementary material (S1) to demonstrating the contradictions of palaeography-based dating and the necessity of tools like Enoch.

The authors state that radiocarbon dates are “more reliable time markers” and “palaeographic estimates do not provide absolute or fixed dates” (lines 572-576, Appendix S4.1). In addition, they “compare the radiocarbon dates with previous palaeographic estimates only in a general sense, not as a rigid application of these estimates” (lines 520-521, Appendix S4.1). However, when working with calibrated radiocarbon dates, the selection or rejection of the C14 temporal ranges used to train Enoch are based on very specific palaeographic temporal proposals (e.g., Appendix S4.1.1). In this regard, the dependence of the C14 dating use from palaeography might appear as an important contradiction.

Concerning this, author’s arguments are better explained in Appendix S5.The statistical calculations and the functioning of Enoch are discussed in detail by the authors. The limitations of the sample size (24 radiocarbon dated scrolls) is explained too. Conclusions are supported by the data.

Finally, in addition to the 95 pages of supplementary material, the authors provide access to other data, such as the OxCal codes, raw data or a video where the rationale behind the research and the control tests conducted can be better understood.

In the opinion of this reviewer, the article should be published with only a couple of minor improvements:

1- In the case of 5/6 Hev1b, the discrepancies between the C14 results and the paleographic estimates are explained (lines 711-716, S4.1.1). However, the discrepancy between those dates and the ones proposed by Enoch, which is clearly shown in Figure 1, is not sufficiently detailed.

2- For practical reasons, table 21 should include Q-numbers.

**********

6. PLOS authors have the option to publish the peer review history of their article (what does this mean?). If published, this will include your full peer review and any attached files.

If you choose “no”, your identity will remain anonymous but your review may still be made public.

Do you want your identity to be public for this peer review? For information about this choice, including consent withdrawal, please see our Privacy Policy.

Reviewer #1: No

Reviewer #2: No

**********

[NOTE: If reviewer comments were submitted as an attachment file, they will be attached to this email and accessible via the submission site. Please log into your account, locate the manuscript record, and check for the action link "View Attachments". If this link does not appear, there are no attachment files.]

While revising your submission, please upload your figure files to the Preflight Analysis and Conversion Engine (PACE) digital diagnostic tool, https://pacev2.apexcovantage.com/. PACE helps ensure that figures meet PLOS requirements. To use PACE, you must first register as a user. Registration is free. Then, login and navigate to the UPLOAD tab, where you will find detailed instructions on how to use the tool. If you encounter any issues or have any questions when using PACE, please email PLOS at figures@plos.org. Please note that Supporting Information files do not need this step.

Decision Letter 1

Carlos Odriozola

4 Apr 2025

Dating ancient manuscripts using radiocarbon and AI-based writing style analysis

PONE-D-24-53510R1

Dear Dr. Popović,

We’re pleased to inform you that your manuscript has been judged scientifically suitable for publication and will be formally accepted for publication once it meets all outstanding technical requirements.

Within one week, you’ll receive an e-mail detailing the required amendments. When these have been addressed, you’ll receive a formal acceptance letter and your manuscript will be scheduled for publication.

An invoice will be generated when your article is formally accepted. Please note, if your institution has a publishing partnership with PLOS and your article meets the relevant criteria, all or part of your publication costs will be covered. Please make sure your user information is up-to-date by logging into Editorial Manager at Editorial Manager® and clicking the ‘Update My Information' link at the top of the page. If you have any questions relating to publication charges, please contact our Author Billing department directly at authorbilling@plos.org.

If your institution or institutions have a press office, please notify them about your upcoming paper to help maximize its impact. If they’ll be preparing press materials, please inform our press team as soon as possible -- no later than 48 hours after receiving the formal acceptance. Your manuscript will remain under strict press embargo until 2 pm Eastern Time on the date of publication. For more information, please contact onepress@plos.org.

Kind regards,

Carlos P. Odriozola, Ph.D

Academic Editor

PLOS ONE

Additional Editor Comments (optional):

Reviewers' comments:

Reviewer's Responses to Questions

Comments to the Author

1. If the authors have adequately addressed your comments raised in a previous round of review and you feel that this manuscript is now acceptable for publication, you may indicate that here to bypass the “Comments to the Author” section, enter your conflict of interest statement in the “Confidential to Editor” section, and submit your "Accept" recommendation.

Reviewer #1: All comments have been addressed

Reviewer #2: All comments have been addressed

**********

2. Is the manuscript technically sound, and do the data support the conclusions?

The manuscript must describe a technically sound piece of scientific research with data that supports the conclusions. Experiments must have been conducted rigorously, with appropriate controls, replication, and sample sizes. The conclusions must be drawn appropriately based on the data presented.

Reviewer #1: Yes

Reviewer #2: (No Response)

**********

3. Has the statistical analysis been performed appropriately and rigorously?

Reviewer #1: Yes

Reviewer #2: (No Response)

**********

4. Have the authors made all data underlying the findings in their manuscript fully available?

The PLOS Data policy requires authors to make all data underlying the findings described in their manuscript fully available without restriction, with rare exception (please refer to the Data Availability Statement in the manuscript PDF file). The data should be provided as part of the manuscript or its supporting information, or deposited to a public repository. For example, in addition to summary statistics, the data points behind means, medians and variance measures should be available. If there are restrictions on publicly sharing data—e.g. participant privacy or use of data from a third party—those must be specified.

Reviewer #1: (No Response)

Reviewer #2: (No Response)

**********

5. Is the manuscript presented in an intelligible fashion and written in standard English?

PLOS ONE does not copyedit accepted manuscripts, so the language in submitted articles must be clear, correct, and unambiguous. Any typographical or grammatical errors should be corrected at revision, so please note any specific errors here.

Reviewer #1: Yes

Reviewer #2: (No Response)

**********

6. Review Comments to the Author

Please use the space provided to explain your answers to the questions above. You may also include additional comments for the author, including concerns about dual publication, research ethics, or publication ethics. (Please upload your review as an attachment if it exceeds 20,000 characters)

Reviewer #1: The comments have been addressed by the authors and some minor modifications have improved the interpretability of the work.

Reviewer #2: (No Response)

**********

7. PLOS authors have the option to publish the peer review history of their article (what does this mean?). If published, this will include your full peer review and any attached files.

If you choose “no”, your identity will remain anonymous but your review may still be made public.

Do you want your identity to be public for this peer review? For information about this choice, including consent withdrawal, please see our Privacy Policy.

Reviewer #1: No

Reviewer #2: No

**********

Acceptance letter

Carlos Odriozola

PONE-D-24-53510R1

PLOS ONE

Dear Dr. Popović,

I'm pleased to inform you that your manuscript has been deemed suitable for publication in PLOS ONE. Congratulations! Your manuscript is now being handed over to our production team.

At this stage, our production department will prepare your paper for publication. This includes ensuring the following:

* All references, tables, and figures are properly cited

* All relevant supporting information is included in the manuscript submission,

* There are no issues that prevent the paper from being properly typeset

You will receive further instructions from the production team, including instructions on how to review your proof when it is ready. Please keep in mind that we are working through a large volume of accepted articles, so please give us a few days to review your paper and let you know the next and final steps.

Lastly, if your institution or institutions have a press office, please let them know about your upcoming paper now to help maximize its impact. If they'll be preparing press materials, please inform our press team within the next 48 hours. Your manuscript will remain under strict press embargo until 2 pm Eastern Time on the date of publication. For more information, please contact onepress@plos.org.

If we can help with anything else, please email us at customercare@plos.org.

Thank you for submitting your work to PLOS ONE and supporting open access.

Kind regards,

PLOS ONE Editorial Office Staff

on behalf of

Dr. Carlos P. Odriozola

Academic Editor

PLOS ONE

Associated Data

    This section collects any data citations, data availability statements, or supplementary materials included in this article.

    Supplementary Materials

    S1 Appendix. The dating problem of the Dead Sea Scrolls.

    (PDF)

    pone.0323185.s001.pdf (168.3KB, pdf)
    S2 Appendix. Radiocarbon dating of the Dead Sea Scrolls.

    (PDF)

    pone.0323185.s002.pdf (11MB, pdf)
    S3 Appendix. 14C determinations and calibrated date plots.

    (PDF)

    pone.0323185.s003.pdf (289.8KB, pdf)
    S4 Appendix. Palaeography and radiocarbon dating of the Dead Sea Scrolls.

    (PDF)

    pone.0323185.s004.pdf (213.5KB, pdf)
    S5 Appendix. Artificial intelligence (AI) in dating the scrolls.

    (PDF)

    pone.0323185.s005.pdf (23.7MB, pdf)
    S6 Appendix. On the use of pre-trained deep learning methods for image-based dating.

    (PDF)

    pone.0323185.s006.pdf (759.2KB, pdf)
    S7 Appendix. Enoch’s date predictions for 135 previously undated manuscripts.

    (PDF)

    pone.0323185.s007.pdf (4.5MB, pdf)
    S8 Appendix. Comparative plots for different information sources.

    (PDF)

    pone.0323185.s008.pdf (329.5KB, pdf)
    S9 Appendix. List of images for different tests.

    (PDF)

    pone.0323185.s009.pdf (157.4KB, pdf)
    S10 Appendix. Radiocarbon sample information.

    (PDF)

    pone.0323185.s010.pdf (228.2KB, pdf)
    S11 Appendix. Data-sheet radiocarbon runs.

    (PDF)

    pone.0323185.s011.pdf (258.7KB, pdf)
    S12 Appendix. Worksheet of comparative data for 2σ 14C dates and traditional palaeographic estimates.

    (PDF)

    pone.0323185.s012.pdf (182.8KB, pdf)
    Attachment

    Submitted filename: PLOS ONE Response Review Comments.docx

    pone.0323185.s013.docx (25.7KB, docx)

    Data Availability Statement

    All data, code, and test film associated with this article are publicly available on Zenodo with the following DOIs: - Data and prediction plots (v3): https://doi.org/10.5281/zenodo.10998958. - Code and feature files (v6): https://doi.org/10.5281/zenodo.13319794. - Film (see details in S7 Appendix): https://doi.org/10.5281/zenodo.8167946.


    Articles from PLOS One are provided here courtesy of PLOS

    RESOURCES