Why Change Is Not Always Linear: Understanding Nonlinear Change

Change is often described as though it should proceed in a recognisable direction. Something improves, the improvement continues, and enough small gains eventually produce a stable new outcome. This linear picture is intuitively appealing because it makes change easier to observe, measure and explain. It also corresponds to some genuine forms of learning and behavioural development, where repeated practice or altered conditions can produce relatively gradual improvement over time.

Human change, however, does not always follow that pattern. Improvement may accelerate after a long period in which relatively little appears to happen. A new behaviour may become available and then temporarily disappear under different conditions. Performance can improve in one area while remaining unchanged in another. Periods of instability can occur during otherwise meaningful change, and an apparent breakthrough may prove temporary once the circumstances that supported it are removed.

Describing change as nonlinear does not mean that all change is chaotic, unpredictable or dramatic. It means something more precise: the amount, direction or form of change observed at one point in time does not necessarily continue at the same rate or in the same direction at the next. Human trajectories may contain plateaus, accelerations, temporary reversals, context-dependent variation and relatively abrupt shifts alongside periods of gradual development.

This distinction matters because a linear expectation can distort how change is interpreted. A temporary setback may be treated as evidence that previous change was unreal. A sudden improvement may be mistaken for a complete transformation. A period of little visible movement may be interpreted as evidence that nothing is changing at all. In each case, the problem lies partly in assuming that meaningful change should be smooth enough to recognise immediately.

Research across developmental psychology, behavioural science and psychotherapy process research provides good reason to question that assumption. Dynamic-systems approaches have long treated development as something produced through interacting processes unfolding over time rather than as a simple accumulation of identical increments. Psychotherapy research has likewise documented trajectories involving sudden gains, spikes, plateaus and other discontinuous patterns that disappear when individual change is reduced to an average line.

The more difficult question is therefore not whether change can be nonlinear. It is what different patterns of change actually mean.

Linear averages can hide nonlinear lives

One reason human change appears more linear than it sometimes is comes from the way change is measured. If a group of people is assessed at the beginning and end of a period, or at only a small number of widely separated intervals, the resulting averages can make improvement appear relatively smooth even when the underlying individual trajectories were not.

Behavioural medicine researchers have pointed out that infrequent measurements can miss important temporal patterns because behaviour unfolds within time rather than merely between two assessment points. Someone may fluctuate substantially while ultimately arriving at a better outcome, while another person may appear unchanged for much of the observation period before improving rapidly. A third may show an early improvement that later reverses. Similar beginning and end points can therefore conceal very different processes.

Psychotherapy research provides an unusually visible example because symptoms and processes are sometimes measured repeatedly across sessions. Hayes and colleagues reviewed evidence showing that treatment change can include early rapid responses, sudden gains, temporary increases in distress and other discontinuous patterns. Their argument was not that psychotherapy must produce instability, but that assuming gradual linear improvement in advance can prevent researchers from noticing other meaningful trajectories.

Later research strengthened part of that picture. A 2020 meta-analysis by Shalom and Aderka examined 50 studies involving 6,355 participants and found that sudden gains (relatively large improvements occurring between consecutive treatment sessions) were associated with better outcomes at both the end of treatment and follow-up. Importantly, the strength and stability of these gains varied, and reversal rates influenced their relationship with subsequent outcome.

The significance of these findings extends beyond psychotherapy, although they should not be generalised carelessly. They illustrate a methodological principle that applies much more broadly: the shape of change matters. Knowing that someone is different at two points in time does not necessarily tell us how that difference emerged, whether it was stable throughout the interval, or whether the same pattern would appear under different conditions.

Nonlinear does not mean random

The term nonlinear can easily create the wrong impression. In everyday language, describing change as nonlinear sometimes becomes a way of saying that progress is messy, unpredictable or impossible to understand. Scientifically, those claims do not follow.

A nonlinear process can be highly structured. The defining point is simply that the relationship between change and time, input or another variable cannot be adequately described as a constant proportional relationship. Small differences in conditions may sometimes produce little observable effect and sometimes contribute to larger shifts, while apparently significant inputs can produce relatively little immediate change.

Dynamic-systems theories of development have been especially influential in drawing attention to this possibility. Thelen and Smith approached development as emerging from multiple interacting components operating across time, with behaviour arising from the organisation of the system rather than from a single controlling cause. Their work drew explicitly on ideas from nonlinear systems while applying them to developmental questions involving movement, cognition and learning.

The relevance here is not that every form of personal or behavioural change should be explained through dynamic-systems theory. That would replace one oversimplification with another. The more useful contribution is conceptual: when several influences interact, the observable trajectory does not necessarily mirror the contribution of each influence in a simple, additive way.

Consider a behaviour that depends on knowledge, opportunity, environmental cues, available skills and repeated practice. Improving knowledge may initially make little visible difference if opportunity remains limited. Once the environment changes, the same knowledge may suddenly become useful. Repetition may then increase familiarity, while later changes in context may temporarily reduce performance again. The observable trajectory could appear flat, then steep, then variable, even though no single moment contains the entire explanation.

That kind of pattern is nonlinear without being mysterious.

Change can occur at different rates in different parts of a system

Another reason change can appear uneven is that the relevant components do not necessarily change together.

Someone may revise an important belief before their behaviour changes consistently. A new skill may be learned before it becomes readily accessible under pressure. Environmental circumstances may change rapidly while learned expectations adjust more slowly. A new behaviour may become reliable in one context while remaining difficult in another.

This is closely related to the distinction explored in Insight Is Not the Same as Integration. Understanding can change meaningfully without every process relevant to functioning changing at the same rate. Similarly, observable behaviour can alter before it becomes reliable across a broad range of circumstances.

These findings make a perfectly smooth trajectory less likely whenever meaningful change depends on several interacting conditions. If one influence changes while another remains relatively stable, the overall effect may initially be small. If several conditions later align, change may accelerate. If one supporting condition disappears, some previous gains may become harder to express. This broader way of thinking about interacting conditions is developed further in What Do We Mean by Human Organisation? The resulting pattern can look inconsistent when viewed only at the level of outcome, but may make considerably more sense when the organisation of the relevant conditions is examined.

Contemporary behavioural science also resists treating behaviour change as one homogeneous event. A 2026 review in the Annual Review of Psychology synthesises evidence around different challenges involved in producing behaviour change, including developing motivation, following through and establishing durable habits. Those processes are analytically related, but improvement in one does not guarantee equivalent movement in the others.

A 2024 review in Nature Reviews Psychology similarly examined individual and social-structural determinants of behaviour and found substantial differences in the effectiveness of interventions targeting different determinants. Knowledge, attitudes, emotions, behavioural skills, habits, norms and structural conditions do not contribute identically across all behavioural problems.

The resulting pattern can look inconsistent when viewed only at the level of outcome. It may make considerably more sense when the organisation of the relevant conditions is examined.

A temporary disruption is still a change, but not necessarily a durable one

The language of transformation can encourage another conceptual mistake: treating every observable difference as evidence that something fundamental has changed.

Temporary disruption can produce dramatic effects. A new environment, relationship, responsibility, constraint, opportunity or period of concentrated effort can interrupt an established pattern. The behaviour that follows may look markedly different from what came before, but the duration and conditions supporting that difference still matter.

This is why a sharp change in trajectory should not automatically be interpreted as a stable new organisation. Psychotherapy studies of sudden gains are useful here because some sudden improvements remain stable while others reverse. Earlier research also found that sudden gains identified in different treatment contexts differed in stability, demonstrating that the existence of a large change and the durability of that change are separate empirical questions.

Outside clinical research, the same distinction can be expressed more generally. Someone may change a behaviour while travelling because the usual environmental cues are absent. A new workplace may temporarily support different routines. A period of unusually high motivation may produce consistent behaviour for several weeks. External accountability may alter performance while that accountability remains present.

None of these changes is unreal. Each provides information about what the person can do under particular conditions. What cannot be concluded from the observation alone is whether the same functioning will remain available once those conditions change.

This is one reason before-and-after thinking can be misleading. It collapses change, stability and durability into a single judgement when they are separate properties of a trajectory.

Adaptation should not automatically be mistaken for deeper change

Adaptation introduces a further distinction. Human systems are capable of adjusting to changing demands without necessarily transforming every process that produced the previous pattern.

This can be highly functional. A person may develop a strategy that allows them to perform effectively in a difficult environment. Someone may modify routines to accommodate a new responsibility, rely on external structure to support attention, or alter communication in response to a particular relationship. These adjustments can represent genuine learning and meaningful improvement.

Yet adaptation is inherently relational: it occurs in relation to conditions. If those conditions change substantially, the usefulness or accessibility of the adaptation may change with them.

The distinction matters because the word change is sometimes treated as though it describes one phenomenon. In reality, a system can vary within its existing organisation, compensate for constraints, adapt to new demands, acquire a new behaviour, lose access to an old behaviour, or develop a pattern that persists across increasingly varied circumstances. Observationally, all of these may look like change. Analytically, they are not necessarily the same.

This does not mean that one form is inherently better or more authentic than another. A well-supported adaptation may be exactly what effective functioning requires. External structure is not inferior simply because it is external, and compensatory strategies are not false forms of change. The distinction becomes important only when stronger claims are made about what an observable difference demonstrates.

A professional account of change therefore needs to ask not only whether something changed, but what changed, under which conditions, and for how long.

Periods of instability do not have one universal meaning

One of the most tempting claims about nonlinear change is that instability must precede transformation. Variations of this idea appear frequently in therapeutic, coaching and wellness language, where worsening, uncertainty or disruption may be interpreted as signs that a major shift is underway.

There is some research showing that instability and discontinuity can accompany particular change processes. Hayes and colleagues, for example, discussed patterns in psychotherapy involving temporary symptom spikes that were followed by improvement. Complex-systems approaches to psychotherapy have also investigated increased variability and discontinuous trajectories around transitions.

That evidence does not justify a general rule that worsening means growth is occurring. Instability can have many meanings, including changing conditions, measurement variability, loss of support, increased demands, temporary experimentation, genuine deterioration or transition. Its interpretation depends on the phenomenon being observed and the evidence available.

This distinction is particularly important in public-facing wellbeing content because romanticising destabilisation can become clinically irresponsible. A difficult period should not automatically be reframed as evidence that a person is “breaking through”, nor should persistence through worsening conditions be encouraged simply because nonlinear-change language makes disruption sound purposeful.

The scientifically responsible position is more restrained. Instability can accompany change, but instability by itself does not tell us whether a durable beneficial change is occurring.

Sudden improvement does not necessarily mean sudden causation

Nonlinear trajectories also complicate explanations of causation.

If a large behavioural shift becomes visible at a particular moment, it is tempting to search for an equally large event immediately preceding it. Sometimes such an event may indeed matter. In other cases, the visible shift may depend on conditions that accumulated gradually before the change became observable.

This is familiar in many areas of learning. Practice can occur over time before performance crosses a threshold at which the improvement becomes conspicuous. Multiple small changes in environment, skill and opportunity can combine until a behaviour that was previously difficult becomes comparatively easy. Conversely, a sudden loss of functioning can sometimes reflect several accumulating demands rather than one discrete cause.

The observation that change was abrupt therefore does not establish that its causes were abrupt.

This is one reason nonlinear thinking can improve causal reasoning when used carefully. Instead of asking only, “What happened immediately before the change?”, it invites attention to how relevant conditions may have accumulated, interacted or changed in importance over time.

It also protects against retrospectively assigning excessive power to one insight, conversation, intervention or event simply because it occurred near a visible turning point. Temporal proximity can generate useful hypotheses, but it is not sufficient evidence of causation.

Durable change requires more than a dramatic moment

For many forms of human change, the most informative question emerges after the initial improvement: what happens next?

A behaviour that appears once demonstrates possibility. Repetition demonstrates something different. Continued availability when circumstances vary provides additional information, while stability across time adds another layer again.

The recent behaviour-change review by Voelkel, Milkman and Duckworth is useful in this respect because it distinguishes initial motivation and follow-through from the development of durable habits. The literature they synthesise emphasises that starting a behaviour and maintaining it involve overlapping but not identical challenges.

This helps explain why apparently significant early change can later weaken without making the earlier change meaningless. The person may genuinely have demonstrated a new capability while the conditions required for durability were still developing. Conversely, durable change may sometimes emerge without a dramatic moment at all, through repeated small adjustments whose significance becomes visible only retrospectively.

The word durable should also be used with care. No human behaviour is completely context-free or permanently guaranteed. Changes in health, environment, relationships, demands or opportunity can alter functioning that had previously been stable. Durability is therefore better understood comparatively: a pattern becomes more reliable across relevant time and conditions rather than absolutely permanent.

This distinction is considerably more useful than treating change as complete or incomplete.

Progress and reversal can coexist

A nonlinear perspective changes how apparent reversal is interpreted, but it should not be used to explain reversal away.

If a new behaviour becomes available for a period and an older pattern later reappears, two conclusions should be avoided. The first is that no meaningful change occurred because the old behaviour returned. The second is that the reversal is automatically part of a healthy process and therefore requires no further examination.

Both interpretations exceed the evidence.

The return of an older pattern may indicate that it remains highly accessible under certain conditions. It may show that earlier change depended on supports that are no longer present, that learning has not generalised broadly, that competing demands have increased, or that the original explanation of the pattern was incomplete. In some cases, it may simply reflect ordinary variation.

What matters is the structure of the trajectory. Is the older response appearing as frequently as before? Under the same range of conditions? For the same duration? Does the newer response return more easily afterwards? Has the range of available responses expanded even though the original pattern has not disappeared?

These questions provide a richer account than asking whether someone has “gone backwards”. Movement through a complex behavioural landscape is not adequately described by a single forward–backward axis.

Nonlinear change does not mean that progress cannot be evaluated

There is a possible danger in taking the nonlinear argument too far. If every reversal, plateau and disruption is treated as compatible with progress, then the concept becomes impossible to challenge. Any outcome can be reinterpreted as part of the process, and failure to improve can always be explained by saying that change is nonlinear.

That is not scientifically useful.

The fact that change can be nonlinear does not remove the need to evaluate outcomes. It makes evaluation more demanding. Instead of relying solely on the direction of movement at one moment, it becomes important to examine duration, recurrence, context, variability, functional consequences and the conditions under which a change appears or disappears.

Repeated measurement becomes especially valuable for this reason. A trajectory observed over time contains information that a single retrospective judgement cannot provide. It can distinguish a brief fluctuation from a sustained difference, show whether a new response is expanding across contexts, and reveal whether apparent improvement is becoming more or less stable.

This is one of the central lessons of process-oriented research: time is not simply the space between measurements; it is part of the phenomenon being studied.

A more precise way to think about human change

The statement that change is nonlinear is useful only if it leads to greater precision rather than becoming another reassuring slogan.

Human change may proceed gradually in some circumstances and discontinuously in others. It can accelerate, plateau, vary across contexts or temporarily reverse. Different aspects of functioning can change at different rates, and an observable improvement can represent temporary disruption, context-specific adaptation, newly acquired capacity or a more durable shift. The trajectory alone does not always reveal which interpretation is correct.

A better approach therefore separates several questions that everyday language often combines. What exactly has changed? How broadly does the change generalise? Under what conditions is it available? How stable is it across time? What appears to support or constrain it? Has a different response become reliably available, or has the immediate environment simply made the previous response less likely?

These questions do not make human change unnecessarily complicated. They recognise complexity that is already present.

The expectation of smooth progress can make normal variability look like failure and dramatic moments look more conclusive than they are. A nonlinear perspective provides a more disciplined alternative, but only when it remains evidence-aware. It allows for periods in which little appears to change, abrupt improvements, temporary reversals and uneven trajectories without automatically assigning any of them a predetermined meaning.

The central question is therefore not whether change is moving steadily forwards. It is whether the organisation of functioning over time is becoming meaningfully different, under the conditions that matter.

That question is harder to answer than drawing a straight line between a beginning and an endpoint. It is also considerably closer to the way human change actually needs to be studied.

Selected research

Hayes, A. M., Laurenceau, J.-P., Feldman, G., Strauss, J. L., & Cardaciotto, L. (2007). Change is not always linear: The study of nonlinear and discontinuous patterns of change in psychotherapy. Clinical Psychology Review, 27(6), 715–723.
Shalom, J. G., & Aderka, I. M. (2020). A meta-analysis of sudden gains in psychotherapy: Outcome and moderators. Clinical Psychology Review, 76, 101827.
Thelen, E., & Smith, L. B. (2007). Dynamic Systems Theories. In Handbook of Child Psychology.
Albarracín, D., Fayaz-Farkhad, B., & Granados Samayoa, J. A. (2024). Determinants of behaviour and their efficacy as targets of behavioural change interventions. Nature Reviews Psychology, 3, 377–392.
Voelkel, J. G., Milkman, K. L., & Duckworth, A. L. (2026). Behavior Change. Annual Review of Psychology, advance online publication.