Monday, March 24, 2008

Tractable and intractable computations human individuals are faced with.

In an uncanny manifestation, as I would call it for the lack of a better word available in my mind right now, sources unravelled before me, without a consciously prepared plan, only to lead me, almost effortlessly, to a sought after solution of a nagging problem. One seemingly intractable problem, in personal terms, on the grounds of the unyielding amount of operations in the process of arriving to a satisfactory solution.

Similar with what I mentioned in that post, the anticipation built-in in the firing sequences of neuron groups, with the additional element of intractable problems. Does that go beyond a simple immediate future anticipation? To processes connected to situations where ever ready, constantly on standby, lingering bifurcations sweep away the thoughts toward new, concluding attractors or falling under the influence of powerful trajectories of all-surpassing, universal attractors? As for example the attractor-notion of knowledge already there, awaiting your mind's arrival? Severely cutting down the number, by-passing unyielding operations? Arriving to a solution sooner?

Computational problems can be "efficiently solvable" or "tractable" or "intractable" as they would require a huge amount of operations, at least n^1000000 (n to the power of 1 million), as it is mentioned here,

"P is often taken to be the class of computational problems which are "efficiently solvable" or "tractable", although there are potentially larger classes that are also considered tractable such as RP and BPP. Also, there exist problems in P which are intractable in practical terms; for example, some require at least n^1000000 (n to the power of 1 million) operations."

These are the kind of problems human individuals face in life situations as it is mentioned in "Fractal Neurodynamics and Quantum Chaos: Resolving the Mind-Brain Paradox Through Novel Biophysics", in Chapter 6.1, The Computational Intractability of Survival in the Open Environment.,

"The principal task of the brain is to compute the survival strategy most likely to enable the organism to evade death and produce viable offspring. A computational problem is intractable if the number of computational steps required grows super-exponentially with the complexity of the problem. The travelling salesman problem (Bern & Graham 1989), finding the shortest route round n cities illustrates this, growing with (n-1)! A problem may also be formally undecidable in the sense of Gödel. Many adaptation-survival problems in the open environment share the characteristics of intractable problems, because each strategy tends to be matched by a competing strategy in another organism and the number of options rapidly exponentiates. An active organism must also complete a processing task within 0.1-1 second if it is going to have survival utility, regardless of its complexity. Such arguments make it clear why parallel processing is an integral feature of vertebrate nervous systems."

In each step in our modern lives, though no different in real terms with the lives of human individuals in any era in human history for that matter, we are required to make decisions about effectively intractable problems. The human individual has largely managed to tackle successfully the computational problems associated with survival, and it did so by utilising our brain's chaotic potential. Thanks to our innate ability to engage and utilise chaotic processes led to the establishment of numerous attractors, providing solutions for many problems. Attractors manifesting in numerous forms and shapes, tangible and intangible, matter-transforming or social and mental constructions, tools in the constant grappling with nature, while at the same time continuously transforming into new shapes and forms.

Saturday, March 15, 2008

Visualising fractal dynamics

Fractal dynamics, the communication between the macroscales with the microscales. In the 'Mind and Brain, Chaos and Quantum Mechanics' paper, page 19, I read:

"The dynamics of many important biological molecules may be fractal in this way, which involves the linkage between a variety of quantum excitations of differing energies, and feedback between tertiary structures and active sites."

Communication of higher scales with lower scales. In this example the higher scales being the tertiary structures and active sites of biological molecules and lower scales being the quantum states of the atoms of the biological molecules.

Quantum excitations of differing energies of the atoms of the biological molecules linked with the tertiary structures and active sites of the biological molecules. As the active sites of the biological molecules define the function(s) of the biological molecule and by that the function(s) of the cell organelles it is part of, the higher level of organised matter.

Different levels of matter organisation, fractally connected.

"... structures behaving, not only in a geometrical sense, but also dynamically ..."

Fractal dynamics surpass in breadth and depth, vertically and horizontally, all aspects of human activity among many other aspects of reality. And in each level of organised matter established attractors, a range of stable states as they are defined by optimally maximised local variables and parametres. Such attractors in turn by virtue of the fractal connections determine the establishment of attractors in higher levels as the local variables exert an influence on global variables and parametres.

And since the fractal dynamics provide a two-way path and local variables are influenced by global variables in turn, it leads to the establishment of new attractors by chaotic bifurcations.

If however global variables induced adjustment of local variables and parametres requires tweaking of variables and parametres outside the limits permitted by the local system, the local system will cease to be.

Wednesday, March 12, 2008

Individuals assume arbitrary standpoints to deal with reality.

On page 45, of "Chaos, Dynamics and Fractals, an algorithmic approach to deterministic chaos", by J. L. McCauley, I read:

"By successive stages of simplification (by making approximations that are abstractly equivalent to discarding information), Lorenz finally constructed a model that he could analyze, and found deterministic chaos ..."

and in the footnote it further elucidates that process.

"Here we must admit that the word 'discard' is not quite appropriate, because we do not have such detailed information to begin with. If one had all the appropriate information (solutions for different initial conditions), one could start by systematically ignoring large amounts of detailed information about complicated trajectories."

So it is not only, that we do not have all the information that there is, meaning that the information already exists, despite our inability to witness it and take it into consideration, but on top of it, even if we had the information, we would still systematically ignore it, as we can not deal with complicated trajectories. Our intellect is not equipped, our intellectual capacity is not enough, to deal with all the information that there is.

This statement freely associated in my mind, generalised, epitomises the standpoints all human individuals assume when it comes to deal with reality.

Since knowledge is limited this leads individuals to make arbitrary choices and based on these choices to define their stance. The objective approach is not enough, it can not unravel reality. The only thing achieved or achieves is to construct structure upon structure, that primarily exists in the minds of individuals who invented them in the first place. As it becomes more elaborate it grows bigger and bigger, a labyrinthine construct that serves little purpose in assisting the majority of individuals to achieve meaning.

Its goal being, to become easily accessible, within reach of more and more individuals, avoiding the constant introduction of obscure concepts, with tiny traces of meaning, unable to confer clarity, prone to multiple interpretations, to as many as the individuals it is exposed to. It becomes the goal not the means. Therefore becomes detached from reality and assumes an essence of its own.

A human construct, on a par to any elaborate architectural construction therefore described as elegant or other similar decorative definition. Its goal should have been to become accessible to more and more individuals by curtailing the plethora of concepts used, instead of lost in the relentless pursuit of inventing more stringent rules and rigorous procedures, to devote as much time towards simplifying the technical language used, by the use of widely accepted, firm footed concepts. Take an extra effort to present models to be, within reach of ever wider audiences, engage that audience in the reality search, increase the lines of attack as they will be provided by the plurality of approach, as each one engaged will contribute.

Propagate the subjective to conquer the objective.