Bennett’s Systematics (not edited)

From the 1920s until his death in 1974, Bennett (1897-1974) sought to develop a conceptual method— what he called systematics—to clarify the pattern and order of wholes by drawing upon the qualitative significance of number. From a phenomenological perspective, one can argue that Bennett’s achievement is a phenomenology of wholes in which each integer—1, 2, 3, 4, and so forth up to 12—points toward a different mode of togetherness and belonging in regard to the thing being studied, which, in Alexander’s case, is largely order and wholeness. In this presentation I draw on Bennett’s understanding of three, threeness, and what Bennett calls the triad to give clues to the remarkable conceptual and applied power of Alexander’s work. Most broadly, my tack in the presentation is to use one approach to wholeness— Bennett’s—to understand better another approach to wholeness—Alexander’s [1].

The First Eight Systems

(1) Monad = Wholeness

(2) Dyad = Complementarity

(3) Triad = Action & relatedness

(4) Tetrad = Activity

(5) Pentad = Potential

(6) Hexad = Event

(7) Heptad = Transformation

(8) Octad = Completedness

Above From: David Seamon
Department of Architecture Kansas State University Manhattan, KS 66506 triad@ksu.edu http://www.arch.ksu.edu/seamon

The Q model’s eight defining terms in relation to Bennet’s first eight systems.

The Q Ontological Axiom of Agency:

  • A State is an actual being. An actual being has a becoming; it is always a potential becoming.
  • A Mode is potential action. A potential action has a difference; it is always an actual difference.

Slide2

  1. State: the length of a temporal cycle i.e. actual_begin → potential_end
  2. Mode: a realm of spatial factors i.e. potential_out → actual_in
  3. Active: refers to more experience necessary i.e. active_ power
  4. Passive: refers to no more experience necessary i.e. passive_ power
  5. Temporal Center: being-in-time i.e. active-actual state_subjective
  6. Spatial Factors: acting-in-space i.e. active-potential mode_expansive
  7. Apt Events: temporal-becoming i.e. passive-potential state_objective
  8. Location Relation: spatial-measure i.e. passive-actual mode_reductive
How The First Eight Systems might relate to the Q:

We will refer to this exercise as, eight ways sensibility proves itself.

1. Wholeness = State

One relates to a cycle in time. A Cycle proves the sense of wholeness.

2. Complimentary = Mode

Two relates to spatial factors. A sense of self proves alterity.

3. Action & relatedness = Active Power (more experience necessary)

Three relates to processing power. Seeking proves a sense of Relationship.

4. Activity = Passive Power (no more experience necessary)

Four relates to power identified. The sense of power available.

5. Potential = Temporal Center (active-actual subjective state)

Five relates to being in time. The sense of nowness proves transition.

6. Event = Spatial Factors

Six relates to spatial activity. The sense of activity that proves events.

7. Transformation = Apt Events

Seven relates to temporal becomings. The sense of events that proves change.

8. Completedness = Location Relation

Eight relates to spatial measure. The sense of resolution that proves belonging.

Triads refer to scripts:

  1. Being
  2. Becoming
  3. Resolve

Resolve may take any number of cycles to reach its completedness. Being and becoming create one unit or one cycle. Resolve may end the cycle or begin another frame.

  1. unit
  2. script
  3. layer

Senses begin in units. Units become scripts. Scripts become layers.

Sensibility is about our interactions and relationships to things and the responses that are generated. Consider that there are things we like and don’t like – drawn to or repelled by – make us anxious or relaxed. Sensibility is a term often used to denote these kinds of responses. We suggest, that our responses are repurposed where their dynamics become part of our communicative nature, dynamics that inform our word-sensibility orientations and processes. This repurposing of our responsive dynamics is a essentially a way to play with our experiences. One way we do this is by holding our responsiveness to the different ways we are constrained to play. Each a way to contain a complete system of play.

To help illustrate this Q perspective of play. Consider the pattern and order of wholes as described by J.G. Bennett (1897-1974). By drawing upon the qualitative significance of number (Ed. 1993), Bennett illustrates a method in which the underlying patterns of things are sensed. That is, through a sense of numberness, a oneness, twoness, threeness and so on. Each sense of numberness is a discrete way to contain the dynamics of thought. Each demonstrates a general way to predict how our thoughts will respond. We suggest, that in this way, we can organize our thoughts by holding our sense of responsiveness to different numberness systems and play.

The twelve systems are not scientific models but insights into degrees of organisation. In his first major essay in this field, The Dramatic Universe (Vol.

Next, consider the Eight Terms of the Q Ontological Axiom of Agency.

  1. State: the length of a temporal cycle i.e. active_begin → passive_end
  2. Mode: a realm of spatial factors i.e. active_out → passive_in
  3. Active: refers to more experience necessary i.e. active_ power
  4. Passive: refers to no more experience necessary i.e. passive_power
  5. Subjective: being-in-time i.e. active-actual state_temporal center
  6. Expansive: acting-in-space i.e. active-potential mode_spatial factors
  7. Objective: temporal-becoming i.e. passive-potential state_Apt Events
  8. Reductive: spatial-measure i.e. passive-actual mode_location relation
We can now consider how the eight terms might apply to Bennett’s Systematics (At least the First Eight Qualitative Significance of Numbers).
Know your Ps & Qs
The polynym semantic system can deal with the full scope of Bennett’s system and can correlate more directly. For those familiar with Bennettian Systematics, you may not see the correlations between Q-unit terms and Systematic terms at first. For instance, in the Bennettian description, oneness is understood as wholeness or a totality of systems and not just a simple cycle as presented in the terms of the Q unit. Systematics holds that the diversity of the wholeness is the qualitative sense of oneness. In our scheme, polynym structures are consistent with the classic Bennettian sense of numberness (e.g., monad = mononym and so on). However, on the  quadranym level, the sense of numberness are fundamentally detailed. Each number is a component of the process of playing itself. It might be helpful to think of these correlations below as mapping an autonomous sense of play to a conscious sense of play. That is, the polynym is about the way the system may choose to play or think. For instance, one may choose a sense of threeness over fourness. The Q-unit is not about a system of choice but about the process that underlies the system to choose. Still, we suggest, that the sense of numberness as correlated below is about the same basic containing dynamics essential to both levels at play.
Eight Terms of The Ontological Axiom of Agency = General Systematics

1. Wholeness (J.G. Bennett) = Q State:

Oneness relates to a full cycle in time. A sense of cycle proves wholeness. STATE

2. Complimentary (J.G. Bennett) = Q Mode:

Twoness relates to spatial difference. A sense of alterity proves the complement. MODE

3. Action & relatedness (J.G. Bennett) = Q Active Power:

Threeness relates to processing power. A sense of action proves relatedness. ACTIVE

4. Activity (J.G. Bennett) = Q Passive Power: 

Fourness relates to the powers of a being. A sense of order proves activity. PASSIVE

5. Potential (J.G. Bennett) = Q Temporal Center:

Fiveness relates to being in time. A sense of limit proves potential. SUBJECTIVE

6. Event (J.G. Bennett) = Q Spatial Factors:

Sixness relates to spatial identity. A sense of freedom proves the laws of events. EXPANSIVE

7. Transformation (J.G. Bennett) = Q Apt Events:

Sevenness relates to temporal becomings. The sense of developing proves transformation. OBJECTIVE

8. Completedness (J.G. Bennett) = Q Location Relation:

Eightness relates to spatial measure. The sense of location proves completedness. REDUCTIVE

The Q active-actual quadrant doesn’t represent the actual world but that which is driven by the actual world, like our motivations and tendencies e.g., hunger, sex, survival, discomfort and so on. So, if one is hungry one negotiates the world for something to eat (FROM neg TO pos). What you eat is not actual, it is potential. That is, being hungry is actual and food in the world is potential. Or, as another dynamical context trajectory: what is between what – is not actual, it is potential. That is, being in empty space is actual and being between things in empty space is potential.
Slide016
Above, in the quadrant, between represents a representation of the objective field. The objective field can be any large knowledge base (Not necessarily part of the q system. It could be conceptnet’s system maybe!?
Theoretically, it is where the rules of all systems are, and is always positive info about the world, always truth conditional. It represents those things that others can or should be able to perceive as being either true or false. It is the job of the q system to make that information easily tractable for commonsense understanding and knowing. It aims to represent an organismic system.
The zero point of reference represents the subjective quadrant (void). That is, it is about those things not seen by others or are unattended by the subjective sense itself. For instance, one does not attend the emptiness of space if not necessary. It is those things that are in the emptiness of space that generally concern us. The objective sense is always positive (between), even if only theoretically. the earth we walk on and the obstacles we avoid will usually belong to the positive quadrant of space. Earth may also begin to fade into an unattended position in this model.
Q-unit: [-+(–) ⊇ +-(++)] = x
Mostly Negative: Infinite(void) = superset
Mostly Positive: Finite(between) = subset
According to this graph layout, the byte correspondence to the q active-passive would look like this:
  • 00 = active-actual (–)
  • 01 = active-potential (-+)
  • 10 = passive-actual (+-)
  • 11 = passive-potential (++)
Active as 0 does seem a bit counter intuitive;)
Because as you where thinking…
  • active is on = 1
  • passive is off = 0
makes simple sense, still…
The question is, in which way is it more intuitive for this model? For me it is the way belonging to the C graph. It better reflects the subjective nature of sensibility – when sensibility is active most of that activity is unattended (or off to our awareness). Most of our own thoughts are unattended according to most cognitive scientists. The Q is about the connection between pre-reflective and reflective thoughts. However passive means no more experience necessary because when a thought is positive (i.e., there or that) there is no more processing of past experiences necessary and also no experience is needed in the future. The positive remains a passive potential of attended sense until the environment drives it again where it becomes active-actual and stimulates its passive potential to find its positive trajectory in away that fits a context. This creates the cycle for scripts.
Scripts function like frames and can be edited like a movie film. A q unit represents a unit of memory: [a –> b]. A flux represents the connections between units [b] –> [a]. When b comes upon a that means the environment is driving. When a comes upon b that means the organism is remembering within an already coupled unit: [a –> b] .
The dynamical context positive quadrant represents that which is probable on the Q level – but not necessarily true on the objective field level. The Q doesn’t really deal with truth, it deals with dynamics or those things that could be true. Really, it is about coping and ways to respond quickly in ways that is frugal with time and energy.
Passive potential or (++) refers to the objective field potentials, it represents virtual perceptual memory. Still, it is only a dynamic of truth like, I feel up even though I’m laying down. The dynamic of up fits the dynamic sense of good mood.
If a condition needs to be deemed actually true or false then this is beyond the dynamical context and becomes a matter of the objective field – this refers to the situational context level. It is a deliberative level of thought. This level is a matter of lexical semantics, which is about word relation frequency, and conceptual semantics. On the other hand, the Q is a episodic framework in the sense that a meaning or knowing is based on experiential traces or subjective experience and not about semantic representations. It is about how users and computers interface by way of the dynamic sense of things. The benefit of the dynamical context is that trajectories or units can be repurposed (metaphorically) on some layer of a situational context. In this way, it can help to better understand or describe a situational condition. It is about heuristics. The idea is to quickly and easily align a dynamical context with a situational context to help confirm a way something can be organized and easily understood. Organisms are about organizing. In the q model this is done with units, scripts and layers. And like you suggested, maybe triads can help that dynamic.
In short, subjective and objective quadrants are part of the same monism or oneness and are only separated to fit a dynamical context (trajectory or coupling). Active-actual is about a subjective sense that is being driven by the environment and always deals with a negative dynamic of a topic. Passive-potential is about a objective sense that is responsive to the subjective sense. For instance, between represents a positive sense to the subjective sense of void, in the dynamical context of space. Here, between may include locomotion or spatial relations between objects based on the virtual motivation of the organismic model.
Sorry it’s so long and probably needs more work. Anyway, back to graph papers:)
Q-Unit & Systematics
“The twelve systems are not scientific models but insights into degrees of organization. Everything ‘begins’ from simple wholeness and has the promise of progressing in depth to something significant for the greater whole.” (Systematics)
The tetrad of power:
  1. Subjective: Active relates to power that drives entities.
  2. Objective: Passive relates to powers entities use.
  3. Expansive: Active refers to more experience necessary.
  4. Reductive: Passive refers to no more experience necessary.

A Q-unit deals with a progression toward wholeness that begins in itself toward a greater whole between other units.

1. State: the length of a temporal cycle i.e. active_begin → passive_end.

2. Mode: a realm of spatial factors i.e. active_out → passive_in.
3. Active: refers to more experience necessary i.e. active_ power.
4. Passive: refers to no more experience necessary i.e. passive_power.
5. Subjective: being-in-time i.e. active-actual state_temporal center.
6. Expansive: acting-in-space i.e. active-potential mode_spatial factors.
7. Objective: temporal-becoming i.e. passive-potential state_Apt Events.
8. Reductive: spatial-measure i.e. passive-actual mode_location relation.
9. Being: harmony in time i.e. actual is given_subjective-entity_self_identify_instance.
10. Actual: substance in space i.e. actual is excepted_reductive-object_specific_value.
11. Becoming: substance in time i.e. potential is given_objective_other_identify_instance.

12. Potential:harmony in space i.e.potential is excepted_expansive_object_general_value.

Q-Unit & Systematics
“The twelve systems are not scientific models but insights into degrees of organization. Everything ‘begins’ from simple wholeness and has the promise of progressing in depth to something significant for the greater whole.” (Systematics)
The tetrad of power:
  1. Subjective: Active relates to power that drives entities.
  2. Objective: Passive relates to powers entities use.
  3. Expansive: Active refers to more experience necessary.
  4. Reductive: Passive refers to no more experience necessary.

A Q-unit deals with a progression toward wholeness that begins in itself toward a greater whole between other units.

1. State: the length of a temporal cycle i.e. active_begin → passive_end.

2. Mode: a realm of spatial factors i.e. active_out → passive_in.
3. Active: refers to more experience necessary i.e. active_ power.
4. Passive: refers to no more experience necessary i.e. passive_power.
5. Subjective: being-in-time i.e. active-actual state_temporal center.
6. Expansive: acting-in-space i.e. active-potential mode_spatial factors.
7. Objective: temporal-becoming i.e. passive-potential state_Apt Events.
8. Reductive: spatial-measure i.e. passive-actual mode_location relation.
9. Being: harmony in time i.e. actual is given_subjective-entity_self_identify_instance.
10. Actual: substance in space I.e. actual is excepted_reductive-object_specific_value.
11. Becoming: substance in time i.e. potential is given_objective_other_identify_instance.

12. Potential: harmony in space I.e.potential is excepted_expansive_object_general_value.

Reference From:

Here’s a brief but helpful look at orientation as represented in the Q model.

  • In theory, imagining situations require engaging various orienting functions.

Think of imagining as finding orientation with other mental orientations. Situations become individuated based on the orientation functions used.

  1. In theory, orienting functions are analogs used for situational understanding.
  2. Orienting functions are in one’s mind and are used to orient with other minds.

(Note: Orienting functions refer to embodied analogs used as a way to learn by comparing abstract symbols to sensory modalities, which can create analogies.)

In the Q model, quadranyms represent orienting functions or analogs. Quadranym units form RF units, scripts or layers for virtual orientation.

  • Q units represent embodied analogs such as, agent, energy, time & space.

Each unit represents a unique sensory experience captured in a semantic framework that pivots on self identification opportunity and affordances.

  • Embodied analogs require potential states to emerge from actual states.

In the Q, the actual state is the primary, definitive aspect of the embodied analog, while the potential state exists as a kind of capacity and possibility.

  • Q units represent the agent’s recall in terms of actual and potential states.

(Note: Quadranyms aim to capture the structure of some event in the world by representing the actual and potential states of the agent’s sensory experience.)

All orienting functions represented by quadranyms follow basic templates:

Prime Superordinate (Template): Potential(actual) ➝ Actual(potential)

(Note: Potential–Actual modes modify actual–potential states. The actual state receives Potential attributes, and the potential state receives Actual attributes.)

Prime Subordinates (Templates Representing Embodied Analogs):

  • Agent: Positive(self) ⊇ Negative(goal)
  • Energy: Active(motion) ⊇ Passive(matter)
  • Time: Future(present) ⊇ Past(event)
  • Space: Infinite(void) ⊇ Finite(between)

Above quadranym examples from section a) Quadranym Theory

(Note: Attributes refer to additional information beyond the basic properties of a condition state.  Potential attributes are always a response to Actual attributes.)

General analogs such as space, time and energy are routinely used and shared

  • Primary orientations are about analogs common between embodied agents.

(Note: In the model, the quadranym is a representation of dynamic sense found between semantic word relations derived from perception and action processes.)

Reference frame models for AI orientation use the template below:

RF Model Template: Topic = Y(source) ⊇ X(target)

 Quadranyms provide faceted categorization for RF models.

  • The Y responds to X is based on the situation and the source–target.
  • The ontological presupposition will anchor for the relevant potentials.

(Note: When constructing orientation the source and target have different roles to play — a source is the actual condition and a target is the potential condition.)

Inferences are conclusions and orientations are from where they evolve.

  • One is oriented, in some manner, to how tendencies evolve in the world.

(Note: source–target relates to affordance: what the world offers the agent; source and target evolvement predicates on what the X factor offers the Y).

See examples in the full article: Orientation