The Modeling Relation

Enter the modeling relation. It turns out that there is a nice, formal theory to talk about all of this.  It was done by a systems biologist named Robert Rosen.  He called this theory ‘the modeling relation’.    

Rosen’s Modeling Relation What the modeling relation portrays is as follows:  on the left (#1) we have a natural system of some kind (things happen in the natural system and causality is involved).   On the right (#3) we have a formal system.  (Formal systems might be math, logic statements, computer simulations, etc.) We can run many experiences, thought experiences, predictions, in the formal system to see what that implies about what a corresponding action should mean in the natural system.   Rosen claimed that if we have a means of going between the two—the encoding (#2 or how to represent in the formal system a potential action occurring in the natural system) and the decoding (#4 or how to carry out in the natural system a prediction made in the formal system ) —then we have a model. If one can’t make all of the four elements work as shown, one doesn’t have a model, but rather merely a representation.   Rosen’s work was about distinguishing between the existence of modeling relations and representations that people were mislabeling as models.   The key to a model, in Rosen’s world, is the ability to use the model to make predictions, to have implications that are then observable in the natural system.  If the model can do that, it is a model; if it cannot, then it is merely a representation. 

 

Observations re the Modeling Relation

Rosen’s modeling relation presumes some kind of objectivist stance.  Nowhere on this chart does one see a “perceiver” or “self.”   Thus, Rosen’s modeling relation assumes a realist world — the same world as traditional management teachings. Rosen’s modeling relation assumes that we can do one-to-one mapping, world to model and model to world.    This same one-to-one mapping exists in how managers are taught to rely on the Gaussian distribution. As long as Gaussian predictions hold up, it is fine to use Gauss as a model. As a manager I can make predictions.  Those predictions have implications for the world.  Most of the time those implications are validated.  Sometimes as a manager I need to tweak my encoding and decoding schemes, but in general the schemas are okay.  Once we accept, however, that the Gaussian description of the world isn’t the real world because it ignores partial dependence and partial correlation, how do we fix this?    

Rosen assumes that one validates models via prediction.  In general, when one is dealing with physical aspects of physical things, Rosen’s conception works pretty well.  However, when one gets into things that are more abstract, semiotic or conceptual, Rosen’s modeling relation has some problems.  Rosen’s modeling relation assumes that that mapping’s existence is the definition of a model.  No self; no perceiver; no observer.   The absence of self is a big deal, not a little deal. One of the things we do in this book is to rebuild the modeling relation from a constructivist point of view.  Complexity theory tells us that a model only works if there is a self included.

 

Bringing Back the Self

Thus, we sought to fix the modeling relation by putting the self back into the model.   Rosen started with a natural system. Instead of a natural system, in our revised approach we are going to refer to an “external item”.  Our goal is to create a model of that external item which allows us to deal with its complexity or gives us the belief that we can deal with the complexity.  We need to believe we can cope, to refer back to that Rorty quote.   Such beliefs are of course dependent on self and context.  Rosen then tells us that one needs all four elements (external item, self, context, and model) in order for the model to in fact  function as a model, and that one needs to make explicit recognition of the four.  The problem with the chart above is that it starts in the wrong place.  We need a chart which starts with self. 

 

The Constructivist Modeling Relation

 

On the above chart, there is a subject existing in a context and doing the perceiving. Since it is important to be explicit, we state that the goal is to recognize the essence of whatever the external thing is, however one may want to go about defining essence.  Once we have recognized that essence, we create the possibility for acting upon or with it.  We are going to define “model” as a reduced representation of the thing.  It’s a reduced representation of the essence. The chart includes three hermeneutic circles, and all three are important.  The circles recognize that the self will have some ongoing, continually revised relationship with a reduced representation, which will change as one goes about making predictions and seeing whether they get validated by one’s understanding of the essence as one deals with it. Notice that there is no room to ascribe a label to the essence. This chart relies on an activity-based conception of the external thing and not on categories. Changing the modeling relation in this way puts the self back, but it also changes how managers go about dealing with their world because once they recognize that the ascribed labels are reduced representations that only get validated in activity, they’re no longer fixed and stable.  They’re always open for questioning.  They’re always part of a hermeneutic circle.  The questioning and thought embodied by a hermeneutic circle are not how we teach our managers to behave.  The traditional approach of define, label, and then act in accordance with the label is no longer sufficient.  Instead, there is a dialogue between temporary definition and potential action that must be attended to.

By doing this, the perceiving subject has been restored to prominence.  The very notion of encoding and decoding that was at the top and bottom of Rosen’s chart have been replaced by a set of hermeneutic circles – I come up with a representation; it cues me into meaning; I have a dialogue with context that may alter the representation, which cues me into more meaning, repeat.The real world has been replaced, instead, by a notion of an essence of whatever the external item is.   A model’s validity becomes a function of its usefulness in articulating that essence to self and to others.   If the model doesn’t help articulate something about the essence that is at least potentially actionable, then the model is no good.This is a very different test than can one make predictions and do the predictions have implications in the real world?

 

The Manager’s Two by Two Matrix

We will begin as manager and look at a two-by-two matrix. In the upper left-hand corner, we have certain occurrences with defined meanings, which we can call ‘the known’.   On the diagonal, moving down, we have things that either occur with probability or when they occur, we don’t really necessarily know their meaning, because the meanings are assigned with probability.   In the lower right-hand corner we have the things that are every manager’s nightmare, or they’re golden opportunities, which are the Miracles and Nasty Surprises.  These are things that occur with undefined meaning and uncertain occurrence. 

Consider a classical but oft told myth.  There is no way that when Pierre Omidyar decided that he needed to get rid of his wife’s Pez dispensers and put up a website to get rid of them, that he had any idea that eBay would emerge.  That was a miracle.  All the people whotried to follow him on the Internet and create something similar thought they were operating in one of the other three squares.  The fact that eBay wasn’t replicable — well, that was a nasty surprise.

 

Let’s Change the Two by Two

From this perspective, using the same quadrant labels, what was known to the manager is the self and the coherent. Probabilistic meaning is found in groups, whose members do not all share the same meaning.  We don’t have codes that function in a lookup table all the time. There are multiple models and probabilistic meaning notions.  Probabilistic occurrences occur out in the environment; there are always multiple possibilities for future events.  There are multiple affordances that are open to us.  In that quadrant of miracles and nasty surprises, we have emergence. 

 

Emergent Coherence

This chart is the same two-by-two matrix, but we have relabeled it by putting a self back into it.   If we draw the action perspective, the outside elements move around a little bit.  Action stays pretty much in the same place.  Story stays pretty much in the same place.  But in-between the quadrants there’s questioning.  Out between probabilistic occurrences and emergence is the field of adjacent possibles, the things we actually can move to as next steps.

Resonance now becomes part of the hermeneutic circle, because we have to include emotion. If we can tell a story that resonates, if we can find a vignette that resonates, then it can help propel understanding and action.   The mere repetition of a label does not. 

If we simplify the chart, we now have self in one corner, group in the other, along with environment and emergence.   Things between self and environment tend to be embodied things that we encounter.  Things between self and group are where the ascribed labels come in.  Where the group is trying to cope with emergence is the space of beliefs. 

 

Resistant to Analysis

 We have added to the chart above an area marked “resistant to analysis.”  We’re not very good at figuring out how to deal with the unknown. There are things that are occurring out in the environment and adjacent possibilities that haven’t occurred yet; those are the puzzle.  This is the stuff that the manager is now faced with as a real challenge.  The manager can guide people through the rest of this circle.  The challenge lies in the area that is marked as resistant to analysis.