DECISIONS, STRUCTURE, AND NATURAL LAW
##plugins.themes.bootstrap3.article.main##
##plugins.themes.bootstrap3.article.sidebar##
Abstract
The object here is to show that our thinking processes and our physical forms and those of all things that exist, are a result of response in nature to influences as stimuli, brought about by natural occurrences. The ideas are developed through a generalization of the role judgment plays in decision making. Judgment serves as the basic link between our conscious awareness and the stimuli of the natural world. The mathematics used to represent natural laws is derived from stimulus-response theory and this in turn from the representation of judgment as it is used in decision-making. The representation of discrete judgment as a principal eigenvalue problem is generalized to the continuous case through Fredholm theory. Solving the resulting fundamental functional equation, which is a necessary condition for the existence of a solution, gives rise to damped periodic oscillation. The Fourier transform of the real valued solution has a perturbed inverse square representation that poses a question raised on occasion in science about the full accuracy of exact inverse square laws of gravitation, optics and of electric charges. The Fourier transform of the complex valued solution is a linear combination of Dirac type distribution of impulsive functions representing how the brain must operate to respond to external stimuli. A generalization is made to a functional equation in operator form with its solution. These solutions describe all forms that exist in nature as anything that responds to influences. These considerations that originate in the mathematics of judgment, serve as a unifying approach to our understanding and to creating tools for modeling and solving complex physical and behavioral problems.
http://dx.doi.org/10.13033/ijahp.v1i1.13
How to Cite
Downloads
##plugins.themes.bootstrap3.article.details##
Judgment, stimulus-response, natural law, response function, operator, Fundamental Equation
Mathematics 5-21. Basel: Birkhäuser Verlag (1991).
Brillouet-Belluot, N. “On a Simple Linear Functional Equation on Normed Linear
Spaces.” Ecole Central de Nantes, (1999).
Huxley, J.: Man in the Modern World, New York: Mentor Books, 1953.
Kolmogorov, A.N. (1957). “On the Representation of Continuous Functions of Many
Variables by Superposition of Real Functions of One Variable and Addition. American
Marthematical Society Translations Issue Series 2, 28:55-59 (1963).
Saaty, T.L.: The Brain, Unraveling the Mystery of How it Works, the Neural Network
Process, Pittsburgh, Pennsylvania: RWS Publications, 4922 Ellsworth Avenue,
Pittsburgh, PA 15213 (2000).
Saaty, T.L. and L.G. Vargas: A Model of Neural Impulse Firing and Synthesis. J. of Math. Psych. 200-219, 2 (1993).
Saaty, T.L., and L.G. Vargas: Representation of Visual Response to Neural Firing. Math.
and Comp. Mod. 17-23, 18/7 (1993).
Copyright of all articles published in IJAHP is transferred to Creative Decisions Foundation (CDF). However, the author(s) reserve the following:
- All proprietary rights other than copyright, such as patent rights.
- The right to grant or refuse permission to third parties to republish all or part of the article or translations thereof. In case of whole articles, such third parties must obtain permission from CDF as well. However, CDF may grant rights with respect to journal issues as a whole.
- The right to use all or parts of this article in future works of their own, such as lectures, press releases, reviews, textbooks, or reprint books.
- The authors affirm that the article has been neither copyrighted nor published, that it is not being submitted for publication elsewhere, and that if the work is officially sponsored, it has been released for open publication.
The only exception to the statements in the paragraph above is the following: If an article published in IJAHP contains copyrighted material, such as a teaching case, as an appendix, then the copyright (and all commercial rights) of such material remains with the original copyright holder.
CDF will receive permission for publication of copyrighted material in IJAHP. This permission is not transferable to third parties. Permission to make electronic and paper copies of part or all of the articles, including all computer files that are linked to the articles, for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage.
This permission does not apply to previously copyrighted material, such as teaching cases. In paper copies of the article, the copyright notice and the title of the publication and its date should be visible. To copy otherwise is permitted provided that a per-copy fee is paid.
To republish, to post on servers, or redistribute to lists requires that you post a link to the IJAHP article, which is available in open access delivery mode. Do not upload the article itself.
Authors are permitted to present a talk, based on a paper submitted to or accepted by IJAHP, at a conference where the paper would not be published in a copyrighted publication either before or after the conference and where the author did not assign copyright to the conference or related publisher.