Design: Business Design Induction/Deduction


This is my latest incarnation of the Business Design Process.  Induction (Brainstorming–generation of ideas) is Counter-Clockwise.  Deduction (Refinement–elimination of ideas) is Clockwise.

Below is the Intelligence Architecture:


Here is the Media Architecture:


This is the Data Architecture for this model.  Note that all values are accepted even if they are wrong:


Below is the Network Architecture of this model.  Note that the values are unique (nodes) and they are sequential (edges):


Here is the Text Architecture:


Here is the Numeric Architecture:


Here is the Octonion Architecture:


Icons: Buttons: 03: Patrix








  1. Nodes – A series of Entities
  2. Edges  – A series of Nodes
  3. Faces – A series of Edges
  4. Solids – A series of Faces
  5. Lines – A series of Solids
  6. Areas – A series of Lines
  7. Volumes – A series of Areas

The Zen of Systems and Networks


My own work with Enterprise Frameworks and Networks has led me to come up with the following table.  It describes the Nodes and Links in a Complete System Network.  I am saying that the Nodes representing Goals, People, Time, Locations, Code, Data, Qualities and Quantities can all be represented as Scale-free Networks and that each of these Node Networks require only one datatype.  I am also saying that there are only three types of links in networks: recursive links within a set, multiple links between sets, single links between sets.  I know of no case where this has been attempted in the manner I am attempting to represent it.


If you have been following my blog you are aware that I have been struggling for a long time to come up with a framework and a clean terminological set to describe systems.  I think I have come one step closer to that goal today.  The table above describes a Fact composed of eight Nodes (first white row illustrating entities) and the Links (last three white rows illustrating recursive, multiple and singular relationships) for each of the System Networks (Interrogative columns).  One of the interesting aspects of this System Network Model is every Fact is composed of a Unique Set of all eight Nodes.  However, all the Nodes in one Fact do not have to have Links to all the Nodes in another Fact.  Each Node within a Fact is independent regarding its Links.  Therefore you have a single set of System Facts with each Fact containing a single set of Interrogative Nodes each connected by their respective Link Networks.

I have recently been writing with the intent to challenge centrism on any one of these networks and advocate a more integrated view. I still remember dealing with data centrism, event centrism, user centrism, goal centrism, program centrism and schedule centrism over the course of my career. All of them have a role to play. My insight into all of these Nouns being Linked by Verbs in only three ways required me to look at all of the Enterprise Architectures and disengtangle the Nouns, Links and Verbs from the reasoning and representations that extend back beyond computing itself.

The Data Model below is a hybrid of Relational Models and Dimensional Models.  I call this an Associational Model.  It is using Relational Architecture to represent it.  However, I think that an alternate Entity-Attribute-Value (EAV) architecture called the Associative Model of Data would be better suited to the task.  I am using relational representation as I am still trying to communicate with a community only familiar with Relational technology.

The first thing to note about this model is Links are represented by Associations.  Associations link two Nouns using a Verb.  What is interesting about this model is every Verb, Association, Noun and Fact is unique.  The vertical connections are Many to Many relationships which allow two vertically adjacent Verbs, Associations or Nouns to have multiple unique relationships between each other.  What this means is there are no integrity problems (duplicate values) as the system network would enforce uniqueness.


The premise of this model is that the Nodes are not dimensions at all.  I am rejecting the traditional concept of dimensionality instead I am saying that there are three dimensions of Links: recursive, multiple and singular.  All we perceive are Facts, Nodes and the Links between them.

So you could come away with the following Zen koan:

entity without entity,

source without source,

path without path,

target without target,

size without size,

dimension without dimension.

Icons: Systema Iconic Language: Part IV


I have been thinking about all I have read to this point and something occurred to me this evening.  There are no such thing as nodes and links.  There are only equilibrium and non-equilibrium states respectively.  Newtonian Thermodynamics only describes equilibrium states.  It does not account for the transition between states when equilibrium does not exist.  So it is with all networks.

When you navigate the web, you are actually moving from one HTML equilibrium state to another HTML equilibrium state.  The page metaphor is concealing the conceptual character of the process.

Back to Basics

The web navigation buttons on a browser are also deceptive.  They do not reveal the logical consistency between the navigation of hypertext networks and goal networks, contact networks, service networks, product networks, location networks, event networks and unit networks.  The consistency between the many forms of media is also concealed by not recognizing that all forms of media are networks transitioning between equilibrium and non-equilibrium states.  It is important to recognize that any form of process or data structure is really a network, even relational databases are simply lattice networks.


The above Icons are the only ones you need to deal with “step” and “loop”, two of the three “linear” processes for navigating any network.  In reality there is no such thing as a linear network.  There is only a path through a set of equilibrium states connected by these non-equilibrium states.  The remaining “decision” is not a binary decision, but a case or switch which is represented by hyperlink icons.

In reality, with the option to back track and break continuity by creating new browser windows, navigation of the web is much more like Prolog than say Basic or C.

It is that simple.  The above icons are the universal icons for navigation of any network, the rest irregardless of conceptual and physical meaning are hyperlinks.

I think it is significant to indicate the target state for hyperlinks through use of icon background shape and color, and to indicate target context through the use of icon foreground content.  This would make hyperlink icons much more communicative and universal.  As also discussed, hyperlink content could be presented as picticons (picture icons), graphicons, (graphic icons), liticons (text icons), sonicons (sound icons), anicons (animated icons) or vidicons (video icons) that exhibit proscribed behavior when rolled over.

Systema: Geodesates as Singularities

“No one untrained in geometry may enter my house” — Plato

Over the past year I have been working with associative and relational databases attempting to find out more about how to develop a better database architecture.  This has taken me into many realms including network theory, chaos theory, state transition theory, geometry, logic, chemistry, biochemistry and physics.  Recently, I began to put these things together and I think I have had a valuable insight.  I call this insight “Geodesate Singularities”.

Geodesate Singularities regard networks as transitions between geodesates which are a group of convex polyhedrons.  Convex polyhedron networks have vertexes as nodes and edges as links.

What is of primary importance to this concept is the vertex enumeration (number of vertexes) and the polytope (number of edges per vertice) in these convex polyhedrons as geodesates are regarded as the most stable states.

First frequency Geodesates are a subset of the Platonic Solids and the Archimedean Solids:

  1. 3 edges per 4 vertices – 6 edges  – Tetrahedron
  2. 4 edges per 6 vertices – 12 edges  – Octahedron
  3. 3 edges per 12 vertices – 18 edges – Truncated Tetrahedron
  4. 5 edges per 12 vertices  – 30 edges – Icosahedron
  5. 3 edges per 20 vertices  – 30 edges – Dodecahedron
  6. 3 edges per 24 vertices – 36 edges – Truncated Cube
  7. 4 edges per 30 vertices – 60 edges – Icosadodecahedron
  8. 3 edges per 60 vertices – 90 edges – Truncated Icosahedron
  9. 3 edges per 60 vertices – 90 edges – Truncated Dodecahedron
  10. 5 edges per 60 vertices – 150 edges – Snub Dodecahedron
  11. 3 edges per 120 vertices – 180 edges – Great Rhombicosidodecahedron

Higher frequency Geodesates are triagulations of the above solids.  I recommend downloading the Mathematica Player and the Mathematica Demonstrations Project Geodesate Demonstration to view the polygons for each frequency.

Again, what is important in the Geodesates are the number of vertexes (nodes) and edges (links).

My hypothesis is when the growth of a network achieves the vertex enumeration and polytope of a geodesate at the first frequency or higher, a singularity state exists in the network order and results in a state transition of the network when exceeded.

Increasing a Geodesate’s frequency involves dividing the faces of the chosen polygon into sub-triangles:

The first frequecy subdivision is termed as 1V, second as 2V, third as 3V and fourth as 4V.

1V Icosahedron Geodesate

12 Vertexes – 12 5 Edge Polytopes

2V Icosahedron Geodesate

42 Vertexes – 12 5 Edge Polytopes – 30 6 Edge Polytopes

3V Icosahedron Geodesate

92 Vertexes – 12 5 Edge Polytopes – 80 6 Edge Polytopes

4V Icosahedron Geodesate

162 Vertexes – 12 5 Edge Polytopes – 150 6 Edge Polytopes

I think geodesate singularites have  implications for Telic, Organic, Chemic, Physic, Static and Gegonic networks.  This has implications for Ray Kurzweil’s Singularities, Malcolm Gladwell’s Tipping Points, Stuart Kauffman’s Self-Organization and Howard Rheingold’s Cooperation Theory.

Convex polyhedrons and geodesates could create and limit new organizational structures for enterprise goals, personnel, products, measures, spaces and schedules.

Related Links:

Icons: The Czerepak Framework

Beyond the Singularity

Physics: Observer as a State

Sociology: The Six Adopter Types

Rules: The Connecting Tissue


The nodes for the network graphics are Cause states, Observer states, Energy states, Mass states, Space states and Time states.  To make this more relevant to business we can use the terms Goals, People, Functions, Data, Locations and Events.  The edges that connect the nodes in all the networks are Cause rules, Observer rules, Energy rules, Mass rules, Space rules and Time rules.  Nodes give the system its concepts, while edges give the system context.  States provide extegrity (new term) while Rules provide integrity.

Each of the networks is composed of finite steps between the starting and terminal node called paths, the potential ways of following the rules to perform the steps are called the strategies, the actual strategy followed is called the tactics, the edges operations and the  nodes are states .

Whether you are negotiating Goals, People, Functions, Data, Locations or Events, you have to create and observe the rules to maintain the integrity of the networks.  Goals are connected by Rules, People are connected by Rules, Functions are connected by Rules, Data are connected by Rules, Locations are connected by Rules and Events are connected by Rules.  Even Events (Time) is a network, because we are continuously referring to different clocks in different frames of reference.

All rules have the same characteristics:


We’ll explore how we will model this for each of the Six Hats, Six Coats networks in a subsequent post.

Now we have the connecting tissue of our networks.  Knowing this, we can embark on a course to model all six networks separately.  Once that is complete we can work on integrating two, three, four, five and finally all six networks into a single set of conventions.

Related Posts:

Systema: Seven Hats, Seven Links