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Juola, Patrick, Duquesne University, USA,

It is common to hear assertions that culture is complex, that language is complex, and that while the complexity of language is a universal constant, the complexity of culture is increasing as technology and the increased pace of modern life creates new complexities. These statements are usually based on subjective assessments, often tinged by nostalgia for the ‘good old days.’ Can questions of cultural complexity be addressed quantitatively?

Previous work (e.g. Juola 1997, 2008) has been able to use information theory to address this question. The basic idea is that a sample of language is ‘complex’ if it contains a lot of information, defined formally as the size of the computer program that would be necessary to (re)create the sample from scratch, a measure more formally known as Kolmogorov complexity. This can be approximated by compressing the text sample and looking at the size of the resulting file – the larger the resulting file, the more complex the original. Alternatively, one can compute complexity directly using Shannon’s (1948) famous formula for information entropy based on a concept of the underlying linguistic ‘events.’ In any case, linguistic complexity can be measured observing discourse-controlled samples of language, essentially by comparing several (linguistic) versions of the same text, such as translations of the Bible or of a specific novel, and observing whether one language yields systematically larger measurements than another. Previous work suggests that no such systematic pattern exists, and that all languages are indeed roughly equal in complexity.

Key to this approach is the idea of discourse control; we are measuring how difficult it is to express a specific fixed concept in a given language and comparing it to the same concept expressed in an another language. Culture, however, can be treated as the set of concepts that people choose to express. By eliminating the restriction of discourse control and instead investigating language chosen freely by the cultural participants, we may be able to tease apart the interaction between cultural and linguistic complexity. In particular, we can distinguish between linguistic and cultural complexity as follows: a language is complex if there is a lot of information contained in a topic-controlled discourse. A culture is complex if there is a large range of topics for discourse, or alternatively a lot of information contained in topical choice. Therefore, if we compare the complexity (however measured) of two language samples that are not topic-controlled, but instead are in some sense representative of the breadth of discourse present in a culture, we can calculate the differences attributable to discourse variation, and hence to cultural complexity.

As an illustrative example, we follow the approach of Spenser (1900; cited by Denton 2004), in that ‘complex’ means ‘containing many different interdependent parts.’ A complex political system has many parties and power groups, many different roles and offices, and many relationships among them. In a political discourse, many if not most of these parties and power groups would need to be explicitly named and distinguished from each other. By contrast, an autocratic monarchy is relatively simple: there is the monarch and then everyone else. A game is complex if it has many rules and strategies. A culture is complex if it contains many heterogeneous aspects such as technological specifications, social stratification, multilevel administrative hierarchies, or a large amount of object or object-types. Continuing this line of reasoning, a complex culture is one with lots of ‘stuff’ and where people do lots of things to or with ‘stuff,’ where ‘stuff’ here refers not only to physical objects but also to people, groups, activities, abstractions, and so forth – anything that can be discussed among the group.

We therefore apply the previous methodology to a different sort of corpus; an uncontrolled corpus that represents the breadth of cultural experience. If the information contained in such a corpus is high, then we can say the culture is complex. Several corpora may be suitable for this purpose; we have chosen to study the Google Books Ngram Corpus (Michel et al. 2010). This contains all of the n-grams from the millions of books in the Google Books database, something like 20 million books, or approximately 4% of all books ever printed. While not strictly speaking representative (for example, ‘publishing was a relatively rare event in the 16th and 17th centuries,’ and ‘many more books are published in modern years’), and of course typically only the literate can write or publish books, this nevertheless gives us a time-stamped window into the scope of culture. Furthermore, by focusing on n-grams (and specifically on 2-grams, word pairs), we can observe not only the distribution of ‘stuff,’ but also some of the relationships between ‘stuff’ – for example, the number and range of word pairs beginning with ‘expensive’ will inform us about changing opinions regarding money and the types of goods considered luxurious and pricey.

We therefore used the Google Books American 2-Gram Corpus to measure changes in the complexity of American culture at ten-year intervals between 1900 and 2000. This corpus simply contains a frequency list of all two word phrases used in American-published books in any given year. For example, the phrase ‘hamburgers with’ appeared only 8 times in print in 1940, compared to 45 in the year 2000. Focusing strictly on the US during the 20th century avoids many of the problems with mass culture, as publishing was a well-established industry and literacy was widespread. However, the number of books published in this time of course tended to increase. Our first observation, then, is that culture may be increasing simply from the number of different things to talk about. The number of different word pair types per year increased dramatically, nearly doubling from 1900 to 2000, as given in table 1.

Table 1
Year # types
1900 17,769,755
1910 22,834,741
1920 22,409,426
1930 19,745,549
1940 20,369,679
1950 23,632,749
1960 27,379,411
1970 34,218,686
1980 34,458,083
1990 37,796,626
2000 41,654,264

This alone indicates an increase in the complexity of written culture, although this process is not continuous and some years during the Depression show a loss. To confirm the overall upward trend, we have also calculated the Shannon-entropy of the 2-gram distributions, attached as table 2.

Table 2
Year Entropy (bits)
1900 17.942357
1910 18.072880
1920 18.072325
1930 18.133058
1940 18.241048
1950 18.336162
1960 18.391872
1970 18.473447
1980 18.692278
1990 18.729807
2000 18.742085

This further analysis illustrates that a more sophisticated measure of complexity shows a continuous process of increasing complexity, even in times when (for example due to economic downturn) the actual volume of words published decreases. Even when people are writing less, they still have more ‘stuff’ about which to write, showing the cumulative nature of culture (today’s current events are tomorrow’s history, but still suitable material for discussion and analysis – part of culture).

We acknowledge that this is a preliminary study only. Google Books offers cultural snapshots at much greater frequency than ten-year intervals. Google Books also offers corpora in other languages (including German, French, Spanish, Russian, and Hebrew) as well as another English-speaking culture. Use of a more balanced corpus (such as the Google Books English Million corpus, a corpus balanced at about 1 million words/year to offset increased publication), or the BYU Corpus of Historical American English might help clarify the effects of publication volume. Analysis of n-grams at sizes other than 2 would illustrate other types of complexity — in particular, 1-grams (words) would show changes in lexical but not syntactic complexity and hence an analysis of ‘stuff’ but not what people do with ‘stuff.’ Despite these weaknesses, we still feel this paper illustrates that culture-wide analysis of abstractions like ‘increasing complexity’ is both practical and fruitful.


Denton, T. (2004). Cultural Complexity Revisited. Cross-Cultural Research 38(1): 3-26.

Juola, P. (1998). Measuring Linguistic Complexity : The Morphological Tier. Journal of Quantitative Linguistics 5(3): 206-213.

Juola, P.. (2008). Assessing Linguistic Complexity. In M. Miestamo, K. Sinnemaki, and F. Karlsson (eds.), Language Complexity: Typology, Contact, Change. Amsterdam: John Benjamins.

Michel, Jean-Baptiste, Y. Kui Shen, A. Presser Aiden, A. Veres, M. K. Gray, W. Brockman, The Google Books Team, J. P. Pickett, D. Hoiberg, D. Clancy, P. Norvig, J. Orwant, St. Pinker, M. A. Nowak, and E. Lieberman Aiden (2010). Quantitative Analysis of Culture Using Millions of Digitized Books. Science (Published online ahead of print: 12/16/2010).

Spencer, H. (1900). First principles (6th ed.). Akron, OH: Werner.