Time comprises a burgeoning mode of inquiry in substance use scholarship, as much as its study remains disparate and, in large part, under-explored within the field. Explorations of how time, temporality, and memory are experienced, perceived, reckoned with, and at times actively harnessed, however, lay bare complex experiences of addiction and intimate aspects of everyday life for both people who use drugs and those in abstinence-based recovery (1–3). Temporality, for example, materially impacts how services are engaged with, the diverse ways in which services structure and organize time often being at odds with service users’ own situation in time (2). Reith (4) notably argues that addiction “reorders” time, her participants retrospectively characterizing long periods of drug use as fractious and non-linear, and yet defined by a sense of the present as “extended” or “frozen.” Abstinence-based recovery, in sharp contrast, “reanimated” time, opened up the future, and was typified in linear, spatialized terms of “moving forward” and “looking backwards” (4).

During Laura Roe’s ethnographic fieldwork–on which this paper is based–services, people who used drugs, and those in recovery, consistently employed spatial metaphors while portraying temporalities of drug use, intoxication, and recovery (5). In abstinence, time was framed as a “forward” progression from past, present, to future, although often cyclically looped back on itself or recessed if drug use was returned to. Active polydrug use and intoxication alternatively gave rise to temporal incoherence, fragmentation, and disorder–at times near impossible to express in language. Time was keenly distorted in the high itself, often felt to pause or stretch indefinitely, depending on combinations of drugs taken and physical circumstances. Throughout the fieldwork, questions around how to grapple with such spatio-temporal complexity–and how to account for multitudes of diffuse, shifting, and contradictory experiences that often seemed to sit outside of language–were ever present; questions that this paper aims to address. It does so in part through an engagement with fractal geometry.

Applications of fractal geometry have long occurred outside of mathematics, comprising a prolific area of research across the natural and social sciences. The use of fractal analysis in studies of substance use remains disparate, although notable works have used fractal dimension to map neurological processes altered through substance use (6); explored the relationship between alcohol-related aggression and dopaminergic transmission through fractal analysis (7); and evidenced significant differences in the structural complexity of carotid bodies when deaths were related to opioids (8). However, although fractals have had diverse applications, never has fractal mathematics been applied in qualitative or ethnographic studies of addiction and substance use. Neither have time experience and temporality been seriously theorized in relation to fractals. As this paper demonstrates, however, fractal patterning is evident across many aspects of life for people who use drugs, and particularly in experiences of time shaped by substances.

This paper traces the intimate and intersubjective experiences of people who use heroin and other drugs, many of whom were attempting to negotiate multiple institutions, financial and social precarity, and their own specific reckonings with time and memory. Presenting snapshots of sustained ethnographic fieldwork from two Southeast counties in Scotland, the paper delves into time consciousness in active drug use, illustrated through individual experiences of intoxication. Laura’s fieldwork initially took place over 12 months between 2016 and 2017 in Southeast Scotland, continuing sporadically over several years (5). The first 7 months of research were largely spent in recovery and harm reduction services, including a community abstinence-based recovery group and a third sector needle exchange. During the subsequent 5 months of research, Laura accompanied one scattered group of people who actively used heroin and other drugs in their day to day lives. Primary methods included participant observation, semi-structured interviews, and casual conversation, although the nature of the research necessitated a reflexive, adaptive methodology to account for frequently difficult, unexpected, and ethically complex situations. Findings indicated that time profoundly shaped experiences of addiction and recovery, and that addiction in turn impacted upon senses of time (5).

This paper contends, overall, that a meaningful engagement with fractal theory contains the potential to open up new vocabulary, imagery, and theoretical avenues with which to grasp complex and non-linear time experience. The aims of the paper are, therefore, twofold; to both provide a nuanced ethnographic exploration of substance use time and to propose a reflexive analytical framework for temporal experience through fractals.

Mathematician Kenneth Falconer notes the difficulties of giving a precise definition to fractals, arguing that fractals are best understood as exhibiting certain characteristics (10). One common characteristic is the fractal tendency to exhibit recursive, self-similar patterns across multiple scales. That is, fractals often contain nested patterns within patterns, which appear near identical from any perspective. Coral reefs are frequently given as examples of natural fractals, as magnified “parts,” at any scale, broadly resemble the “whole” in appearance and structure. Coral reefs also exemplify exceptional structural complexity that renders their study challenging. Falconer likewise notes that mathematics has often excluded objects deemed too irregular to be examined within the methods and bounds of classical calculus, or described in “traditional geometric language,” but that fractal geometry offers the potential to better grasp and express complexity (9).

Anthropological and mathematical understandings of complexity are admittedly very different, and the term possesses an array of meanings in both disciplines that make analytical use problematic. Time described as “complex” might connote, in a simple sense of the word, the complicated, the intricate, and the obscure, each of which can be used to characterize the temporalities experienced through substance use. Outside of common parlance, however, complexity may also be considered in the mathematical sense, broadly relating to the nature of systems and their relationships with their component parts. As with fractals, however, there is no one definition of complexity in mathematics, the concept instead depending upon the context it is applied in (10). And as also with fractals, anthropology has a rich history of engaging with complexity theory, perhaps most notably within linguistics (11, 12). In contrast with structuralist approaches to language–which broadly hold that “root” oppositional pairs of signifiers give rise to binary metonymic associations, from which spring “trees” of symbolic classificatory systems–post-structuralist models of language consider signifiers as unfixed and operating in a complex network (13). That is, there exists an “indefinite referral of signifier to signified,” in which the meaning of signs is “endlessly deferred” (12, 14). Language and signification are as such composed through the endlessly complex interactions of individual parts, which comprise classificatory systems. Our interest, too, in understanding time as “complex,” lies largely in the intermingling of dynamic, infinitesimal, and ever-shifting components of temporal experience and memory–that is, in the “non-linear relationships between constantly changing entities” (10).

How, then, might time be viewed as complex in a manner accounting for the co-implication of interrelating components? To take the example of substance addiction, it was apparent during Laura’s research that time was often experienced as fractured and continually fracturing, due to specific forms and means of intoxication and overlapping experiences of trauma and loss. Time alternately splintered, slowed, accelerated, and was lost altogether, to produce an overarching sense of time that was composed of shifting and fluid parts, but which could not be reduced to those parts. Senses of fractures and fragmentation in moments of time were often felt to accumulate, interact, and replicate across wider spans of days, months, and years. Complexity arose in the coalescence of conflicting temporalities to forge forceful senses of time as non-linear, recursive, and self-similar across scales: that is, of time as fractal.

Most well-known images of fractals, such as the Cantor set, the Julia set, and the Sierpinski triangle, illustrate only coarse approximations of the fractal, which are too complicated to represent visually due to their infinitesimal details. An example is that of the Mandelbrot set (Figures 1, 2), publicized by Benoit Mandelbrot, images of which depict infinitely fine and recursive details at increasing magnifications.

The set somewhat adheres to the fractal principle of self-similarity across scales, as it contains rough copies of itself, and yet each magnification of the set brings new features and “surprises” (15). Mandelbrot himself is noted by James Gleick to have been continuously astonished at the set’s complexity, with Gleick noting that “there were always new kinds of seahorses, new curling hot house species…no part of the set exactly resembles any other part at any magnification” (15). Gleick goes on to describe the set as “a miracle of miniaturization in which every new detail was sure to be a universe of its own, diverse and entire” (15). It was such that prompted Marilyn Strathern to remark that “the whorls and involutions of these self-similar shapes that repeat motifs through any scale of magnification produce the most seductive visuals” (16).

The innate representational challenges of fractal mathematics bear relevance to the difficulties faced in anthropology and other disciplines to reckon with the full complexity and multiplicity of time and temporal consciousness. These challenges are, moreover, keenly felt in describing time experienced through poly-substance intoxication. In striking resemblance to the fractal characteristics outlined above, Laura’s participants emphasized the intricate variety of instances of getting high, which come to take on broad qualities of sameness, or “self-similarity” through time. The highly embodied, individual, and situated nature of polydrug use, however, was ever-difficult to render in words.

Through explorations of time, temporality, and memory, fractals can provoke new avenues of thought–providing a means with which to better understand, excavate, and portray experiences that sit outside of classical conceptions of linear time, and for which language is often insufficient to grasp. An engagement with fractal theory, as such, not only illuminates ways in which time comes to bear on everyday life across multiple temporal scales, but provides expanded linguistic, epistemic, and hermeneutic frameworks with which to apprehend (mathematically) complex, incoherent, and ineffable experience. Greater attention to time experience in addiction is something that, we propose, should accompany an ethical embracing of uncertainties, gaps, and complexities, and a refusal of over-simplified or generalized portrayals of substance use.

While the focus of this piece was experiences of active drug use and intoxication, the research also highlighted fractal-like patterns in experiences of abstinence, recovery, and relapse. Many participants related time as endlessly repetitive in their attempts to stop using drugs and experiences of relapse, some emphasizing that nesting within each new attempt to recover was the memory of the last unsuccessful attempt, and within it the preceding, and so on. Clinical neuroscience literature attempts to evidence a similar pattern, positing that each attempt at abstinence followed by a return to heroin makes the chances of recovering less and less likely (22). It is our perspective, overall, that fractal theory has rich potential to investigate a range of aspects of addiction; for example, critically interrogating simplistic linear/cyclical framings of recovery, abstinence, and treatment. Fractal analysis could likewise be employed to explore state and institutional treatment of temporal complexity; stigmatizing stereotypes associated with “chaotic” and recursive temporal experience; and the damaging insistence of recovery organizations on service users’ pursuit of a linear timeframe. More broadly, an engagement with fractals underscores the potential of interdisciplinary collaborations, toward a translatory dialectic in ethnographic praxis and participant-led theory.

An orientation to time, overall, aids in tracing the invisible structural, social, and historical processes that operate at the level of everyday experience, as well as the minutiae of such experience. Where time and experience are difficult to trace, express, and make sense of, fractals open up space for analysis without imposing rationality or coherence: one in which time as dust and depth is made possible.

The original contributions presented in this study are included in the article/supplementary material, further inquiries can be directed to the corresponding author.

The studies involving human participants were reviewed and approved by University Teaching and Research Ethics Committee (UTREC), University of St Andrews. The patients/participants provided their written informed consent to participate in this study. Written informed consent was obtained from the individual(s) for the publication of any potentially identifiable images or data included in this article.

LR conducted the ethnographic research that informs the manuscript. SD, LR, and HW developed the concept for the manuscript. All authors contributed to the drafting and revision of the work.