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Tuesday, May 26, 2009

Conversation as Combinatorial Geometry

{link » Politics as conversation}
“To try to understand better, in its genuine - epistemological - meaning, is always a worthwhile exercise. At the same time, where one's purpose is dialogic, aiming at an understanding that is reciprocal, it is as well to be clear what one's own values are and how they differ from other values. [...] Dialogue with others who do not subscribe to the same values is, indeed, the stuff of politics and it is an indispensable mode of living with others in a morally tolerable way. [...] [T]hough dialogue and a search for common ground are still to the point, the secular liberal would do well to remember that secular liberalism permits more of a conversation than certain types of politics-faith inseparability do[.]”
 — Norman Geras
Some of the points that Norm makes in his interesting essay can be illustrated by 3-D modeling techniques, variously called solids modeling, constructive solid geometry, combinatorial geometry, as well as others.

Boolean Operations in Constructive Solid Geometry
union = box.OR.balldifference = box.NOT.ballintersection = box.AND.ball
union is merger of box with balldifference is subtraction of ball from box intersection is common to box and ball

We can visualize Norm's discussion by letting the red box represent secular liberalism and the blue ball represent politics-faith inseparability. Then the search for the Holy Grail of common ground is reduced to finding the combinatorial intersection of red box and blue ball.

In this fashion we can easily visualize some general conclusions about such politically charged endeavors. Foremost among these — it is abundantly clear that common ground (i.e., an intersection) may not exist! Its existence depends entirely on the specifics defining the political boundaries (i.e., bounding surfaces) of the potential communicators (i.e., box and ball) and their relative positions in the dialogosphere.

It seems to me that eternal optimists (some may say naive optimists), such as President Obama, may not realize that common ground may not exist in some situations. There are several high profile international confrontations in which parties to the disputes have been seeking common ground for decades, to no avail. Such searches may be futile if a combinatorial intersection does not exist.

Post #768 Conversation as Combinatorial Geometry

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