Quotient Spaces In Politics

by: Paul Rosenberg

Sun Oct 05, 2008 at 13:30


Lately, I've been thinking about quotient spaces in politics.  What's a quotient space?  Take a look at a wall calender, dividing the continuous flow of time into days, weeks, months and years-cycles within cycles within cycles, or an analogue clock, dividng time into seconds, minutes, hours and 12-hour cycles.  These are commonplace examples of what mathematicians call quotient spaces. Wikipwedia explains:

In topology and related areas of mathematics, a quotient space (also called an identification space) is, intuitively speaking, the result of identifying or "gluing together" certain points of a given space. The points to be identified are specified by an equivalence relation. This is commonly done in order to construct new spaces from given ones.

For a mathematician, time is a space-a one dimensional space, a line.  We glue it together by identifying all midnights, thus making every day, and every time equivilent with the same day and time of every other day.  Or we glue it together by identifying all January firsts, making every year, and every day of the year equivalent with the same day of every other years.  Okay, you say, big deal.  A fancy poants way to talk about time.  But what's that got to do with politics?

Ah, I thought you'd never ask!

Paul Rosenberg :: Quotient Spaces In Politics
Remember this chart?  It's an overview of Robert Kegan's model of cognitive development:

Kegan's Subject/Object Schema of Cognitive Development
StageWe Are:
Subject
(structure of knowing)
We Have:
Object
(content of knowing)
Underlying Structure
1Perceptions

SOCIAL PERCEPTIONS

Impulses
Movement


Sensation
2Concrete

POINT OF VIEW

Enduring Dispositions
Perceptions

SOCIAL PERCEPTIONS

Impulses
3
Traditionalism
Abstractions

MUTUALITY/
INTERPERSONALISM
Relationship


Inner states
Concrete

POINT OF VIEW

Enduring Dispositions
Needs, Peferences
4
Modernism
Abstract Systems

INSTITUTION
Relationship-Regulating Forms

Self-authorship
Abstractions

MUTUALITY/
INTERPERSONALISM
Relationship

Inner states
Subjectivity
Self-consciousness
5
Post-
Modernism
Dialectical

INTER-
INSTITUTIONAL

Self-transformation
Abstract Systems
Ideology

INSTITUTION
Relationship-Regulating Forms

Self-authorship
Self-regulation
Self-formation

Just as we can structure time into a series of ever-expanding quotient spaces--seconds, minutes, hours, days, weeks, months, years, we can structure our perceived reality into a series of ever-expanding quotient spaces as well: the underlying structures in the chart above.  Of course, there is one very significant difference:  we are embedded one place or another in the chart above, and where we are embedded determines the quotient space that in turn determines how we see the world.  One of the most significant dividing lines in politics is between level 3, the level at which our reality is ultimately socially determined, and level 4, the level at which we begin to fundamentally determine our reality for ourselves.

At level 3, we accept the world as it is, because we are embedded in the world of social roles and relationships, and we lack the capacity to take that world as object.  Individuals within that world can be mapped in terms of quotient spaces-the roles defined by society: husband, wife, father, mother, son, daughter, boss, co-worker, etc. At level 4, we have the capacity to stand back from the world of social roles and relationships, and to chose how to relate to it, not just how and where to fit in, but how to change things, as well. Once upon a time, whatever a father did, his son followed the same line of work.  This still remains an option, of course, but it's no longer an ironclad rule.  It's no longer built into the structure of social roles and relations.  That happened in part because people began to consciously challenge and change that aspect of the world of social roles and relationships.

While the social world can change gradually over time without requiring specific individuals to consciously drive the change, such changes are certainly facilitated by having individuals who can take a step back, and see how things can be different.  Such was the case with the choice of careers becoming commonplace, and such was the case also with marriage choice replacing arranged marriages.  Such is the case with gay marriage today, as well.  Those who see the social world from inside, in terms of fixed social roles inevitably see changes to them or deviations from them as threatening or destructive, while those who see the world of social roles form the outside, as a malleable object, see such changes or deviations as simply an inevitable part of life: change happens.

This is one of the funamental cleavages between liberals and conservatives, although not an absolute one.  There are egalitarian social roles and relationships that are liberal in character, and there are new social roles and relationships that are authoritarian.  But generally speaking, the shift away from level 3 embededness in traditional social roles and relationships is a shift toward greater equality as well as greater autonomy.

At level 3, whatever one takes to be the right social structure can be seen as functioning as a mental quotient space, determining the nature of the world-or at least the nature of the world as it should be.  Naturally, this is a setup just made for conflict, unless different groups with different quotient spaces are kept "in their place"-meaning either social or else physical segregation.  Indeed, it was the bloody turmoil of the wars of Reformation that lead to the emergence of liberalism as an intellectual tradition that could mediate between such groups that could not be effectively segregated, and that had to learn to live with one another.  The liberal, level 4 quotient space is not composed our of fixed social relationships, but rather out of systemic intellectual relationships-not in the sense of an abstract, philosophy-class intellect, but simply in the sense that the level 4 person reflects on how values, ideals, beliefs, etc. relate to one another, not in order to understand them as they are taught, but to decide for themselves their proper relationship.  This is what Kegan calls "self-authorship."

In In Over Our Heads [p 185], he writes about how level 4 involves:

"...a qualitatively more complex system for organizing experience than the mental operations that create valeus, beleifs, convictions, generalizations, ideals, abstractions, interpersonal loyalty, and intrapersonal states of mind."

And goes on to say about it:

"It is qualitatively more complex baecause it takes all of these as objects or elements of its system, rahter than as the system itself; it does not identify with them but views them as parts of a new whole.  This new whole is an ideology, and internal identity, a self-authorship that can coordinate, integrate, act upon, or invent values, beliefs, convicsitons, generalizations, ideals, abstractions, interpersonal loyalties, and intrapersonal states.  It is no longer authored by them, it authors them, and thereby acheives a personal authority."

A mature level 4 consciousness can recognize that others see things differently, even-among those at level 3-in arbitrary or irrational ways, but their quest is to make sense of things for themselves, and this involves, of necessity, a degree of tolerance for others to work things out differently.  Thus, their mental "quotient space" does not result from gluing together the received structure of the world, but rather derives from the much more expansive realm of conceivable and defensible relationships that can potentially make sense of the world.  It is, in essence, the mental space of combined possibilities of how one might possibly construct a worldview-an ethics, a politics, an aesthetics, a personal code of conduct, whatever one feels one must have in order to make sense of the world, and act responsibly towards it, and towards others, as well as oneself.

Naturally, those functioning at Level 3 have no experience of the inner ordering process of self-authorship inherent in Level 4.  To them, stepping outside of their Level 3 framework is quite literally inconceivable.  Anyone who would do so would be opening the door to anarchy, nihilism, unbounded moral relativism.  For them all order must come from without, from the world they embrace as the only possible one that makes sense, and to abandon that world is to abandon reason, order, and morality itself.  This constitutes, in one form, the basic disconnect between liberalism and conservatism.  It is, in one sense, an unbridgable gap.  Intellectually, Level 3 cannot comprehend the world as seen by Level 4.  Yet, it is still possible for people to communicate, and even to love and trust one another across such divides.  Indeed, much deeper divides separate every parent from their newborn child.  And so the point of understanding the existence of such differences is not to despair, but to begin the process of finding ways to build bridges based on understanding both what we share in common, as well as what we do not.  It is, in short, a reality-based approach to bridge-building, rather than a fantasy-based one.


Coda

Back on September 23, Chris wrote a  diary, "A Rare Moment", in which he talked about his fascination with the early 20th Century as a period of clashing ideologies.  In a follow-up diary, I will write about ideological struggle with this notion of quotient spaces in politics as a sort of deep background.


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Nerdiest post ever? (4.00 / 2)
And watch out...this discussion's about to get even nerdier!

Paul, if I remember right from previous discussions, you were a math major?  Or maybe you got an advanced degree in math?  Well, I'm a math Ph.d., so get ready for some nerd rank-pulling. :)

Seriously, though...it seems to me that your "quotient space" approach might be more robust if you centered it around the defining concept of equivalence relations, as per Wikipedia.  In terms of human relationships, perhaps it might help to focus on the "transitive" property of equivalence relations.  

For instance, a sibling relationship is transitive: if person X is a sibling of person Y, and person Y is a sibling of person Z, then person X must be a sibling of person Z.  On the other hand, being friends is not transitive: if X is friends with Y, and Y is friends with Z, X does not necessarily have to be friends with Z.

Just throwing this out there; the mathematical concept behind your reasoning is certainly interesting to me.  


Oh Those Wonderful RST Relationships! (4.00 / 2)
Yeah, I'm a math deliquent, I must admit.  Undergrad only, but it was relatively advanced.  Unfortunately, also, quite some time ago, so I appreciate all the help I can get!

As for the diary development, I think the applications of quotient spaces are potentially quite vast, and I certainly thought of writing more about equivilence relationships.  But as it happens this diary was written to provide a lead-in for another diary I actually wrote last weekend, but just didn't have time to post.  I've just retooled it a bit so that the two fit together better, and as a pair they only develop one line of thinking out of many possibilities that I think could be developed here.

I eagerly encourage folks to jump in with other ideas.  We can be nerdie as we wanna be!

"You know what they say -- those of us who fail history... doomed to repeat it in summer school." -- Buffy The Vampire Slayer, Season 6, Episode 3


[ Parent ]
Paul -- interesting points... explains judgements btwn levels (4.00 / 1)
This is a great explanation for why people at "lower" levels tend to negatively judge those at "higher" levels of cognitive development. (One of the most frustrating situations is being a Level 4 working for a Level 3 boss, for example.)

Still, I was hoping you were going to tie it all together to describe ways in which different levels view time differently... :-) I don't know if it generalizable that Level 3's view "one time" (the past is the present and will be until the end times) whereas Level 4's view time as a process of unfolding sequences.

Finally, Robert Wright's book "Nonzero" may fit in here, too. He talks about how over the long expanse of history people, individually and collectively, have grown to view more and more others as sharing an identity. This may be another way in which classifications impact thinking by level.


One Thing About Time (0.00 / 0)
People at Level 3 can have all sorts of different views about time, depending on what the society (or subsociety) they live in thinks.  What they can't do is take a comparative view or two more different conceptions.  Of course, they can hold incompatible views, without ever being bothered that they are incompatible.  It's the rational comparison that stumps them.


"You know what they say -- those of us who fail history... doomed to repeat it in summer school." -- Buffy The Vampire Slayer, Season 6, Episode 3

[ Parent ]
DUGG IT!!!!! (0.00 / 0)
Quotient Spaces In Politics
openleft.com - An article by Paul Rosenberg. It helps explain why conservatives are (or appear to be) so dense.

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