Actor: Database Modelers automate weakness and agony.

Proactor: Database Designers automate power and pleasure.

Reactor: DBAs automatically complain.

You may be wondering about the title of this post. I’ve decided to reject John Zachman, a non-businessman completely, and name my discovery to honor someone I respect much more highly, an archetypical businessman, Peter Drucker.

The first thing to do is abandon the term “hierarchy”. You are working with networks. You are also dealing with seven networks, not one. This means you are dealing with not seven by seven (49) but seven to the power of seven (over 800,000) nodes in the business space. This is called a seven dimensional hypercube. The main difference between the associative model and the relational model is that the associative (node-link) business area grows into the space while the relational (relation-inferred relationship) business area has to be completely defined. When you are talking about almost one million cells in the schema alone the traditional relational model with all of its NULL values for unused space in tables becomes quite cumbersome. The SQL is resource intensive in both models.

Another thing to abandon is your language. Lay English is often imprecise and inconsistent. I am creating a taxonomy as part of this work to provide a seven dimensional vocabulary. Every one of the terms was thoroughly examined for its definition.

Finally, abandon preconceptions. Look at the data and let it guide you.

There are key levels of abstraction: The schema which are entities and entity associations and instance and instance association. I highly recommend going to Simon William’s site lazysoft.com and reading some of his short white papers on the architecture.

A chart of associations is below:

Let’s look at these associations in the context of physics and business:

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

After considerable struggle with the data it became clear to me that I was not dealing with a table in the normal sense. I could not reconcile a data cube with the seven dimensions I had discovered. Then it occurred to me that I was not dealing with a cube at all. I was dealing with a simpler solid, the octahedron. The octahedron has six dimensions (spokes) and *seven vertexes.*

This gives us a Hauy Construction (this figure is an eight degree):

Using my new taxonomy gives us the following views:

Front:

Side:

Top:

The age of the cube is over. Welcome to the age of the Octahedral Hauy Construction.

In this context we can deduct the following equation:

In the Business Interpretation E can represent Everything (Monopoly) and M can represent Market.

First, we create the generic table:

We are now ready to create the schema:

We can also look at the role of long tails (exponential curves) and tipping points (singularities, pluralarities). Singularities occur when the taxonomy reaches it’s cost/benefit optimum and plurality when the data utilizes the entire business space. Benefit declines from that point.

What I am saying here is systems are not tabula rasas. Systems have a hardwired architecture and schematic that obeys simple physical laws that are in many ways understood as well as softwired structure that is unique to the system. We don’t have to create a unique architecture and unique schema for each system. Now they need only to be refined and applied across the spectrum of human endeavor. We need only learn how to classify the data.

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.

*“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:

- To identify a positity, positifies an identity.
- To objectify a projectity, projectifies an objectity.
- To chronify a chronity, chronifies a chronity.
- To projectify a quantity, quantifies the projectity.
- 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.

*“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:

- 3 edges per 4 vertices – 6 edges – Tetrahedron
- 4 edges per 6 vertices – 12 edges – Octahedron
- 3 edges per 12 vertices – 18 edges – Truncated Tetrahedron
- 5 edges per 12 vertices – 30 edges – Icosahedron
- 3 edges per 20 vertices – 30 edges – Dodecahedron
- 3 edges per 24 vertices – 36 edges – Truncated Cube
- 4 edges per 30 vertices – 60 edges – Icosadodecahedron
- 3 edges per 60 vertices – 90 edges – Truncated Icosahedron
- 3 edges per 60 vertices – 90 edges – Truncated Dodecahedron
- 5 edges per 60 vertices – 150 edges – Snub Dodecahedron
- 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:

Sociology: The Six Adopter Types

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?

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:

- Computers
- Machines
- Goals
- Observers
- Elements
- Particles
- Points
- Events

The new Links are:

- Operations
- Processes
- Rules
- Names
- Bonds
- Quanta
- Distances
- 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: