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**CHAPTER 3: Research Design and Methodology**

The literature review in Chapter 2 suggested a bias in the conceptualization of CAS such that they are perceived as being emergent, distributed, and unpredictable

These generalizations have themselves been built on the work of several Nobel Laureates who have all interpreted fundamental quantum-level phenomena in the same way. The resultant perception of the lack of centralization in CAS does not allow for a meaningful kernel of innovation to be constructed. The mathematics constructed to-date has perhaps therefore also tended to be piece-meal and as a result there does not appear to be a single centralized mathematics that can frame CAS as a cohesive whole animated by the essential property of innovation.

In a way of looking at this it is apparent that the lack of a single mathematical framework for innovation for CAS may be the result of a bottom-up look at CAS. If however, CAS were to be perceived from the outside-in then its holistic nature and the nature of the innovation inherent in it might surface more easily.

The research problem, building on the gap identified in theory in Chapter 2 and as summarized in Section 2.2, is what would a mathematical framework for innovation in CAS look like?

The following research strategy, research methodology and research instruments illustrate the investigation of the fundamental research problem.

**Research Strategy**

In his book ‘Supersymmetry and Beyond: From the Higgs Boson to the New Physics’ Kane (Kane, 2013) states that only now scientists are beginning to ask why the world works the way it does, as opposed to the normal research focus of how the world works the way it does. What was considered to be in the realm of philosophy has now become normal in the realm of particle physics research. Einstein asked that question decades ago, but it is only now that the question can be answered with the birth of theoretical, as opposed to experimentally-based frameworks, such as String Theory. Development in String Theory has proceeded through studying the theory itself, as opposed to the interaction of experiment with theory. In perhaps a similar vein the mathematical model developed here is also primarily grounded in theoretical as opposed to experimental ponderings. Subsequently the theoretically constructed mathematical model is then applied and ‘tested’ in several ways as elaborated by the following components of the research strategy. The research strategy follows from the nature of the research question, to frame a holistic mathematical engine for innovation in CAS, and can be thought of as the essential approach to be employed to further explore the research problem under consideration (Creswell, 2013). The framing of such a mathematical engine that addresses the key attributes, design principles, and working hypotheses therefore employs a qualitative approach and is elaborated in the research strategy outlined below:

- Construction of a conceptual analytical framework: Construct a conceptual analytical framework that incorporates the design principles and hypotheses generated in the literature This analytical framework will be expressed as series of equations that will define a mathematical kernel of innovation in CAS.
- Application of the conceptual framework: The mathematical framework will then be applied to sample CAS domains to arrive at relevant conclusions about the domains to further the understanding of these domains, using a process of deductive The difference between deductive and inductive logic is illustrated by Vickers in the Stanford Encyclopedia of Philosophy (Vickers, 2016): “Deductive logic, at least as concerns first-order logic, is demonstrably complete. The premises of an argument constructed according to the rules of this logic imply the argument’s conclusion. Not so for induction: There is no comprehensive theory of sound induction, no set of agreed upon rules that license good or sound inductive inference, nor is there a serious prospect of such a theory. Further, induction differs from deductive proof or demonstration (in first-order logic, at least) not only in induction’s failure to preserve truth (true premises may lead inductively to false conclusions) but also in failing of monotonicity: adding true premises to a sound induction may make it unsound.”
- Simulation of the key equation in the analytical framework: The key mathematical equation that frames a possible process for innovation in CAS will then be simulated to descriptively research how innovation in CAS may be altered through manipulating key parameters contained in the equation.
- Case study: The derived equations will then be applied to a case study to gain further insight into a process of organizational innovation
- Reinterpretation of piece-meal CAS math: The piece-meal CAS math will be reviewed in light of the mathematical model developed here
- Hypotheses review: The initial set of hypotheses will be reviewed in light of the results of the previous components of the overall research strategy
- Qualitative proof of structure of mathematical model: A qualitative proof or need for the essential mathematical structure of the model, comprising of several layers each focused on some essential dynamic, will be explored

**Research Methodology**

The research methodology elaborating how each component (Buys, 2014) of research strategy will be fulfilled is the following:

- Construction of a conceptual analytical framework: The methodology is to use the process of induction in arriving at the mathematical Note that while a deductive argument “is intended by the arguer to be (deductively) valid, that is, to provide a guarantee of the truth of the conclusion provided that the argument’s premises (assumptions) are true”, “an inductive argument is an argument that is intended by the arguer merely to establish or increase the probability of its conclusion” (IEP Staff, 2016). Existing mathematical functions will be leveraged where appropriate, and new mathematical functions will be defined and used where none currently exist. Starting from the outside-in, certain pervasive and relevant patterns will be mathematized. Then using induction, several equations will be derived to reflect observations and hypotheses about the outside-in view of CAS. Equations will in general build on the previous one and the simplest initial observations will then be converted into summary equations using previous equations developed.
- Application of the conceptual framework: The resultant framework will then be applied to several CAS domains. Since the process of induction was used in constructing the conceptual analytical framework, the process of deduction is used in the application of the framework to each of the CAS domains to thereby increase the validity of the The first CAS domain is at the level of the cell, where a substantial body of knowledge about cell-function has already been developed. The mathematical framework will re-interpret certain observations about molecular plans being used by all cells to suggest an equation of innovation at the cellular level. Second, it will be applied to the domain of quantum properties to reinterpret some fundamental conclusions that several Nobel Laureates have arrived at, and that stand at the bases of many perceptions about CAS itself. Third, it will be applied at the level of quantum-particle classification. Fourth, it will be applied to the domain of atoms by studying a four-fold classification of the Periodic Table. Fifth, it will be applied to the domain of CAS itself to deduce conditions for sustainability of CAS. Sixth, it will be applied to reinterpret fundamental properties of CAS itself. Note that the application to the corporate level of complexity will take place by means of a case study as elaborated in point 4 below.
- Simulation of the key equation for innovation in the analytical framework: Using Vensim Simulator, the key equation for CAS innovation will be constructed. A graphical user-interface will allow key parameters that cause a jump in the level of system-innovation to be modeled. Interactive sessions will allow the level of system-innovation to be graphed and studied as parametric inputs
- Case study: An approximately three-year case study conducted by the researcher of this dissertation at Stanford University Medical Center will be discussed to illustrate the practical action of several key equations for innovation in Hence a descriptive illustration of how the equations may work practically will be highlighted.
- Piece-meal CAS math review: The question is to what degree are the piece-meal areas that have been considered able to integrate into the general mathematical model as being developed here. If this integration is noticeable the degree of confidence may be higher that the developed model may be considered deep and wide enough to be a basis of thinking about a more general mathematics for CAS
- Hypotheses review: The hypotheses initially generated will be reviewed in light of the research conducted in the preceding The associated body of knowledge for System Dynamics and CAS as laid out in the literature review will be revisited.
- Qualitative proof of structure of mathematical model: Implication of Einstein’s special and general theory of relativity will be leveraged to gain insight into essential structure that must exist in any coordinate

**Research Instruments**

Given that the research problem is the construction of a mathematical model of innovation in CAS, the instruments used are qualitative in nature and are essentially reduced to ‘codes’ (Cooper & Schindler, 2014) such as ‘cohesiveness’, ‘simplification’, ‘relationship’, ‘ability’, amongst others, as summarized in Figure

The choice of research instrument by which each component of the research strategy is probed into is also elaborated by Neuman (Neuman, 2013) who draws a distinction between data used in quantitative versus more qualitative research. Being that the research question is qualitative in nature data would be more in the form of trends, generalizations, taxonomies, as opposed to precisely measurable variables:

- Construction of a conceptual analytical framework: The cohesiveness of the derived mathematical equations becomes the instrument of It will need to be observed if the generation of a new equation is consistent with the equations already generated and the understanding of innovation in CAS as a whole.
- Application of the conceptual framework: The mathematical equations will have to be applied to CAS domains to deduce Further insight and simplifications to the properties in the target domains are the instrument of research.
- Simulation of the key equation in the analytical framework: As different input parameters are selected in the simulation, the overall level of system innovation will change. Detailed graphs depicting relationships will be highlighted to illustrate some of the relationships in the derived equations. The relationship of adjustable parameters to system innovation is the instrument of research
- Case study: The ability of equations to frame organizational innovation and change is the instrument of research.
- Piece-meal CAS math review: Cohesiveness of integration of piece-meal math equations into the main model is the instrument of Data about how well they integrate into the derived math model is the focus of analysis.
- Hypotheses review: Addressing generated hypotheses in the derived mathematical model is the research instrument
- Proof of structure of mathematical model: Ease with which existing established theory suggests structure of mathematical model derived here

ABSTRACT

ACKNOWLEDGMENTS

INDEX OF FIGURES

INDEX OF DERIVED EQUATIONS

CHAPTER 1: Introduction & Background

1.1 Introduction

1.2 Research Problem

1.3 Key Attributes of the Desired Theory

1.4 Summary of Core Mathematical Framework

1.5 Chapter Summary

CHAPTER 2: Representative Literature Review

2.1 Theory and Research Review

2.1.1 Systems Dynamics

2.1.2 Bottom-Up Approach to Complex Adaptive Systems

2.1.2.1 Distributed Control

2.1.2.2 Inter-Connectivity

2.1.2.3 Sensitive Dependence on Initial Conditions

2.1.2.4 Emergent Behavior

2.1.2.5 Far from Equilibrium

2.1.2.6 State of Paradox

2.1.3 Rule-Based Systems

2.1.4 Top-Down Approach to Complex Adaptive Systems

2.1.5 Mathematics in CAS

2.1.5.1 Prigogine’s Dissipative Structures

2.1.5.2 Turing’s Activator-Inhibitor Equations

2.1.5.3 Complicated vs. Complex

2.1.5.4 Measuring Complexity

2.2 Literature Conclusion & Need for a New Theory

CHAPTER 3: Research Design and Methodology

3.1 Research Strategy

3.2 Research Methodology

3.3 Research Instruments

3.4 Summary

CHAPTER 4: Model Development

4.1 Inherent System Bias

4.2 Nature of a Point in a System

4.3 Architectural Forces

4.4 Uniqueness of Organizations

4.5 Emergence of Uniqueness

4.6 Varying Culture of Organizations

4.7 Inherent Dynamics of Any System

4.8 Equations for Stagnation and Dynamic Growth

4.9 Qualified Determinism of Complex Adaptive Systems

4.10 Framing Organizational Transitions at Layer U

4.11 Framing and Modeling Shifts in Innovation at Layer U

4.12 Framing Complexity

4.13 Summary

CHAPTER 5: Theoretical Model Application

5.1 Application of Generalized Equation of Innovation at the Cellular Level

5.2 Application at the Quantum Level

5.2.1 Dual wave-particle nature

5.2.2 Independent states as specified by superposition

5.2.3 Quantum tunneling

5.2.4 Canceling out of quantum dynamics

5.2.5 Traveling faster than the speed of light

5.2.6 Entanglement

5.2.7 Going backward in time

5.2.8 Quantum Fluctuations

5.2.9 Summary

5.3 Architecture of Quantum Particles

5.4 The Periodic Table

5.4.1 The S-Group

5.4.2 The P-Group

5.4.3 The D-Group

5.4.4 The F-Group

5.5 Sustainability of CAS Systems

5.6 General CAS Mathematical Operators

5.6.1 Presence-Based Mathematical Operators

5.6.2 Power-Based Mathematical Operators

5.6.3 Knowledge-Based Mathematical Operators

5.6.4 Nurturing-Based Mathematical Operators

5.7 Summary

CHAPTER 6: System Simulation of Quaternary Model

6.1 Overview of Modeling

6.2 Only Untransformed Layer Active

6.3 With Meta-Level M1 Active

6.4 With Meta-Level M2 Active

6.5 With Meta-Level M3 Active

6.6 Activation of Point Summary.

6.7 Simulation Summary

CHAPTER 7: Stanford University Medical Center Case Study

7.1 The Objectives and The Equations

7.2 The Beginning of the Work

7.3 Results of Work at Stanford Hospital & Clinics Leadership Academy

7.4 Work With the Pediatric Intensive Care Unit

7.5 The Fractal Organization Field Guide

7.6 Summary

CHAPTER 8: Evaluation

8.1 Evaluation of Mathematical Equations

8.2 Evaluation of CAS Target Application Domains.

8.3 Evaluation of System Simulation

8.4 Evaluation of Stanford Case Study

8.5 Evaluation of Existing Math in CAS

8.6 Evaluation in Relation to Generated Hypotheses from Literature Review

8.7 Evaluation in Relation to Einstein’s Theory of Relativity

8.8 Summary

CHAPTER 9: Conclusions

9.1 Overview

9.2 Contributions

9.3 Further Research

APPENDIX 1: APPLICATION OF THE DERIVED MATHEMATICAL MODEL TOWARD THE FRAMING OF A UNIFIED FIELD THEORY

APPENDIX 2: QUBITS AND QUANTUM COMPUTING

APPENDIX 3: INTEGRATING LIGHT INTO THE EQUATION OF SPACE-TIME EMERGENCE

APPENDIX 4: LISTING OF DERIVED EQUATIONS

APPENDIX 5: VENSIM EQUATIONS AND VARIABLES

APPENDIX 6: STANFORD UNIVERSITY MEDICAL CENTER CASE-RELATED COMMUNICATION AND ENDORSEMENTS

APPENDIX 7: EXISTING EQUATIONS LEVERAGED IN DERIVED MATHEMATICS

APPENDIX 8: AUTHOR’S PUBLISHED ARTICLES AND AWARDS RELATED TO THIS DISSERTATION

REFERENCES

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