Analyzing Scientific Progress: Models of Knowledge Growth

Science never stands still. Every year, millions of new papers add to a vast and expanding body of recorded knowledge. But how exactly does this knowledge grow? Does it pile up neatly, brick by brick, with each discovery resting on the one before it? Or does progress arrive in sudden bursts that overturn what came before? Scientometrics, the quantitative study of science, treats these questions as measurable problems rather than philosophical puzzles. By counting publications, tracking citations, and mapping how ideas connect over time, researchers have proposed several models to explain how the structure of knowledge develops. Three of these models stand out, and together they offer a surprisingly complete picture of scientific progress.

Why measuring the growth of knowledge matters 🔗

Before looking at the models, it helps to understand why anyone bothers to measure knowledge growth at all. Scientometrics was first described as the quantitative study of science as an informational process, and one of its central concerns is measuring the degree to which knowledge advances over time. The field grew out of the sociology of science and has direct applications in science policy and research management.

For students and policymakers, the practical value is clear. If we can model how a field expands, we can forecast where it is heading, decide where to invest research funding, and identify emerging specialities before they become crowded. Patterns in publication counts and citation links act as fingerprints of how knowledge actually behaves. The three models that follow each interpret these fingerprints differently.

The cumulative progression model 🔗

The first and most intuitive model treats scientific knowledge as something that builds steadily on what came before. Each new finding develops from antecedent ideas, adding another layer to a continuously growing structure. This is the view captured by Isaac Newton’s famous remark about seeing further by standing on the shoulders of giants.

Knowledge as an accumulation of facts 🔗

In the cumulative model, scientific development happens through the gradual addition of verified facts, refined concepts, and improved methods. One of the most striking features of science is precisely this progressive accumulation of content over time, growing at an exponential pace through much of the twentieth century. Mathematics is a clear example. Babylonian numerical notation made Greek geometry possible, which in turn supported the later development of algebra and, eventually, calculus. Each stage depended on the foundations laid earlier.

This model is often linked to a positivist view of science, in which knowledge moves incrementally toward an increasingly accurate picture of reality. It is also the version of science that most textbooks present, showing discovery as an orderly sequence where each scientist extends the work of predecessors.

What citation data reveals 🔗

Scientometric evidence lends real support to the cumulative view. A large study published by the Royal Society analysed major discoveries and methods across many fields and found that scientific methods and resulting findings are highly cumulative across both fields and time. The researchers point out that complex tools such as mathematics, lasers, and particle accelerators, and whole fields such as biomedicine and atomic physics, simply could not exist if knowledge were not built up cumulatively.

The main criticism of this model is that it can oversimplify reality. By presenting progress as a smooth, predictable upward climb, it tends to hide the false starts, dead ends, and messy debates that characterise real research, especially during periods of major conceptual change.

The random selection model 🔗

The second model challenges the tidy logic of cumulative growth. It proposes that a new idea can emerge from almost any point in the scientific timeline, not only from the most recent work. A researcher in 2026 might draw a crucial insight from a paper published decades ago that was overlooked at the time.

Drawing on the whole history of a field 🔗

This view recognises that knowledge does not always advance in a straight line from the latest publication. Citation patterns often show scientists reaching back across long stretches of a field’s history, reviving forgotten findings or recombining old ideas in new ways. Progress, in this reading, depends less on a strict chronological chain and more on which earlier contributions happen to be selected and developed further.

Some big-data analyses of publications and citations use exactly this kind of random sampling across the literature, and the picture they produce can look far more irregular than the cumulative model suggests. Ideas appear scattered across time rather than neatly stacked.

An evolutionary reading of science 🔗

The random selection model shares conceptual ground with evolutionary thinking. Ideas undergo variation through creative work, selection through peer review, replication, and citation, and retention through textbooks and teaching. This framing has been applied widely, including to technological change, where advance is driven by a combination of chance events, deliberate selection between rival approaches, and incremental improvement.

One useful consequence of this model is that it explains why scientific progress can look unpredictable as it happens. Promising theories sometimes languish in obscurity for years while less obvious ideas gain rapid acceptance. The model captures this uncertainty better than a strictly cumulative account can.

The model of growth with discontinuities 🔗

The third model brings the previous two together. It accepts that knowledge accumulates for long stretches, but argues that this steady growth is interrupted by periods of disruption. This view is most closely associated with Thomas Kuhn and his influential 1962 book on the structure of scientific revolutions.

Normal science and paradigm shifts 🔗

Kuhn argued that science does not progress in a smooth, continuous fashion. Instead, it alternates between two phases. During normal science, researchers work within an accepted framework, or paradigm, solving smaller problems that Kuhn called puzzle-solving. Knowledge accumulates steadily here, much as the cumulative model describes.

Problems arise when anomalies that the paradigm cannot explain begin to pile up. If these resist resolution for long enough and trouble enough members of the community, the field enters a crisis. The crisis is resolved only when scientists discard the old paradigm and adopt a new one. Kuhn called these dramatic transitions paradigm shifts, and he saw successive paradigms as necessarily incompatible with one another. The shift from Newtonian physics to relativity is a classic example.

Tracing discontinuities through scientometrics 🔗

What makes this model especially interesting for scientometrics is that Kuhn himself suggested studying shifts in the technical literature cited in research footnotes as possible indicators of paradigm change. Researchers have taken up this idea directly. A bibliometric study by Marx and Bornmann examined the emergence of plate tectonics and connected it to the Kuhnian model of paradigm shifts using citation evidence.

Other work has shown that major conceptual breaks leave detectable traces in the data. A study of the reverse transcriptase discovery in tumour virus research found that the paradigm shift was associated with a break in citation patterns and the sudden appearance of previously unknown technical terms. These findings suggest that discontinuities are not just philosophical claims; they can be observed and measured in the literature itself.

It is worth noting, however, that the prevalence of grand revolutions is debated. The Royal Society analysis mentioned earlier concluded that genuine paradigm shifts of the kind Kuhn described apply to only about one percent of major breakthroughs, with the vast majority of progress remaining cumulative. The discontinuity model, then, may describe rare and dramatic moments rather than the everyday texture of science.

Bringing the three models together 🔗

These three models are best understood not as rivals but as complementary lenses. The cumulative progression model captures the building-block nature of most research and the long-term exponential rise in publications first studied in depth by Derek de Solla Price and later scientometricians. The random selection model accounts for the irregularity and unpredictability that real citation data reveals. The growth-with-discontinuities model explains the rare but significant moments when an entire field reorganises itself.

A useful way to hold them together is to picture knowledge growing cumulatively most of the time, drawing selectively and somewhat unpredictably on its entire past, and occasionally undergoing a sharp break that resets the foundations. For anyone studying scientometrics, recognising which model fits a particular field or period is an important analytical skill, because each model points to different questions worth asking and different patterns worth measuring.

What do you think? Which of these three models best describes a field you are familiar with, and can you identify a moment in its history that looks more like a paradigm shift than steady accumulation? Where in the scientific timeline have important but neglected ideas waited years before being selected and developed further?

References

1. https://arxiv.org/pdf/1201.0676
2. https://arxiv.org/pdf/1802.05941
3. https://royalsocietypublishing.org/rspa/article/480/2302/20240141/66777/Debunking-revolutionary-paradigm-shifts-evidence
4. https://www.researchgate.net/publication/243768027_Technological_Discontinuities_and_Dominant_Designs_A_Cyclical_Model_of_Technological_Change
5. https://en.wikipedia.org/wiki/Normal_science
6. https://en.wikipedia.org/wiki/Paradigm_shift
7. https://link.springer.com/article/10.1007/s11192-018-2931-3
8. https://arxiv.org/pdf/1412.2416
9. https://link.springer.com/article/10.1007/s11192-007-1958-7