Universe: Interrogative Spaces

iconuniverse14

In my previous post I gave thought to Tim Brown of IDEO’s “design thinking”, Clayton Christensen’s “Innovator’s Dilemma”, Malcolm Gladwell’s “Tipping Point”, and Buckminster Fuller’s “Synergetics” concepts.  What emerged was the above Czerepak Framework.  My claim is this framework is fundamental to designing a system.

The thing that the above table shows is interaction within what I am now going to call the “Interrogative Spaces”: HowSpace, WhatSpace, WhySpace, WhoSpace, WhenSpace, WhereSpace, HowMuchSpace, HowManySpace.  Each ellipse I call a “vortice”.  The Interrogative Spaces are composed of one or more vortices.  The Framework above shows how Spaces are composed within the Interrogatives,  but what about interactions between the Interrogative Spaces?   A good example is speed or velocity.  Speed is the intersection of WhenSpace and WhereSpace:

v = r / t

Where v is velocity, r is radius and t is time.

If you are increasing Speed, which is acceleration, you have one dimension of WhereSpace and two dimensions of WhenSpace:

a = r / t’ * t”

Where a is acceleration, r is radius, t’ is the first clock and t” is the second clock.  You cannot measure acceleration with one clock. This uniqueness of every vortice applies to all the Interrogative Spaces and all inter-relationships between all of the Spaces.  .

Another way to look at the Interrogative Spaces is as sets and subsets.  The first row are the complete Space vortice sets.  The second row are the first Space vortice subsets.  The third row is the intersect between the row two and row three Space vortice subsets. And the fourth row are the intersects between the row two and row three and row four Space vortice subsets.

I do not believe that anything is constant.  Not the speed of light, not gravity, not cosmology.  Every intersection of dimensions creates a vortex in Universe and every one is unique.  We are simply unable to measure and manage the uniqueness of everything, therefore we make generalizations which create models that can always be falsified.

Jared Diamond: Societal Collapse

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more about “Jared Diamond: System Collapse“, posted with vodpod

If you listen carefully to what Jared Diamond is saying in the TED video above, he is describing not a five part, but a six part power curve into a systemic singularity. This has been one of the core themes of discussion of this blog.  We all seem to be too close to our problems to see the commonality.  The interrogatives come into play here:

  1. Goals
  2. People
  3. Functions
  4. Forms
  5. Times
  6. Distances

Times and Distances being the basis on which the higher orders are built.

When we look at the recent economic “crisis” we see 300 trillion in currency circulating and roughly 1 trillion to 2 trillion shifting suddenly and unexpectedly.  We witnessed a systemic collapse, a singularity, a tipping point, a power curve, an exponential change, a phase transition or whatever label you want to call it.  These have been happening everywhere since Time and Distance began in different contexts and orders both in human and non-human systems.

What Jared Diamond and other alarmists are implying is that human society is now a system approaching its final singularity in this century on this planet.  We are implying that today we are experiencing a less than one percent crisis on a power curve into a singularity.  How many more iterations will the global system withstand?  Will humanity make the step into space successfully before we experience a global dark age?  How will the six or more factors in the power curve play out?

The truth to me appears to be that power curves whether they play out or not result in either a systemic climax or anti-climax followed by a systemic collapse.  Would it not be better if we experienced a systemic climax that led to us expanding into the solar system?

Systemic collapse seems to be the fashion of this generation.  Every generation looks with fascination at its own youth, maturition, reproduction and acceleration into mortality.  Some die early, some die late, but all die.  It is an irrevocable law of nature.  It is not about self-interest.  It is about what self-interest is defined as.

Related Posts:

Beyond the Singularity

Servitas and Libertas

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If You Don’t Like the Speed, Get Off the Ride

We have lived in “exponential times” since the big bang (if there was one)

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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.

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

Singularity, Pluralarity and Lorentz Transformation

Working with Malcolm Gladwell’s Tipping point, Ray Kurzweil’s Singularity and the Pareto Principle lead me to begin thinking about a pattern that presented itself. In an earlier post here and here I discussed how there had been many Singularities in history. It also lead me to talk about Pluralarites. Then it struck me there is an oscillation between Singularity and Plurality, giving us the Singularity Pluralarity Plot above. And the implications are interesting.

Any innovation follows the Singularity Pluralarity Plot as a complete life cycle. Kurzweil’s singularity will be no exception. The first working AI will be the domain of specialists it will not be unleashed uncontrolled on humanity and it will have been accomplished after several incremental developments that will leave humanity more than prepared for it. The AI will then have to be molded into compatibility to a variety of purposes. After that it will have to be iterated until it is reliable. Once it is reliable then the true singularity happens: the cost benefit ratio is achieved and AI becomes accessible to the general public. The next step is availability on the global market. Finally, AI will have to be always on and pluralarity is achieved. AI will be ubiquitous and the next innovation will take place. The commoditized original AI will begin its descent and a new innovation in AI or a completely new technology will take its place and begin its ascent.

There will be social upheaval, but I don’t think it will be as dramatic or as immediate as some think.  The anthropomorphization of AI will fade and it will just be considered another tool.

The first thing that occurred to me is that as there is a positive and negative infinity there is also a positive and negative zero. Whether the zero is positive or negative is determined by whether you approach it from positive values or negative values. The second thing that occurred to me is that a pluralarity to singularity transition is divisive while a pluralarity to singularity transition is multiplicative. The third thing that occurred to me is that it is possible to have a positive to negative transition. For example you could follow a positive singularity to positive pluralarity curve with a negative pluralarity to negative singularity curve which would ascend like a staircase. The fourth thing that became obvious is that on an exponential curve the Pareto Principle applies at both ends. It’s like applying Lorentz transformations. Fifth, I am currently reading Peter Drucker’s Innovation and Entrepreneurship and have discovered that seizing opportunity, Entrepreneurship, requires recognizing whether you are approaching a Singularity or a Pluralarity while creating opportunity, Innovation, is making a Singularity or Pluralarity. The final thought that occurred to me is what are the implications of this knowledge on network design, physics, chemistry, biology, databases, complexity, simplicity, organization, history, anthropology, evolution, commoditization? I’ll leave it there.

Beyond the Singularity

I have been doing some work on a new greater-than-social networking concept and was struggling with singularities and the term “religion”. Instead of abiding by the conventional definitions of the term I decided to look into the roots of the word itself.

Broken down, religion means repeatedly binding oneself to what you rely upon. But what is it upon which we rely?

Religion when taken in its 13th century context was synonymous with “conscientiousness”. But what did conscientiousness mean? I decided to dig deeper.

Conscientiousness means living according to conscience meticulously. Now we had the word conscience.

Science, as most of us understand, means “knowledge”. But what does the prefix “con-” mean?

“Con-” as a prefix means “combined”.

Therefore, in its unadulterated form “religion” means “repeatedly binding oneself to one’s combined knowledge meticulously”. Or in otherwords, “Observing all I know”.

This is the true failure of most religions. They limit what they know to a few texts and deny any further expansion of knowledge. Judaism stops at the Old Testament. Christianity stops at the New Testament (No one comes to the Father except through me). Islam stops at the Koran (There will be no prophets after me).

In reality, all the wise men that have existed despite all their conviction were, are and will be wrong. There will always be more knowledge. And what each of us knows is unique to us because every human experience is unique. And no person’s combined knowledge is the same as any other person’s.

To homogenize ourselves by standardizing our conscience, standardizing our organization, standardizing our professions, standardizing our education, standardizing our climate and standardizing our terrain will ultimately lead to a singularity. And we have had countless singularities throughout history. We’ve just used other terms for them.

Facility was a series of singularities produced by the standardization of land from hunting ground, to farm, to storehouse, to factory, to palace, to temple. Chronology was a series of singularities produced by the standardization of time from herd migration, to growing season, to supply levels, to production cycle, to communication cycle, to cognition. Commodity was a series of singularities produced by standardization from sources, to seasons, to measures, to trades, to connections, to conscience. Industry was a series of singularities produced by the standardization of hunting practice, agricultural practice and accounting practice, trades practice, organizational practice and religious practice. Community was a series of singularities produced by the standardization of tribe, village, colony, city, state, empire. Conscience was a chain of singularities produced by the standardization of geographic worship, climactic worship, possession worship, trades worship, organization worship, combined knowledge worship.

We have always been in an age of exponentials. We have always been experiencing singularities. The outcome of any singularity is predictable: A new media is created and moves from Macro (Mainframe), to Meso (Mini), to Micro (Personal), to Nano (Portable). Literacy went through this evolution. The Gutenberg press went through this evolution. Telecom is going through this evolution. Transportation went through this evolution. Computers went through this evolution. The internet will go through this evolution. Artificial Intelligence will go through this evolution.

Looking at a singularity from this perspective it becomes obvious that for every black hole of standardization there is a white hole of diversity beyond. It could be also said that Ray Kurzweil’s singularity is actually Malcolm Gladwell’s tipping point–a transition from scarcity to ubiquity. Kurzweil’s mistake is the same or similar to Zeno’s Paradox.

Imagine a series of professional AI’s giving way to an explosion of amateur AI’s.

Simply put, a tipping point is the transition point where benefit finally comes to exceed cost.

Related Post:

Jared Diamond: Societal Collapse

Servitas and Libertas