This is an Open Thread / Coffee Hour and all topics of conversation are welcome. What is for dinner? How are you doing? What is on your mind. If you are new to Street Prophets please introduce yourself below in a comment. This Coffee Hour series is brought to you by a taxonomy of elementary frames.
René Thom in his book Structural Stability and Morphogenesis presented a general theory of theory of models. Of interest to students of politics is how the models can denote the semantic the interpretation of actions on an object. As an application of his theory of models Thom used it to lay the foundation for a new understanding of linguistics.
Wolfgang Wildgen’s Zero Unfolding. This is simple or elementary “frame” for the word being. The little orange ball resting in the “valley” of the geometric form can represent an object or a concept. The geometric form represents the frame that contains the object of concept.
Thom’s initial theory of semantics was extended by Wolfgang Wildgen by building on Charles Fillmore’s theory of Frame Semantics. Simply stated a word can evoke a frame. And a frame can determine the words we use.
Fillmore started a project at the University of California called FrameNet that uses an electronic database to catalog over 13,000 pairings of word with meanings that Fillmore calls lexical units. In addition the database lists over 1200 frames that are related to the lexical units. For the purposes of this article these frames will be called complex frames to distinguish them from Thom’s elementary frames. Click here to visit the FrameNet website.
George Lakoff in his numerous books on politics made Fillmore’s framing model the central idea for understanding how Democrats can communicate our values better. While Lakoff focuses on complex global frames such as matriarchal and patriarchal Thom drills down to the local and catalogs elementary frames.
It is my thesis that a complete theory of political frames requires integration of the complex or global frames with the simple or local frames. Wolfgang Wildgen gives us the local or simple frame theory we need in his book Catastrophe Theoretic Semantics where he updates and develops Thom’s original ideas.
For today's Coffee Hour we will take a quick look at four of Thom’s Elementary Catastrophes that are defined by the dimensions of action that controls them. These four are distinguished by one dimension of behavior. These become the building blocks for the needed elementary frames.
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The Zero Unfolding, introduced by Wolfgang Wildgen, above is considered “trivial” as it is defined in two dimensions and not one of Thom’s original seven elementary catastrophes. However, it is tacitly contained within all seven and is a useful element of Wildgen frame theory.
The Fold can be used to create models to understand the framing of beginnings, endings, being and existential change. This geometric form can be visualized in three dimensions easily because the equation only has three variables. It is one of René Thom’s Elementary Catastrophes.
The fold is the simplest frame as it has one dimension of control and one dimension of behavior. In future Street Prophet’s articles I will exactly explain how these form or unfoldings are use to model objects acting within a frame. But, for today I am just introducing the geometric forms and mentioning their potential modeling use.
The Fold can be used to create models to understand the framing of beginnings, endings, being and existential change. This geometric form can be visualized in three dimensions easily because the equation only has three variables.
Imagine our little orange ball sitting on the fold surface and imagine its behavior determined by gravity. The one dimension of control determines where the orange ball is on the form. If the orange ball is in the valley it is cradled by the sides of the valley and exists. If the one dimension of control moves the orange ball out of the valley over the hill to the left it falls off the fold and ends its stable existence. This action can be reversed and our orange ball can be moved so that its stability comes into existence. Lastly there is a configuration that is functionally identical the Zero Unfolding contained within the Fold. But, the frame is different. This distinction will be covered in future articles.
The Cusp can frame models of beginnings, endings, being, capture, existential change, and bipolar change. In addition it can model simple homeostasis and hysteresis. The graphic is a projection of cusp into the three dimensions of space. It is one of René Thom’s Elementary Catastrophes.
The Cusp is defined by two dimensions of control and one dimension of behavior. The interpretation of the actions defined by the Cusp frame are more complex than can be visualized by the use of gravity because our little orange ball can be moved around the surface and fall over the edge of the top surface to the bottom surface or move on the bottom surface and jump up to the top surface. It is this behavior of a sudden catastrophic jump that inspired René Thom to name his theory Catastrophe Theory.
The cusp can model being, beginnings, endings, change just like the zero unfolding and the fold. In addition the cusp can model the relationship of a predator and prey as found in the predation loop. Capture is one of the words that can be framed by the cusp.
The Swallowtail combines the qualities of the Fold and the Cusp to create frame models of beginnings, endings, being, capture and different types of change including metastable change. In addition it can model the concepts of almost and eject. The graphic is a projection of a section of the Swallowtail into the three dimensions of space. It is one of René Thom’s Elementary Catastrophes.
The Swallowtail is the next more complex frame of the four being discussed today and it has three dimensions of control and one dimension of behavior. This unfolding is fully realized in an higher dimensional space and we can only view it by looking at slices projected into in three dimensions. The Swallowtail gets it name from the shape in the graphic being similar to form of the bird called the swallowtail.
By adjusting the control parameters our little orange ball can model everything the fold and cusp can model with the addition of the concepts of almost and eject. This unfolding, in my opinion, plays an important role in rehearsing actions and playing with ideas. Also, Wildgen postulates that the swallowtail can be used to model adverbs.
The Butterfly combines the qualities of the Fold, Cusp and Swallowtail to create frame models of actions on objects. In addition it can model the concepts of passage, mediated effects, giving, compromise, transfer, and indirect action. The graphic is a projection of a section of a Swallowtail into the three dimensions of space. It is one of René Thom’s Elementary Catastrophes.
The Butterfly has four dimensions of control and one dimension of behavior. It is impossible to property visualize it with one graphic. Thom named it the Butterfly because of an projection that suggests the form of a butterfly. I have been using Wolfram Mathematica to generate the graphics in this article directly from the unfolding equations. I’m sorry that at this time getting the graphics generation ability of Mathematica to display the butterfly form has eluded my programing skills.
The Butterfly combines all the elements of the Zero Unfolding, the Fold, the Cusp, and the Swallowtail. It adds the ability to model concepts of passage, mediated effects, giving, compromise, transfer, and indirect action.
Politically and philosophically and the Butterfly frame is the place that Democrats want to be. Thinking and acting in the world of ideas in a progressive way demands the ability to have a full range of actions available.
George Lakoff’s global or higher view of framing, while valuable in giving complex stories to describe and talk about our options for action, makes a fundamental framing error. He inadvertently frames his writing about Republicans and Democrats in using the Cusp model. This implying a false equivalency. I propose modeling political behavior on a value hierarchy based on complexity. The idea is to remove all equivalency between the parties.
A New Politics Defined
- Democrats act and vote in ways that model reality using all four frames presented above.
- Republicans act and vote in ways that model reality using the Zero Frame as its distinguishing metaphor.
A direct application of the taxonomy of elementary frames is used in cognitive category collapse theory.
Vertical Category Collapse is framing a communication with a lower complexity cognitive frame rather than with a more complex one. Complexity can be ranked by the unfolding formulas. The unfoldings are based on René Thom’s Elementary Catastrophes.
