Mathematics Meets Archaeology: Discovering the Mesolithic Origins of Car Dyke

Robert John Langdon August 23, 2024August 23, 2024 Archaeological Discoveries, Archaeological Methodology, Bayesian Analysis in Archaeology, Car Dyke Construction Date, Data-Driven Archaeology, Mathematical Models in Archaeology, Mesolithic Archaeology, Prehistoric Britain, Scientific Archaeology, Spatial Analysis in Archaeology

Contents

1 Introduction
2 The calculations
3 Further Reading
4 Other Blogs

Introduction

In archaeology, theories about ancient structures and sites have traditionally been shaped by subjective interpretations, often constrained by the limited evidence. The lack of precise data, historical bias, and conflicting narratives have left the field somewhat speculative. However, recent advancements in mathematical modelling have introduced new ways to derive data-driven conclusions. We can dig deeper into the ancient past by applying Bayesian and Spatial Analysis, extracting valuable insights with greater certainty. One particularly compelling case study is the re-evaluation of Car Dyke, a linear earthwork historically associated with Roman engineering. Through these combined mathematical approaches, we have uncovered evidence that suggests Car Dyke may have been constructed much earlier than previously thought, potentially dating back to the Mesolithic period. (Mathematics Meets Archaeology: Discovering the Mesolithic Origins of Car Dyke)

Bayesian Analysis

Bayesian analysis, a statistical method for updating the probability of a hypothesis as new evidence is introduced, has become a powerful tool in archaeology. Rather than concluding solely on static data, Bayesian analysis allows researchers to adjust their assumptions and probabilities as more evidence becomes available. For example, when archaeologists find artefacts from a particular period, Bayesian analysis helps calculate the likelihood that the site was occupied or used during that time. This method is precious for refining timelines and revising outdated interpretations, as it constantly evolves based on the influx of new data. In archaeology, it has traditionally been applied to analyse when sites were in use rather than when they were constructed.

However, focusing solely on the usage of a site can leave gaps in understanding its origins. This is where Spatial Analysis comes into play. Spatial Analysis examines the geographic distribution of artefacts and features, revealing patterns that might indicate when and how the site was built. By analysing the concentration of artefacts across a landscape, Spatial Analysis can help pinpoint periods of significant activity and uncover the construction date of ancient structures. When combined with Bayesian analysis, this approach offers a more comprehensive understanding of a site’s construction and use, leading to data-driven and contextually rich conclusions. (Mathematics Meets Archaeology: Discovering the Mesolithic Origins of Car Dyke)

Car Dyke

Car Dyke is an ideal case study for demonstrating the power of this dual approach. The Dyke stretches across Lincolnshire and Cambridgeshire, and for years, it has been a topic of debate among archaeologists. Traditionally, scholars have attributed its construction to Roman engineering, primarily due to the presence of Roman artefacts in the broader region. However, our research applied Bayesian and Spatial Analysis to challenge this assumption. By focusing on the distribution of artefacts found specifically along the Dyke, we uncovered evidence suggesting that its origins might be much older, potentially tracing back to the Mesolithic or Neolithic periods.

We began our investigation by applying Bayesian analysis to calculate the likelihood of different periods being associated with the construction of Car Dyke. This required gathering data on all artefacts found across Lincolnshire and using it to calculate the prior probabilities for each period. Given the abundance of Roman artefacts in the region, our initial Bayesian model favoured a Roman construction date. However, as we incorporated new evidence from the area surrounding Car Dyke, a different pattern began to emerge. Spatial Analysis revealed that a significant number of Mesolithic and Neolithic artefacts were clustered in proximity to the Dyke, suggesting that it might have been constructed much earlier than previously believed. (Mathematics Meets Archaeology: Discovering the Mesolithic Origins of Car Dyke)

Spatial Analysis

Spatial Analysis allowed us to go beyond the surface-level examination of artefacts. By mapping the geographic distribution of Mesolithic and Neolithic finds, we could see that these early artefacts were concentrated in key areas along Car Dyke, particularly where it intersects with ancient landscapes like river valleys and elevated terrain. This pattern indicated that the Dyke was more than just a Roman infrastructure project—it may have been a significant site for earlier peoples as well. The concentration of Mesolithic artefacts along the Dyke strongly suggests that the site was either constructed or heavily used during that period.

The integration of Bayesian and Spatial Analysis was essential in refining our understanding of Car Dyke’s history. While Bayesian analysis initially supported the Roman origin theory due to the larger body of Roman artefacts across Lincolnshire, the localised data revealed by Spatial Analysis shifted the probabilities significantly. This combination of methods allowed us to challenge the traditional narrative and propose a new hypothesis: Car Dyke may have been constructed during the Mesolithic period and later used or modified by the Romans. This shift in focus—from usage to construction—helped us uncover a deeper history of the site that would not have been apparent through Bayesian analysis alone. (Mathematics Meets Archaeology: Discovering the Mesolithic Origins of Car Dyke)

Data-Driven Methos of Identification

This dual approach also highlights a broader shift in archaeology toward more data-driven methods. Traditionally, archaeology has relied on subjective interpretations, with researchers filling in the gaps when evidence was sparse. While this has yielded valuable insights, it has also introduced biases and inconsistencies. By incorporating mathematical models like Bayesian and Spatial Analysis, we reduce the subjectivity inherent in archaeological interpretation and increase the accuracy of our conclusions. These methods offer a more transparent and repeatable framework for analysing archaeological data, allowing researchers to refine their hypotheses as new evidence is discovered.

The benefits of this approach extend beyond just Car Dyke. By applying Spatial Analysis alongside Bayesian calculations, archaeologists can uncover hidden patterns that might go unnoticed. For example, Spatial Analysis considers the broader context of artefacts within the landscape, revealing relationships between artefact concentrations and natural features such as rivers, hills, and valleys. This level of analysis helps archaeologists understand not just when a site was used but also why it was built in a specific location. In the case of Car Dyke, Spatial Analysis allowed us to see that the site’s significance extended far beyond the Roman period, providing a more complete picture of its history and purpose.

Our Revaluation of Car Dyke

The re-evaluation of Car Dyke’s construction date demonstrates the power of combining Bayesian and Spatial Analysis in archaeology. Bayesian analysis is invaluable for updating our understanding of site usage, but Spatial Analysis provides critical insights into ancient structures’ construction and broader significance. These methods allow archaeologists to move beyond speculation and embrace a more scientific approach to uncovering the past. Integrating mathematics into archaeology marks a crucial step forward, helping researchers develop more accurate and evidence-based conclusions.

Car Dyke North Section – (Mathematics Meets Archaeology: Discovering the Mesolithic Origins of Car Dyke)

As we refine these techniques and apply them to other sites, the potential for discoveries grows exponentially. The case of Car Dyke is just one example of how mathematical analysis can reshape our understanding of ancient history. By embracing data-driven methods like Bayesian and Spatial Analysis, archaeology is evolving into a discipline that is less reliant on conjecture and more focused on scientific rigour. The future of archaeology lies in this marriage of mathematics and empirical evidence. As we continue to push the boundaries of what we know, we can expect to uncover even more of history’s mysteries with confidence and clarity.

Conclusion

The combination of Bayesian and Spatial Analysis has revolutionised our understanding of Car Dyke’s construction date, suggesting that it may have been built during the Mesolithic period rather than the Roman era. This new approach has reduced the subjectivity in archaeological interpretation and allowed us to develop more accurate, data-driven conclusions. As these mathematical models continue to be refined and applied to other archaeological sites, they will undoubtedly pave the way for even more significant discoveries and a deeper understanding of our ancient past.

The calculations

Bayesian Analysis

To calculate the prior probabilities for each period based on the total number of finds in Lincoln, we first calculate the total number of finds across all periods:

Step 1: Total Number of Finds

Total Finds=13,723(Roman)+8,994(Medieval)+5,619(Post Medieval)+1,680(Early Medieval)+2,451(Iron Age)+2,091(Neolithic)+634(Mesolithic)+980(Bronze Age)=36,172\text{Total Finds} = 13,723 (\text{Roman}) + 8,994 (\text{Medieval}) + 5,619 (\text{Post Medieval}) + 1,680 (\text{Early Medieval}) + 2,451 (\text{Iron Age}) + 2,091 (\text{Neolithic}) + 634 (\text{Mesolithic}) + 980 (\text{Bronze Age}) = 36,172Total Finds=13,723(Roman)+8,994(Medieval)+5,619(Post Medieval)+1,680(Early Medieval)+2,451(Iron Age)+2,091(Neolithic)+634(Mesolithic)+980(Bronze Age)=36,172

Step 2: Calculate Prior Probabilities

Divide the number of finds for each period by the total number of finds:

P(Roman)=13,72336,172≈0.3794P(\text{Roman}) = \frac{13,723}{36,172} \approx 0.3794P(Roman)=36,17213,723≈0.3794 P(Medieval)=8,99436,172≈0.2487P(\text{Medieval}) = \frac{8,994}{36,172} \approx 0.2487P(Medieval)=36,1728,994≈0.2487 P(Post Medieval)=5,61936,172≈0.1554P(\text{Post Medieval}) = \frac{5,619}{36,172} \approx 0.1554P(Post Medieval)=36,1725,619≈0.1554 P(Early Medieval)=1,68036,172≈0.0465P(\text{Early Medieval}) = \frac{1,680}{36,172} \approx 0.0465P(Early Medieval)=36,1721,680≈0.0465 P(Iron Age)=2,45136,172≈0.0678P(\text{Iron Age}) = \frac{2,451}{36,172} \approx 0.0678P(Iron Age)=36,1722,451≈0.0678 P(Neolithic)=2,09136,172≈0.0578P(\text{Neolithic}) = \frac{2,091}{36,172} \approx 0.0578P(Neolithic)=36,1722,091≈0.0578 P(Mesolithic)=63436,172≈0.0175P(\text{Mesolithic}) = \frac{634}{36,172} \approx 0.0175P(Mesolithic)=36,172634≈0.0175 P(Bronze Age)=98036,172≈0.0271P(\text{Bronze Age}) = \frac{980}{36,172} \approx 0.0271P(Bronze Age)=36,172980≈0.0271

Summary of Prior Probabilities:

Roman: 0.3794
Medieval: 0.2487
Post Medieval: 0.1554
Early Medieval: 0.0465
Iron Age: 0.0678
Neolithic: 0.0578
Mesolithic: 0.0175
Bronze Age: 0.0271

Step 1: Define Prior Probabilities

Using the prior probabilities:

Roman: P(HRoman)=0.3794P(H_{\text{Roman}}) = 0.3794P(HRoman)=0.3794
Bronze Age: P(HBronze Age)=0.0271P(H_{\text{Bronze Age}}) = 0.0271P(HBronze Age)=0.0271
Neolithic/Mesolithic: P(HNeolithic/Mesolithic)=0.0753P(H_{\text{Neolithic/Mesolithic}}) = 0.0753P(HNeolithic/Mesolithic)=0.0753

Step 2: Evidence Likelihoods Based on Local Data

Given the distribution of finds:

Roman: P(ERoman∣HRoman)=24132≈0.1818P(E_{\text{Roman}}|H_{\text{Roman}}) = \frac{24}{132} \approx 0.1818P(ERoman∣HRoman)=13224≈0.1818
Bronze Age: P(EBronze Age∣HBronze Age)=47132≈0.3561P(E_{\text{Bronze Age}}|H_{\text{Bronze Age}}) = \frac{47}{132} \approx 0.3561P(EBronze Age∣HBronze Age)=13247≈0.3561
Neolithic/Mesolithic: P(ENeolithic/Mesolithic∣HNeolithic/Mesolithic)=61132≈0.4621P(E_{\text{Neolithic/Mesolithic}}|H_{\text{Neolithic/Mesolithic}}) = \frac{61}{132} \approx 0.4621P(ENeolithic/Mesolithic∣HNeolithic/Mesolithic)=13261≈0.4621

Step 3: Apply Bayes’ Theorem

Posterior Probability for Roman:

P(HRoman∣E)=0.1818×0.3794P(E)=0.0689P(E)P(H_{\text{Roman}}|E) = \frac{0.1818 \times 0.3794}{P(E)} = \frac{0.0689}{P(E)}P(HRoman∣E)=P(E)0.1818×0.3794=P(E)0.0689

Posterior Probability for Bronze Age:

P(HBronze Age∣E)=0.3561×0.0271P(E)=0.0097P(E)P(H_{\text{Bronze Age}}|E) = \frac{0.3561 \times 0.0271}{P(E)} = \frac{0.0097}{P(E)}P(HBronze Age∣E)=P(E)0.3561×0.0271=P(E)0.0097

Posterior Probability for Neolithic/Mesolithic:

P(HNeolithic/Mesolithic∣E)=0.4621×0.0753P(E)=0.0348P(E)P(H_{\text{Neolithic/Mesolithic}}|E) = \frac{0.4621 \times 0.0753}{P(E)} = \frac{0.0348}{P(E)}P(HNeolithic/Mesolithic∣E)=P(E)0.4621×0.0753=P(E)0.0348

Step 4: Normalise the Posterior Probabilities

Sum of the calculated values for normalisation:

P(E)=0.0689+0.0097+0.0348≈0.1134P(E) = 0.0689 + 0.0097 + 0.0348 \approx 0.1134P(E)=0.0689+0.0097+0.0348≈0.1134

Now, calculate the normalised posterior probabilities:

Roman:

P(HRoman∣E)=0.06890.1134≈0.6074P(H_{\text{Roman}}|E) = \frac{0.0689}{0.1134} \approx 0.6074P(HRoman∣E)=0.11340.0689≈0.6074

Bronze Age:

P(HBronze Age∣E)=0.00970.1134≈0.0855P(H_{\text{Bronze Age}}|E) = \frac{0.0097}{0.1134} \approx 0.0855P(HBronze Age∣E)=0.11340.0097≈0.0855

Neolithic/Mesolithic:

P(HNeolithic/Mesolithic∣E)=0.03480.1134≈0.3069P(H_{\text{Neolithic/Mesolithic}}|E) = \frac{0.0348}{0.1134} \approx 0.3069P(HNeolithic/Mesolithic∣E)=0.11340.0348≈0.3069

Analysis and Interpretation:

Neolithic/Mesolithic: The higher frequency of finds in this period significantly increases its posterior probability to approximately 30.69%, which is quite substantial.
Roman: Despite having fewer finds in this area, the Roman period still has a high posterior probability due to its higher prior, but it is now only about 60.74%.
Bronze Age: The probability for the Bronze Age period remains lower at approximately 8.55%.

Conclusion:

The calculated probabilities show a more balanced view, with the Roman period still favoured but with a much stronger case for the Mesolithic/Neolithic period. This suggests that while Roman use of the Dyke is still likely, the Mesolithic/Neolithic period also holds significant importance, potentially indicating earlier use or occupation before the Romans.

Langdon Mathematics

While Bayesian theory often yields definitive results, its accuracy can be compromised due to its dependence on subjective prior assumptions, which may only sometimes reflect reality. If these priors are not well-chosen or are based on incomplete or biased information, the resulting analysis might be misleading.

Therefore, relying solely on Bayesian methods without considering the variability and complexity of archaeological data could lead to conclusions that only partially capture the nuances of the actual distribution of artefacts. My method, which focuses on Spatial Analysis and empirical data, addresses these limitations.

My approach to calculating finds would differ significantly. First, I would define the area where artefacts could be discovered—using Lincolnshire as a reference due to its comprehensive archaeological data. By doing so, we can estimate the expected number of artefacts per square meter of Lincolnshire land, offering a more objective and spatially grounded method for understanding artefact distribution.

As IA reports:

To calculate the percentage likelihood of finding an artefact from each period in a single square meter of Lincolnshire, we can follow these steps:

Step 1: Determine the Area of Lincolnshire

Area of Lincolnshire: Approximately 6,959 square kilometres (6,959,000,000 square meters).

Step 2: Calculate the Find Density

For each period, calculate the density of finds per square meter by dividing the total number of finds by the area of Lincolnshire.

Find Density calc 1 — Mathematics Meets Archaeology: Discovering the Mesolithic Origins of Car Dyke 16

Step 3: Calculate the Likelihood for Each Period

Roman:

Find Density calc 2 1 — Mathematics Meets Archaeology: Discovering the Mesolithic Origins of Car Dyke 17

Likelihood: 0.000156%

Neolithic:

Find Density calc 3 1 — Mathematics Meets Archaeology: Discovering the Mesolithic Origins of Car Dyke 18

Likelihood: 0.000011%

Mesolithic:

Find Density calc 4 2 — Mathematics Meets Archaeology: Discovering the Mesolithic Origins of Car Dyke 19

Likelihood: 0.000004%

Bronze Age:

Find Density calc 5 1 — Mathematics Meets Archaeology: Discovering the Mesolithic Origins of Car Dyke 20

Likelihood: 0.000003%

Summary of Likelihoods in order of expectation:

Roman: 0.000156%
Medieval: 0.000129%
Post Medieval: 0.000081%
Early Medieval: 0.000024%
Iron Age: 0.000021%
Neolithic: 0.000011%
Mesolithic: 0.000004%
Bronze Age: 0.000003%

These percentages represent the likelihood of finding an artefact from each period in a square meter of Lincolnshire. Given the extensive activity during that time, the highest is for the Roman period, just marginally ahead of the Medieval period.

We now need to look at the search area (63 miles of the Northern End of Car Dyke) as listing on the LiDAR maps in the previous section of the book. We must first calculate the total search area in square metres, count the number of finding within this area, and then compare against the expected number.

Summary of Expected Finds:

Roman: 15.83 artefacts
Medieval: 13.07 artefacts
Post Medieval: 8.19 artefacts
Early Medieval: 2.44 artefacts
Iron Age: 2.17 artefacts
Neolithic: 1.07 artefacts
Unknown: 0.59 artefacts
Modern: 0.50 artefacts
Mesolithic: 0.36 artefacts
Bronze Age: 0.34 artefacts

Summary of Items Found:

Mesolithic/Neolithic: 61 finds
Bronze Age: 47 finds
Roman: 24 finds

Calculate the Odds of This Kind of Find

For each period, the odds ratio of finding this many artefacts compared to the expected finds:

Odds 1 — Mathematics Meets Archaeology: Discovering the Mesolithic Origins of Car Dyke 21

Odds 2 — Mathematics Meets Archaeology: Discovering the Mesolithic Origins of Car Dyke 22

Step 4: Interpret the Results

Mesolithic/Neolithic: A massive 5589.72% increase and an odds ratio of 57.01 suggest significant activity during this period, far beyond what was expected.
Bronze Age: An even higher increase of 13723.53% and an odds ratio of 138.24 indicate the area was very important during the Bronze Age.
Roman: A modest 51.60% increase with an odds ratio of 1.52 suggests Roman activity, but not as dominant as the earlier periods.

Conclusion

The very high percentage increases and odds ratios for the Mesolithic/Neolithic and Bronze Age periods strongly suggest that the Car Dyke area was occupied and actively used during these times, with significant archaeological activity that exceeds what would be expected based on general Lincolnshire data. While still represented, the Roman period is less prominent in this area compared to the earlier periods.

This confirms other Dyke surveys such as Offa’s and Wansdyke that also show design (wibbly-wobbly) in construction attributed to the builders seeking natural springs rather than a direct line of route to maintain water levels which were achieved at a later date in history by locks.