Simmel : On Number Mills>>Sociology>>Ryan>>SOC116

Outline

    1. "On the Significance of Numbers for Social Life"
      1. Small Groups
        1. Socialism
        2. Religious Sects
        3. Aristocracies
      2. Large Groups: The Mass
      3. Group Size, Radicalism, and Cohesiveness
      4. Paradoxes in Group Structure
      5. Numerical Aspects of Prominent Group Members
      6. Custom, Law, Morality
    2. The Quantitative Determination of Group Divisions and of Certain Groups
      1. Introduction
      2. Numerically Equal Subdivisions
      3. The Number as a Symbol of Group Division
      4. Group Organization on Numerical Principles and Its Effect upon the Individual
      5. The Social Gathering ("Party")
      6. The Extended Family
      7. Quantity and Quality
    3. The Isolated Individual and the Dyad
      1. Introduction
      2. The Isolated Individual
      3. Isolation
      4. Freedom
      5. The Dyad
      6. Characteristics of the Dyad
        1. Triviality
        2. Intimacy
      7. Monogamous Marriage
      8. Delegation of Duties and Responsibilities to the Group
      9. The Expansion of the Dyad
        1. The Triad vs. the Dyad
        2. Two Types of Individuality and their Connection with Dyadic and Other Relationships
        3. Dyads, Triads, and Large Groups
        4. The Formal Radicalism of the Mass
    4. The Triad
      1. The Sociological Significance of the Third Element
      2. The Non-Partisan and the Mediator
      3. The Tertius Gaudens
      4. Divide et Impera
    5. The Importance of Specific Numbers for Relations Among Groups
      1. Group Subdivisions
      2. The Decimal Principle
      3. The Outside Regulation of Groups According to Their Maximum and Minimum Sizes

      Simmel On Number -- Outline

    6. "On the Significance of Numbers for Social Life"
          1. Positive aspect = number makes something happen; negative aspect = something cannot happen until numerical threshold is reached.
          2. "Two’s company, three’s a crowd."
          3. Legacy. Mancur Olson on tragedy of commons/free rider problem – collective action only in small groups. Rosabeth Kanter on tokens in organization – social psychological effects independent of attitudes of numerically dominant members. Peter Blau – ratios between groups determine levels of interaction and meanings associated with proportions (e.g., in a 90:10 situation you have more minority pairings with majority than vice versa and so it seems like a different kind of phenomenon to the two groups).
      1. Small Groups
        1. Socialism
          1. Works in small groups because of mutual surveillance. In large groups you need a complex division of labor (e.g., for mechanical solidarity) but this differentiation inevitably extends to wishes and feelings as well as occupations. Size may also be limited by need to depend on a surrounding world for things. Not everything can be planned so existence of groups with planned economy depends on their being surrounded by society living under different conditions (88.8-89.5).
        2. Religious Sects
          1. If groups get too large it gets difficult to do things like all looking alike, being the same vis a vis the outside world, being connected by shared sense of one another’s direct religious experiences. So, either such religious groups stay small or they grow but change their sociological character (90.1-5).
        3. Aristocracies
          1. Seems to be a limit on size. Group must be "surveyable" by all members. Relations must be traceable. Thus, aristocracies often have practices which serve to limit their numerical growth (e.g., primogeniture). Simmel seems to think there is something inherently unstable in this approach. If the aristocracy grows too much it disappears, but, if it does not, then it is more at risk of disappearing as well.
      2. Large Groups: The Mass
      3. Group Size, Radicalism, and Cohesiveness
      4. Paradoxes in Group Structure
      5. Numerical Aspects of Prominent Group Members
      6. Custom, Law, Morality
    7. The Quantitative Determination of Group Divisions and of Certain Groups
      1. Introduction
          1. This is not a matter of quantitative exactness.
      2. Numerically Equal Subdivisions
          1. Lots of ways to divide groups (e.g., hierarchies of ancestry). Dividing groups by number plays a role in development of idea of equal or corresponding parts. Councils of 100, township system in midwest, "divide up into groups of N," etc.
      3. The Number as a Symbol of Group Division
          1. Leadership by "the six" or "the group of seven." The sociological irony is that the most "special" group in a society is labeled by its most generic quality, its number (107.5). The number, Simmel says, is not 1+1+1+… but rather it stands for the group as a unity, the group in its groupness. By focusing on the number rather than some other quality we emphasize the shere interactivity that constitutes the group without reference to any particular content of that activity (107.5). "It is exactly the characterless and impersonal nature of numerical designation which is characteristic here: more forcefully than any other less formal concept could do it, it indicates that it refers not to individuals but to a purely social structure" (107.8).
          2. Sometimes things referred to by a number do not need to be numerically exact. "The number becomes independent even of its arithmetic content: all it indicates is that the relation of the members to the whole is numerical; the number, which has become stable, represents this relation" (108.5).
          3. Coins/money, tithe, "Hundred" – symbols for subdivisions according to objective principles.
      4. Group Organization on Numerical Principles and Its Effect upon the Individual
          1. Under such numerically "objective" arrangements as democracy we have a curious irony. In exactly that society based on the liberal ideal of the individual, votes are "counted rather than weighed." The individual disappears in its numerical equality. The full specificity of individual personality is replaced by the fact that it is just one (111.3).

          2. Individual voices matter. Consensus or individual veto.
          3.  
          4. One person,
            one vote.

      5. The Social Gathering ("Party")
          1. "…the question of how many persons must be invited before a ‘party’ results" (111.9). Number may vary but given a set of conditions, the number makes a difference. Some non-numerical factors include:
          1. The more people the less they need to invest their "higher natures" – to balance this we compensate by intensifying external and sensuous attractions – (e.g., how is a big class not a party?) – key factor is easy formation of subgroups (partly from lack of complete harmony of mood).
          2. Twofold nature of party. Everyone can be involved in interactions with specific others but at the same time they must acknowledge that they are at a larger event. Goffman talks about this as honoring the larger situation.
          3. The formal ball is archetypical "party" : people intimately dance, but change partners frequently; all are guests of the host and this links them together, but their relations are quite impersonal.
      1. The Extended Family
      2. Quantity and Quality
        1. Intermediate value problem. One is not a party, 25 is. So there must be a number in between where "partiness" sets in. But we can’t identify it in practice or in theory. Where’s the way out of the conundrum?
        2. DJR: this is a basic question in the non-linear, emergent properties of the social world. Qualitative discontinuous differences emerge from amidst continuous quantitative change.
        3.    
        4. 6 *
        5. 15
        6. 20
        7. 7
        8. 21
        9. 35
  • *The number of combinations of n things taken r at a time is defined to be: C(n,r) = n!/(r!*(n-r)!) where n! = n(n - 1)(n - 2) . . . 1

      1. The Isolated Individual and the Dyad
        1. Introduction
        2. The Isolated Individual
        3. Isolation
        4. Freedom
        5. The Dyad
        6. Characteristics of the Dyad
          1. Triviality
          2. Intimacy
        7. Monogamous Marriage
        8. Delegation of Duties and Responsibilities to the Group
        9. The Expansion of the Dyad
          1. The Triad vs. the Dyad
          2. Two Types of Individuality and their Connection with Dyadic and Other Relationships
          3. Dyads, Triads, and Large Groups
          4. The Formal Radicalism of the Mass
      1. The Triad
        1. The Sociological Significance of the Third Element
        2. The Non-Partisan and the Mediator
        3. The Tertius Gaudens
        4. Divide et Impera
      2. The Importance of Specific Numbers for Relations Among Groups
        1. Group Subdivisions
        2. The Decimal Principle
        3. The Outside Regulation of Groups According to Their Maximum and Minimum Sizes