Self Organization

"Meanwhile, back on earth.."

Self-organization is driven by the goal such as expansion or by a disturbance that may call for defense. While the hyperflight site deals primarily with the self-organization of matter, self-organizing principles also apply to the organization of individual minds, social groups, and machines. In this article, your organization takes the front seat.

Self-organization is difficult to figure out but easy to embrace. If you are a scientist, you will have hard time until you understand different computational modalities of the duality. It is not possible to arrive at self-organization with words such as order, hierarchy or statistics, for these words belong to but the domain of the left brain. The inclusion of true and full infinity is required (not just unbounded kind of "in potentia" Aristotelian infinity), and then the stability in the midst of the infinite environment is also required. So, take it easy and do not mind taking a step back. You are integrating a big domain -- the virtual domain of the infinite.

Your brain functioning may change, however, and you should not be compelled to continue. For better or for worse, the virtual domain is a very divergent environment with slippery slope, and some even claim the choice may at times not be yours. It is not as easy as if caught in a riptide -- there is a procedure to use if caught in that -- and 'what works' is now subjective, indirect, and non-causal. What works for you is what works for you. It is not as bad as "abandon all hope, ye who enter here" kind of thing, but you will not be able to see the shore until you shore the sea.

To see a world in a grain of sand
And heaven in a wild flower
Hold infinity in the palm of your hand
And eternity in an hour.

    William Blake
    from 'Auguries of Innocence'

If you are familiar with the Riemann sphere, you can apply it to the first line -- imagine being at the North Pole. The second line is the shoring of the sea, the third and fourth line -- well, take it from there.. ..

While the right brain thinking is understood in terms of relationships and artistic preference, the down side could be seen as the mind that seems a "leaf in the wind," pursuing tangents and associations that may come by. Some discipline will be called upon, although it is not the strength but a broad and integrated knowledge that gels the discipline. Perhaps the best summary in dealing with the infinite is in the book The Fog, for which we have a book review. Finally, not all is about psychology and poetry. As you read on, you may appreciate that dealing with the infinite may be something the upcoming technology could be able to handle. Building upon the Pythagorean and alchemical foundation, you are in charge of your brain and the pill is the stopgap measure at best.

      In a way of the background you can check the geometry of hyperstates, which is about self-organization of matter. Hyperstates is the one organizing framework for any and all real systems, which issues from the Tetractys of Pythagoras. Hyperstates framework has a mathematical and physics foundation from which all hard (real) topologies issue. Each dot is a particular and real manifestation of a topology such as the planetary ring, multi-ring, planet in an orbit, spiral galaxy, spherical galaxy, barred galaxy, and the galactic cluster. By definition, every topology (every dot) is a tractable solution. Moreover, self-organization via hyperstates is scale-independent inasmuch human-defined micro and macro scales is concerned. Scale-independence holds even though the gravitational force does not dominate within the atom.

      In another piece for a background, you may want to read about at least some concepts associated with chaos. The present published work on chaos is weak and science writers in particular dwell on parts that are not relevant.

      Oftentimes the work with infinities is trivialized under labels such as 'imagination' or thinking 'outside the box.' In the realm of infinity we get a lot of stuff, which can be a lot of crap, too. The point is that there is not a general simple description for infinity, and in the end descriptions such as 'imagination' become those of a simpleton. Infinity can be managed only through relationships and the consequent relevance such relationships may have.


Your Mind

Self-organization consists of ongoing actions of selected separations and joining, depending on your objectives and your current disposition. A small number of relationships are disconnected at any one time. Dissolved relationships have weak, conflicting, or low frequency outcomes. Such separation-joining actions allow subsequent (mental) computing to happen faster and with fewer what-if considerations. Hyperstates will help; yet, the self-organization via hyperstates takes time because the "mass and momentum" of various systems (mental processes) need to find their own new equilibrium (new computable state or new non-conflicting state) by moving to another context that belongs to (is associated with) another hyperstate. For that reason, all possible hyperstates are to be considered concurrently while keeping in mind that we are dealing with real systems.

New computing state is based on systems that are perceived as dependent (following, inferior) and independent (leading, superior). Any physical variable can be dependent or independent and this is a function of the interacting context, which, in turn, is a function of relative scale but is not determined by scale alone.

Growth (reach), individuation, and organization of your mind necessitates a rearrangement of relationships.

The real component of your mind is continuously searching for determinism. Things that can be measured (quantified) and controlled in a repeatable fashion provide the real mechanism for your mind. Turing machine (our current computer) is the best example of the power and the limitation of real thinking.

The virtual component of your mind is continuously searching for the most relevant context and is also necessary for self-organization. When engaging the virtual, changes can be spontaneous. They are not easy to predict as to when and what, and a considerable risk entails the subjective "churning of the virtual" without the changes being realized. One needs to find and have faith in the most relevant belief system but one cannot abdicate its own self (core, soul, fire, eye, light, center, pilot, or other designations of self). In the most fundamental definition of existence, "You are the keeper of your fire."

Moreover, when or if the virtual component is prevailing strongly, there is no clear indication that the organizing actions have completed, for the virtual is infinite. In this situation a guide is necessary to help you get grounded. Under certain circumstances, the number of dissolved and new relationships rises from easily managed minority to a substantial reshuffling of virtual relationships. One can appreciate that self-meditation, for example, may exacerbate this condition. Again, a guide is necessary because permanent physiological changes may result.

Your mind is
where your consciousness arises

Any attempt at unifying (merging) the components of the real and the virtual creates paradoxes and confusion. Self-organization of your mind, then, consists of

A: Obtaining a separate representation of the environment in both the real and the virtual context, and

B: Applying real or/and virtual methods, depending on which method is the most effective. Use real methods for the accomplishment of the objective and use virtual methods to bring about the most relevant context

Duality affords a
good definition of consciousness

The paragraph A above serves well as the definition of consciousness. When a particular situation is perceived in both contexts, there is a presence of a separate and dual arousal to the external stimulus. When there are separate arousals that correspond to the real and virtual aspects, then there exists consciousness in one's mind.

If mostly the real component is perceived, the situation is managed using the if-then method. Essentially a Turing machine (present computer) method, the if-then process allows predetermined situations to be addressed with a particular response. While action is inherent in the real method, the relevancy of such action depends on a priori knowledge. The effectiveness of the real method can be narrow. In the limit, the response may not be tractable with respect to the desired outcome. The improvement can only come from knowledge enhancements but, intrinsically, real method has no capability to do so — that is, there is no self-organizing aspect within the real method alone. We can also say that real thinking is "table driven."

If mostly the virtual component is perceived, the situation is managed with the what else method. The virtual what else method searches for associations that may be relevant to the situation at hand. By improving relevancy, one improves effectiveness. While obtaining many possible arousals (virtual method is concurrent without bound), there is no inherent action within the virtual method since the inference/causality is absent (inference limits concurrency). It also makes sense to say that the virtual approach brings about enlightenment when highly relevant contexts are found.

Your Brain

Reality rests on repeatable and finite properties of things. The goal of reality is invariance or periodicity. The prized possession is an equation that yields computable, and therefore predictable and repeatable outcome [here is a tangent on the fourth degree of independence and its implication to real system's inference and repeatability]. Some problems such as three-body or N-body instability are not tractable. Although 100% real in their manifestations, N-body problems do not have a general solution and the outcome is either approximate (in the short run), irrelevant (in the long run), or intractable. Therefore, if or when the number of relationships increases or becomes unbounded, the application of real methods is no longer adequate.

The brain's separation into left and right hemispheres deals with the emulation of the real and the virtual domain, respectively. Left Brain Dominance can be defined as thinking (computing) activity that addresses the problems of the virtual while using real methods. The compensatory action of the left brain in light of the increase in relationships is the invocation of parallelism, but the parallel method requires processed objects to be independent of each other or have invariant properties. Thus, either the relationships (linkages) are ignored or the threads are pursued one at a time. When relationships are ignored the oucome has lower relevance. When threads are pursued sequentially, the outcome moves out of reach because the process becomes intractable.

Repeatability (and hence causality and inference) is the cornerstone of reality and the foundation of engineering. Repeatability, along with measurability, form the present definition of the scientific method. Repeatability, however, diminishes as relationships increase. Real methods that attempt to deal with the issues of the virtual — that is, when relationships are unbounded — result in lack of relevancy or in intractability. In the extreme, one can reach some conclusion only by generalization that strips objects of their unique qualities. Such conclusions, then, can quickly become irrelevant. Similarly, one can spend much time contemplating all possibilities where each thread receives equal weighting with the result that all objects are being assessed without regard to their degree of relevancy. Processing of objects will spawn other threads and without relevancy the entire process becomes intractable.

Another way of distinguishing between real and virtual domains is through the commutative property. We say that two variables are commutative if AoB=BoA, where 'o' is some operation on variables A and B. If the commutative property does not hold — that is, AoB is not the same as BoA, we are in the virtual domain and causality does not hold. It is likely the brain (or a machine) tests for the commutative property and thus differentiates between variables that represent (emulate, are derived from) the virtual and the variables that represent the real. For example, if we say

    'Good variables are hard to find,' and
    'Hard variables are good to find,'

we see that the properties and attributes in these two sentences are not commutative unless "hard" is in most respects the same as "good." The commutative property is inherent in algebra and describes a subset of the real domain for which mathematical solutions exist.

The engine of your mind

A closed system provides a construct for real methods to yield repeatable results (via stochastic or other statistical or averaging methods). The tradeoff here is the increase in entropy and consequent decrease in organization. However, there is a "critical mass" or a certain quantity of relationships that can acquire self-organizing capacity, even in a closed system. For the relationship-poor inorganic matter, this critical quantity appears to be in the hundreds of billions of formally organized objects (with the relationship count much in excess of that). The issue here is the possibility for a brain to atrophy irreversibly and, also, that some very large amount of relationships is a condition for self-organization.

Another construct that enables real methods is that of infinite or inexhaustible supply of real resources. Big bang theory is fueled by the (sudden) availability of enough kinetic energy to explain the expansion of the entire universe. Similarly, the 'Oort cloud' is postulated — in effect invented — to supply the apparently inexhaustible quantity of new comets. Our mind surrenders to real methods by envisioning deep pockets of governments or investors which, in turn, make anything possible. Even nonexistent black holes are put to work here, for the bottomless capacity to suck can be used to construct many inexhaustible free-energy theories. One can also see that the contrivance of dark matter took hold as yet another unlimited real constructor. Dark matter can be stuffed in as-needed quantity to explain why galaxies do not fly apart [we have as many turtles for you to stand on as you want — all the way down]. In summary, the virtual is intangible and infinite but, for better or for worse, real things (can become organized but) are not infinite.

By far the most popular real method is that of hierarchy. When applied in the virtual environment, however, relevant linkages are severed or ignored because the hierarchical (vertical) structure cannot manage unbounded relationships. Branching hierarchies can have many stems, and relationships cannot be described unambiguously or in a tractable manner. (Here is a tangent on often used condition of completeness. Classical scientist uses the term freely and without appreciation of intractability that often arises with completeness. Intractability forecloses solutions in practical timeframes.) The same can be said about differentiation, which is a real method that separates things along a particular level within the hierarchy. Differentiation helps by creating new objects with narrower/reduced meaning (or focused functional grouping) — alas at the expense of linkages. Real reorganization — that is, the replacement of one hierarchy with another will be only marginally successful while carrying reorganization cost of its own. Ideally, the brain addresses real issues with only the real methods.

To demand something or to order someone is to apply real methods. When applying virtual methods, one raises expectations because one manages the context. As you may suspect, neither the real or the virtual domain contain methods that are panaceas. In general, we desire both methods to be applied while understanding that both methods stand apart and cannot be merged.

Free will

While each individual does have a free will, some wills are better than others. In the supply-side environment, a free will can be seen as 'free choice.' In the demand-side environment, free will can be characterized as a 'stronger will.' In either case it is your will that you apply and you live with. You are free to apply your will as long as you are willing to be accountable for its consequences.

Your brain is best visualized as an economics engine that seeks efficiency and effectiveness. Your brain's business, particularly in the open market environment (supply-side), is highly virtual and is not driven by rules or equations. In the demand-side economic environment your brain operates in a closed system where real methods are applicable but real methods have no self-organizing property and such system will remain the same or atrophies through the corruption or real resources

Parallel and Concurrent

There is a subtle yet distinctive difference between parallelism and concurrency. Parallelism applies a plurality of instances of one method while concurrency applies many methods of one instance each. The increase in parallelism produces the output sooner or produces more output. Parallelism is not concerned with efficiency, only in earlier and/or greater output. Concurrency is not concerned about producing things only in higher quantity. Concurrency deals with deployment of many different methods that operate simultaneously and with overall greater effectiveness.

It is said that if one bricklayer can build a house in one hundred days, one hundred bricklayers cannot build a house in a single day. One hundred bricklayers working in parallel cannot build a house in one day but one hundred people with different skills working concurrently can build a house in a single day

Your Organization

Vertical (Hierarchical) organization mimics real systems with the benefit or predictability. Input can be related to the structure yielding deterministic processing times. The output of such system can be labeled as being a matter of execution, done deal, or a slam dunk. The weakness is its lack of flexibility and tendency to resolve issues -- should these arise -- in a contentious manner. The lack of relationships (lack of virtual perspective) in a real organization tends to perpetuate such organization past its relevant and useful life and, consequently, organizations that deploy mostly real methods can take on a role of a spoiler or adversary.

Virtual: The second ingredient

Horizontal organization mimics the virtual. Everything relates to everything while the outcome is difficult to ascertain. However, new, more efficient, or innovative output is likely to emerge. The outcome or timing are difficult to predict and some say that neither the outcome or the timing is possible to control. (Self-test: Is control a real method?) Knowing the virtual behavior, we apply coherence to yield computable process. Knowing the real world, we collapse some linkages to materialize the outcome. Valuing concurrency, we apply constructs that do not entirely reduce superposition but promote coherence. Constructs themselves determine the outcome, which, although not "as ordered," is within the family of desired outcomes.

Your Life and Life

Hyperstates depict the actual balanced and self-organized realization (see, touch, measure) of matter. Hyperstates, therefore, are a depiction of the physical and organized reality. The virtual domain is not discussed in breadth at this site (but it gets much attention in the Quantum Pythagoreans book). By itself, the virtual domain has its own quadrature symbolism, is highly divergent (at least NLogN — lest it could be processed with real methods), the commutative property does not hold, causality or inference are absent, and objects are "replaced" with intangible conglomerations. The collection of relevant entities is concurrent without bound. (Parallelism in the real domain is constrained by the condition of independence.) Virtual components cannot be argued because the degree of relevancy and the large quantity of variables are at its heart.

Virtual symbolism takes on forms that are described by some (Alchemy) as "based on number four." Squares, diamonds, and crosses — including their rotation — represent the virtual symbolism and these are best left to the individual to appreciate. The real domain is formed through hyperstates and there is only one format, even though this one format produces one real plane with a large number of real computable topologies (geometries, structures).

Virtual conglomerates can be bonded or bounded via relationships but this cannot be done exclusively because the virtual cannot be "owned" by some; the virtual domain is accessed and shared by all and by "everything" because the virtual domain is a repository of all knowledge that exists in the infinite superposition.

The virtual domain is intangible and cannot be destroyed by real means. [Here is a tangent on Supernova.] Virtual entities cannot be destroyed by virtual means but can be spun or weaved or attached to relate to other virtual entities. As a whole, the virtual domain is neither favorable or unfavorable or good or bad because the virtual domain "just is." However, the virtual domain deals with relevancy and context, and then new relationships can be considered as favorable or unfavorable. The virtual domain can be defined as relationships that are infinite and, since the relevance (or truth) becomes apparent with a large number of relationships, we can conclude that {1} The virtual domain appears highly subjective to an individual and {2} A large quantity of relationships need to be explored to obtain a good representation of what is relevant to a situation or to an individual.

The virtual domain can also be defined as knowledge and can be converted to real (can be materialized). In fact, no organized entity can exist without both the real and the virtual components and, for example, it is not possible to create an atom with real energy alone. The virtual domain deals with infinities of relationships and associations and is indispensable to life, to life's creation, and to the creation or extinction of life forms.

Two Points of Balance

The virtual domain, being based on the number four stands apart across a discontinuity and in balance with the real domain that is based on the number three. Mandala represents the inner (subjective, virtual) variables that are based on number four and that are oftentimes balanced by meditation. Also, concurrent consideration also needs to be given to obtain a computable context in the real domain that is based on the number three.


Should one seek to balance only the virtual, the second balancing point may be missed to the extent as to dissociate the real domain altogether.

Enjoy, for it is now complete. {May 11, 2001}

You will also need an objective. Something big that may take many years to complete -- and it may not even complete in this lifetime. The idea is that the idea you have becomes physically [I'd even say geometrically] represented inside your brain. Consequently, you will begin to grow this objective by acquiring relevant knowledge from, well, ether -- for it is all there. So, don't be shy and pick something that's really big but not something that would take away too much from your obligations.

 Vibrations create charka nodes with body's backbone geometry

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Added introduction summer 2005

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Last update August 11, 2007