It has been reported, possibly as apocrypha, that when South Sea islanders were asked to explain their cosmology about what supported the World Turtle (who supported the world), one bright spark replied: “It's turtles all the way down!” The take-home message from the target article is analogously: “It's distributions all the way down!” Though the message may seem obvious, it is interesting to note that most of the current textual, big-data literature either doesn't get it or fails to appreciate its richness.

The lion's share of the textual, big-data literature (that analyses, e.g., words, sentiment terms, tweet tags, phrases, articles, blogs) really concentrates on what could be called first-order effects, rather than on second-order effects. First-order effects are changes in a single, statistical distribution of some measured text-unit (word, article, sentiment term, tag) – usually from some large, unstructured, online dataset – that can act as a predictive proxy for some population-level behaviour. So, for instance, Michel et al. (Reference Michel, Shen, Aiden, Veres, Gray, Pickett, Hoiberg, Clancy, Norvig, Orwant, Pinker, Nowak and Aiden2011) show how relative word frequencies in Google Books can reflect cultural trends; others have shown that distributions of Google search-terms can predict the spread of flu (Ginsberg et al. Reference Ginsberg, Mohebbi, Patel, Brammer, Smolinski and Brilliant2009) and motor sales (Choi & Varian Reference Choi and Varian2012), and the numbers of news articles and of tweet rates can both be used to predict movie box-office revenues (Asur & Huberman Reference Asur and Huberman2010). In these cases, the actual distribution of the text data is directly reflected in some population behaviour or decision.

Second-order distributional effects are changes across several, separate distributions that can predict population-level behaviour; usually, where these separate distributions span different time periods. Big-data research on such effects is a lot less common; to put it succinctly, most of the work focuses on either the wisdom of crowds (Surowiecki Reference Surowiecki2005) or herd-like behaviour (Huang & Chen Reference Huang and Chen2006) but not on how a wise crowd becomes a stupid herd (for rare exceptions, see Bentley & Ormerod Reference Bentley and Ormerod2010; Bentley et al. Reference Bentley, Garnett, O'Brien and Brock2012; Onnela & Reed-Tsochas Reference Onnela and Reed-Tsochas2010; Salganik et al. Reference Salganik, Dodds and Watts2006). Bentley et al. recognise the importance of such second-order effects in stressing that population decision-making may shift from one signature distribution to another. However, we believe that there is more to be said about such second-order effects.

For instance, second-order effects can be further divided into between-distribution and within-distribution effects. Between-distribution effects concern the types of changes, mentioned by Bentley et al., where there is change from one signature distribution to another over time (movement between the quadrants of their map): for example, from the Gaussian distribution of the wisdom of crowds to the power-law distribution of herd behaviour. In physical phenomena, such distributional changes are often cast as phase transitions; for example, when water turns to ice or when a heated iron bar becomes magnetised (see Barabasi & Gargos 2002). Bentley et al. raise the prospect that there are a host of similar phase transitions in human population behaviour, transitions that can be tracked and predicted by mining various kinds of big data. We find this prospect very exciting, given the notable gap in the big-data literature on such effects.

Bentley et al. say a lot less about within-distribution effects, the systematic changes that may occur in the properties of a given signature distribution from one time-period to the next; for example, the specific properties of separate power-law distributions of some measured item might change systematically over time. Research on such within-distribution effects in textual, big-data research is even rarer than that on between-distribution effects – one of these rarities being our own work on stock-market trends (Gerow & Keane Reference Gerow, Keane and Walsh2011). In this study (Gerow & Keane Reference Gerow, Keane and Walsh2011), we found systematic changes in the power-law distributions of the language in finance articles (from the BBC, the New York Times, and the Financial Times) during the emergence of the 2007 stock-market bubble and crash, based on a corpus analysis of 18,000 online news articles over a 4-year period (10M+ words). Specifically, we found that week-to-week changes in the power-law distributions of verb-phrases correlated strongly with market movements of the major indices; for example, the Dow Jones Index correlated (r=0.79) with changes in the 8-week-windowed, geometric mean of the alpha terms of the power laws. These within-distribution changes showed that, week-on-week, journalists were using a progressively narrower set of words to describe the market, reporting on the same small set of companies using the same overwhelmingly positive language. So, as the agreement between journalists increases, the power-law distributions change systematically in ways that track population decisions to buy stocks.

In Bentley et al.’s map, this analysis is about tracking movement within the southeast quadrant. Naturally, we also find the prospect of such within-distribution effects very exciting, especially given the lack of attention to them thus far.

So, it really is “Distributions all the way down!” Current research is only scraping the surface of the possible distributional effects that may be mined from various online sources. Bentley et al. have provided a framework for thinking about such second-order effects, especially of the between-distribution kind, but there is also a whole slew of within-distribution phenomena yet to be explored.