For some time I have been working on a basic model of scientific progress (or, since “progress” is a value-loaded term, a model of how science progresses). It has implications for certain issues related to scientific publication, so I thought I would share it here, especially as I do not write for journal publication. This blog is my journal, as it were.

The model has two parts, each of which I have described elsewhere, so all I will do here is first to briefly introduce them and tie them together, then talk a bit about publication issues. The first part of the model is called an “issue tree,” which is a logical form that I discovered way back in 1973. The second part I call “leaping concepts.”

Both parts are described in short articles on the blog of the Office of Scientific and Technical Information (OSTI), U.S. Department of Energy. Note that each is written in the context of discussing OSTI’s mission, but that is not the focus here. OSTI sponsored this research, as a way of exploring innovations related to their extensive scientific publishing activities. They are one of the world’s biggest publishers of gray literature, via portals such as The Science Accelerator, Science.gov, and WorldWideScience.org.

The issue tree model of scientific progress is described in “Sharing Results is the Engine of Scientific Progress” (17 June 2009). Central to that description is a schematic issue tree diagram:

The issue tree works as follows. Someone gets a major research result. This result raises several new scientific questions, which could not have been asked before. Different people go to work to answer these questions (including getting different answers to the same question). The results of these efforts raise new questions, and the process repeats itself. The result is a tree structure, which I call an issue tree, in which the number of questions and answers grows exponentially with each successive level.

Note that in addition to questions and answers, one can also have objections and replies, though this is not shown in the diagram. This logical form is found in many sorts of human activities, not just in science. In fact the name issue tree is due to my first finding it in public policy issues, not in science.

My conjecture is that this form of dendritic or tree-like growth is frequently found in science. In particular, it is probably how multiple subfields grow from single discoveries. It may also characterize larger fields. It is in fact a form of divergence, showing how one idea can lead to many lines of thought.

However, the issue tree looks far too isolated and self contained. What is missing is the fact that the answers produced are often based on ideas brought in from prior work in other fields. This is what is meant by “leaping concepts.” The idea of leaping concepts is discussed in “Leaping Concepts and Global Discovery” (28 October 2009). I do not have a graphic for leaping concepts, but one can imagine an issue tree with arrows coming in from other realms of scientific activity, both present and past. Regarding the past, one of the fascinating things about science is how someone will reach back many years to get the concept they need to answer a new question.

Leaping concepts are also a form of divergence, because one idea may go many places. But when multiple ideas or concepts come together in the local issue tree of a scientific field, they are a form of convergence. The convergence is that ideas from different places come together. Combining the divergence of the issue tree with the convergence of leaping concepts gives us a rich and dynamic network structure. This structure is my simple model of how science progresses. Of course any particular case is going to be far from simple, but structurally there are just a few basic elements, namely the issue tree and the leaping concepts.

Before looking at publication, let’s look at science for a bit. The potential for exponential growth in the issue tree suggests several interesting features. First is the potential for explosive growth. Given a growth rate of just three nodes per node in the tree, the tenth layer alone will have almost 60,000 nodes. That could be a lot of research, so we can see how a new idea can quickly take off, once it does. That scientific fields can take off this way has been known since the 1950s. The issue tree provides a possible structural analysis of this phenomenon.

But conversely, one can see that there will typically be many more questions than can be answered; given limited resources to fund research. This helps explain why so many proposals get rejected. The potential for explosive growth is everywhere pressing on the funding system.

On the publication side it is easy to see why new journals are always springing up. The frontier is constantly evolving, and subdividing into new specialties, which then grow into journal size, as it were. It is very organic; in fact I tend to view issues as living things, and science is an issue driven environment.

What citations mean is particularly interesting in this model. A given citation may represent one of a number of very different linkages. It may refer back up into the issue tree, to a key progenitor. Or it may refer to a parallel effort, or a prior result that did not work. Or it may refer to the source of a leaping concept. Or it may refer to a review article that basically summarizes the issue tree. Or it may do something else entirely. I have found that citations often range across all of these cases.

On the leaping concept side, I have already posted here about how new methods and math can spread from field to field. See “My Utopian Vision for Communication of Scientific Methods” (October 11 2011). This flow itself calls for new journals.

I hope you find my simple, two part model useful when thinking about science.

Note: for more on issue trees, see my little textbook “Issue Analysis: An Introduction to Issue Trees and the Nature of Complex Reasoning.”