Fractality of informativity in 300 years of E nglish scientific writing (2023)

Abstract: Scientific writing is assumed to have become more informationally dense over time (Halliday, 1988; Biber and Gray, 2016). By means of fractal analysis, we study whether over time the degree of informativity has become more persistent with predictable patterns of gradual changes between high vs. low informational content, indicating a trend towards an optimal code for scientific communication.

## introduction fractals are the product of dynamic systems and refer to structures that are self-similar, i.e. repeat themselves on every level of scale, indicating recurrent patterns. while fractality has its origin in mathematics by researcher benoît mandelbrot, it has been applied to a wide range of fields which consider complex dynamic systems, such as biology @xcite or music @xcite . language is a complex dynamic system that shows inherent fractal patterns, especially in language evolution, language processing, change in language use, acquisition or development (e.g., @xcite ; @xcite ; @xcite ). this dynamic perspective on language allows us 'to tease out the processes through which a phenomenon unfolds' @xcite . in this paper, we are interested in how english written scientific communication has evolved over a period of ∼ 330 years from its beginnings (1660s) up to modern science @xcite . one general hypothesis for the development of scientific writing is that it has become increasingly informationally dense over time @xcite , moving from increased clausal to increased phrasal complexity (i.e. from a verbal towards a heavy nominal style). given that scientific writing is intended for communication between experts, we hypothesize a tendency towards optimizing language use by striving for a balance between highly informative content and a conventionalized style of writing. we measure the informativity of scientific texts using the information-theoretic measure of surprisal, i.e. a word's predictability in context. the more predictable a word is in its context, the less its informativity (e.g. function words are low in informativity as they are quite predictable given particular contexts, consider e.g. the expression on behalf of, were of is quite predictable given on behalf ), while lower predictability indicates high informativity (as e.g. for scientific terms). by means of fractal analysis, we compute the hurst exponent @xcite of informativity arcs, asking whether over time the degree of informativity has become more persistent with texts showing gradually increasing and decreasing patterns of informativity (higher hurst exponents) which repeat themselves in a text (indicated as self-similarity) or whether informativity tends to fluctuate within a text (low hurst exponents) without a recurrent pattern. ## analysis using the hurst exponent, we ask whether the distribution of informativity within the rsc texts becomes more persistent over time, which would indicate a more uniform and smooth distribution of information within articles, i.e. a more persistent informativity profile. informativity is measured by surprisal (cf. section 2.2). example (1) shows a sentence with low informativity on average (4.6 of surprisal), where words are relatively predictable given their previous context (such as newton given sir isaac). example (2) shows a sentence which is higher in informativity on average (surprisal of 8.1), where illustrated is relatively unpredictable given its previous context (compare to the more explicit version which occurred and which illustrated which would lower the average informativity). example (3) presents a highly informative sentence (surprisal of 10.9) due to the terms used in it. we compute the hurst exponent on the articles' sentence-based informativity arcs. figure 1 and 2 show the lines of two arcs with extremely high (@xmath0.92) vs. low (@xmath1.27) exponents. informativity is on the y-axis of figure 1a and 2a with the time series of the texts (i.e. sentences) on the xaxis. figure 2a shows high fluctuations around the mean with rather abrupt changes in surprisal values, while figure 1a shows a much smoother trend, with smaller and gradual changes in informativity from low to high and vice versa. figure 1b and 2b present a globally smooth trend signal, represented as a polynomial fit on the detrended informativity profile foot_3 . a detrended profile is a profile where the datapoints' values are subtracted to the mean; polynomial fits on such a signal allow us to estimate the series' underlying systematic components and to forecast its long-term behaviour (see also @xcite on obtaining global lines, i.e. detrended lines). in general, texts with a low hurst exponent contain sentences with strongly varying averages in surprisal (low-high-low etc), while texts with a relatively high hurst exponent are built up by sequences of sentences presenting a gradual increase or decrease in surprisal (low-lower-high-higherhighest-higher-high-lower-low etc). thus, a hurst exponent @xmath2.5 indicates long-term trends in the informativity profile of a text and more persistent patterns (e.g. a gradual increase in informativity followed by a gradual decrease or vice versa). a hurst exponent of 0.5 indicates abrupt changes with unpredictable peaks and troughs in informativity, while a value @xmath3.5 suggests an antipersistent trend, i.e. a trend reverting constantly to the mean through a "zig-zag"-like behaviour. figure 3 shows an overall trend of the hurst exponent for the rsc texts averaged over each year, with the averaged exponent value on the y-axis and years on the x-axis. for almost all years the hurst exponent @xmath4.5. from the 1650s to 1800 there 4 to best show mean-reverting patterns, (b) excludes the first and last ten sentences of the article. figure 3: hurst exponent of rsc texts over time averaged on each year. however, after a relatively stable period, informativity profiles become slightly less persistent in the 20th century. this could indicate a development of a scientific code at pressure given the highly demanding process of increased specialization, i.e. growing specialized domains, in which formulaic language and grammatical consolidation are combined with an increasingly diverse, domainspecific use of terminology. these high demands might introduce sharper changes in the informativity profiles of more contemporary articles, leading to the slight disrupt of the "smoothness" of the informativity trends, slightly lowering the overall hurst score. finally, it is worth noting that while the texts' average hurst exponent oscillates through macroperiods (here centuries), its variance and standard deviation decline steadily ( measure spearman corr. kendall corr. mean 0.160 0.076 variance -0.664* [-0.83, -0.4] -0.517* [-0.74, -0.2] std -0.619* [-0.8,-0.33] -0.476* [-0.71,-0.13] ## conclusion we have modeled fractality for english scientific texts given their informativity over time on the rsc corpus, showing a general trend towards the use of smoother informativity profiles. this is in line with previous accounts on information density, which hypothesize uniform distributions to ease processing cost @xcite . here, we have shown that this also adheres at the textual level. considering that scientific writing is meant for expert-to-expert communication, being subject to increased processes of specialization, more contemporary scientific writing shows trends towards slightly less smoothed signals, with stronger alternations between more conventionalized, formulaic vs. highly specialized informational content. at the same time, we observed a strong converging trend indicated by a significant reduction in variance and standard deviation of the hurst exponent. in future, we would like to see whether this notion of an optimized informativity signal is observable in the development of other registers. also, there might be discipline-specific trends which would shed light on processes of specialization and diversification among scientific disciplines. moreover, as we continuously work on enhancing corpus quality, we would like to have a through analysis of possible confounds that might have an impact on surprisal as well as fractality calculation. this will lead us to uncover more comprehensively source for changes in fractality. also, as we here have applied one of the most simple ways of calculating fractality, we want to experiment with other measures in order to evaluate their performance for this task.