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.


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