Derivation Of Principles & Strategies For Creative Development And Problem Solving:

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Universiality of Generalized Model

When considering the sciences and arts, a useful perspective that includes both wholistic and reductionist advantages is that of universal adaptation. This perspective is that everything may be viewed as being adaptive to varying degrees, from 0 to 100%, with typical cases being somewhere in between these extremes. And by "everything" we neccessarily have to include the boundaries and contexts that define anything. If this perspective seems objectionable for any reason(s), have patience for it will become clear later on why this perspective has many advantages when one is interested in creative, problem solving, analysis or related tasks.

Overview

• Universality of adaptation
• Interactions as coadaptation => Universality of coadaptation
• Universality of coadaptation => Universality of "self-similarity" of interactions
• Universality of "self-similarity" of interactions => Possibility of experimental evidence of "self-similarity" of interactions
• Similarity detection as fundamental to thought, emotion, aesthetic, life
• Similarity is generally multidimensional and cross-dimensional
• Adaptability vs contexts => contexts as boundaries & boudnaries as context
• Adaptive boundaries (as contexts) => adaptive contexts
• Incompleteness of contexts => incompletness of models: Lack of perfect isolation (ubiquitous interconnectedness), uncertainty principle, etc.
• Incompleteness of models => multiple models representing multiple/mutual & incomplete contexts
• Order of adaptation (of boundaries, constraint structures) determines order of complexity (and the combination of model complexity and/or order of model multiplicity)
• A general strategy for finding "self-similarity": solve for system response F1(params) = F1(remap(params))
• F1(params) = F1(remap(params)) solutions => "Eureka!"
• "Eureka!" moments of insight, finding solutions, creativity, etc. come when recognizing these similarities, identities, mutual contexts, etc.
• An important ingredient in aesthetic experience is the "eureka" component that comes with such recognition.

More Detail

• Universality of adaptation: Here adaptation is generalized to mean there is interaction. This interaction occurs across a "boundary" between two or more objects. If we view an individual object (reductionist view), we see input (stimulus, energy, information, material, etc.) and output (of the same and/or differing dimensions).

  input => interactive (adaptive) object => output

  A classic systems theory view of such an object has a canonical form description as:

  
           input =>(difference) => feed forward mechanism, H => output
                         \\                                      //	
                           <======= feedback mechanism, G <======		
  
  

  In the classic systems theory Laplace transform form:
  F(s) = H(s)/(1 + G(s)*H(s))

  In the classic logistic map form:

  F(n) = (input(n) - G(n)*F(n-1))*H(n)) or F(n) = input(n)*H(n) - F(n-1)*G(n)*H(n)

  For the corresponding canonical recursive integrator (infinite impulse response low pass filter or IIR LPF), H(n) = b0 = constant and G(n) = -a1/b0 = constant:

  F(n) = input(n)*b0 + F(n-1)*a1

  For the unity DC gain version of this IIR LPF, b0 = 1-a1, for a1 being a parameter that has values of 0 (no adaptation) to 1 (infinite integration):

  F(n) = input(n)*(1-a1) + F(n-1)*a1

  Examples of things often considered

  • non-interactive, non-adaptive (though close examination generally reveals exceptions), G=0: a river (water enters input and exits as output)
    • a river: water enters input and exits as output
    • the sun: chemical energy is input and light and heat are output
  • First order interactive/adaptive:
    • Anything well modelled using linear systems theory, linear differential equations, etc.
      • Classical Newtonian physics models (covering much of mechnics, extended to much of electromagnetics and wave theory)describing laws of momentum, acceleration, etc. including:
        • first order orbits (excluding perturbations from tertiary objects) of satellites
        • decay, resonance and damping of electronic (RC, L/R, etc.), accoustic, mechanical (discharge & damping) and other systems,
  • Second and higher order interactive/adaptive:
    • Generally non-linear systems (including classes of systems associated with fractals, chaos theory, etc.)
      • Biological systems including
        • the most common energy production mechanism: ATP production in mitochondria and chloroplasts
        • cellular function mechanisms of various regulation including detection and production of various chemical consituents of life functions.
        • systemic regulation: nervous system, circulatory system, respiratory system, endocrine system, etc.
        • perceptual systems (again, see for example U.S. No. 6907143 ( 6/14/2005), Adaptive Spatio-Temporal Filter for Human Vision System Models)

• Interactions as coadaptation => Universality of coadaptation

• Universality of coadaptation => Universality of "self-similarity" of interactions: The term "self-similiary" is in quotes because it is meant in a super generalized way: similarity may be measured (adaptively) in many ways including, but not limited to dirrect difference (error), statistical trends and tendencies inlcuding but not limited to correlation (including both positive and negative), etc. For sake of simplicity, in many cases, using some mapping (translation, transform, etc.) mechanism between inputs, outputs or other parameters being compared may be used in conjunciton with correlation and error measurement in order to measure "self-similarity" within an interaction.

  As a concrete example,

• Universality of coadaptation => Universality of "self-similarity" of interactions
• Universality of "self-similarity" of interactions => Possibility of experimental evidence of "self-similarity" of interactions
• Similarity detection as fundamental to thought, emotion, aesthetic, life
• Similarity is generally multidimensional and cross-dimensional
• Adaptability vs contexts => contexts as boundaries & boudnaries as context

  There are advantages to view contexts as boundaries and vice versa. In doing so, there are two main points to make here regarding adaptability of boundaries:

  • Boundaries have degrees of rigidity (which are rarely, perhaps never 100% rigid). Recognition of boundaries not being "fine lines" or inflexible, etc. has historically lead to breakthroughs such as:
    • Boundaries between true and false: fuzzy logic for probabilistic decision making, etc.
    • Boundaries among dimensions (spatial directions such as up and right, etc.): Mobeus (Listing) Strip, Escher (& Godel, Escher, Bach: self-referencing recursions).
    • Boundaries between integer dimensions (such as 1-D and 2-D, etc.): fractal dimensions, fractals, etc.
    • Boudaries between real and imaginary: i.e., +imaginary and -imaginary extremes in Z-plane: lead to doubly efficient reconstruction filter:
    • U.S. No. 7406493 ( 7/29/2008), Up-Sampling Half-Band Reconstruction Filtering: Method of design and example design of reconstruction and resampling filtering using about one half of the resources (pole and zero equivalents, gates, MACs, cycles, etc.) of prior art.
    • Boundary between mass and energy: e = m*c^2
    • Boundaries between economies
    • Boundaries between eco-systems
    • Boundaries between cultures
    • Boundaries between science disciplines
    • Boundaries between the arts
    • Boundaries between the arts and sciences
  • The "inverted-U" relationship between complexity and boundary constraints (i.e. rigidity):
    • Boundaries with rigid constraints have static behavior and have minimum complexity relative to boundaries with slightly less rigid constraints.
    • Boundaries with no constraints whatsoever are not boundaries at all.
    • In between these extremes, interaction across boundaries is influenced by the boundary and may influence and/or redefine the boudnary. Such interaction may be seen as adaptation. The degree of rigidity may be seen as a measure of the boundary, and may be normalized to values in the continuum from 0 to 1.0.

• Adaptive boundaries => adaptive contexts
• Incompleteness of contexts => incompletness of models: Lack of perfect isolation (ubiquitous interconnectedness), uncertainty principle, etc.
• Incompleteness of models => multiple models representing multiple/mutual & incomplete contexts
• Order of adaptation (of boundaries, constraint structures) determines order of complexity
• A general strategy for finding "self-similarity": solve for system response F1(params) = F1(remap(params))
• F1(params) = F1(remap(params)) solutions => "Eureka!"
• "Eureka!" moments of insight, finding solutions, creativity, etc. come when recognizing these similarities, identities, mutual contexts, etc.
• An important ingredient in aesthetic experience is the "eureka" component that comes with such recognition.