Models Learning Change
Feb, Mar, 2010
Connecting theoretical systems to the natural world of complex systems

P. F. Henshaw, HDS complex systems science
680 Ft. Washington Ave, NY NY USA, 
tel & fax: 212-795-4844, email:


[note: This is a draft of essay to be published in Cosmos and History June 2010 Models Learning Change (author copy)]


Because "the map is not the territory" it's valuable to learn how to watch the territory to see when to change your maps of it.   That is can be foreseeable and important for our maps of the irreversible processes that lead to natural systems changing form.   They're signals that new maps will be needed.    For theoretical models it serves to replace equals signs with question marks at times of change, prompting you to look for new assumptions and rules of the road as they emerge.

Theoretical models can be complete abstractions, or based on information to represent states of physical organization in some individual physical system.   Those that have physical subjects are valid as information about their subjects only if people use them with a wider understanding of the complex nature of the real subject and its real environment.   Models can describe all kinds of feats of change that physical systems are unable to, and physical systems can do all kinds of feats that abstract models can't, like change by themselves.    Anticipating such change in the organization of physical processes prompts searching for new information and adapting the models.   A method for doing so follows from how the conservation of energy limits the kinds of change that are physically possible.   In practical terms, for lasting change to begin or end, the conservation of energy requires that it's energy flows not have instantaneous leaps, and  so incorporate irreversible developmental processes of accumulative change, such as growth and decay.   These can serve as markers for anticipating changes in form for the physical systems that display them, and be ready to adapt the theoretical models that describe them. 

These signs of irreversible change can be empirically located by their observable mathematical signatures to determine by observation if there are complex growth and decay processes associated with them.    A practice of watching both models and environments for such processes of irreversible change can then help maintain a connection between models and their subjects.   It can provide added time for effective response to changes arising from the complexity of the physical system beyond the information in the model.   It's especially valuable for learning how to respond to the behavior of natural systems with independently learning parts.   They change direction according to what the parts are learning, not any map or model at all.   The unpredictability of what the parts are learning may be highly consequential so early understanding quite useful.

Science has not usually maintained a duality between information systems and physical systems, though, except to refer to physical systems as 'undefined'.   That would then mean restricting terms like "system", "organization" or "object" to exclusively apply to the world of theory and information, and relate to the world of physical things with no particular reference to them, except data.    Here "physical things" are referred to as existing prior to any information gathered about them and to be observed as individuals somewhere in particular.   "Information" is implicitly defined everywhere in general but is solely a human construct and meaningful only within the culture of those that invent it.    Human language, though, did not originally arise from information, but for referring to the things of the physical world around us.   Presently language often confuses the distinctions, though.   So, though one cannot refer to organization in physical things as made of information as organization in our models is, it's quite possible to refer to and study the physical organization of nature as a subject, and keep the two quite usefully distinct.  

Whether one is referring to information or to physical things mostly needs to be understood from context.   That is aided by studying the major differences between what information can describe and that things can do.   Theoretical models depicting physical systems are necessarily self-contained in their own unchanging definitions, and are also necessarily represented as existing in isolation without an environment.   The person who uses a theoretical model needs to supply the rest of the relationship between the model and the physical subjects it points to in the world.   Natural physical systems, in contrast, are complex beyond the reach of information and arise from within an open environment in an undefined way.   They also continually change everywhere at once without having a way to apply general rules from somewhere else.  These are quite large differences.   Models and things can fit each other loosely, as between the weather and weather forecasts.    For some subjects they can fit snugly, as between hand and glove.   

An example of responding to natural change in the physical form of economic systems, and in the models and "rules of the game" implied, introduces a discussion of the window of opportunity for doing so. 


scientific method, mathematical modeling, physical systems, models, learning, change, adaptation, foresight

Working draft - mostly 9/2/09

1.  Introduction

The understanding of natural systems found embedded in open environments and changing form continually, has been limited by representing them with theoretical models.   Natural systems display local organization that accumulates as an environmental learning process around the movement of energy.   Models are useful for times when natural systems are regular, but cannot predict complex organizational change, or environments.    That and other inherent differences between theoretical models and natural systems can be exploited to train researchers to adapt their models to changing physical organization they otherwise could not predict.   

All physical systems have natural limits of scale, for example, and models tend not to, so systematic progressions of scale predict physical system changes to look for that models will not reflect.   Some difficulty arises in overcoming the language problem of discussing differences between physical and theoretical systems.    Normal discussion frequently refers to both mental abstractions and physical things with the same terms, as with the word “apple”.   Normal usage is to use words to refer to both our ideas and information about a subject, and the physical thing with features beyond our information at the same time as if to not distinguish. 

The method proposed here is to develop indicators for when to look for changes in physical systems that require model changes beyond the information previously available.   It provides timely indicators for when to change assumptions and some general indication of how.   It does not offer the "holy grail" of modeling, to define the systems of nature, but helps give apparently vague forms successively clearer features and allow our fixed rules and definitions to fit them more responsively.   It is not always successful but it generally exposes productive questions that would not be asked otherwise.   The particular strategy to be proposed is a way to represent processes of regular proportional change as having both different organization and environments at their beginnings and ends.   That prompts, or you might say 'forces', one to pay attention to the interior details of complex autonomously changing systems that models are so useful for ignoring. 

What models and explanations do for us, where we get them to work, is represent one scale or regular aspect of organization, assuming the regularities of others are constant.   That helps predict what those regularities would result in, but is valid only as long as those assumed constant properties remain so.  That assumption is always highly uninformed, is the key, a matter of faith.  Due to the natural complexity of physical things most of what is assumed constant is completely unknown, so we can't possibly know all of what we assume.  There are useful indicators of when some assumptions will certainly need to change, though.

For example, if you have a simple computable model of ocean waves, changing the scale of the variables does not change the behavior of the model.  Increasing the scale of actual waves leads to a point where they break, however, due to physical system scales not represented in the model.  That difference in behavior due to scales of organization that models contain no information about, is itself predicable.  It helps predict the emergence of new realities and lead to discovering them, whether the circumstance concerned is familiar or not.   In that case it raises the certainty that the old model will not continue to be valid. 

The usual aim of modeling is to finding what regularities can be relied on.  The interest here is rather the opposite, what regularities can be relied on to fail.   It's like a "check engine light" for environmental models.   The object here is to exploit common regularities certain to be temporary for pointing to what parts of a system will change for reasons beyond your present information.  That can help locate where change has or will occur to raise good questions about the missing information needed. 

The learning isn’t over when a good set of regularities and a useful model are found, but really just begun.  Learning how to use models to help anticipate natural system changes would teach a great deal about how to adapt to or avoid conflict with them.  Because natural systems are learning processes themselves, requiring coordination of environmental changes and complex responses, there are hair raising complications of trying to change them ever more rapidly, complications not found in models.

The issues are framed in a conversational style both for wider audiences and because the real subject is a new scientific method for raising unanswered questions, a hypothesis generator as it were.   A scientific method not designed to produce equations, but to raise better questions, is unusual.     It might benefit from revisiting issues from various perspectives.  After discussing the main conceptual problems and describing the method, a conceptual application addresses what constitutes timely decision making about approaching changes in kind for natural systems and the models used to represent them. 

2.  The basic method

If one can identify systems that are naturally temporary it raises the question of how they begin and end.  Beginnings like either the germination of a seed, a handshake between people or the tipping of an environmental balance, are events on other scales of organization than the processes that develop from them.  Process ending events are similarly different from the processes they end.  They include the slight jerk that occurs as breaks bring a vehicle to a stop, the death of an organism, the completion of a task, and a circuit burning out from increasing load.  They are organizational events on other scales than the subject process as beginning events are.  As you learn to look for them you recognize the kinds of processes that begin and end with them, and it develops foresight for what to expect and what processes are naturally temporary because of it.   Processes that are necessarily temporary include regular positive feedback systems.  They begin somehow (with smaller scale processes) and lead to conditions that make them end somehow (with smaller scale processes).  Watching for them leads one’s questions beyond the information available to unexplained but connected processes and relationships, and so to a path of inquiry where you can be sure of there being information to find.  The ability to predict them helps you to find them and serves to expose other scales of system organization to view.  Simple temporary processes include the four types of systems of regular proportional change, which are usually present where you find evidence of regular proportional change (Fig.  4). 

Fig.  4         growth  | integration  | disintegration  | decay

For example, in studying plants you discover they come from the germination of seeds, and that the end of their explosive seed growth is when they use up their seed resource and switch to growing responsively to their environments to begin their maturation.  One needs to validate that any curve that looks like regular proportional change represents a system of proportional change to use this approach, of course.  There are a variety of mathematical tests to help verify the apparent systemicity of apparent developmental processes as part of that (Henshaw 1999, 2007).  As with any search what you find depends on the combination of what is there and how resourceful in looking for it one is. 

As with testing a hypothesis, the validity of each question is then to be confirmed by having it lead to useful discoveries about the system producing the evidence.  Because feedback networks that are dominant enough to show in measures of accumulative change tend to be system-wide, finding them also tends to clearly localize the boundaries of individual system networks that are acting as a whole and that is often a useful way to validate the original question about them.  The powerful question is asking how each kind of system of proportional change begins and how its own development will lead to its own end.  As such it is also a new way of considering time, organized as a one-way ladder of accumulative change by locating some of the rungs. 

If a system model itself implies either continual growth or decay for a physical system, or an inflection from growth to decay, learning to read those as a question about the implied behavioral changes in physical system is the task.  In each case once you’ve identified the likely behavioral change approaching then that would probably lead to changing the model at some point to correspond.  Though the physical system features hidden from view one looks for remain quite undefinable, this exploratory approach still leads you to more and more details of how they are organized and discovering better and better questions about them. 

Chained together as they commonly occur in nature, the four temporary systems of regular proportional change become a general map of “how things come and go” and “a typical life story” of developmental processes and their punctuating smaller scale events.  Fig.  5. 

Fig 5.  A Model of Change, six punctuating smaller scale events and five periods of regular proportional change.  Showing one possible naming convention for the natural sequence of developmental processes  (Henshaw 1985, Salthe 1993)


In any case of either a model or an observed physical process exhibiting the character of any place on the model of change prompts the questions about how the physical system would be connected to the other parts and where in the model to replace the “=” signs with “?” marks. 

3 Conceptual application & discussion

Keeping with the conversational format the example application is discussed in relation to the following diagram of alternative paths for a system making a switch from growth to maturation, either early or late.  The change symbolized is from having a limitless environment and changing in proportion to itself to having a limited environment and changing in proportion to its distance from its limit, fig.  6.  The equation is the same for each, with only a different point in time for the switch from responding to the past to responding to the future.  It is almost self-explanatory that delayed response results in disruptive change and timely response in smooth change, but it helps to see it visually too. 

Arbitrary units are used and the response rate of 10% is used before and after.  An arbitrary point of failure  (the Cap = 75) is set at 2.5 times the arbitrary stable limit set at 30, as well as to to keep the graph small enough for the page.  What varies is the time when switching from multiplying to limiting accumulation occurs. 

Fig.  6 - Growth toward a limit with delay in recognizing the limit: IFY0<cap,Y1=Y0*(1+RateConst*(1Y0*(IFBefore=0,else=1/limit)))

The model represents any growth system as it changes from its independent seed growth, and then switches to integrating with its environment, as in maturation.  The question asked is how does it affect the system if the switch in response occurs early or late, with the time of the change marked for each series.  The clear implication is that switching early has little effect on the future and switching late has a very large effect. 

One need not know anything more to acknowledge the general principle displayed, that in environments presenting a need to respond to new conditions the window of opportunity for responding gets shorter and shorter.  The important recognition is that system response problems are all about the fact that systems start without the information that a responses will become needed.  The practical opportunity is that the simple information that the starting process will end does provide the information that responding to the end will be needed.  The model shows generally how the timing of beginning that response determines whether it will be made gracefully.  The key is contradiction implied, that systems growing independent of their future constraints need to “encode and decode” information about a world of relationships they have no information about, before they make contact.  If systems don’t have information about the future, how do so many seem to demonstrate exceptionally graceful self-limiting development.  The hypothesis here is that it is by the growth system itself becoming increasingly sensitive to disturbance as the progression of the whole pushes its unseen parts beyond their organizational limits, producing instability of  the whole. 

Once a system is sensitized to the need for change, brought on by its own internal instability, the continuity of the process requires time for change.  For people involved in steering growth system responses to environmental limits the difficulty is that the momentum of institutional habits from the past seems to necessitate going well beyond the point where changing directions of development cannot be made gracefully.  That is the default case for when the sensitivity to the need to respond did not come early enough.  That’s where the inherent temporary nature of systematic change needs to be the information needed for drawing the conclusion that you need to prepare to turn already, long before any contact with natural limits is made.  Many kinds of natural systems that gracefully respond to limits seem to do just that. 

The trick seems to be needing to start to turn before you really need to, otherwise the time needed to adapt to new conditions would make a system unable to or to not do so smoothly.  For example, as in paddling a canoe on a winding river (or generally for any craft of steering) you quickly discover that taking the last possible opportunity to turn risks capsizing and spoiling the trip.  So the earliest opportunity that is not premature is the one you choose.  That means being very sensitive to the need to steer.  You’d take the earliest opportunity to think of how to turn and then focus attention on determining the optimal time to do so, ready to turn before the need to turn, and particularly before the turning point is determined by external forces.  In the real world we have a choice just like that, the need to steer our economic system with it’s practice of adding to things by %’s built into the culture, practice, projections and needs of society.  It’s not even yet discussed in public whether there is a question of needing to end the institutions of growth somehow, let alone have a ready response for doing it.  In responding to the limits of growth the question of delay seems to be in how late we are in seeing the need to turn at all.  We seem likely to be following a path like series 3, 4 or 5.  Series 1 or 2 would have made the most graceful turns, but the noticeable resource strains and series of major growth disruption crisis for systemic causes suggests the system has already gone past the period of unfettered growth it is thus already too late to climax smoothly.

For people, understanding how to respond to limits is complicated by how the limits themselves always seem moveable, allowing us to use our creativity to make successive delays in dealing with it.  The need to learn how to turn doesn’t go away, but can be successively ignored, making the question one of whether to respond to “soft signals” or waiting for “hard signals”.  With increasing effort and creativity it starts off being fairly easy to disguise the mounting difficulty in moving natural limits.  That ends in approaching back breaking resistance from nature, though, and then much too late to gracefully respond.   One can see a possible “Darwinian” cause for why nature is so full of systems that are highly responsive to soft signals, then.  Organisms and weather systems and lots of other things do, though, seem to have a way to respond to the approach of limits by completing their development rather than extending their development to points of failure.  The rarity of complex systems that delay their responses to the last opportunity might be because they tend to not survive.  It’s certainly true in business and personal relationships, that the people insensitive to emerging lines of conflict and the need to adapt to change around them don’t tend to prosper.  Perhaps that’s also why what we mostly see in nature are kinds of systems that respond to real limits at their earliest opportunity.  The implied principle for modeling is that for models to sensitize us to the need to change assumptions in the future, models should include leading questions for when to look for information beyond the model. 

For our present situation the standing world plan for economic growth to multiply wealth forever includes the design of all our institutions being organized for that, rather than sensitized to steer away from that.  If, say, this is the first moment the real necessity of that is being noticed, the rational response would then be to first ask how and when, and the observation that it seems we are already too late to do it smoothly.  Those are things you can know without knowing very much, is the point.  These questions naturally deserve longer discussion than is possible here.  One way to begin exploring the physical system for answers is to ask what new conditions it’s parts will run into, and look for the things that would disrupt its positive feedback mechanisms.  Those mechanisms will be partly identified by anything that increases by %’s.  Without even knowing what they are, one can conclude as you identify them that the question is how it would be best to have them end.  Using energy to multiply our uses of energy and using money to multiply our uses of money to keep track of what we do with energy both display the basic features of positive feedback mechanisms and so pose the question of how to end them.  Responsive steering would mean being prepared to end them in a constructive way at the right time, to avoid having them end disruptively.

4.  Conclusion

Learning much better how to also shape our way of thinking to fit nature’s, relying less on increasingly controlling nature to fit our own logics and values,  seems to be a necessary part of successfully responding to even our own designs on earth.  Perhaps the time has come when people can finally understand the formal value of maintaining two explanatory worlds in our minds, one of connections within our information and one of questions about things beyond our information.  We have actually lived with those two worlds in our minds all along, of course, while often confusing things by treating them as one.  One gives us our cultural world of meanings that occupies most of our thoughts mentally, and the other is made of our questions pointing to a physical world of natural systems we live in physically.  Learning to separate them provides a possible way to understand their connection, having a use for a world beyond our real understanding supporting an awareness of how separate that reality is from our own explanations of things.  Science would seem to clearly need both, at least, and the difference in perception might also be of use to the other parts our own personal and cultural worlds of arts, values and relationships

6.  Acknowledgments

Considerable help in this work was provided by years of correspondence with Stan Salthe as well as many other valued critical thinkers who offered me their time, attention and insight.



Supplemental Resources

1.    An appendix of theoretical issues & added references cut from this edit.


Elsasser, Walter, 1987. Reflections on a Theory of Organisms - Holism in BiologyJohns Hopkins
- found that the persistence of diversity in natural form (heterogeneity) would conflict with the assumption of statistical causation that underlies mathematical science. 

Henshaw, P. F., 2010. Complex Systems - Encyclopedia of the Earth

Henshaw, P. F.,  2007. Notes - Mathematical tests for punctuated equilibrium in draft plankton evolution paper “ Flowing processes in a punctuated species change”

Henshaw, P. F., 1999. Features of derivative continuity in shape. Journal of Pattern Recognition and Artificial Intelligence (IJPRAI), Special issue on Invariants in Pattern Recognition, V13 No 8 1999 1181-1199

Henshaw, P. F.,  1985Directed Opportunity, Directed Impetus: New tools for investigating autonomous causation. Proceedings; Society for General Systems Research 1985, Louisville KY

Rosen, R.,1991. Life Itself. Columbia Univ. Press

Rosen, R., 1993 On The Limitations Of Scientific Knowledge, in: Casli, J. L. (Ed.), On The Limits To Scientific Knowledge. Perseus Books

Salthe, S., 1993. Development and Evolution: Complexity and Change in Biology, MIT Press.

Sterman, J.D., 2002. All models are wrong: reflections on becoming a systems scientist. Jay Wright Forrester Prize Lecture. Syst. Dyn. Rev., 18, 501–531

P. F Henshaw