Databases: Hyperbolic Schema Example

hyperbolic-geometry

In a TED.com talk, Margaret Wertheim proudly relates how a craft predominantly practiced by women solved the physical representation of Hyperbolic Geometry.  Click on the image to view a video of the talk.

This got me to thinking about the representation of Hyperbolic Schemas and Hyperbolic Data.

An example of a Hyperbolic Schema is as follows:

Take the name “John”.  “John” can be seen as an word element or as a composite of “J”, “o”, “h”, “n”.

The left side of the brain sees the element, the right brain sees the composite. This applies level after level.  Phrase element and composite of words.  Sentence element and composite of phrases.  Paragraph element and composite of sentences and so on.  The associative database can support both representations.  This give you very powerful editing capabilities at many levels of granularity as well as powerful searches and applications.

Our product does this using the Sentences Associational Database from Lazy Software.  A relational database cannot do this effectively or efficiently.

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The Zen of Systems and Networks

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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.

systemnetworkslinks1

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.

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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.

Systema: Six Interrogatives and Four Associations

enterpriseassociations2

Since I have been thinking about the dimensionality of Einstein’s universe and the associations within the six interrogatives, it has led me to wonder about how the two fit together.  I have expressed it in the above diagram.  The association types are the rows and the interrogatives the columns.  We immediately have four dimensions for each interrogative.  Food for thought as I think about my current reading on network theory.

This hearkens back to a model I did in June 2007:

enterprisehybrid

You can see by using an association table for each interrogative this model provides for all the possible associations within the ontology.  However, I do not think this model is complete.  I’ll discuss that a bit later.