The Withers in Morpeth, Northumberland

The mid-word from left to right

normalsize profiles}\label{F2}\end{figure}

It looks like the resulting models have a promising similarity to the previously obtained models for mid-words and late-words. The AIC and the percentage of the variance explained by each model are also very high and analogous with previous estimations. Indeed, the substantial reduction of words that such a restriction entails (from around 1.7 million to just over seventeen thousand) might actually have sharpened the modelling. The two sets of models are also very similar, which tentatively suggests that a partial implementation using data from tritangents should therefore also be useful. I tentatively conclude that this proof of concept has been successful. This has great importance for the wider research prospect of verifying or falsifying quantitative models through experimental verifications, since it is possible to currently perform magnetic resonance with up to seven letters, and with the possible extensions for up to fourteen (Seymour \cite{sey2014exercising}; Birn et al. \cite{bir2014parsing}).

Discussion

Advantages and downsides of this approach

Exit information and the three-dimensional approach

This approach is unique in a number of ways. For example, unlike the new developments in quantitative data-age research grounded on digital humanities and corpus-based methodologies, it does not require direct access to original documents, collections or archives. It only depends on secondary sources, which also implies that the potential of this approach is inevitably limited to already existing digital texts. The theoretical archaeological and inscriptional model for the evolution of writing systems described above shows that the three-dimensional and typological dynamics of graphemes is possibly connected to the basic elements that architecture and urbanism would share across cultures. The three-dimensionality of the paper, the antenna and the cloth might offer an explanation in cognitive terms of the patterns of stylometric signatures that are explained in detail in the previous sections. The mental preference for parallelograms lower than squares supports the view that their width is more readable and had a clearer exit strategy (Yan et al. \cite{yan2015exit}), and is in agreement with the exit information hypothesis which also affects urbanism (Hillier \cite{hill2009spatial}) and that argues for widths proportional to and greater than heights as being more natural and easier to read, provided that they were at equal distance (Bernard \cite{ber2001finding}; Larson \cite{lar2007influence}; Yan \cite{yan2015exit}). It is also relevant that learning to read might enthrone minimum letter widths as an average threshold for processing the relation of vertical and horizontal visual fields. The novelty of the present work, therefore, would also be related to the fact that the computational implementation of the relationship between the architecture of writing (system) and its spatial semantics (network) has not been studied extensively, although compartmental models have been explicitly recognised by O'Brian and Glowacki (\cite{br2007feasting}) as a key to study the political economy, and further developed with regard to architecture (Bevan \cite{bev2013models}), by adding a spatial variable ('compartment') rather than letters.

Attenuated effects through time-distance

I started this work with the question of whether any given model of average word lengths and actual word lengths distribution found in current English texts, as in the previous examples from Moby Dick and the works by Lovecraft, the very same styles and patterns could have been registered in late- and mid-antique Greco-Roman writings. Conversely, if there is any variability across stylistic periods, then I expected to see it reflected in models connecting average word lengths and actual word length distributions. The results even outperform the expected correlations between early writing systems, their usage and material culture. As previously demonstrated in Figures~\ref{F1},~\ref{F2} and~\ref{F3}, the proportions derived from averaged word lengths are not entirely random and correspond to theoretical models of visual preference also explained in Section~\ref{S3}.

Another reason for choosing the data sources comes from the fact that architectural studies so far have not been utilising contemporary textual evidence, which can be supported by the models proposed in this article. Textual data might have been considered as not suitable for primarily longitudinal studies, even though they could offer more precise longitudinal (in time rather than space) information, which is particularly relevant in the case of archaeological excavations. As there could be observed some variances in later Roman sources and samples covered by Pompeian evidence, the model for these reasons cannot be easily generalised since there may be some fluctuations due to the size of the walls and related spatial limitations, which also have to be taken into account. This outcome represents no more than a tiny fraction of the vast documentary source, suitable for the methods described; it would be possibly interesting to test this model also on Etruscan periods, as well as other periods in Greek and Roman art and architecture and compare it to later monumental and palatial styles. The documentation of early styles is much less accessible, and therefore the database that could be tested for this work is, unfortunately, more limited. Nonetheless, the Greco-Roman textual datasets tend to support the findings also for some of the prehistoric models. The implemented methodology could be useful in reconsidering the relationships between architectural canons and their ideological or identity aspects, given their conformity to proportion, symmetry, alignment and material culture. The importance of cultural constraints on the readability of written words was confirmed in primates, who seem to show a preference for an equilateral, rather than a rectangle, parallelogram or trapezium, during the random recognition tests (Spinozzi et al. \cite{spi2009global}). Hence, the preferences for horizontal rectangles wider than squares above other shapes as cultural conventions could be evolutionary determined and imitate or reproduce typical archetypal patterns in spatial environments and built landscapes, aside from their relationship with the physical infrastructure.

Conclusions

The very similar distributions between textual (as in (A-B, Figure~\ref{F2})) and architectural data (as in (C, Figure~\ref{F3})) would confirm that proportions in textual culture can be heuristically traced back in typological terms not only to architectural patterns but also to the monumental inscriptions, despite their inevitable differences. Equipped with a limited set of analytical lenses focused on the correlations of textual with archaeological lines of evidence, I attempted here to propose a more comprehensive model for understanding the origins of ancient aesthetics from a cognitive perspective accountable for dimensions that go beyond the domain of letters and written culture. At first, it might be surprising that the Canons, buildings and monumental inscriptions have so much in common, and that the literary strategies of producing writing preserve so much of the classic architectural proportions. The predominance of oral culture in explaining early testimonies has been contested, also in light of finding that writing systems might be older than previously thought. According to S. Houston (\cite{hous2004writing}), writing was not tightly connected with the administrative or supra-personal, abstract economic systems. As a result, the communicative and social functions of writing were instead tightly interwoven: writing is embedded within speech, and canonical texts could be used to invite discourse and conversation, over an ale in the alehouse, or wine in the tabernae or popinae. One obvious advantage of this research is that it can be applied iteratively to much larger textual datasets: its usage does not demand much philological expertise, and the naive, not domain-specific ontology of letters seems to perform well in delivering a stylistic analysis. Consequently, I hope that the identification of three-dimensional and typological strategies behind the materialities of writing could provide important stimuli towards our understanding of the affinity of texts towards different material cultures. In that sense, this work could also be relevant for archaeological theory, anthropology and studies of material culture, which all would benefit from considering the quantitative aspects and data-driven evidence in textual corpora, and insights into the more robust modelling of written culture which crosses borders between disciplines and periods.