The Math Forum

Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Math Forum » Discussions » Education » math-teach

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

Topic: 'Complex Systems' and important relationships within them
Replies: 7   Last Post: Apr 4, 2014 3:22 PM

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
GS Chandy

Posts: 8,307
From: Hyderabad, Mumbai/Bangalore, India
Registered: 9/29/05
'Complex Systems' and important relationships within them
Posted: Apr 1, 2014 10:12 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

I've long been suggesting at Math-teach that a great many of the issues and problems we discuss here at Math-teach (and, indeed, at almost every forum - from international forums like the UN or the G-8 [now reduced to G-7]; the House of Representative and the Senate, USA; to Parliaments in the UK and India, etc; as well online forums such as Math-teach, etc) where problems are confronted and 'debated' (but rarely if ever resolved satisfactorily) - MOST of these unresolved issues are problems are rooted in the lack of adequate understanding by 'stakeholders' in the various 'systems' under consideration of just how they should debate and act on the issues, difficulties, problems at play in the respective systems.

Some specific systems that have not yielded to 'conventional thinking' are:

- -- the public school system in the USA (and elsewhere); the 'math education' system;

- -- systems of national governance;

- -- economic systems;

- -- health-care systems;

- -- systems of debating complex issues;

- -- motivation systems in most organisations;

- -- systems to enable individuals to overcome the frustrations and difficulties they confront when they are working to accomplish complex Missions;

- -- and so on. It is, in fact, rare to find an individual, organisational or societal system that is working 'satisfactorily'. I dare to suggest that most of the deeper issues and problems within these systems will NEVER be resolved *effectively* (or even just *adequately*) by use of the 'conventional mode of thought' to which we're unfortunately addicted.

Complex systems and stakeholders in the systems
Some aspects of these issues and problems may be rooted in 'irreconciliable differences' between stakeholders - but in practice we find that most such issues can definitely be resolved (to considerable extent) if the 'stakeholders' in the respective systems simply learn how to handle issues in those systems.

In particular, this claim is almost self-evidently true in all 'human-made systems': the issues and problems in such systems arise from human actions within those systems.

There are exceptions, of course: for instance, it is unlikely indeed that the 'irreconciliable differences' between, say, a murderer and his/her victim would ever be 'satisfactorily resolved' - for both parties - by way of both of them learning how to 'handle' the issues dividing them through effective debate!

However, it is clearly true that, in the great majority of issues and problems confronted within human-made systems could be happily 'resolved' if the stakeholders in those systems were to learn how to discuss and debate the issues relating to the systems. (It does appear that we have progressed somewhat since medieval times in the learning of how to resolve issues through debate and discussion rather than by committing violence against each other).

Practical 'tools for thought' to help clarify complex systems
The late John N. Warfield, in a series of seminal contributions to 'general systems theory' (GST), devised a remarkably simple approach that could enable us learn how to 'handle' issues and problems within complex systems of all kinds: all that's needed is for the 'stakeholders to become aware that the way the system functions is strongly (perhaps entirely) dependent on the 'inter-relationships' between the factors in the system under consideration. Warfield also developed practical modeling tools that can help us clearly perceive the quite abstract inter-relationships between factors at play in the specific system under consideration. More information about Warfield's developments in systems science is available at and from the "John N. Warfield Collection" held at the library of George Mason University, where Warfield was Professor Emeritus - see

Complex systems and relationships within complex systems
The stakeholders' understanding of the complex systems within which they function and work is based on their understanding of the factors ('elements') within those systems and the relationships of those elements to each other AND to the 'purpose(s)' of the systems under consideration.

Conventional management sciences have devised a number of ways and means (tools) to discuss the factors within complex systems - but they've never seriously considered the 'relationships' of the factors within the systems. Tools that Warfield developed now make it possible for stakeholders to explore and understand the inter-relationships of the factors in the systems to each other.

'System relationships' and how to deal with them:
There are a number of relationships that are important in complex systems. Mathematicians have long explored relationships in mathematics in very sophisticated waysw. However, Warfield found that - in order to enable effective exploration of complex systems - a very productive approach is simply to consider 'system relationships' in just two categories:

- -- 'Transitive' relationships (i.e. relationships that obey the following rule:
If element 'A' is transitively related (some specific relationship) to element 'B'; AND

if element 'B' is transitively related (in the same relationship) to element 'C'; THEN

it follows that element 'A' MUST be transitively related (in the same relationship) to element 'C'.

- -- 'non-transitive' relationships (i.e., those NOT obeying the above rule).

Probably the most important of 'transitive systems relationships' in the context of enabling enhanced understanding by stakeholders in the specific system under consideration is "CONTRIBUTES TO" (along with its 'system negatives' "HINDERS" and "PREVENTS"). [More below on "CONTRIBUION" relationship in complex systems].

The conventional 'management sciences' somehow early on became enamoured with the transitive relationship "PRECEDES" and developed the whole discipline of 'Project Management' based on modeling to find out how 'Events' or 'Milestones' in complex systems "may PRECEDE" one another.

What was apparently forgotten by management 'scientists'** is that it's highly unlikely indeed that the "PRECEDENCE" of Events or Milestones can be figured out in any complex system from scratch. In brief, we stakeholders in complex systems are likely to understand how 'Events' and 'Milestones' in any complex system under consideration "MAY PRECEDE" one another only after we have gained considerable understanding of and insight into the 'other behaviour' of the specific system. We need to study the system to begin with through other, more appropriate, system relationships.

**The 'management sciences' (particularly in the discipline miscalled 'Project Management') have expended HUGE resources in studying complex systems by way of the "PRECEDENCE" relationship - and a great deal of those resources have been simply wasted, because our understanding of how 'Events' and 'Milestones' in the system may "PRECEDE" one another in the system is bound to be extremely vague until we have become quite familiar with the behaviour of things within that system.

It is quite amusing (but also very sad indeed) to note that a HUGE amount of efforts and resources have been wasted by practitioners of so-called 'Project Management' in constructing models based on the "PRECEDENCE" relationship. For example, Robert Hansen has proudly informed us that he and some of his colleagues had put up "30-foot PERT Charts", on the walls of the halls and corridors of the various offices he had worked in!!!

OTHER RELATIONSHIPS could be more fruitful and productive:

It turns out that there IS indeed a transitive system relationship in any system that could be most productive for the purpose of bringing us some understanding of the behaviour of that system: as noted earlier, this relationship is "CONTRIBUTES TO".

In fact, all of us human beings have actually from infanthood onwards been intuitively exploring (with considerable success) the complex systems that confront us using this very relationship!

We have all grown up conducting 'thought experiments' in all the systems we encounter, basically trying to discover how an action performed in the system may help performance of some other action in the system: in brief: how are the factors of interest in the system ('system elements') transitive related to each other by way of the "CONTRIBUTION" relationship!

The 'systems modeling tools' developed by the late John N. Warfield can very significantly help help us choose the appropriate transitive relationships in complex systems that could lead to enhanced understanding of those systems. Had the management 'scientists' and the 'Project Managers' ever troubled to understand 'systems' effectively, they'd had saved themselves all this wasted effort.

A few useful transitive relationships are listed below:

- -- "CONTRIBUTES TO" (along with its 'system negatives', "HINDERS" and "PREVENTS") - very definitely the first relationship that should be studied;

- -- "enhances"; "leads to"; "supports"; ...

- -- "reports to" - useful for development of 'responsibility structures' in organisations;

- -- "PRECEDES" - the relationship taken up with full force by the management 'scientists (without, alas, adequately understanding just how and when these relationships may be applied in complex systems). It is very sad indeed that so much potentially effort has been expended in such wasteful efforts as putting up 30-foot PERT Charts!

- -- "IMPLIES": a most important system relationship (in particular in 'thought systems', 'idea systems', 'philosophical systems; 'learning systems'; 'legal systems', etc, etc. (I must note that Warfield's 'Interpretive Structural Modeling [ISM], the tool par excellence to help us study and explore transitive relationships, is inadequate to help us explore and understand the "IMPLICATION" relationship. I would hope that, after we have the OPMS website up and running, we shall be able to put some effort to try create some effective modeling tools to help us explore "IMPLICATIONS".

There is a great deal to write about 'system relationships' - but we shall do that later, after we have the OPMS website up and running.


Message was edited by: GS Chandy

Message was edited by: GS Chandy

Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© The Math Forum at NCTM 1994-2018. All Rights Reserved.