These chains of events follow a strict sequence, speeding up and then slowing down. They absolutely never start in the middle, with slowing down for example, but always start at the beginning of the succession and end at the natural succession's end. No matter what you do you can't get either a physical or intellectual model of a process of change to work properly without the tell-tale these little start-up and shut-down sequences that mark its departure from a past form and a final arrival at a new one.
Scientific tools can partly test the question by allowing us to take direct measures of change to see if transitional curves, developing rates, are to be found connecting steady states. Such growth rate curves are a sign of history dependent processes and locally developing causation. It is not so much whether a sequence of measurements fits a growth equation. It's whether there's any process at all connecting the end points of change. What is commonly found connecting steady states are the ever-present logistic ('S') curves, frequently regular, but non-steady state, smooth transitional progressions connecting changes in kind.
Logistic curves are unusually pervasive in the measures of transitional events of every scale and duration. They occur precisely during the time intervals where fundamental change is occurring, where the past and future formulas do not apply, and where it is especially hard to describe what's going on. This coincidence is a marvel of nature that goes relatively unnoticed in the body of science. I don't believe there is a chapter in any physics text simply called 'change', 'happening' or its equivalent. We work around it all the time, but never really address the subject. The question is, what do those easily observable orderly in-between periods represent?
Are they the evidence of evolving systems, exploding and fading successions of events too complex for us to yet understand, the smooth and silent workings of radical transformation, the pervasively evident but completely mysterious way it all works?
Great respect is owed to the traditions, and practical achievements, of classical and modern science. It is also true that an evolutionary perspective of events isn't theoretically necessary. No model of nature is ultimately right or wrong, just more or less satisfying and more or less useful. An evolutionary model of events is possible, however, and that is interesting.
The classical and modern world view of science is composed of deterministic rules, postulated to be embedded in the cosmos (rather than just in our notebooks), and exceptions to those rules called uncertainty. As the origin and development of everything else, these rules and exceptions are truly models of how we study nature, tools for using nature, not a models of it. No event so simple as a spark or a water drop was ever so simple as the equations that describe it. Several things are missing. Variables have no substance, no hierarchy of complex interactions such as the parts of all things have. Equations are not collections of independent parts. Equations can't represent beginnings or ends as all organization in nature has. Equations are helpful is guiding us on how to predict and exploit nature. Does that mean that equations is what nature does?
Some of the rules of science survive by our creating ever more intricate 'epicycles' of determinism, from perfect circles, to perfect ellipses, to chaos attractors. It's still the same form of equation. This is undoubtedly useful in searching out the facets of nature we can control, but it fails to provide satisfying answers on a number of questions. It is somewhat antithetical to science but the next frontier may be an exploration of events over which we have no possible control, the locally emergent autonomous structures, what in nature systematically disobeys its own rules in the process of evolving new ones. This is what you see in its most elemental form in the study of the transitions between definable states, the creative realm of the undefined.
When both a change in organization and a recognizable history of events are evident, a graph of any measure of the subject will provide a simplified image of the way the chain of events reverberated within its environment. As with single sparks, whole industries, crystal formation, combustion, scientific discovery itself, or the development of an organism, any sequential record of a change recording its history from beginning to end begins with some form of discontinuity and then acceleration, reflecting the formation of the event process itself, leading to deceleration in its maturation or decay. The complete event appears as locally self-organizing, acting as a whole, reflecting its circumstances but displaying uniquely individual design, appearing to have had a direction, but having been a process of local discovery.
People tend to have ideas before they set out
accomplish something, and we've built our scientific models of nature
that image, but the master of the art, this place called nature, thinks
only by doing. Why are there all those 'S' curves?
We can see that
they coincide with the time period and location of nature's
discovery of organizational change. Is there anything simpler and more
visible, or more
hidden and complex, than this mysteriously elegant form of nature's
This approach to building some new scientific tools is a work in development, with some good pieces done, and many loose ends. The current focus is on an aid for recognization processes in historical records of change, derivative reconstruction (DR), which extracts implied dynamic continuities from sequential data. Both spurious and chaotic signals exist, and do effect the resolution of the data and one's choice of methods. False positive and false negative identifications of organizational change are real concerns, but useful new useful information of locally evolving events can usually be found.