150: A Network Threshold

I was thinking about Malcolm Gladwell’s interesting book Tipping Point and it occurred to me that there is a network that is similar to his “The Magic Number 150” chapter that says communities break down when the membership reaches 150.

It is the C60 Buckminsterfullerine or a truncated icosahedron.

Truncated icosahedron

This interesting little geodesate has 60 vertexes and 90 edges.

In the context of an associative database that is 60 entities and 90 associations or 150 Entity Types.

It is interesting that the most symmetrical of shapes might as a network correspond to the threshold he describes in communities.

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Encouragement

“If at first an idea isn’t absurd, there’s no hope for it.”
Albert Einstein (1879 – 1955)

Garrett Lisi on his theory of everything

I agree with Garrett Lisi. It’s sets and geometry.

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The Lie E8 is a beautiful structure mathematically with 248 dimensions:

However, I think what he wants to achieve is even simpler to model physically.

This is a 3V Icosahedron Geodesate:

This structure gives us 92 vertexes (entities) and 270 edges (associations) or 362 particles.

Employing Occam’s Razor, I suggest that some form of Icosahedron Geodesate theory is more likely the answer.

Dune: One Loose End

Dune: Battle of Corrin is the conclusion of the three volume prequel to the original Dune anthology by Frank Herbert.  It documents the events leading to the destruction of the Omnius Empire and the final battle of the Butlerian Jihad at the planet Corrin.  All of the loose ends are neatly tied up by Brian Herbert and Kevin J. Anderson but one:  The essential connection between the Bene Gesserit maternal ancestral recall and the Spice Agony.  I found their patch to be wholly unsatisfactory.  Otherwise a good read.

Universe: Hexahedron Theory

Hexahedron Schema:

  1. 4 Axes are Dimension Particle Sets
  2. 8 Vertexes are Space Particle Sets
  3. 12 Edges are Force Particle Sets

Additional Schema Components:

  1. 4 Axial Plane Sets
  2. 6 Edge Plane Sets
  3. 16 Axial Plane Triangulation Sets
  4. 24 Edge Plane Triangulation Sets

Look at the vertexes of the hexahedron as entities.

Entities are Sequence->Value->Type

Look at the edges and axes of the hexahedron as associations.

Associations

are: SourceEntity->VerbEntity->TargetEntity

or: SourceAssociation->VerbEntity->TargetEntity

The instances for the entities and associations are the sets we are working with.

The key is the universe is composed of particles of a broad variety.  But every particle is simply an association in the form of a set.  The lowest order particles are event and point.  They are one dimensional particles.  All subsequent higher dimension particles can be reduced to a subset of these particles.

I have revised my theory to include the observer in the system.  I am of the opinion that the observer is not unary but binary having two hemispheres to the brain.  Position and Velocity are composed of sets not points and are observed separately by the ordinal and cardinal hemispheres of the observer.  Consequently, the universe is not probalistic, but wholly deterministic.

Where – When : Space – Time

Sequa is an ordinal point set while frequa is a cardinal event set.

What – How : Mass – Light

Quala is an ordinal sequency set while Quanta is a cardinal frequency set..

Why – How Much :  Gravity – Energy

Grava is an ordinal quality set while Erga is a cardinal quantity set.

Who – Whom : Ordinality – Cardinality

Orda is an ordinal gravity set while Erga is a cardinal energy set.

I think there are even higher order entities and associations, but I have still to work them out.

Octahedron Theory (cont’d)

I have been updating the previous post and will continue to update it as I receive feedback from my peers over at dbforums.com.  I want to thank them for helping me to express my concept more clearly.

Universe: Octahedron Theory

The octahedron:

  1. 3 Axes (I thought this was a triangular point)
  2. 4 Planar Corners (I thought this was a tetrahedral shell)
  3. 6 Vertexes (I thought this was an octahedral shell)
  4. 12 Edges (I thought this was an icosahedral shell)

The key is the universe is composed of particles of a broad variety.  But every particle is simply an association in the form of a set.  The lowest order particles are event and point.  They are one dimensional particles.  All subsequent higher dimension particles can be reduced to a subset of these particles.

The three axes of the octahedron are the universes of different orders.  They are simply subsets of one another.

The six vertexes of the octahedron are the vertex dimension sets of the system.

The twelve edges of the octahedron are edge dimension sets between each of the vertex dimension sets.  These edge sets are also particles and the same set equations can be applied to them that were applied to the vertex sets.

To understand the tables you will require high school level physics knowledge and an understanding of basic set theory.

First, I am taking ordinal sets and performing three set operations on them to get subsets.

Second, I am then plugging the subsets into a standard set equation that describes the “space” for that dimension set.

Third, I am then introducing the result into a higher order dimension set.

When

How

How Much

Why

What

Where