Contribution
A lecture to the American Philosophical Society proposing that one road to a non-trivial theory of complex systems is a theory of hierarchy. It joins four arguments: hierarchy is common; hierarchies evolve faster than non-hierarchic systems of the same size; hierarchies are nearly decomposable; and near decomposability makes them describable. It is not a technical paper. Proofs and data are in cited work.
Key insight
Complex systems are built, and persist, as wholes of stable parts whose inside runs faster than their outside. The two consequences, faster evolution and simpler description, both come from that one fact.
Assumptions
- Pragmatic holism. The whole is more than the sum of its parts “not in an ultimate, metaphysical sense, but in the important pragmatic sense that, given the properties of the parts and the laws of their interaction, it is not a trivial matter to infer the properties of the whole”.
- Arbitrary floor. Where partitioning stops, and what counts as elementary, “is somewhat arbitrary”.
- Random assembly with stable intermediates. The evolution model assumes parts arrive at a constant rate and disperse with constant probability unless a stable state is reached. Simon calls the assumptions “not particularly realistic” and says they understate the advantage of hierarchy.
Key results
- Hierarchy, widened (Hierarchic systems).
- Defined as a system “composed of interrelated subsystems, each of the latter being, in turn, hierarchic in structure until we reach some lowest level of elementary subsystem”.
- It includes “systems in which there is no relation of subordination among subsystems”. “In fact, even in human organizations, the formal hierarchy exists only on paper”.
- Span is the number of subsystems at a level. A diamond or a gas is a “flat” hierarchy.
- Social hierarchies are identified “by observing who interacts with whom”. The spatial and social views “can be reconciled by defining hierarchy in terms of intensity of interaction”. “One of the interesting characteristics of nerve cells and telephone wires is that they permit very specific strong interactions at great distances.”
- Books and music are hierarchies too.
- The watchmakers (Evolution of complex systems).
- Hora builds from subassemblies of about ten parts; Tempus builds each watch of about 1,000 parts in one piece, and an interruption scatters it. With an interruption probability of .01 per part, Tempus takes about 4,000 times as long.
- “The time required for the evolution of a complex form from simple elements depends critically on the numbers and distribution of potential intermediate stable forms.”
- No teleology: “Direction is provided to the scheme by the stability of the complex forms, once these come into existence. But this is nothing more than survival of the fittest—i.e., of the stable.”
- Problem solving is the same process. Cues that signal progress are the stable subassemblies (the clicking safe: 10 × 50 tries instead of about 10
- Empires: “if one would be Alexander, one should be born into a world where large stable political systems already exist.”
- Near decomposability.
- Two propositions: “(a) in a nearly decomposable system, the short-run behavior of each of the component subsystems is approximately independent of the short-run behavior of the other components; (b) in the long run, the behavior of any one of the components depends in only an aggregate way on the behavior of the other components.”
- The worked example is a building of rooms divided into cubicles. Within hours each room equalizes; over days the building does. “After the intraroom short-run equilibria have been reached, a single thermometer in each room will be adequate”.
- The matrix of interaction coefficients is block-diagonal, with off-diagonal entries below some small ε. The theorem is from Simon & Ando (1961), cited, not reproduced.
- “In the dynamics of social systems, where members of a system communicate with and influence other members, near decomposability is generally very prominent.”
- Limits on span in social systems: “a human being is more nearly a serial than a parallel information-processing system”.
- Frequency separation in organizations: “It is probably true that in social as in physical systems, the higher frequency dynamics are associated with the subsystems, the lower frequency dynamics with the larger systems.” Executives’ planning horizon is “generally believed” to lengthen with rank, and “It is probably also true that both the average duration of an interaction between executives and the average interval between interactions is greater at higher than at lower levels.”
- Description.
- Hierarchic systems are redundant and so describable briefly. Few kinds of subsystem, near decomposability (the “empty world hypothesis”: “most things are only weakly connected with most other things”), and recoding a time path as the law that generates it.
- “If there are important systems in the world that are complex without being hierarchic, they may to a considerable extent escape our observation and our understanding.” Simon leaves open which way the dependence runs.
- State against process descriptions: blueprints against recipes. “While RNA is a blueprint for protein, protein is a recipe for metabolism.” Problem solving is translating between the two.
- Ontogeny partially recapitulates phylogeny where descriptions are stored as processes, and so does teaching.
Claims
| id | claim | strength | support |
|---|---|---|---|
| C1 | Complexity frequently takes the form of hierarchy | moderate, empirical generalization | examples across physics, biology, society and symbol systems; no count |
| C2 | Hierarchic systems evolve far faster than non-hierarchic ones of comparable size | strong as a model, illustrative as a number | the watchmaker calculation; “we cannot … take the numerical estimate seriously” |
| C3 | Nearly decomposable systems have short-run subsystem independence and long-run aggregate dependence | strong (a theorem) | Simon & Ando (1961), cited and not shown |
| C4 | Social systems are prominently nearly decomposable | moderate | formal organizations and channels of communication; asserted |
| C5 | In organizations, higher levels have lower-frequency dynamics and longer intervals between interactions | weak | ”probably true”, “generally believed”; no data |
| C6 | Hierarchy makes complex systems describable, and non-hierarchic complexity may escape us | moderate as argument | the redundancy argument; the direction of dependence is left open |
| C7 | Organisms store their self-descriptions as process descriptions (programs) | speculative | 1962 molecular biology; Simon calls it speculation |
Concepts
- Hierarchy (Simon’s sense). Successive sets of interrelated subsystems, with or without authority between them.
- Span. The number of subsystems at a level; a flat hierarchy has a wide span.
- Stable intermediate form. A subassembly that persists if the assembly process is interrupted.
- Near decomposability. Interactions within subsystems much stronger than interactions between them (a block-diagonal matrix with small off-diagonal terms).
- Empty world hypothesis. Most things are only weakly connected with most other things.
- State and process description. A description of what a thing is, and one of how to make it.
Connections
- The all-hands (CASE-050). C5 is the case’s cadence, stated sixty years earlier and as weakly. Coordination at the level of the whole firm is the slow dynamics, and it comes in rare, long interactions.
- A boundary for a combined form. Near decomposability gives a criterion the record has not used. A pair or group is one subsystem when its internal interactions are much stronger than its interactions across its edge. The dancing couple (CASE-046) passes while dancing and fails when the song ends. This is a third candidate beside mutual entrainment (CLAIM-172) and reciprocal compensation (LIT-902). The three measure different things: strength, timing and goal-preservation. That bearing is the record’s.
- No governor. Hierarchy without subordination is the shape of THEORY-056 and of Ainslie’s interests (THEORY-067).
- Inscription. The state/process distinction bears on the storage claim (CLAIM-160). A personal rule or a strategy memo is a process description written for a later reader. The bearing is the record’s.
- The analogy objection. The opening paragraph states the caution of CLAIM-163: “Metaphor and analogy can be helpful, or they can be misleading. All depends on whether the similarities the metaphor captures are significant or superficial.”
- Koestler (LIT-908) builds the holon on the watchmaker parable.