Grand Unified Theory

Framework for a Real Enterprise

It was Peter Drucker who revealed undeniably that business was a science that could lead to predictable results.  The way he did so was by collecting and systematizing all the knowledge he could gather on the subject and then testing hypotheses.  After much deliberation on the science of systems and the science of business.  I present the Physics Framework above and the Enterprise Framework below.  As one physics Nobel laureate said, “If you aren’t doing physics, you’re stamp collecting!”

I am working to refine my framework table for a lay audience. It is a vocabulary for a business system. Like the Linnean system, by using the intersection of the row and column (two terms) I can identify any operation of the system. Still needs work, but its getting there.

It is based on an associative (node and link) architecture not a relational (table and relationships) architecture.

At first glance this might be regarded as a Zachman Framework.  The columns by convention are called focuses.  The rows called perspectives.  The interrogatives make up the column header.  John Zachman offered some poorly chosen row headers which I’ve replaced.  There are two major differences.  First, it requires an additional focus as part of the enterprise, the Market which is measured in potential profit.  It’s time for the academics and bureaucrats to stop turning up their noses to the source of their existence:  a market that will pay in currency to fatten their budgets.  Second, REVISE, the nodes, are something obvious to Einstein; RELATE, the links, something obvious to Drucker (remember the links are verbs); REPORT, the node and link attributes, should be obvious to Thomas Jefferson; RECORD, the databases, to Carnegie; REGARD, the datatypes, to Turing; REPOSE, the ordinality, which remembers whats related to what, REVEAL, the cardinality, full of exceptions to the enterprise.

Systema: Geodesates, Nodes and Links

“To every action there is an equal and opposite reaction.” — Isaac Newton

A predominant issue arising from my work is the discovery of the difference between a node and a link.  A node type represents a state type while a link type represents a transaction between state types.  However I am finding there are a limited number of node types (self-ordered states) and link types (self-ordered state actions).

In the diagram below, each polyhedron is a first frequency geodesate and has a unique polytrope/polytype combination.  A polytrope is the number of edges per polyhedron vertex.  A polytype is the number of polyhedron vertexes.  This is not the final version.  I am still working to purify my geodesate concept.

What I am revealing here is that each of the seven Node Types on the Left has only one Link Type on the right.  In the same way that an association is composed of a source node type and target node type, an association is composed of a source link type and target link type.

Here is an example of a homogenous Entity to Entity association:

Here is an example of a hetergeneous Entity to Positity association:

Having considered this it is now possible to conclude that there are a unique set of nodes each with a unique link which can be used to build homogeneous or heterogeneous associations.  In otherwords, each node type can perform only one action type.  It is the reaction type of the target node type that makes the action reaction combination unique in the system.

Let’s look at some examples of node type and link type associations:

  1. To identify a positity, positifies an identity.
  2. To objectify a projectity, projectifies an objectity.
  3. To chronify a chronity, chronifies a chronity.
  4. To projectify a quantity, quantifies the projectity.
  5. To qualify an identity, identifies a quality.

Fourty-nine possible type combinations exist.  I think there are even more types which I will explore with Archimedean Solids and higher frequency Geodesates in later posts.

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

The Vaio is Dead! Long Live the iMac!

It’s a big day here in relationary land.  My trusty Sony Vaio had a physical hard disk failure.  Repair would cost one quarter of the purchase price and weeks between Sony and back.  Fortunately, I do most of my work on Google Docs at home and I backup my iTunes library.  So I went to the local high profile electronics dealer and asked the sales rep what I could get for the original purchase price of a four year old Sony Viao.  The answer was a top of the line iMac and in a matter of 20 minutes for financing I walked out with a big box in hand.

When I reached my apartment and pulled the iMac Box out of the brown cardboard shipping box I looked at the thing and decided to clean my entire apartment in preparation.  This was like bringing my dream date home.  I unpacked the computer and set it up on my desk.  I realized that I would have to get a new chair so I would not hurt my neck looking up into the screen which was bigger than my television display.  Then I turned it on.

Everything about the machine, the OS and the software is superior.  This is American design, Californian design at its finest.  I showed it to my friend and he told me to take time to get a little sleep every night.

I celebrated by downloading a complete Mozart collection from iTunes.  The sound is great.  I’ll be giving away my Vaio, my DVD player and my television set.  I think I will give up my land line and buy an iPhone, too.

iMac, where have you been all my life?

Icons: The Czerepak Framework

Tearing apart the Zachman Framework has yielded great results.  I have identified the core nodes and links (we won’t use the terms entities and associations any more).  The new Nodes of the Czerepak Framework are:

  1. Computers
  2. Machines
  3. Goals
  4. Observers
  5. Elements
  6. Particles
  7. Points
  8. Events

The new Links are:

  1. Operations
  2. Processes
  3. Rules
  4. Names
  5. Bonds
  6. Quanta
  7. Distances
  8. Durations

If you look at the link icons you can see what I am hypothesizing as the optimum cardinality for each.  I am thinking about this from the perspective of the Platonic solids, R. Buckminster Fuller’s work, Stuart Koffman’s work with chaos theory and Boolean networks and Albert Einstein’s own love for geometry.

The set of icons created to this point are below: