A Category Theoretic Thinking Perspective on: Studying Emergence in Teams Using Multiple Methods A...
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Transcript of A Category Theoretic Thinking Perspective on: Studying Emergence in Teams Using Multiple Methods A...
A Category Theoretic Thinking Perspective on:
Studying Emergence in TeamsUsing Multiple Methods
A SymposiumAcademy of Management Annual Meeting
Vancouver BC, August 10, 2015
James K. HazyAdelphi University
Founder, Leadership Science, LLC
Organizing Organization TheoryCategory Theory
Systems Thinking
Complex Adaptive SystemsManagementTheory
Psychology
IO psych
Social Psych
Neuroscience
Natural Sciences
Traditional Economics
Evolutionary Economics
Resource-Based View
Dynamic Capabilities
Behavior Economics
Operations/Logistics
Decision ScienceSoft Systems Method
Chaos Theory/ Dynamical Systems
Linguistics/Semantics
Logic
MathematicalFields
Computer/DB Science
ITC systems
Social media
Social Physics
Neuroscience
Cybernetics
Statistical mechanics
(Adapted from Spivak, 2014; however, errors are mine alone).
Mathematical Category Theory
• Objects (Categories can be Objects)
• Relationships• Identity • Composition
• Associativity
“sets” or “collections”
“arrows” or “maps” object maps to itself f: A B, g: B C implies g ᵒ
f: A Ch ᵒ (g ᵒ f )= (h ᵒ g) ᵒ f
Think (but not exactly)Abstraction
Abstract Representations of Objects & Relationships that preserve Structure or Order (i.e. store “information”)
(Adapted from Spivak, 2014; however, errors are mine alone).
g ᵒ f gA B
C
f
g ᵒ f
A
Group of members, mi
has a
Team“limit”
has a
Project
hasa
has a
Cooperative Structure“colimit”
P X G P
G
“Pullback” or “meet”- ConstructOrdering in Space of Possibilities
Define: Observed “Emergence of a Team Cooperative Structure” as a “Fact” The above statement is “True” iff the diagram commutes, that is, iff …
P G
Π
“Pushout”or “join”Construct Disjoint Union for Clarity
of Role Interfaces & Map of Activities
Team Project Cooperative Structure Team Group Cooperative Structure
Construct broadestachievable Project given Group for planning purposes
Construct simplestProject roadmap &Group structureto enable action
Construction must be rigorous at increasing levels of detail
Universal property is not decomposable; component objects
“reconstructed” as functors, i.e, “integrated- selves.”
Inclusion
Inclusion
(Adapted from Spivak, 2014; however, errors are mine alone).
Projection
Projection
Hypothesis I: The above diagram commutes, iff… Benefit Maximized (PXG) less Cost Minimized (P G) = Value >
Hypothesis II: Autocatalysis occurs iff catalytic Leadership Practices are present
Hypothesis III: The presence of Residual Complexity between• External Complexity in the ecosystem (context) and the • Internal Complexity within the organizing system (category structure) enables the emergence of a new Cooperative Structure (storing additional information) that enhances the system’s predictability.
Π
Implications
OpportunitySeeking
Value Discovering
StrategicAmbiguityDivergence
Fine-GrainInteractions
(FGI)Autonomy
EntrepreneurialOrganizing
Value Gathering
InterpretativeDominanceConvergence
Coarse-GrainProperties
(CGP)Integrative
ChangingEcosystems
Dynamical Systems &Attractors
Information/ Entropy
Computational/Algorithmic Complexity
Identity/Entity
Structural & RelationalComplexity
Many (Plurality) One (Unity)
Abstract Framework
Level 3: Ecosystem-Level Dynamic search on fitness landscapes
Level 2: Event-LevelPredicting future state underuncertainty
Level 1: Identity-LevelDetermining “Logical” Categories of unity, relations & identity.
Human Interaction Dynamics (HID)Difference – Dualities – Sameness Analytical
RepresentationExploration Exploitation
Let’s look at implications of these layers from the bottom up
(Hazy & Backström, 2013b)
7
Research Questions & Methods
RQ1: What category theoretic frameworks can be developed & how can real-time data be gathered and processed to efficaciously solve organizing problems?
RQ2: Which leadership practices are necessary for catalyzing organizing and at what frequency is each required to sustain each requisite leadership function under various circumstances?
RQ3: What mathematical and computational models can be developed to simulate the potential field effects on organizing under various environmental and internal interaction conditions?
Methods Development: Data collection/analysis techniques and algorithms, a Leadership Practices Data Collection instrument, and mathematical & computational simulation models.
Category Theory (Very Partial) Toolkit
(Adapted from Spivak, 2014; however, errors are mine alone).
• Categories of abstract objects or types & inter-relationships – Sets (e.g., roles, workgroups, firms), Graphs (e.g., social networks), Functors, etc. – finite & infinite; discrete & indiscrete; continuous
• Recursively “layer up” or “drill down” (e.g., Power Laws?) – “Categories of Categories” & Sub-categories as Objects
• Database Schemas are Categories as are networks– Cognitive schema?
• Universal objects & properties might signal emergence– initial & terminal objects “constructed ” over indexed Functor Categories– colimit or “join” least upper bound; “simplest” disjunction into components (e.g.
a subway map has Letter-named and Color-named lines representing “train-equivalence”) – limit or “meet” or greatest lower bound; “broadest” still included in all objects
(e.g., the “ordered pair,” cross-product, i.e., multiplication)
• Left & right adjoints translate among categories – “Free” & “Forgetful” Functors between categories and generalized definitions
References1.Goldstein, J. (2015). Reimagining emergence, Part 3: Uncomputability, transformation, and self-transcending constructions. E:CO ,
16(2): 116-176.
2. Goldstein, J., Hazy, J. K., & Lichtenstein, B. (2010). Complexity and the Nexus of Leadership: Leveraging Nonlinear Science to Create
Ecologies of Innovation. Palgrave Macmillan: Englewood Cliffs.
3.Hazy, J. K., & Ashley, A. (2011). Unfolding the Future: Bifurcation in Organizing Form and Emergence in Social Systems. Emergence:
Complexity and Organization, ISSN: 1521-3250, 13(3), 58-80.
4.Hazy, J. K., & Backström, T. (2013a). Human Interaction Dynamics (HID): Foundations, Definitions, and Directions. Emergence:
Complexity and Organization, 15(4).
5.Hazy, J. K., & Backström, T. (2013b). Editorial: Human Interaction Dynamics (HID)—An Emerging Paradigm for Management Research.
Emergence: Complexity and Organization, (15)4: i-ix
6.Hazy, J. K. & Boyatzis, R. E. (in press). Emotional Contagion and Proto-Organizing in Human Interaction Dynamics. Frontiers in
Psychology Organizational Psychology.
7.Hazy, J. K., Millhiser, W., & Solow, D. (2007). Mathematical and computational models of leadership: Past and future. In J. K. Hazy, J.
Goldstein & B. B. Lichtenstein (eds.). Complex Systems Leadership Theory (pp. 345-370). Mansfield, MA: ISCE Publishing.
8.Hazy, J. K. & Wolenski, P. R. (in press). Phase transition and complex social contagion as enabling mechanism s for coordinated action
in populations: A mathematical framework. In E. Mitleton-Kelly, Prof. A. Paraskevas, C. Day (Eds). Edward Elgar Handbook of Research
Methods in Complexity Science: Theory & Application.
9.Holland, J. H. (1995). Hidden order: How adaptation builds complexity. Reading, Massachusetts: Perseus Books.
10.Mac Lane, S. (1978). Category Theory for the working mathematician, 2nd edition. New York: Springer.
11.Spivak, D.I. (2014). Category theory for the sciences. Cambridge, Massachusetts: MIT Press.
Questions?
Back-Up Slides
New Management Imperatives
• Context – Use information to parameterize internal and external complexity and map among categorical representations to enable efficacious decisions and actions
• Catalysis - Engage predictability (cycles) & uncertainty (events) by accelerating information gathering and using by testing ideas through action – “Leadership Practices”
• Categories - Determine and communicate a common understanding of who is acting and what is being done.– Mission: Construct largest Category supporting a Project that can be
accomplished by these People: “limit” as greatest lower bound (GLB) – Roadmap: Construct smallest Category reflecting: connected activities
connected people: “co-limit” as least upper bound (LUB)
ΠTraditional leaders often claim to embody these Categories. By doing
so, they become a personified structural attractor. Because these categories are “universal properties” transcending any individuals, those who seem to embody them may appear to have “charisma”.
A better solution is a rigorous mathematical treatment using diverse input. This enables additional levels of complexity to be layered onto the
mathematical representation that is understood & used by the team.
Five Leadership Functions
• Gathering Information for situational awareness• Generative activities to create options that
accelerate information producing events• Using information by implementing the structures
for resource and information flows• Administering the execution & control of activities,
resources & information• Building community & evolving collective identity
14–
Frequency of LeadershipPractices
Organizing/ Coordinating Mechanism
System Function Performed
Collective-LevelSituational Awareness
Emergence
Ratcheting/Timely & Effective Decision-Making
Entrainment
Shared Identity
Info Gathering/ Learning Culture
Generative/ Creating Alternatives & Options
Info Using/Accountability Culture
Administration/Efficient Executing
Sense of Community/Employee Engagement
Illustrative Practice:- Ask questions of diverse parties
- Bias to“ try something” with others and process feedback
- Promote people & activities for success not politics
- Offer incentives to meet objectives
- Find & promote a common cause or purpose
Culture of Leadership
Among Team Members
Complex Adaptive
System
OrganizationalProperties Enabling
Performance & Adaptation
Social Field Potential
• Action Vectors, ai Persons Directed To Goal• Order Parameters, Higher-scale relevant
observable among ai
• External Complexity, Opportunity/Threat• Internal Complexity, Organizing Potential • Singularities Discontinuous Change
ξ
cint
cext
Proposed definition:Value is created when Information is gathered and used
such that through agency the residual uncertainty that remains between internal and external complexity is reduced.